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Closeness Spaces: Elementary Explorations into Generalized Metric Spaces, and Ordered Fields Derived From Them

University of Illinois at Urbana-Champaign
Department of Mathematics

Closeness Spaces:

Elementary Explorations Into Generalized Metric Spaces, and Ordered Fields Derived From Them

Jonathan Hayward
Master's Thesis
Advisor: John Gray
May 6, 1998

Abstract

A generalization of metric spaces is examined, in which we are able to determine which of two pairs of points is closer (or if both are equally close), but not initially know how to assign a number to a distance. After the spaces are defined in general, we look at some more specific closeness spaces, and establish the the existence of a metric, which we are able to determine, under certain broad circumstances.

After looking at the closeness spaces, more specific attention is devoted to the closenesses themselves. We begin to define arithmetic operations over closeness spaces, and (given certain restrictions on the space) then complete addition and subtraction to develop a totally ordered group in which the closenesses are embedded. We prove that it is indeed a totally ordered field, and look at some examples. Directions are suggested for future research.

[Side note when entering this dissertation two decades later: this research includes a way to rigorously define and use infinitesimals. Infinitesimals were long seen as something you wanted to have but could not rigorously define; epsilon-delta proofs in relation to derivatives in calculus represent a masterstroke of how to do an infinitesimal's job using only standard real numbers for epsilons and deltas. Infinitesimals were spoken of as a ghost to be exorcized, and the entire point epsilon-delta proofs were a way to circumvent obvious use of infinitesimals in a mathematically rigorous way. At the time this thesis was written there appear to have been rigorous treatment of infinitesimals; however, so far as one could tell this approach to providing this kind of squeaky-clean rigorous handling of infinitesimals was new when the thesis was written.]

Introduction

Intuitively, a closeness space is like a metric space, with balls, symmetry, positive definiteness, and a triangle inequality, boundaries, an induced topology, and other familiar attributes of a metric space. However, it is a space for which we do not specifically know a metric: it is possible that we simply do not know a metric or none is given, or that no metric may exist. The latter holds in certain cases where the real numbers are too coarse of an ordered field to describe the space's distances: such a thing is possible, for instance, when there are infinitesimal and infinite distances. A closeness space might not be thought of so much as a generalization of a metric space (at least in the sense that a metric space is a generalization of ℝⁿ), but rather as a metric space with a generalization of real-valued distances. It is a metric space which may potentially have nonstandard real numbers (broadly defined) as its distances, rather than necessarily having real numbers under the standard model as its distances.]

In this sense, what is of interest is not only the spaces themselves, but their distances: what kind of group embeds them (we will look at a field which embeds an arithmetic closure of these distances). We will study the topological spaces, but our interest is not only in the spaces, but in the ordered groups and then fields which embed the closenesses. Throughout this thesis, the aim is both to establish certain elementary properties — laying a groundwork — and also to suggest directions for future research.

It is remarked that the approach is not to start with a field and then see for what kind of spaces it can function like a metric; the approach is rather to start with a space and see what kind of field acts as an arithmetic closure to its closenesses, given a certain construction.

Chapter 1: Notation, Definitions and Terminology

Notation 1:1:

In this document, a lowercase, indexed variable name is generally understood to be an element of the set designated by the corresponding uppercase letter, provided that the letter is 's' or occurs after 's' in the alphabet. For example:

s₁ ∈ S

Furthermore, we associate in the same way α with indexing set J, and β with K. These indexing sets are understood to have no last element.

There will be plainly marked exceptions to this rule.

Definition 1:2:

A closeness space C is a set S, together with a function

ƒ: S ✕ S ✕ S ✕ S ↦ {'<', '=', '>'}

such that the following conditions hold:

Definition 1.2.1:

f is defined for each quadruplet of points in S.

(S is said to be a space, and its elements are referred to as its points, as elsewhere in topology. The function f is said to be a closeness.)

Intuitively, this condition and those following guarantee that ƒ is comparing the distance between the first two points, and the distance between the last two points to see which one is greater. This condition, and the next four, are simply conditions which guarantee that ƒ is well-behaved as a function on a pair of pairs of points, only depends on which pair of pairs of points is given, and defines a total ordering up to equivalence classes.

For every six points s₁, s₂, s₃, s₄, s₅, and s6 (possibly non-distinct), we have the following conditions hold:

Condition 1.2.2:

ƒ(s₁, s₂, s₃, s₄) = ƒ(s₂, s₁, s₃, s₄)
ƒ(s₁, s₂, s₃, s₄) = ƒ(s₃, s₄, 1₁, s₃)

ƒ is not affected by swapping the elements in one pari, or by swapping the pairs. This is the closeness space's version of a metric space requiring symmetry.

Condition 1.2.3:

If ƒ(s₁, s₂, s₃, s₄) = '<', then ƒ(s₃, s₄, s₁, s₂) = '>'.
If ƒ(s₁, s₂, s₃, s₄) = '=', then ƒ(s₃, s₄, s₁, s₂) = '='.
If ƒ(s₁, s₂, s₃, s₄) = '>', then ƒ(s₃, s₄, s₁, s₂) = '<'.

Condition 1.2.4:

If ƒ(s₁, s₂, s₃, s₄) = '<' and ƒ(s₃, s₄, s₅, s₆) = '<', then ƒ(s₁, s₂, s₅, s₆) = '<'.

Condition 1.2.5:

We have

ƒ(s₁, s₂, s₁, s₂) = '='

Condition 1.2.6:

If s₂ and s₃ are distinct, then we have

ƒ(s₁, s₁, s₂, s₃) = '<'

Every point is closer to itself than the distance between any pair of distinct points; this is the closeness space's version of the positive definiteness of a metric space.

Condition 1.2.7:

We have

ƒ(s₁, s₁, s₂, s₂) = '='

In other words, there is only one zero. It may be mathematically interesting to remove this restriction, but we will not investigate that possibility.

Condition 1.2.8:

If ƒ(s₁, s₃, s₁, s₂) = '<' then for every set T ⊂ S containing points arbitrarily close to s₃ (in a sense to be defined below), there exists t₁ ≠ s₃, such that, for every point s₄, if ƒ(s₃, s₄, s₁, s₂) = '<'.

(What this is getting at, is that if you have a boundary point s₂ to a ball (boundary being outside the ball as with metric spaces), then every point closer to the center than the boundary point has a neighborhood entirely contained inside the ball (closer to the center than the boundary point). This means that a ball with a boundary point has a unique radius: there cannot be a second boundary point further than the center than the first boundary point, because then the first boundary point would be inside the ball; there also cannot be a secondary point closer to the center than the first boundary point, because this axiom says that every closer point has a neighborhood.)

Condition 1.2.9:

A set T ⊂ S is said to hold points arbitrarily close to point s₃ (in a sense to be defined below), there exists t₁ ≠ s₃, such that if ƒ(s₂, t₁, s₂, s₄) = '<', then ƒ(s₁, s₄, s₁, s₂) = '>'.

(Here, we say that if you have a boundary point s₂ to a ball, then every point further from the center than the boundary point has a neighborhood disjoint from the ball. Note that these two conditions may be vacuously satisfied by finite or other discrete metric / closeness spaces, with which we are not very much concerned.)

These two stipulations together constitute the closeness space's version of the triangle inequality in a metric space. The slight awkwardness of this definition is necessary to permit discrete metric spaces. This awkwardness will recur in other places where we are defining concepts on a very low level without using familiar tools (because we are developing a more general form of such tools), but it should pass.

Definition 1:3:

A set T ⊂ S is said to contain points arbitrarily close to point s₁ if the following conditions hold:

Condition 1.3.1:

T is nonempty and contains at least one point distinct from s₁.

Condition 1.3.2:

For every distinct pair of points s₂ and s₃, there exists T₁ distinct from s₁ so that ƒ(s₁, t₁, s₂, s₃) = '<'.

(In other words, for every closeness in the space, there is a point in T that is closer to s₁.)

Additional terminology 1.4:

Term 1.4.1:

Point s₁ is said to be closer to s₂ than s₃ is (close to s₂) when ƒ(s₂, t₁, s₂, s₄) = '<'.

Term 1.4.2:

Points s₁ and r are said to be equidistant from s₂ when ƒ(s₁, s₂, r, s₂) = '='.

Term 1.4.3:

Point s₁ is said to be father from s₂ than r is when ƒ(s₁, s₂, r, s₂) = '>'.

Term 1.4.4:

A pair of points is referred to as a distance.

Term 1.4.5:

The pair (s₁, s₂) is said to be the distance from s₁ to s₂.

Condition 1.4.6:

If distance d₁ is the pair (s₁, s₂) and distance d₂ is the pair (s₃, s₄), then the following three conditions hold:

Condition 1.4.6.1:

If ƒ(s₁, s₂, s₃, s₄) = '<', then d₁ is said to be less than d₂, written d₁ < d₂.

Condition 1.4.6.2:

If ƒ(s₁, s₂, s₃, s₄) = '=', then d₁ is said to be equal to d₂, written d₁ = d₂.

Condition 1.4.6.3:

If ƒ(s₁, s₂, s₃, s₄) = '>', then d₁ is said to be greater than d₂, written d₁ > d₂.

Remark 1:5:

Equality induces a partition of equivalence on distance. We will abuse notation slightly by referring to a distance, its equivalence class, and elements of its equivalence class interchangeably. Context should make clear which of these is meant; if context is not sufficient to clarify, then we will be more explicit as to which of these is intended.

Definition 1.6:

A ball about point s₁ is a set of points such that the following two conditions hold:

Condition 1.6.1:

Every point in the ball is closer to s₁ than is every point not in the ball.

Condition 1.6.2:

There does not exist point s₂ in the ball such that the following conditions hold:

Condition 1.6.2.1:

No point in the ball is further from s₁ than s₂ is.

Condition 1.6.2.2:

S contains points arbitrarily lose to s₂, which are not contained in B.

This latter condition guarantees that B does not contain its boundary, if it does have a nonempty boundary.

As the remainder of the definition and terminology, we have:

Condition 1.6.3:

If distance d = (s₁, r), r is not contained in B, and B contains points arbitrarily close to r, then ball B is said to of radius d, or to be the ball of radius d centered at p, and its boundary is said to be the circle of radius d centered at p.

(By the remarks following the triangle inequality, there is at most one equivalence class of distances which satisfy this property. Note that a ball might or might not necessarily have a radius.)

Definition 1.7:

A set T is said to have points arbitrarily close to point s₁ if T contains at least one point t₁ ≠ s₁, and for every t₂ ≠ s₁, there exists t₃ which is closer to s₁ than is t₂.

Definition 1.8:

The boundary of a set T is the set U of points u such that both T contains points arbitrarily close to u, and S∖T contain points arbitrarily close to u.

Definition of values, having different levels, 1.9:

We are using the term value to refer to mathematical objects which we will use in the construction of the field we are working on. Each value has a level; values of higher levels are determined in terms of values of lower level. The highest level of value will be an element of a field. I will define some (not all) levels of values here. If we use the term without specifying its level, it should be understood to be the last level specified, usually the highest level so far defined, if there is ambiguity. In some cases we will leave an ambiguity when what we are saying applies both to a member of an equivalence class, and its class.

Definition 1.9.1:

A level 0 value is defined to be a distance (strictly defined as a pair of points).

Definition 1.9.2:

A level 1 value is defined to be an equivalence class of level 0 values under the partition induced by equality. Level 1 values are ordered, in the same way that their members are ordered.

The remaining levels of values will be defined after I have begun to build up the the machinery necessary to explain and use them.

Definition 1.10:

A level 0 zero is defined to be a distance (s₁, s₁).

Definition 1.11:

A level 1 zero is defined to be the equivalence class of level 0 zeroes. Zeroes will be defined for all levels greater than or equal to level a.

Definition 1.12:

A level n value is defined to be positive if it is greater than the level n zero.

Definition 1.13:

A level n sequence is defined to be a level n sequence {∈_α}_α∈J, with J a totally ordered indexing set.

A level n epsilon is defined to be a level n sequence {∈_α}_α∈J, of positive level n values, such that the following two conditions hold:

Condition 1.13.1:

Every positive level n value v is greater than some ε_α.

Condition 1.13.2:

Every ε_α is greater than or equal to every ε_β.

Condition 1.13.3:

Distance d₁ is said to be within distance d2 of distance d3 if there is a set of points s₁, s₂, and s₃ such that d₁ = (s₁, s₂), d2 ≤ (s₃), and d₃ = (s_{1, ss}₃).

Chapter 2: Examples

Example 2.1:

Every metric space is a closeness space. Two distances are compared by '<'.

Example 2.2:

We derive a space C from ℝ² under the Euclidean metric as follows:

We make C a copy of ℝ², and then we add a point o' to the space, and define closenesses as follows:

O' is as close to every non-origin point as the origin is.

O' and the origin are closer than any other distinct pair of points.

Theorem 2.1.1:

This closeness space cannot be described by any metric.

Proof:

We prove this by contradiction.

Assume that such a metric exists.

If a metric did induce this closeness, it would have a least nonzero distance d, the distance from the origin O to O'.

Let the distance from O to (0, 1) be d'.

By the Archimedean property, there exists n such that d' ÷ n < d.

By repeated application of the triangle inequality on segments from (0, 0) to (i ÷ n, 0) and from (i ÷ n, 0) to ((i + 1) ÷ n, 0), this means that d' is at most equal to n times the distance from (0, 0) to (1 ÷ n, 0).

This means that the distance from (0, 0) to (1 ÷ n, 0) is less than d, but it is positive because they are two distinct points, and d is a minimal positive distance. ⇒⇐

Q.E.D.

This space is in many ways a space very like a metric space; although it boasts unusual decoration, it has a strong amount of stricture, like a metric space, structure that might not be present in an arbitrary metric space.

Example 2.2:

Let M be a metric space with metric μ over a set E of equivalence classes partitioning a set S. Then we can define a closeness space C which has S as its space, and its closeness ƒ defined as follows:

For every four points s₁, s₂, s₃, s₄ in S:

Case 2.2.1:

If μ(s₁, s₂) < μ(s₃, s₄), then ƒ(s₁, s₂, s₃, s₄) = '<'.

Case 2.2.2:

If μ(s₁, s₂) > μ(s₃, s₄), then ƒ(s₁, s₂, s₃, s₄) = '>'.

Case 2.2.3:

If μ(s₁, s₂) = μ(s₃, s₄), then:

Case 2.2.3.1

If s₁ = s₂ and s₃ = s₄ then ƒ(s₁, s₂, s₃, s₄) = '='.

Case 2.2.3.2

If s₁ ≠ s₂ and s₃ = s₄ then ƒ(s₁, s₂, s₃, s₄) = '>'.

Case 2.2.3.3

If s₁ = s₂ and s₃ ≠ s₄ then ƒ(s₁, s₂, s₃, s₄) = '<'.

Case 2.2.3.4

If s₁ ≠ s₂ and s₃ ≠ s₄ then ƒ(s₁, s₂, s₃, s₄) = '='.

In other words, if we have a metric space over equivalence classes, we can compare distances between pairs of elements of the classes by first looking at the distance between the elements' equivalence classes, and then doing something else to break ties — say, seeing where they are the same.

In relation to this, we have:

Definition and example 2.3:

If we have two closeness spaces C and D, with underlying sets S and T, then we can take their cross product E = C ✕ D, with underlying sets S and T, then we can take their product E = C ✕ D, with closenesses compared in the dictionary order.

Specifically, let U be the underlying set for E. We compare two distances d₁ = (u₁, u₂) and d₂ = (u₃, u₄), with u₁ = (s₁, t₁) and d₂ = (u₂, u₂), u₃ = (s₃, s₃), and u₄ = (s₄, t₄), as follows:

Case 2.3.1:

If (s₁, s₂) < (s₃, s₄), then (u₁, u₂) < (u₃, u₄).

Case 2.3.2:

If (s₁, s₂) > (s₃, s₄), then (u₁, u₂) > (u₃, u₄).

Case 2.3.3:

If (s₁, s₂) = (s₃, s₄), then:

Case 2.3.3.1:

If (t₁, t₂) > (t₃, t₄), then (u₁, u₂) > (t₃, t₄).

Case 2.3.3.2:

If (t₁, t₂) < (t₃, t₄), then (u₁, u₂) < (t₃, t₄).

Case 2.3.3.3:

If (t₁, t₂) = (t₃, t₄), then (u₁, u₂) = (t₃, t₄).

N.B. This cross product, in the dictionary order, will be used later.

Example 2.3.4:

Let S, T = ℝ² under the closeness induced by the Euclidean metric. Then U = S ✕ T may be described as a Euclidean plane, where each point is itself a miniature Euclidean plane. It is a plane with infinitesimal distances, or alternately an infinitesimal Euclidean plane.

A typical ball in this space is the ball with center at the origin ((0, 0), (0, 0)) consisting of all points strictly closer to the origin than ((1, 1), (1, 1)). This divides teh large-scale plane into three regions: the interior, exterior, and boundary of the disk of radius 1, centered at the origin. The interior of the disk corresponds to miniature planes which are entirely within the ball, where every point is inside. The exterior of the disk corresponds to miniature planes which are entirely outside the ball, where no point is inside. The boundary of the disk corresponds to miniature planes where the interior of the disk of radius 1 centered at the origin (of the small one, not the large plane or metric space) is inside the ball, and its boundary and exterior are outside. The boundary of the given ball in U consists of, in the miniature planes, all circles of radius 1 centered at the origin which are themselves on the circle of radius 1 in the large plane.

Proof that this satisfies the axioms of the space:

The set of equivalence classes (under equality) of closenesses has a 1-1 order-preserving mapping to the nonnegative real number line cross itself, in the dictionary order. In other words, it is a dictionary order cross product of two totally ordered sets, and therefore totally orders. This satisfies axioms 1.2.1-1.2.7.

To satisfy 1.2.8, we let s₂ be closer to s₃ than is s₃.

If the small planes of s₂ and s₃ are equidistant to the small plane of s₁, then the small plane position position of s₂ is closer to the small plane position of s₁ than is the small plane position of s₃. There is, by topology, an open disk about the small plane position of s₁ and boundary the small plane position of s₃; if we take such a disk in the small plane s₃ is actually contained in, it has points arbitrarily close to s₃, and is contained in the disk of center s₁ and boundary s₂.

Every set T containing points arbitrarily close to s₃ intersects the aforementioned disk infinitely many times. So we take some point inside that as our t_{1; every point s₄ closer to s_e than is t₁ and therefore closer to s₁ than is s₂.}

The same argument holds in the case that the small plane of s₃ is closer to the small plane of s₁ than is the small plane of s₂, save that we simply choose any disk contained in the small plane of s₃.

1.2.9 is satisfied; we simply have an open disk outside the open disk of center s₁ and boundary point s₂ instead of inside.

Remark 2.3.4.1

Note that in this case, a ball in the cross product was not a cross product of two balls, but the boundary of a ball in the cross product was cross product of the boundary of two balls. This leads us to:

Theorem 2.3.4.2:

Let C and D be closeness spaces with underlying sets S and T, both of which consist of more than one point. Let space E = C ×, with underlying set U = S × T. Let ball B be a ball in E which does not contain any points (s₂, t₂) for any point s₂ and some point t₂, contains all points (s₃, t₃) for any point t and some point t₃, and is centered at point u₁ = (s₁, t₁).

Then B is not the cross product of two balls, but the boundary of B is the cross product of the boundaries of two balls. Furthermore, if the aforementioned boundray is nonempty and contains point u₄ = (s₄, t₄), then the boundary consists of the cross product of the circle of radius (s₁, s₄) of radius (t₁, t₄) centered at t₁.

N.B. All of the hypotheses, which informally could be described as looking like clutter, are needed only to rule out degenerate exceptions. There are a number of equivalent replacements for the requirement that B contains no points at one T coordinate and all points at another.

Proof:

Proof by contradiction that B is not the cross product of two balls:

Assume that B is the cross product of two balls. B contains all of the points at one T coordinate, t₃, and none at another, t₂. Therefore, B contains u₅ = (s₅, t₅ with s₅ ≠ s₁. Every point (s₁, t₆) is closer to u₁ than is u₅, so B contains a point at T coordinate t, and also does not contain that point. ⇒⇐

We consider two cases now:

Case 2.3.4.2.1:

B has an empty boundary. In that case, the further claim is vacuously true because the 'if' clause is not met. In addition, the former claim is also at least vacuously true: we observe that an entire space constitutes a ball, and the boundary of the entire space is empty. Therefore we examine the more interesting

Case 2.3.4.2.2:

B has a nonempty boundary. In that case, we observe that all points on the boundary are equidistant from some point u₁; if one were closer to another, we would have an exception to the triangle inequality.

I claim that if (s₇, t₇) and (s₈, t₈) are in the boundary B, then so are (s₇, t₈) and (s₈, t₇):

Assume that (s₇, t₇) and (ss₈, t₈ are in the boundary B. Then we can say the following, both for sets of points contained in B, and sets of points disjoint from B: there exists a set U₇ ⊂ U containing points arbitrarily close to (s₇, t₇), and a set U₈ ⊂ U containing points (s₈, t₈). U₇ is a set of ordered pairs of points, which contain points of arbitrary close S coordinate to s₇, and a set U₈ ⊂ U containing points arbitrarily close to (s₈, t₈). U₇ is a set of ordered pairs of points, which contains points of arbitrarily close S coordinate to s₇, and arbitrarily close T coordinate to t₇, and U₈ is a set of ordered pairs of points, which contains points of arbitrarily close S coordinate to s₈, and arbitrarily close T coordinate to t₈. Take the cross product V of the S coordinates in U₇ and the T coordinates contained in U₈, and the cross product W of the S coordinates contained in U₈, and the T coordinates contained in U₇. As this arguments applies both to sets of points contained in B, and sets of points disjoint from B, we have (s₇, t₈) and (s₈, t₈) as desired.

This establishes the independence of the S and T coordinates of points on the boundary, so the boundary is a cross product of some pair of sets in S and T.

These sets must be equidistant from s₁ and t₁ respectively; if they were not, then we could select two radii of different length for the ball, and violate the triangle inequality. So they are subsets of the boundaries of balls; they must be the whole boundary because the cross product of two accumulation points of different sets is an accumulation point of the cross product of the two sets, as we argued above. And this establishes that the radius of the boundary must be the distance from the center to the cross product of two respective boundary points. So we have the boundary of B, for u₄ = (s₁, s₄) a point on the boundary, equal to the crosss product of the circles of radius (s₁, s₄) and (t₁, t₄) centered at s₁ and t₁ respectively, as desired.

Q.E.D.

Example 2.4:

Any subset of a closeness space is a closeness space.

Remark 2.5:

The operations of taking a cross product of two closeness spaces in the dictionary order, and taking a subset of a closeness space, are together quite powerful. All other examples here are special cases of the operations taking a cross product of two closeness spaces in the dictionary order, and taking the subset of a closeness space.

Example 2.5.1:

The disjoint union of two closeness spaces C and D, in other words a union where C and D retain their closeness functions, and every function in one space is closer than every function in another space, is achievable by taking ℝ × C, paring it down until we have only a copy of (0, 1) where 0 is identified with a copy of C, and then taking the cross product of the result in D, and again paring it down until we only have a copy of (0, 1)where 0 is identified with a copy of C for which each element is identified with a single element, and 1 is identified with a copy of D.

If we allow not only finite but transfinite sequences of these two operations (which must be well-ordered, in order to be well-defined), then possible closeness spaces can take an almost unbelievable complexity beyond what is possible for metric spaces. The faintest hint of this is provided by a transfinite algorithm, and partial proof of correctness which is not reproduced here, which seems (given the Axiom of Choice) to be able to embed an arbitrary partial ordering in a totally ordered field. I believe that the power is sufficient to justify making:

Conjecture 2.5.2:

Assuming the Axiom of Choice, any closeness space can be generated from ℝ under the closeness arising from the usual Euclidean distance metric, by the operation of taking cross products in the dictionary order, and taking subsets.

Example 2.6:

The long line appears to be a closeness space under what could intuitively be described as comparing the absolute value of differences. In general we cannot subtract ordinals as we can finite numbers, but we can do something comparable in this case.

We compare pairs of ordinals (o₁, o₂) and (o₃, o₄) as follows, in the case that both are distinct pairs:

Without loss of generality, assume that o₁ < o₂ and o₃ < o₄.

ƒ(o₁, o₂, o₃, o₄) = '<' if o₁ + o₄ < o₃ + o₂.
ƒ(o₁, o₂, o₃, o₄) = '=' if o₁ + o₄ = o₃ + o₂.
ƒ(o₁, o₂, o₃, o₄) = '>' if o₁ + o₄ > o₃ + o₂.

Example 2.7:

The numbering of items in this thesis may be taken to be a finite and discrete closeness space, with closeness compared with a dictionary ordering on the numberings.

Chapter 3: Towards Constructing a Field

We now define the next level of values:

Definition 3.1:

A level 2 value is defined to be a level 1 sequences of values {d_α}_α∈J which is Cauchy convergent: for every element ε_β of level 1 epsilon {e_β}_β∈K, there exists an element d_β of {d_α such that every subsequent pair of values d_α1, d_α2 are within ε_β of each other.

What we are dong here is taking the closure of the set of level 1 values under the operation of taking limits, which might or might not be embeddable in ℝ and might be finer-grained. A level 1 value is included by a sequence that consists exclusively of that value.

Note 3.2:

We compare two level 2 values v₁ = {d_1α}_α∈J and v₂ = {d_2α}_α∈J as follows:

If there is an element α₀ of J such that, for all subsequent values of α₁ and α₂ we have α₁ and α₂ then v₁ ≤ v₂.
If there is an element α₀ of J such that, for all subsequent values of α₁ and α₂ we have α₁ and α₂ then v₁ ≥ v₂.
If for every element α₀ of J, there exist subsequent α₁, α₂, α₃, and α₄ such that d_1α1 ≤ d_2α2 and d_1α3 ≤ d_2α4, then v₁ = v_2.

Definition 3.3:

A level 3 value is defined to be an equivalence class of level 2 values under the partition induced by equality. Level 3 values are ordered in the same way that their members are ordered.

Definition 3.4:

A level 2 zero is defined to be an infinite sequence of level 1 zeroe.

Definition 3.5:

The level 3 zero is defined to be the equivalence class of the level 2 zeroes.

Lemma 3.6:

The set of points whose distances are less than v₁ from point s₁, for any value v₁ and point s₁, constitutes a ball.

Proof:

It is clear that every point in this set is closer to s₁ than is any point not in the set. So we need only to know that the set does not contain any boundary points.

If there is a boundary point s₂, then there is an epsilon at that boundary point contained in the set, and an epsilon at that boundary disjoint from the set. From these can be chosen a sequence of distances that converges to (s₁, s₂) and is inside the set, whereby v₁ ≥ (s₁, s₂), and can also b chosen by a sequence of distances that converges to (s₁, s₂) and is outside the set, whereby v₁ ≤ (s₁, s₂). So v₁ = (s₁, s₂). The ball contains only points strictly closer than v₁, so it does not contain s₂. ⇒⇐

Q.E.D.

Definition 3.7:

The supremum (resp. infemum) of a nonempty set W of level 2 values is defined to be the equivalence class containing the sequences v₁ of values which satisfy the following three conditions:

Condition 3.7.1:

All elements of v₁ are contained in some element of W.

Condition 3.7.2:

v₁ contains at least one element greater than (resp. less than) or equal to any element of W.

Condition 3.7.3:

v₁ is monotonically nondecreating (resp. nonincreasing).

Remark 3.7.4:

Not all sets will necessarily have a supremum or infemum. This a definition of what the supremum is if it exists, not necessarily a statement that one always exists.

There is at most a single equivalence class containing all such sequences, because any one contains an element greater than or equal to any element of any other, arbitrarily far along in the sequence.

The supremum and infemum of the empty set are undefined.

Now, we begin to develop an arithmetic.

Definition 3.8:

A value v₁ is said to be equal to v₂ + v₃ if v₁ is the supremum over all triplets of points s₁, s₂, and s₃ of the distance (s₁, s₃), such that the following two conditions hold:

Condition 3.8.1:

(s₁, s₂0) ≤ v₂
(s₂, s₃) ≤ v₃

Condition 3.8.2:

There do not exist any three points s₄, s₅, and s₆ such that:

(s₄, s₄) ≤ v₂
(s₅, s₆) < v₃
(s₄, s₆) ≥ v₁

(s₄, s₄) < v₂
(s₅, s₆) ≤ v₂
(s₄, s₆) ≥ v₁

Notation 3.8.3:

A value v₁ is said to be a difference of v₂ and v₃ if v₂ = sub₁ + v_{3_.}

Remark 3.8.4

This definition does not guarantee the existence of a sum of two values; it only tells how to tell if a given value is equal to the sum of two others.

This value is chosen for its simplicity, specificity, and power; there numerous other ways of defining addition, some of which would seem to be a more generalized version of addition, doing to addition in ordered, cyclic, abelian groups as we know them what metric spaces do to ℝ². However, we will not investigate that generality here, and in particular, we are going to restrict our attention to a specific subset of closeness spaces, those for which addition as here defined is associative and uniquely defined.

If we not only do not restrict our attention, but replace the given condition with the stipulation that v₁ is the supremum over points s₁ of distances from s₁ is the supremum over points s₁ of distances from s₁ to a point in the union of all closed balls of radius v₃ whose centers lie in a closed ball of radius v² centered at s₁, then we further lose commutativity; at least in the case of the long line, though, we have reproduced ordinal addition.

It appears that looking at those more general cases may be of mathematical interest and may allow the creation of an arithmetic that is looser and more general than that of an ordered, abelian group. However, we do not investigate that possibility here, and have not investigated it, beyond the brief attention paid in this remark.

This definition provides commutativity, and unique subtraction where defined (i.e. v₁ - v₂ may not be defined, but if it is, it is unique; provided that v₁ - v₂ may not be defined, but if it is, it is unique; provided that v₁ = v₂ + v₃, if v₄ < v₃, then the distances between pairs of points eligible for the definition of addition will be less by at least a minimum positive amount, by the triangle inequality, so v₂ + v₄ < v₂ + v₃ = v₁. This observation, as well as establishing that subtraction is not ambiguous (though possibly undefined), proves for us:

Theorem 3.9:

For any three values v₁, v₂, and v₃ for which v₂ + is defined, we have:

If v₁ < v₂, then v₁ + v₃ < v₂ + v₃.
If v₁ = v₂, then v₁ + v₃ = v₂ + v₃.
If v₁ > v₂, then v₁ + v₃ > v₂ + v₃.

Sketch of Proof 3.9.1:

The first case is established above. The second case is established from the first case by the symmetry of an ordering, and the third case is established by the contradiction which would arise from the transitivity of the ordering if one sum was less than the other.

We now define our next level of value; as we earlier developed a closure under the operation of taking limits, we now define a closure under the operation of addition. Again, we are going with the more specific and powerful definition of addition given, at the loss of some generality.

Hunch 3.10:

Addition of values is associative.

Suggestion of Proof Idea 3.10.1:

It seems that this arises from condition 3.8.2. Definition 3.8 is a refined version of earlier, less powerful definitions; we have not devoted enough time to the matter to establish associativity. We will continue on the assumption that this is true; one might say if need be that we are restricting our attention to spaces where addition is associative. We will further restrict attention to spaces which are closed under addition (although a slightly weaker condition is needed for my work, namely that any two level 4 values as defined below are uniquely comparable).

Definition 3.11:

A level 4 value is defined to be a finite string of symbols as follows:

Part 3.11.1:

If v₁ is a variable referring to a level 3 value, then "v₁" is a level 4 value.

Part 3.11.2:

If "s₁" and "s₂" are two level 4 values, then "(s₁ + s₂) is a level 4 value.

Part 3.11.3:

If "s₁" is a level 4 value, then so is "— s₁".

Part 3.11.4:

Nothing else is a level 4 value.

We compare level 4 values as follows:

Comparison 3.11.5:

If for level 3 values we have v₁ < v₂, then for level 4 values, we have "v₁" < "v₂" and "— v₁" > " — v₂".

If for level 3 values we have v₁ = v₂, then for level 4 values, we have "v₁" = "v₂" and "— v₁" > " — v₂".

If for level 3 values we have v₁ > v₂, then for level 4 values, we have "v₁" > "v₂" and "— v₁" < " — v₂".

And we complete comparison by allowing certain manipulations, namely:

Part 3.11.6

If for level 3 values we have v₁ = v₂ + v₃, then inside a level 4 value v₁ may be substituted or back-substituted for v₂ + v₃ and v₃ + v₂, then inside a level 4 value v₂ may be substituted or back-substituted for v₁ + — v₃.

Part 3.11.7:

We may associate and commute while preserving equality.

Part 3.11.8:

We may add a like value to two different values without affecting their comparison.

Part 3.11.9:

Comparison is transitive.

We now define:

Definition 3.12:

A level 5 value is an equivalence class of level 4 values under equality, with addition, additive inversion, and comparison of equivalence classes defined according to the equivalence classes of those operations on respective members.

We now have an ordered abelian group.

Remark 3.13:

It is well known that an ordered abelian group may be embedded in a field. (Source: Anand Pillay).

Definition 3.14:

For any two values v₁ and v₂, v₁ is said to be of the same magnitude as v₂ if there exists a positive natural number n such that either v₁ + v₁ + ⋯ + v₁ > v₂ (with v₁ added to itself nn times) and v₂ + v₂ + v₂ ⋯ v₂ >
v₁(with v₂ added to itself n times), or v₁ + v₁ + ⋯ + v₁ < — v₂ (with v₁ added to itself nn times) and — v₂ — v₂ — v₂ ⋯ — v₂ < v₁ (with v₂ added to itself n times).

It is clear that the magnitudes are equivalence classes of values.

The value 0 resides in its own magnitude, which will not be named.

Part 3.14.1:

Magnitude M₁ is said to be greater than (resp. less than) magnitude M₂ if it is a different magnitude, and M₁ contains at least one positive value that is greater than (resp. less than) at least one positive value in M_2.

Part 3.14.2:

The magnitude which contains 1 is said to be finite.

All greater magnitudes than the finite magnitude are said to be infinite.

All lesser magnitudes than the finite magnitude (excluding the magnitude of 0), are said to be infinitesimal. The variable ε will hereafter refer to an infinitesimal.

To give a specific example of what kind of ordered field we have, let us look at

Example 3.15

Let closeness space C be the space examined in example 2.3.4, namely ℝ² × ℝ², under the closenesses induced by the dictionary order on Euclidean closenesses.

Then the closenesses are of type ℝ² × ℝ², in the dictionary order.

The elements of a minimal imbedding field are of order type S ⊂ ℝ²ℤ, such that all but finitely many of the coordinates of an element of S are zero.

Comparison of values is a dictionary comparison of their coordinates.

Addition of two values is coordinate-wise addition of reals. I.e. if v₁ and v₂ are values and v_1i, v_2i are the i^th coordinates of v₁ and v₂ respectively, then the i^th coordinate of v_3i of v₃ = v₁ + v₂ is equal to v_1i + v_2i.

Multiplication of two values is as follows:

If v₁ and v₁ are as above, then v₃ has coordinate v_3i equal to _Σj+k=i = v_1j × v_2k.

This is isomorphic to the field of ratios of polynomials in a single variable, over the real numbers. Note that, although the order type is fixed, a constant c chosen so that c⁰ = 1, c¹ is a number of the lowest infinite magnitude and zero coordinate in other magnitudes, and c^-1 is a number of the highest infinitesimal magnitudes, is not a unique constant. Any one such value can be arrived at by multiplying another such value by a nonzero real number.

The interpretation of this representation as given is that the 0-coordinate is the finite component, components of positive ℤ value are infinite components, and components of negative ℤ value are infinitesimal components (or vice versa).

Under this interpretation, we can say that the given closeness space is like a metric space, using the given field instead of ℝ as the measure. It could be stated to use the 0 coordinate for the large plane, and the — 1 coordinate for the miniature planes at each point of the large plan (in which case the space is interpreted as a roughly Euclidean plane with infinitesimal distances, or to use the 1-coordinate for the large plane, and the 0 coordinate for the small planes (in which case the space is interpreted as an infinite plane of real planes — it is to the Euclidean plane roughly as ω² is to ω among ordinals), or indeed z and z - 1 for any integer z.

Example 3.15.1: Non-Standard Analysis

This allows achievement of at least some of the results of nonstandard analysis. For example:

Definition 3.15.1.1:

For the duration of this example, we define the nearest real number to a finite value to be the value of the same first coordinate, and zero component in the second coordinate. (I.e. a distance of 3.7 × 0 is the nearest real number to 3.7 × — 23.4. 3.7 × — 23.4 or 0 × 14 are not the nearest real numbers to anything.)

Definition 3.15.1.2:

We define the limit of a function ƒ at point x to be equal to the nearest real number to ƒ(x + ε), if such a real number exists and is uniquely defined across all infinitesimals ε.

For example, the limit of ƒ(x) = x + 1 at x = 1 is the nearest real number to

ƒ(x + ε) =
f(1 + ε) =
1 + ε + 1 =
2 + ε

which has 2 as its nearest real number.

Definition 3.15.1.3:

We define a function ƒ(x) to be continuous at point x if f is defined at x and if, for every infinitesimal e, we have ||ƒ(x + ε) — ƒ(x)|| at most an infinitesimal.

For example, if we have

ƒ(x) = x + 1 if x ≥ 0
ƒ(x) = 0 otherwise

then we have f continuous at -1 and 1, but not continuous at 0:

ƒ(-1 + ε) - ƒ(-1) = 0 - 0ƒ(1 + ε) - ƒ(1) = 1 + ε + 1 - 1 + 1 = ε
but problems when we examine a negative value of ε with nearest real number at 0:

If ε < 0, then ƒ(0 + ε) = ƒ(ε), but we have f(0) = 0 + 1 = 1, and 0 — 1 = &mdash 1 is not an infinitesimal.

Definition 3.15.1.4:

We define the derivative of a function ƒ at point x to be the nearest real number to

(ƒ(x + ε) - ƒ(x)) / ε

if such a number exists and is well-defined across all infinitesimals ε.

For example, the derivative of ƒ(x) = x² is equal to the nearest real number to:

x + ε)² - x²) / ε =
(x² + 2xε + ε² - x²) / ε =
(2xε + &epsilon²) / ε =
2x + ε

and the nearest real number to 2x + ε is 2x. So we have the derivative of x² equal to 2x.

Closing remark

Providing a nonstandard analysis with derivatives seems straightforward enough; notwithstanding the fundamental theorem of calculus, it is not clear to this author how to adapt these findings to create an integral, although just as epsilon-delta arguments provide a finite workaround to infinitesimals, the core concept of integration in calculus find a finite workaround to summation of an infinite number of infinitesimally thick slices. It might be noted that this system does yet have the infinite sums and infinite integers of non-standard analysis. Perhaps our restricted attention disregarded some closeness spaces or other matters yielding fields that would allow a more powerful non-standard analysis; perhaps work with the closeness spaces involving the ordinals cross [0, 1) — a nonnegative long real number line — would achieve such things. However, we will draw a limit to the investigation here.

Frankincense, Gold, and Myrrh: A Look at Profound Giftedness Through Orthodox Anthropology

A look at profound giftedness through Orthodox anthropology

Thesis Statement

Gold, frankincense, and myrrh are emblems of Christ's kingship, divinity, and suffering respectively, applying to humans as Christ's image, studied in the profoundly gifted.

Abstract

The purpose of this paper is to look at the features of Christ confessed gifts of gold, frankincense, and myrrh as features playing out in humans, and exploring what concrete shape this playing out takes in the so-called "profoundly gifted." (Kingship, divinity, and suffering play out in equally significant ways for other populations, but the scope is primarily limited to a segment of the stated population.) "Profound giftedness" is used a standard psychological technical term, if a quite flattering label for a more ambivalent experience.

Profound giftedness is explored as one of many experiences that looks different from the inside and from the outside; paradoxically, what looks different from the inside and outside is in large measure its particular expression of human commonalities. (This could be said for many other populations as well.) Profound giftedness as an expression of being human is explored, in the (royal and) divine image, in particular the rule over Creation through work, alongside a particular expression of suffering, while being attentive to the fact that profoundly gifted people both suffer and cause others to suffer. Suffering is explored in light of Orthodox experience before the essay closes by applying lessons learned in looking at profoundly gifted difference to human difference as such. Profound giftedness experience combines extremes, including both privilege and marginality. This study looks at the profoundly gifted experience of being human, and owes a considerable debt to studies of the human experience of the marginalized, while drawing from other traditions including the Orthodox.

Profound giftedness is not described as exception to the normal human rule but as the univocally applied human rule given further specification that could be given different further specification for other populations.

Symbols, humans, and Christ

There is an understanding of symbol/image that plays out in this paper's treatment of the image of God and the symbolic character of the magi's gifts. If we look at the question, "Does a symbol represent and embody or represent only?" an Orthodox perspective is that a symbol or image both represents and embodies.[1] A proper symbol is neither arbitrary nor detached but connected to what it represents. Hence Kallistos Ware answers the question of whether Orthodox pay undue devotion to wood: "The icon is... a symbol; the veneration shown to the images is directed, not to stone, wood, and paint, but towards the person depicted."[2] We shall see in a moment that the person is in turn a symbol of Christ, but the immediate point is the understanding of symbol that undergirds such a position. It is the same understanding of symbol that says that the Gifts of the Magi were not given arbitrary imputed symbolism, representing without embodying. Not only do they both represent and embody, but there are layers of symbolic resonance, and that resonance informs this paper as does the precedent in Ephrem the Syrian, a poet of the first rank,[3] treating a fluid rather than inflexible treatment of the symbols' precise meaning.

It is a deceptive understatement to call Christ a norm to humanity. To be human is to be made in the image of God, classically understood as "in the image of the Trinity,"[4] as Ware attests, and this image specifically includes the image of Christ. Part of this image plays out in treatment of others: Ware writes "Monastery guests, as St Benedict of Nursia (c.480-c.550) wrote in his Rule, are to be received 'as Christ himself.' In similar terms, the fourth-century Egyptian Abba Apollo insisted, 'We should bow down before those who come to see us, for we are bowing down not before them but before God.'"[5] This principle is in no sense unique to monastery guests: in Mt 25.31-46 the righteous are separated from the wicked in the last judgment according to how they treated Christ through their treatment of the downtrodden, with no distinction being made for religious persuasion. One's treatment of another is one's treatment of Christ tout court. Christ lies at the heart of humanity and his image in every human reaches the point that one cannot do good or ill to another human, Christian or not, as someone detached from Christ because there is no such thing as someone detached from Christ. This is tacitly tied to a norm in a much deeper sense than a norm extrinsically imposed de jure, whether or not it fits a person originally independent of that arbitrarily imposed norm. One can have something to do with Christ without encountering Christianity: the relevance of Christ does not enter the picture only in relation to explicit identification with Christianity.

As a limitation of scope, this paper looks at the image of Christ as it is expressed in the profoundly gifted. "[God] doesn't make two blades of grass the same: how much less two saints, two nations, two angels."[6] The image of Christ is specified equally but differently in other human populations, and other papers might look at other populations. The scope of this paper is to offer analysis and description for the profoundly gifted and talk about how the image of Christ in the human constitution plays out specifically in this locale. If the profoundly gifted are explored as connected to Christ and the Theotokos or Mother of God, this is intended as an exploration of something common with other populations rather than a specific distinction that applies to the profoundly gifted and not others. Then why focus on the profoundly gifted? Human basics can be further specified in exploring the particularity of their expression in different populations, and this paper is intended to offer specific characterization and thick description for the group in its focus, a methodology one would expect to be able to apply to any number of groups. (Other papers with different focuses might give comparable specification to the human rule through thick description of other populations.)

Chrism, frankincense, and myrrh

Chrism was not "mere" oil but a sacramental emblem of the Holy Spirit. Cyril of Alexandria compares aromatic holy oil, or chrism, which produces "the advent of deity,"[7] to consecrated bread that has become the Body of Christ,[8] and Cyril does not mean this as extrinsic and arbitrary symbolism but understands symbol along the lines outlined above. Oil is an emblem of the Holy Spirit so that anointing with oil may be hard to disentangle from anointing with the Spirit,[9] and oil carried rich resonances: Susan Ashbrook Harvey writes: "Most important for early Christians were the ideas of priesthood, kingship, and prophecy as offices of sacred activity conferred through an anointing with holy oil. Early Christians applied these concepts to the figure of Christ, as well as themselves as his followers. [emphasis added]"[10]

Ashbrook Harvey mentions a "universal patristic exegesis"[11] of gold as emblematic of Christ's kingship, frankincense of his divinity, and myrrh of his suffering. In patristic sources this exegesis can be tersely stated,[12] but at other times there is fluidity and resonance: in Ephrem the Syrian myrrh intercedes for swords used in aggression, gold intercedes for treasures plundered from King Hezekiah, and frankincense appeased divinity.[13] The three basic meanings are here cast in a touching light of reparations for the magi's ancestral offenses against Mary's ancestors. This paper's method is informed by how in Ephrem the three gifts were not limited to a single rigid meaning but could be flexibly applied in different ways.

Frankincense was a complement to anointing oil; Ashbrook Harvey writes, "...incense took its base meaning from its identification with sacrifice. Incense served as a medium for human initiative towards the divine, and its fragrance marked the process of human-divine encounter. Holy oil, by contrast, represented divine initiative towards the human."[14] Incense could signify human approach to divinity, or divinity itself.[15]

Myrrh was associated with suffering and death. Concordance search results for "myrrh," "spices," or "ointment" (in the RSV) reveal an overwhelming number of Gospel references explicitly connected to the passion: the Gospel reference to myrrh, spices, ointment, etc. pave the way for the Fathers to tie myrrh to suffering and death.

Gold is less thoroughly explained in Ashbrook Harvey and seems to be one of those objects of study poised to slip through the cracks of what is considered "doctrinally significant:" prior research to support an argument appears scanty, leaving primary sources the best available resource. Kittel[16] and Fitzgerald[17] lack entries for "chrysos"/"gold." This may be a difficulty, but it does not stop one from looking at the other two gifts, and patristic treatments of kingship can presumably illuminate gold as an emblem of kingship.

Chrism is almost a fourth gift besides the three, and in a way is prior: it cuts deeper, and we call Christ "the Christ," meaning anointed Prophet, Priest, and King. The oil and the Holy Spirit are paradigms for each other.[18] Anointing was important in baptism[19] and some sources make baptism more a matter of oil than water.[20] John the Baptist announced one who would baptize with the Holy Spirit and with fire,[21] and perhaps oil rather than water explained baptismal anointing, with the Holy Spirit and with fire, to make little Christs. Not only myrrh for suffering, but gold for kingship and frankincense for divinity, are basic to being human and constituted by the image of Christ. The anointing with the literal-and-more-than-literal chrism that makes prophet, priest, and king applies to Christ and Christians. It is not only the pre-eminent gift of chrism that is connected with what it means to be human. The Gifts of the Magi are ultimately gifts to humans who bear Christ's image.

Gold and frankincense in human work

The gifts have something to say about the human person. It is the Last Adam[22] who received frankincense, gold, and myrrh, and this Last Adam is tied to the First Adam: Genesis 1.26-8 (RSV) reads:

Then God said, "Let us make man in our image, after our likeness; and let them have dominion over the fish of the sea, and over the birds of the air, and over the cattle, and over all the earth, and over every creeping thing that creeps upon the earth." So God created man in his own image, in the image of God he created him; male and female he created them. And God blessed them, and God said to them, "Be fruitful and multiply, and fill the earth and subdue it; and have dominion over the fish of the sea and over the birds of the air and over every living thing that moves upon the earth." [emphasis added for words relating to human rule]

Genesis 1 ties the divine image to human rule. The language used is of an idol image of a deity that carried the deity's essence and through which the deity's work was accomplished.[23] Furthermore, a good portion of the words in Genesis 1.26-8 are devoted to the relationship between the human and the rest of material Creation. To cite one patristic example, Basil of Caesarea can spiritualize rule over animals by discussing rule over oneself,[24] but alongside an a fortiori implied argument, "Let them rule over the fish. We were, in the first instance, given power over animals who live elsewhere. [God] did not say, Let them rule over domestic animals, but over fish:" humans have a powerful authority over the animals that goes beyond domestic animals to even effectively apply to fish.[25] Our relation to the natural world is a relation as royalty made to rule. Anestis Keselopoulos explains this point: "[St. Symeon] has a strong feeling for the fact that man was created to function as king of creation."[26] Gold and frankincense do not begin to describe humanity in Christ's shadow. They already describe the divine image in Genesis 1.

That the texts above connect to work is foundational to John Paul II's Laborem Exercens.[27] He argues, "Man is made to be in the visible universe an image and likeness of God himself, and he is placed in it in order to subdue the earth. From the beginning therefore he is called to work,"[28] making subduing the earth and human rule the bridge between the imago dei and work. The royal, divine image expresses itself in work—perhaps not only work, and perhaps "work" needs to be more broadly understood than "remunerated labor," but on the Genesis 1 account the one holy day of rest is only achieved after the six days of the Creator himself working. One can scarcely ask for a higher valuation of work than to say the world was created by God's work (perhaps over billions of years), and as the Father works, so does the Son (John 5.17). Work is a defining feature of humanity (although not the only important feature). Work is part of human glory, part of the gift of gold and frankincense. The archetypal command to rule Creation is a command to work, and to be king is to rule through work.

Properly understood, work is at the core of what Keselopoulos gives great moral weight, one's "relationship with the things in creation."[29] Work is the outward operation of the image of God, and relating to the world virtuously is partly a matter of loving work. Madeleine l'Engle describes service that is close to the heart of work: "If the work comes to the artist and says, 'Here I am, serve me,' then the job of the artist, great or small, is to serve."[30] The artist does not take first initiative but responds by serving an as yet unformed Creation that needs to be loved into its full being. We will further explore this image later.

Conceptualization of profound giftedness

I am wary of using the term "genius" for several reasons. Of all the common terms in psychological literature, "genius" is most problematic. It is difficult to say "genius" and only imply a claim of ability; invariably there are half-conscious associations evoked which approach being a morally separate class of creature who has a higher calling and is not bound by the same rules as mere mortals, much like the pathological conceptualization of the "exceptional man" critiqued in Crime and Punishment.[31] "Genius" comes with a mystique, or, to be more precise, is largely a mystique.

"Profoundly gifted" is not a synonym for "genius," and I will use the imperfect "profoundly gifted" not because it is perfect (it isn't), but to avoid forcing readers to deal with my own invented term when a standard term exists. "Genius," even besides its connotations, denotes someone who leaves behind work of enduring value, and I believe it is possible for profoundly gifted to make no such achievement, and for that matter to do poorly at certain ordinary achievements like economic self-sufficiency. The narrow technical term "profoundly gifted" overlaps the term "genius" (if the latter is stripped of its mystique), but the overlap is incomplete, with one neither necessary nor sufficient to ensure the other. Having considered what amount to limited options, all of which have drawbacks, I will use the term "profoundly gifted" as being the least problematic, even if it is a flattering way of describing an ambivalent condition.

While the language of "giftedness" has Biblical origins,[32] I am using technical terms which depart from the Biblical usage and which I treat as having important differences from the Biblical way of framing gifts. Theologically, the quite different Biblical conceptualization is to be preferred, and I will use psychological terms even if it might be theologically preferable to have another terminology besides that of giftedness to refer to this particularly obscure form of human giftedness. I Corinthians 12 never speaks of "gifted" (as opposed to "non-gifted") people, and in the parable of the talents,[33] the servants admittedly differ in how much they receive, but they do not differ in having at least one substantial "talent" entrusted to them, meaning at least sixty-five pounds[34] of precious metal.[35] It is not only the profoundly gifted who have a place and a quite significant gift for the greater, common good, nor does one need to be psychologically labeled as "gifted" to count as a human being. Furthermore, this discussion is limited in its scope and does not treat other forms of giftedness even if one departs from the Biblical baseline that true talent and giftedness are for all, not a few. Daniel Goleman's Emotional Intelligence: Why It Can Matter More than IQ[36] is controversial,[37] but Goleman takes a look at one of several of the intelligences treated by multiple intelligence theory, and at very least makes a significant argument of exactly how success may be more a matter of emotional intelligence than the specific type of intelligence treated within the scope of this paper.[38] Even broader would be a serious attempt to treat not only intelligences but the broader category of aptitudes, which seem practically infinite in variety.

Profoundly gifted work at a young age

Work is a defining feature of humanity and can be neither limited to nor centered on the profoundly gifted, but there is something that shines in the work of the profoundly gifted. But before I go further about that, I need to explain a feature of traditional psychological research in this domain. Leta Hollingworth, who was highly influential in how psychology subsequently came to approach giftedness and was the founder of gifted education,[39] expressed concerns that Francis Galton's Hereditary Genius[40] identified gifted people by established adult reputation, after interventions no longer help much.[41] She suggested that one shift focus to gifted children, which has left a curious lacuna in the psychological research: study of gifted people is first and foremost study of gifted children. Therefore, the research that is available deals primarily with gifted children and I will be looking at children.

Hollingworth describes "child L" in middle school:[42]

He was relatively large, robust, and impressive, and was fondly dubbed "Professor." His attitudes and abilities were appreciated by both pupils and teachers. He was often allowed to lecture (for as long as an hour) on some special topic, such as the history of timepieces, ancient theories of engine construction, mathematics, and history. He constructed out of odds and ends (typewriter ribbon spools, for example) a homemade clock of the pendular type to illustrate some of the principles of chronometry, and this clock was set up before the class during the enrichment unit on "Time and Time Keeping," to demonstrate some of the principles of chronometry.

Coming from a slightly different angle, Martha June Morelock offers analysis for Michael Kerney:[43]

The Plato Phenomenon

Mr. Kearney reports that since Michael was very young, he has seemed to spontaneously manifest both factual knowledge and conceptual comprehension that no one has taught him. He recalls an incident when Michael was three years old . . .

Mr. K: Michael at three coming up to me—when I came up to me and he said "Dad, Dad! I've got to show you this, got to show you this!" And he showed me the commutative rule of algebra. And I said "Michael! That's great! Where did you learn that?" "I don't know. I just made it up!" And then he goes "Wait, Wait! There's more! There's more!" And then he showed me the associative rule.

In searching for an explanation for this phenomenon, Mr. Kearney has considered a number of possibilities—including an analogy to Platonic philosophy . . .

Mr. K: Just in terms of some of his mathematical ability—some of the cognitive abilities. Some of the fact knowledge that he knew. But we didn't look at those as telepathy or spiritual things. It was more platonic. I think our experience, if anything, would be related to Platonic Forms. He seemed to be able to go in and take things out of another dimension and apply them—things that you wouldn't normally know, he knew. I mean, I don't think the issue was whether or not anyone taught him or not. It was that they were available to him and on occasion, he could dip into a location and bring things up. He has a cognitive ability to see things whole.

There is a sense in which a staggering intelligence is the baseline of being human: the most important sense of intelligence is not any of the intelligences on a multiple intelligence scale and in fact not something that some people have more of,[44] but something like embodiment that is simply part of the baseline of being human: this sense of intelligence forms a necessary context to achievements like the above which, taken out of context, suggest that there is a very occult phenomenon manifest in a very few, showing "ordinary" intelligence to be trivial. That would be a deep misunderstanding of intelligence in all parties. The intelligence described in the above quotation is in fact something spiritual, along with "ordinary" intelligence, but there is something easier to see in this kind of achievement even if one has grown insensitive to ordinary intelligence as a spiritual feature of the divine image at work. Profound giftedness exists in continuities with broader human intelligence: artwork in a gallery, at its best, need not dazzle in a way that "shows" that nothing outside the gallery is beautiful; one can visit an art gallery and have one's eyes opened not only to the art but the world the art is drawn from.

If the royal, divine image expresses itself in profoundly gifted work, the expression of the image in work is not an ontologically distinct faculty that the profoundly gifted have that not everybody else has. There is, however, a qualitative difference, suitable for thick description. This quality would not be rightly identified in any sense as an exclusive or even primary shadow of the Theotokos in the Annunciation, but among many polarities and many kinds of difference work for the profoundly gifted resembles the Annunciation in one among many ways.

Before identifying the specific contours that might place the work of the profoundly gifted in the shadow of the Annunciation in a particular way, it may help to clarify one Eastern understanding of the Annunciation that I am using as a framework:[45]

The incarnation was not only the work of the Father, by His power and by His spirit, but it was also the work of the will and faith of the Virgin. Without the consent of the Immaculate, without the agreement of her faith, the plan was as unrealizable as it would have been without the intervention of the three divine Persons Themselves. It was only after having instructed her and persuaded her that God took her for His Mother and borrowed from her the flesh, that She so greatly wished to lend Him. Just as He became incarnate voluntarily, so He wished that His Mother should bear Him freely and with her full consent.

The Annunciation of the Theotokos,[46] in the Eastern Tradition, is not understood as a message the angel spoke, but was when the Theotokos gave her full cooperation to the divine initiative, saying, "Behold the handmaid of the Lord. Be it unto me according to thy word."[47] The Theotokos offers the perfect creaturely response to the divine initiative, and the most enduring works of profound giftedness are in its shadow. (There are many other points on the spectrum of human experience that are in its shadow, too.)

Creative work, and much of the serious work of the profoundly gifted, is a minor incarnation and the fruit of a minor annunciation. Madeleine l'Engle writes, "The artist is a servant who is willing to be a birthgiver. In a very real sense the artist (male or female) should be like Mary who, when the angel told her that she was to bear the Messiah, was obedient to the command."[48] It is the bearing of a Creation that comes to one initially unformed, not yet given concrete shape, and one gives to it out of one's nature, loves and serves it into being; one gives it one's own flesh until it has become enfleshed and ready to meet the world. There are other dimensions to the connection—perichoresis or interpenetration of bearer and gift, and a spiritual discipline l'Engle calls "almost identical with adoring the Master of the Universe in contemplative prayer"[49]—and the process, meditated on throughout Madeleine l'Engle's Walking on Water,[50] is not unique to the profoundly gifted, who are not correctly understood if they are viewed simply in terms of differences without attention to human commonalities.

But it is the textured shape taken by the human gold and incense for many profoundly gifted.

Myrrh and the suffering of the profoundly gifted

Suffering is a basic part of human life. It takes different forms, perhaps, but it is constitutive of human experience. Furthermore, there are a great many human experiences that are different from the inside and from the outside. If this is explored with regard to the profoundly gifted, this is not as something that sets the profoundly gifted apart, but exploring further the concrete human form of human universals that are given further specification one way for the profoundly gifted and are given further specification other ways for other populations.

Giftedness as studied in this paper does not automatically include emotional intelligence, but it does not leave emotional life unaffected: for the entire range of giftedness, and not only the profoundly gifted, "giftedness has an emotional as well as a cognitive substructure: cognitive complexity gives rise to emotional depth."[51] This has a marked positive aspect; it makes it easier to have a rich inner life and to experience joy, but "[i]ntensity, in particular, must be understood as a qualitatively distinct characteristic. It is not a matter of degree but of a different quality of experiencing:"[52] it is as if at an age where children of a particular bent are given toy power tools, the range of gifted children are left to contend with real power tools, leaving more positive possibilities but also more ways of getting hurt that for many children simply aren't an issue. This kind of inner life is a mixed blessing when it comes to experiencing difficulties.

What is school like for the profoundly gifted? What is do they experience when they are in a situation which people assume is entirely oriented around them and their interests, where they have life easy and do not need to apply themselves like other people? This is what it meant for two boys:

He would go to school from 8 to 2 and you would think that would be enough. Nope. Cause when he got home at 2 o'clock, he goes "Mom, I want work. They didn't give me any work." It's like "You did all that stuff at school?" "Oh, that's easy stuff.["] He used to complain "Mom, they're making me write "cat" and "dog" and all these three letter words." So I went to the school and I said "He doesn't like to write these things, and why are you having him read cat and dog books? He reads far beyond that level." And they said it was because they wanted his hands—because he was so young and his motor skills had to be developed, that they wanted him to read this little easy book so that he could write. Well, he was like, "Well, let me read the big books and I'll write."[53]

Ian completed Grade 3 in a quiet fury of anger, intellectual frustration and bitterness. His verbal and physical aggressiveness returned in full spate; however, as he was now 2 years older than he had been in Grade 1, he was able to maintain a tighter control on his emotions while at school, and his teachers remained quite unaware of the emotional toll levied on him. At home, however, he released all of his frustration and resentment and became, in Brock's words, "almost impossible to live with." In addition, he began to experience severe headaches, bouts of nausea, and stomach pains. [longer emphasis added][54]

This experience is a hint of the dark side of the profoundly gifted experience. Profound giftedness offers real advantages, and no account of it is complete without accounting for what seem almost like magic powers. Giftedness is a privilege, the more the better, or is commonly assumed to be such kind of unqualified privilege so that saying that giftedness is painful comes across like saying that riches are painful. Yet if it is a privilege, it is a privilege that includes an experience that can be painful enough to cause depression, escape through street drugs, and suicide.[55]

The analogy to wealth could be refined: profound giftedness seems to be like wealth in an odd currency that makes it easy to buy luxuries but difficult to acquire some necessities. The characteristics described under "Gold and Frankincense" are quite significant and a source of joy. In general the profoundly gifted experience is an experience of extremes, where few things are moderate. But there are things some others wouldn't guess at, such what such differences mean for difficulties finding and obtaining steady work, let alone a normal environment experienced as hostile enough to induce nausea in a young boy. Being significantly above average is an advantage, but it must be understood that the "moderately" gifted whom one is tempted to assume are "mediocre gifted" are in fact no such thing: they are almost what giftedness should be like, significantly above average and yet escaping certain problems.[56] "Moderate" giftedness coincides almost entirely with what has elsewhere been called the range of "socially optimum intelligence,"[57] and it resembles the classical image of moderation or a via media which not simply avoids two extremes but in its balance has something positive that both extremes lack. This is a different phenomenon from another range where birth trauma and brain damage seem close to a majority phenomenon,[58] is part of why scholars will speak about "the 'syndrome' of profound giftedness."[59] It's still classified as giftedness, but it not just a further enhanced form of the advantages in moderate giftedness. Doreen Freeman suggests of disability, "How often we hear people say they would 'rather be dead than disabled' yet the suicide rates of the disabled do not reflect this pessimistic view."[60] Disability is a different condition viewed from the inside and the outside, and so is giftedness, for which the suicide rates are apparently higher. We are aware that stereotypes can affect a true appreciation of other groups, which includes race and disability, and also include profound giftedness as an experience difficult to judge from the outside. (Not that the profoundly gifted experience is unique in looking different from the inside versus the outside: there are any number of human experiences that are different from the inside and the outside, and this is not a distinction for the profoundly gifted but only how the phenomenon plays out for them.)

Aharon Lichtenstein writes as he concludes an article on suffering as having a profound place within Judaism:[61]

In conclusion, I return to the sinking feeling that much of what has been said here might fall on deaf ears... any attempt to cry up the purgative nature of suffering might be viewed, especially after the Holocaust, as trite, platitudinous, and—what is worst—callous...

I can understand such a reaction—and indeed, up to a point, share it. But only up to a point... Response to suffering cannot be divorced from the totality of religious experience...

Suffering, and the use of suffering, have a place within religion.

John Behr's central mystery is "life in death" for his appropriately titled The Mystery of Christ: Life in Death.[62] The cross is central: "This scriptural reflection on the Passion of Christ began by the apostles and evangelists was continued, expanded and deepened in the work of subsequent theologians, shaping every aspect of their theological vision."[63] This expands into meaning not only that Christ bore his Cross but we are to bear the Cross: what is normative is for "everything [in our lives to be] encompassed in [Christ's] economy."[64] "Life" is used in terms of the divine life,[65] and "death" holds far more than a merely biological meaning:[66] the mystery of "life in death" is a mystery of "frankincense in myrrh."

There have been people who have found in joy in suffering. Peter and other apostles, after being beaten,[67] left the council "rejoicing that they were counted worthy to suffer dishonor for the name."[68] Ware's closing examples in an article on martyrdom tell of martyrs' joy.[69] This puzzling behavior is difficult to understand but plays out what is said in the Sermon on the Mount, in a passage that is part of the Orthodox Church's main liturgy:[70] "Blessed are those who are persecuted for righteousness' sake, for theirs is the Kingdom of Heaven. Blessed are you when men revile you and persecute you and utter all manner of evil falsely against you for my account. Rejoice and be glad, for your reward is great in heaven, for so men persecuted the prophets who were before you."[71] I cite these not because I expect it to be self-evident how people could respond this way, but precisely to suggest that there's something in their version of suffering that is hard to appreciate today.

Even if it is hard to see how, these texts indicate that there is something that may not be obvious about innocent suffering. Hebrews and I Peter elaborate and clarify: "For it was fitting that [God], for whom and by whom all things exist, in bringing many sons to glory, should make the pioneer of their salvation perfect through suffering,"[72] If Christ himself was made perfect through suffering then it would seem incongruous to say that suffering may have perfected Christ but should not apply to people in his shadow. "For one is approved if, mindful of God, he endures pain while suffering unjustly. For what credit is it, if when you do wrong and are beaten for it you take it patiently? But when you do right and suffer for it and take it patiently, you have God's approval:"[73] God's approval can be on the innocent sufferer even if the suffering is not externally labeled as suffering in the Lord's name.

To say that Christ "the pioneer of their salvation" was made perfect through suffering transforms our understanding of Christ and even more suffering. Elsewhere people learn from Christ, but in Hebrews we read shocking words: "Although he was a Son, he learned obedience through what he suffered."[74] (This is the only New Testament text where the Son is said to learn obedience.) In Hebrews 11.28, suffering is tied to faith, "portrayed as force sustaining God's people in times of opposition and affliction, enabling them to overcome fear and temptation and fulfill his purposes for them,"[75] which is the context to how Moses "considered abuse suffered for the Christ greater wealth than the treasures of Egypt, for he looked to the reward."[76] It may seem that such Biblical statements about suffering in the name of Christ only speak to the case of confessors and martyrs narrowly understood, but I Peter 2.19-20 forestalls such a reading and orients our understanding of innocent suffering as such. After describing Christ's voluntary suffering as normative and monastic living as a manifestation of martyrdom, Ware writes, "What has just been said about Christ, about the martyr and the monk, is also true in a certain measure of every Christian without exception,"[77] specifically in the sufferings of life. There are different forms of martyrdom which do not always include violence and death, but to be Christian is to be called to martyrdom.[78]

This is not resignation. Paul uses paschw of "his readers, Christians in general,"[79] and can have a very active ring, meaning "'to fight,' perhaps 'to fight an enforced fight,'... not 'to be helplessly exposed or subject to alien pressure,'... 'to prevail'. [emphasis added]"[80]But the understanding that filters into the gift of myrrh is not simply a temporary measure for when the problem cannot be properly addressed yet. Cases of truly difficult suffering are not an exceptional case that this teaching also applies to; they are the central case under this view. This view of suffering applies from relative inconveniences up to major suffering including poverty and hunger, the death of loved ones, illness from cancer to depression, and many other cases. If the profoundly gifted are no unique center to the Biblical teaching because they are in no sense the only ones to suffer, that does not make their suffering trivial. Suffering increases as one approaches sainthood, and while suffering does not confer any automatic sainthood, Orthodox hagiography details a number of people with unusually difficult lives—the saints who are canonized as unusually good at living a normal human life—and some of their relics are said to miraculously stream, significantly enough, with myrrh.[81] To see profoundly gifted suffering as outside the bounds of normal human life and to try an activist solution to bring it into the bounds of normal human life is to fail to realize that profoundly gifted suffering is a unique opportunity to live the normal Christian life, a life where gold and incense cannot be separated from myrrh.

The reality of myrrh is a reality of suffering made positive in a context where suffering is no longer the last word, and it is not separate from gold for kingship and frankincense for divinity. Those saints who are fragrant with myrrh are fragrant with Heaven's incense. There are some theologians who talk about humanity as the priest of Creation,[82] and the massive repositories of skills acquired by the profoundly gifted can be a legitimate exercise of kingship—humans properly exercise kingship in the image of God's kingship not only, and perhaps not primarily, when kingship is exercised over other people.[83] There is a kind of joy and pleasure to learning and acquiring skills, and this may not always be situated within an explicit ecclesial setting, but then it no less constitutes part of what is normal and the gift of gold for kingship.

Profound giftedness in its potential to harm others

Profound giftedness is both a gift from God and something whose use is not always good. Without going too far into the word "holy" (Hebr. qds, apparent etymological meaning, "separate"),[84] I would like to talk some about what it means, and why we should not make too facile an identification of holiness with moral goodness. Holiness consists less in the creature's relationship to the Creator than the Creator's relationship to the creature.[85] Giftedness is not unique in this regard, but it is giftedness that is not based on merit but is simply given by the Creator. It may not be achieved by being morally good, and it is misunderstood if it is treated as an accidental arrangement of cognitive faculties. And that lends to something paradoxical: the greater the gift, the greater the potential for evil in the use of that gift, even in the attempt to do good.

Where there is untold human suffering, it may well be related to profoundly gifted plans to improve the world. Stfane Courtois's The Black Book of Communism[86] tells of millions who starved to death under Marx's plan for a better world.[87] One can name Adam Smith and the fathers of the Industrial Revolution as creating a masculinist vision to improve the world, a vision that on the ground left things worse for a number of people, and in particular women: Bob Goudzwaard's Aid for the Overdeveloped West[88] argues that the economic system that some profoundly gifted have helped build in the West is in fact not good for humans qua humans. Much of the industrialization that has led from wives working in adult company to housewives working in solitary confinement, destroying conditions that some feminists would like to reclaim, is transformation of society that stems from profoundly gifted people's "good ideas" to make a better world.[89] It is perfectly coherent to say that a profoundly gifted person will persuasively argue for a vision of a better world that practically results in incalculable human suffering.

Thick description of myrrh: interdependent terms of human weal or woe

There is another feature of human life that gives a shape, allowing thick description, to what myrrh is; and this is not just for the profoundly gifted: this feature is a specific trait of interdependence. How one experiences this specific trait depends greatly on how it is received: if it is approached with joy and acceptance, can be experienced as suffering that is almost Heavenly in how full it is and how deep its grounds for joy,[90] or can be wrongly experienced as vanity, meaningless suffering that approaches dukkha.[91] The story is told of someone who saw Hell, in which wretched pandas were surrounded by rice but miserable and starving because their three foot long chopsticks made it impossible for the pandas to feed themselves. Then the visitor was taken to Heaven and saw pandas surrounded by rice, delightedly feeding and being fed by each other with their three foot chopsticks. The difference between Heaven and Hell is a difference that lies in how one is capable of experiencing the realities one is in. It is not just true in the next life that we can experience certain things as joyful or as meaningless dukkha. It is also true of this life, and more specifically of certain features of human interdependence, and the impossibility of independence, that are perhaps never completely avoidable but seem harder to even pretend to avoid in the profoundly gifted experience. It appears that some profoundly gifted may have no way to present their gifts in a way that a job recruiter will interpret as believable competence.[92] Paradoxically, an unusually impressive list of achievements may not be accompanied by much opportunity to be self-supporting and perhaps not other "necessities."

In the work of Arthurian criticism Arthurian Torso,[93] Lewis discusses Virgil in Charles Williams' Taliessin through Logres:[94]

It is Virgil himself who died without reaching the patria, who saw 'Italy' only from a wave before he was engulfed forever. It is Virgil himself who stretches out his hands among the ghosts ripae ulterioris amore, longing to pass a river that he cannot pass. This poet from whose work so many Christians have drawn spiritual nourishment was not himself a Christian—did not himself know the full meaning of his own poetry, for (in Keble's fine words) 'thoughts beyond their thought to those high bards were given'. This is exquisite cruelty; he made honey not for himself; he helped to save others, himself he could not save.

...The Atonement was a Substitution, just as Anselm said. But that Substitution, far from being a mere legal fiction irrelevant to the normal workings of the universe, was simply the supreme instance of a universal law. 'He saved others, himself he cannot save' is a definition of the Kingdom. All salvation, everywhere and at all times, in great things or in little, is vicarious. The courtesy of the Emperor has absolutely decreed that no man can paddle his own canoe and every man can paddle his fellow's, so that the shy offering and modest acceptance of indispensable aid shall be the very form of the celestial etiquette. [emphasis original]

Lewis is summarizing Williams, and Williams's point has strong theological relevance. Ware introduces one topic of discussion as "what Charles Williams calls 'substituted love', 'coinherence', or 'the way of exchange',"[95] founded precisely on the above "law of the canoe." Profound giftedness is not a help for making honey for oneself but making honey for others, and this is not because the profoundly gifted are any more altruistic: whether one is selfish or generous, profound giftedness helps paddling others' canoes much better than it helps paddling one's own.

Alisdair MacIntyre's Dependent Rational Animals argues that dependence is constitutive of human nature.[96] Self-understanding as being independent requires sweeping acknowledgment of our dependence under the rug: true independence is probably impossible and certainly undesirable. If some people have difficulty achieving even a more relative independence, that is not an exception to how humanity normally works. It is continuous with large segments of humanity besides the profoundly gifted having more difficulty achieving a measure of independence. A few profoundly gifted experience worldly success—perhaps great—while many more experience surprising struggles.[97]

Lewis calls the law "exquisite cruelty," and it is even crueler if a definition of justice in terms of paddling one's own canoe is applied to the world, and one begins to suspect that even the Lawgiver, God, does not meet that standard of justice. But there is something in that picture that is not cruel, something that hinges on being willing to give up that standard of justice and accept the "law of the canoe" as terms of joy. If the profoundly gifted experience has extremes in its glories and difficulties, this form of interdependence is a difficulty that can and should be a glory, even if profoundly gifted may rarely be able to experience it as a particular form of human blessing.

Comparable remarks could be made for other populations and communities.

Conclusion

It seems a strained reading of Midas's tale to argue that whatever Midas said, the king consciously thought he would retain the usual human ability to touch things without changing them into anything else, and in addition have the option to turn things to gold by touch when he so desired. Perhaps that would have been a far wiser thing to ask for. Despite this lack of foresight, it appears that when the king said that he wanted everything he touched to turn to gold, the "everything" he envisioned of course did not include his food and wine, and absolutely did not include his only daughter. It seems that Midas's desire was for a fantasy version of a gift, and he was shocked when he received the real thing.

Profound giftedness is not a curse like Midas's. It offers much better prospects of living to old age, not to mention any number of other benefits. But it is, like any number of other human experiences, different from the inside than from the outside.

There is another king associated with gold—in fact, six billion such royalty on one account, and Midas's gold for his greed is in fact a base metal next to that gold that is from the same fountainhead as frankincense and myrrh. Human difference is not a matter of some people being at the human baseline, with everyone else starting from the same baseline but with added modifiers. In that sense everybody is on the baseline: it is mistaken to say that a profoundly gifted person is an "as modified by" representative of the majority, and neither more nor less mistaken than the opposite claim that most people are "as modified by" versions of the profoundly gifted, or comparable pairs of remarks spanning other human differences. Differences can be a chasm—sometimes requiring a great leap to bridge,—but when one can and does bridge the chasm, one may learn not of one more adjustment that can be made to a baseline centered on one's own group, but a deeper understanding of what the baseline is and is not.

In that sense there is nothing distinctive about profound giftedness being different from the inside and from how one would imagine it from the outside. It is illustrative of the human.

Partly Annotated Bibliography

(The annotation is geared primarily towards profound giftedness as a theological reader may be expected to understand the theological literature better than the literature on giftedness.)

Ashbrook Harvey, Susan, Scenting Salvation: Ancient Christianity and the Olfactory Imagination, Berkeley: University of California Press 2006.

Buttrick, George, The Interpreter's Bible, Abingdon Press 1952.

Carson, D.A. et al. (eds.), New Bible Commentary: 21^st Century Edition, Downer's Grove: InterVarsity Press 1994.

Clark, Stephen, Man and Woman in Christ, Ann Arbor: Servant 1980.

Courtois, Stephane et al., The Black Book of Communism: Crimes, Terror, Repression, Boston: Harvard University Press 1999.

If one wishes to take seriously that profound giftedness and good intentions can cause incalculable suffering, this text covers something that is better not ignored.

Dostoevsky, Fyodor, Crime and Punishment, New York: Random House 1956.

L'Engle, Madeleine, Walking on Water: Reflections on Faith and Art, Wheaton: Shaw 1980.

In my argument about gold and kingship, I have talked about a profoundly gifted accent to work. Giftedness as such is incidental at best to Madeleine l'Engle's focus, but this is a perspective on artistic work, a work that is close to contemplation, and if it does not have a profoundly gifted focus it still has a profoundly gifted perspective as the basis to explore artistic work as a whole.

Feldman, David, "A follow-up of subjects scoring above 180 IQ in Terman's 'Genetic Studies of Genius'", in Exceptional Children, vol. 50 no. 6 1984, 518-523.

This study makes the briefest passing mention that one of Terman 1925's very few profoundly gifted subjects "took his own life," without the briefest passing suggestion of any way this tragedy might be something to learn from, might be something related to the profoundly gifted experience, or could even be preventable. (Statistical analysis is impossible for a small sample, but if one person in a twenty-nine person sample committed suicide, this is hundreds of times higher than the population at large, or even demographics like those suffering from major depression.) This feature is symptomatic of a broader tendency in Feldman to be a generic summary without insight, and this is part of why I prefer the more qualitative studies such as Hollingworth 1975 or Morelock 1995.

Freeman, Doreen, "A Feminist Theology of Disability", in Feminist Theology 29 (2002), 71-85.

Fitzgerald, Allan, Augustine Through the Ages: An Encyclopedia, Grand Rapids: Eerdmans 1999.

Galton, Francis, Hereditary Genius: An Inquiry Into Its Laws and Consequences, London: Macmillan 1892 (1869).

From the introductory chapter Galton takes positions offensive even in his own day, and, to pick one example, his stand for intelligence-centered eugenics as a moral duty earns Galton's vile reputation today. His study seems to be less concerned about describing or studying genius in the sense offered by other sources than making a minimal study of his subjects sufficient to move on to his real interest, identifying whether genius is hereditary enough to bolster the eugenics he advocated. On a more positive view of the study of giftedness, Galton can be read as indicating how far the study of giftedness has come since Galton's approach. Too much of Galton's attitude lingers in later literature, but Webb 1980 bases his argument on a completely different footing: when he appeals for reform and cites a statistic that gifted education is part of special education but receives per capita less than three cents on the dollar compared to other special needs populations,[98] the argument is not that gifted people are entitled to better treatment because they are superior. The argument is that special needs should be treated in proportion to the need. He places giftedness as a greater special need than most people realize.

While acknowledging that the gifted population may be one of few special needs populations which is envied, one may hope that future literature may shift further away from Galton in the direction of recognizing the gifted population as having legitimate if perhaps unanticipated special needs, and given proportionate treatment to the form of special needs.

Goleman, Daniel, Emotional Intelligence: Why It Can Matter More than IQ, New York: Bantam 1995.

This controversial book treats one of several important aptitudes besides those studied here. The reason this article studies only one type of giftedness out of many is not because it's the only interesting kind of intelligence (emotional intelligence may be more important), but a limitation of what can reasonably be treated in a single paper.

Goudzwaard, Bob, Aid for the Overdeveloped West, Oshawa: Wedge 1975.

Gross, Miraca, "The Early Development of Three Profoundly Gifted Children of IQ 200," in Klein, Pnina; Tannenbaum, Abraham (eds.), To Be Young and Gifted, Norwood: Ablex 1992, 94-138.

This article is probably the best short sampling that offers a sense of human encounter through thick description of profoundly gifted children, and may serve as an orientation to the terrain of profoundly gifted children before tackling Hollingworth 1975 and Morelock 1995.

Gross, Miraca, "Factors in the Social Adjustment and Social Acceptability of Extremely Gifted Children," Ohio Psychology Press 1994 as seen online at http://www.gt-cybersource.org/Record.aspx?NavID=2_0&rid=10586 on 1 January 2007.

Rather than thick description this article provides an analysis of social issues surrounding the profoundly gifted and why their position requires them to deal with social challenges that are not as much of an issue for others.

Hayward, Jonathan, Artificial Intelligence, AI as an Arena of Magical Thinking for Skeptics: Cognitive Science, and Eastern Orthodox Views on Personhood, Master's Thesis (Cambridge University), 2004.

A study of the significance and power of basic human intelligence that can sometimes be overlooked in the study of giftedness.

Hollingworth, Leta, Children Above 180 IQ: Stanford-Binet Origin and Development, New York: Arno Press, 1975 (1942).

A classic study offering thick description of profoundly gifted children. Hollingworth has not been superseded.

Honderich, Ted (ed.), The Oxford Companion to Philosophy, Oxford: Oxford University Press 1995.

Howard, Pierce, The Owner's Manual for the Brain: Everyday Applications from Mind-Brain Research, Austin: Bard 2006.

Also readable as "A layperson's introduction to the culture and prejudices of cognitive psychology/cognitive science," but a valuable resource nonetheless, and the only psychological work I know that is not specialized in giftedness but offers an on-target treatment of profound giftedness.

Keselopoulos, Anestis, Man and the Environment: A Study of St. Symeon the New Theologian, Crestwood: St. Vladimir's Seminary Press, 2001.

Kittel, Gerhard, Theological Dictionary of the New Testament, Grand Rapids: Eerdmans 1976.

Klein, Ann, "Fitting the School to the Child: The Mission of Leta Stetter Hollingworth, Founder of Gifted Education," in Roeper Review, 23 (2), 2000, 97-103.

Kreeft, Peter, Three Philosophies of Life: Ecclesiastes: Life as Vanity; Job: Life as Suffering; Song of Songs: Life as Love, San Francisco: Ignatius 1989.

Landy, Frank, "The Long, Frustrating, and Fruitless Search for Social Intelligence: A Cautionary Tale," in Murphy, Kevin (ed.), A Critique of Emotional Intelligence: What Are the Problems and How Can They Be Fixed?, Mahwah: Lawrence Erlbaum 2006, 81-123.

An opposing views piece to (Howard) Gardner theory, including Goleman 1995.

Lewis, C.S., That Hideous Strength, New York: Scrivener 1996.

Lichtenstein, Aharon, "The Duties of the Heart and Response to Suffering," in Jewish Perspectives on the Experience of Suffering, Northvale: Jason Aronson, 1999.

Macintyre, Alisdair, Dependent Rational Animals: Why Human Beings Need the Virtues, Chicago: Open Court 1999.

Maloney, George, Gold, Frankincense & Myrrh: An Introduction to Eastern Christian Spirituality, New York: Crossroad 1997.

McVey, Kathleen, Ephrem the Syrian: Hymns, New York: Mahwah 1989.

Morelock, Martha, The Profoundly Gifted Child in Family Context, UMI 1995.

This dissertation studies in depth two profoundly gifted children who represent two forms of profound giftedness, Bethany Marshall (profound giftedness focused in a single area, in this case music performance) and Michael Kerney (profound giftedness spread out over many areas). The latter represents someone who is exceptional even for someone who is profoundly gifted. In some sense Morelock is a complement to Hollingworth 1975, but includes significant analysis alongside its thick description.

O'Brien, David; Shannon, Thomas, Catholic Social Thought: The Documentary Heritage, Maryknoll: Orbis 1992.

Schmemann, Alexander, For the Life of the World: Sacraments and Orthodoxy, Crestwood: Saint Vladimir's Seminary Press 1973 (1963), 17.

Smets, Alexis; van Esbroeck, Michel (trs. and eds.), Basil de Césare: Sur l'Origine de l'Homme, Paris: Cerf 1970.

Sword, L., "Gifted Children: Emotionally Immature or Emotionally Intense?" Gifted and Creative Services, Australia, as seen online at http://www.gt-cybersource.org/Record.aspx?rid=12310 on 1 January 2007.

Giftedness is not the same as emotional intelligence but it complexifies emotional life, meaning that gifted sometimes have to work harder to reach what others achieve by less effort to reach emotional maturity. (This article is not limited to profound giftedness but tries to address the broader gifted population.)

Terman, Lewis et al., Genetic Studies of Genius, Stanford: Stanford University Press 1925 (vol. 1), 1926 (vol. 2), 1930 (vol. 3), 1947 (vol. 4), 1959 (vol. 5).

Webb offers reasons why Terman's methods of identifying gifted people may have been unintendedly biased in favor of the members of the gifted population who enjoyed the greatest social advantage.[99] Terman uses the word "genius" in the title for a population that mostly overlaps the range of "socially optimal intelligence," without that much attention to profound giftedness. However, Terman offers a landmark study and almost everybody stands on his shoulders even in criticizing him.

Thunberg, Lars, Microcosm and Mediator: The Theological Anthropology of Maximus the Confessor, La Salle: Open Court, 1995.

Vasileios (Archimandrite), Hymn of Entry, Crestwood: Saint Vladimir's Seminary Press 1984.

Walton, John et al., The IVP Bible Background Commentary: Old Testament, Downer's Grove: InterVarsity Press 2000.

Ware, Kallistos, The Orthodox Church, New York: Penguin 1997 (1963).

Ware, Kallistos, The Orthodox Way, Crestwood: Saint Vladimir's Seminary Press, 1995 (1979).

Ware, Kallistos, "Seek First the Kingdom: Orthodox Monasticism and Its Service to the World," in Theology Today, April 2004, 61.1, http://proquest.umi.com/pqdlink?did=623880061&Fmt=7&clientId=9148&RQT=309&VName=PQD as seen 11/12/06.

Ware, Kallistos, "What is a martyr?" in Sobornost Incorporating Eastern Churches Review, London: Fellowship of St. Alban and St. Sergius, V.1 (1983), 7-19.

Webb, James; Meckstroth, Elizabeth; Tolan, Stephanie, Guiding the Gifted Child: A Practical Source for Parents and Teachers, Columbus: Ohio Psychology Publishing Company, 1982.

Webb ties together a great many things in this overview of the spectrum of giftedness (including profound giftedness). Where the sources I recommend for profound giftedness (Morelock 1995, Hollingworth 1974) offer qualitative thick description, this source incorporates theory, thick description, and practical advice into a picture that better than anything else I have seen in its insight into the entirety of the gifted experience.

Williams, Charles; Lewis, C.S., Taliessin through Logres, The Region of the Summer Stars, and Arthurian Torso, Grand Rapids: Eerdmans 1974.

Footnotes

[1] Vasileos 1984, 81-7.

[2] Ware 1997, 32; cf. Ware 1995, 34.

[3] McVey 1989, 4.

[4] Ware 2004, seen online.

[5] Ware 2004, seen online.

[6] Lewis 1996, 370: a character breaks from description of Arthurian grandeur to discuss how this in no way makes Britain superior because each nation has its own characteristic glory: each nation is distinctive and none is superior. Much the same could be said of various populations that are/might be given thick description through the methods of this paper.

[7] Ashbrook Harvey 2006, 73.

[8] Ashbrook Harvey 2006, 73.

[9] Ashbrook Harvey 2006, 66.

[10] Ashbrook Harvey 2006, 66-7.

[11] Ashbrook Harvey 2006, 254n138. I cannot here explore the suggestion, mentioned in Ashbrook Harvey 2006, 33, that "gold" may represent an underlying Aramaic term for another herbal aromatic.

[12] Irenaeus, Adversus Haereses 3.9.2.

[13]Hymns on the Nativity 19.4 in McVey 1989.

[14] Ashbrook Harvey 2006, 74.

[15]Hymns on the Nativity 9.15.

[16] Kittel 1976.

[17] Fitzgerald 1999.

[18] Ashbrook Harvey 2006, 119-21.

[19] Ashbrook Harvey 2006, 67-73.

[20] Ashbrook Harvey 2006, 68.

[21]Matthew 3.11; compare: "There is fire in chrism." (GPh 2.15)

[22] I Corinthians 15.45; cf. I Corinthians 15 and specifically 15.22.

[23] Walton 2000, Genesis 1.27.

[24]Hexameron, Homily 10.8.

[25]Hexameron, Homily 10.9, my own translation. [Emphasis taken from French translation]

[26] Keselopoulos 2001, 57.

[27] John Paul II, Laborum Exercens, 1981.

[28] LE, prologue.

[29] Keselopoulos 2001, 90.

[30] L'Engle 1980, 23.

[31] Dostoevsky 1956, III.5.

[32] Cf. Matthew 25.14-30 and I Corinthians 12.

[33]Matthew 25.14-30.

[34] Balz 1982-3, talentos.

[35] Hagner 1995, Matthew 25.14-5.

[36] Goleman 1995.

[37] Landy 2006 provides an opposing view.

[38] On anecdotal evidence, though, consider the case of one young woman with high enough social intelligence that when she enters a room all the conversations start to run more smoothly and everybody seems to want to be her close friend or romantic partner. It appears that a high enough level of social intelligence may come with unwanted side effects. (Personal conversation with her friend Lydia Klingforth c2000.)

[39] Klein 2000, 97.

[40] Galton 1892.

[41] Hollingworth 1942, xiv.

[42] Hollingworth 1942, 217-9.

[43] Morelock 1995, 223-5.

[44]Hayward 2004, 13-16.

[45] Nicolas Cabasilas, in M. Jugie, 'Homélies mariales byzantines,' Patrologia orientalis, XIX, fasc/, 3, 1925, p. 463, as quoted in Lossky 1976, 141.

[46] http://www.holyannunciation.org, as seen on 22/11/06.

[47]Luke 1.38, RSV.

[48] L'Engle 1980, 18.

[49] L'Engle 1980, 194.

[50] L'Engle 1980.

[51] Sword, online.

[52] Michael Pichowski as cited in Sword, online.

[53] Morelock 1995, 161.

[54] Gross 1992, 103.

[55] Webb 1982, 191-204: an entire chapter treats this.

[56] Gross 1992, 97.

[57] Gross 1994, seen online.

[58] Morelock 1995, 293-4.

[59] Morelock 1995, 295.

[60] Freeman 2002, 73.

[61] Lichtenstein 1999, 60.

[62] Behr 2006.

[63] Behr 2006, 33.

[64] Behr 2006, 143.

[65] Behr 2006, 35.

[66] Behr 2006, 143.

[67]Acts 5.40.

[68]Acts 5.41 RSV.

[69] Ware 1983, 18.

[70] The Divine Liturgy of St. John Chrysostom.

[71]Matthew 5.10-2.

[72]Hebrews 2.10 RSV.

[73]I Peter 2.19-20 RSV.

[74]Hebrews 5.8 RSV.

[75] Carson 1994, Hebrews 11.23-8.

[76]Hebrews 11.26 RSV.

[77] Ware 1983, 10.

[78] Ware 1983, 16.

[79] Kittel 1976, paschw.

[80] Kittel 1976, paschw.

[81] One hagiographical account may be seen at http://www.roca.org/OA/25/25d.htm, "And lo, the Star... St. Simon the Myrrh-gusher," as seen on October 9 2006. Like most hagiography, this is considered part of the Orthodox tradition of "biography as theology," theology given flesh in a person's life.

[82] Schmemann 1973 (1963), 17; Keselopoulos 2001, 57.

[83] See i.e. Keselopoulos 2001, 57, 64 and comments about Genesis 1:26-8 above.

[84] Botterweck 2003, qds.

[85] Kittel 1964, hagios.

[86] Courtois 1999.

[87] Courtois 1999, 4.

[88] Goudzwaard 1975, 4-5.

[89] If one is prepared to accept that truly traditional societies are something other than traditional roles attemptedly imposed on post-Industrial Revolution living conditions, then Clark 1980 provides an analysis largely of how women have suffered under certain changes, even if it doesn't focus on who contributed "good ideas" behind the changes.

[90] The Heavenly/Purgatorial suffering found in Job, in Kreeft 1989, 59-96.

[91] The Hellish suffering found in Ecclesiastes, in Kreeft 1989, 13-58.

[92] Personal conversations with different profoundly gifted, 2001.

[93] Lewis 1974.

[94] Lewis 1974, 305,7.

[95] Ware 1983, 11.

[96] MacIntyre 1999, 1ff.

[97] Personal conversations with profoundly gifted, 2001.

[98] Webb 1982, 3.

[99] Webb 1982, 10.

Dark Patterns / Anti-Patterns and Cultural Context Study of Scriptural Texts: A Case Study in Craig Keener's "Paul, Women, and Wives: Marriage and Women's Ministry in the Letters of Paul"

CJS Hayward
christos.jonathan.hayward@gmail.com
CJSHayward.com

Diploma in Theology and Religious Studies, 2003
Faculty of Divinity
University of Cambridge
20 May 2003

Abstract

The author suggests how the concept of 'patterns' in architecture and computer science, or more specifically 'dark patterns' / 'anti-patterns', may provide a helpful vehicle to explicitly communicate tacit knowledge concerning problematic thought. The author also provides a pilot study which seeks to provide a sample analysis identifying indicators for the 'surprising cultural find' pattern in which cultural context is misused to explain away offending Bible passages.

Introduction to Patterns, Dark Patterns, and Anti-patterns

The technical concept of pattern is used in architecture and computer science, and the synonymous dark patterns and anti-patterns refer to patterns that are not recurring best practices so much as recurring pathologies; my encounter with them has been as a computer programmer in connection with the book nicknamed 'GoF'[1]. Patterns do not directly provide new knowledge about how to program; what they do provide is a way to take knowledge that expert practitioners share on a tacit level, and enable them both to discuss this knowledge amongst themselves and effectively communicate it to novice programmers. It is my belief that the concept is useful to Biblical studies in providing a way to discuss knowledge that is also held on a tacit level and is also beneficial to be able to discuss explicitly, and furthermore that dark patterns or anti-patterns bear direct relevance. I hope to give a brief summary of the concept of patterns, explaining their application to Biblical studies, then give a pilot study exploring one pattern, before some closing remarks.

Each pattern consists of a threefold rule, describing:

A context.
A set of forces within that context.
A resolution to those forces.

In the contexts of architecture and computer science, patterns are used to describe best practices which keep recurring and which embody a certain 'quality without a name'. I wish to make a different application, to identifying and describing certain recurring problematic ways of thought in Biblical or theological inquiry which may be understood as dark patterns, which often seem to be interlaced with sophistry and logical fallacy.

Two examples of what a dark pattern, or anti-pattern might be are the consolation prize, and the surprising cultural find. I would suggest that the following provide instances of the consolation prize: discussion of a spiritual resurrection, flowering words about the poetic truth of Genesis 1, and Calvin's eucharistic theology. If you speak of a spiritual resurrection that occurs instead of physical resurrection, you can draw Christians far more effectively than if you plainly say, 'I do not believe in Christ's physical resurrection.' The positive doctrine that is presented is a consolation prize meant to keep the audience from noticing what has been taken away. The context includes a text that (taken literally) a party wants to dismiss. The forces include the fact that Christians are normally hesitant to dismiss Scripture, and believe that insights can give them a changed and deepened understanding. The resolution is to dress up the dismissal of Scripture as a striking insight. Like other patterns, this need not be all reasoned out consciously; I suggest, via a quasi-Darwinian/meme propagation mechanism, that dismissals of Scripture that follow some such pattern are more likely to work (and therefore be encountered) than i.e. a dismissal of Scripture that is not merely undisguised but offensive.

In the surprising cultural find, a meticulous study is made of a passage's cultural context to find some basis to neutralise the passage so that its apparent meaning does not apply to us. The context is similar to that of the consolation prize, if more specific to a contemporary Western cultural setting. The forces, beyond those mentioned for the consolation prize, include ramifications of period awareness and the Standard Social Science Model: there is a very strong sense of how culture and period can influence people, and they readily believe claims about long ago and far away that which would seem fishy if said about people of our time and place. The resolution is to use the passage's cultural setting to produce disinformation: the fruits of careful scholarly research have turned up a surprising cultural find and the passage's apparent meaning does not apply to us. The passage may be presented, for instance, to mean something quite different from what it appears to mean, or to address a specific historical situation in a way that clearly does not apply to us.

It is the dark pattern of the surprising cultural find that I wish to investigate as a pilot case study in this thesis.

Case Study

Opening Comments

The aim of this case study is to provide a pilot study of how the surprising cultural find may be identified as a dark pattern. In so doing, I analyse one sample text closely, with reference to comparison texts when helpful.

I use the terms yielding to refer to analysis from scholars who presumably have interests but allow the text to contradict them, and unyielding to refer to analysis that will not allow the text to contradict the scholar's interests. Yielding analysis does not embody the surprising cultural find dark pattern, while unyielding analysis does. I consider the boundary to be encapsulated by the question, 'Is the text allowed to say "No!" to a proposed position?'

Ideally, one would compare two scholarly treatments that are alike in every fashion save that one is yielding and the other is unyielding. Finding a comparison text, I believe, is difficult because I was searching for a yielding text with the attributes of one that was unyielding. Lacking a perfect pair, I chose Peter T. O'Brien's The Letter to the Ephesians[2] and Bonnie Thurston's Reading Colossians, Ephesians & 2 Thessalonians: A Literary and Theological Commentary[3] to represent yielding analysis and Craig Keener's Paul, Women, Wives: Marriage and Women's Ministry in the Letters of Paul [4] to represent unyielding analysis. I was interested in treatment of Ephesians 5:21-33. When I use Biblical references without a book, I will always be referring to Ephesians. All three of secondary sources present themselves as making the fruits of scholarly research accessible to the layperson. O'Brien provides an in-depth, nonfeminist commentary. Thurston provides a concise, feminist commentary. Keener provides an in-depth, Biblical Egalitarian monograph. Unfortunately, the ordered copy of Thurston did not arrive before external circumstances precluded the incorporation of new materials (and may have been misidentified, meaning that my advisor and I both failed after extensive searching to find a yielding feminist or egalitarian treatment of the text). My study is focused on Keener with comparison to O'Brien where expedient.

There seems to be an interconnected web of distinguishing features to these dark patterns, laced with carefully woven sophistry, and there are several dimensions on which a text may be examined. The common-sense assumption that these features are all independent of each other seems to be debatable. One example of this lack of independence is the assumption that what an author believes is independent of whether the analysis is yielding: the suboptimal comparison texts were selected partly because of the difficulty a leading Christians for Biblical Equality scholar and I experienced trying to locate yielding feminist analyses other than Thurston in Tyndale's library. I do not attempt to seriously investigate the interconnections, beyond commenting that features seem interconnected and less independent of each other than most scholars would assume by default.

The substance of my inquiry focuses on observable attributes of the text. I believe that before that point, observing a combination of factors may provide cues. I will mention these factors, but not develop them; there are probably others:

Is the book a monograph organised around one of today's hot issues, or e.g. a commentary organised around the contents of a Biblical text?
If you just open the book to its introduction, do you meet forceful persuasion? Are those first pages written purely to persuade, or do they attempt other endeavours (e.g. give factual or theoretical background that is not especially polemical)? What is the approach to persuasion?
Does the book contain anything besides cultural arguments finding that Biblical texts which apparently contradict the author's camp need not be interpreted that way?
How much does the author appear able to question our Zeitgeist (in a direction other than a more thorough development of assumptions in our Zeitgeist)?
What, in general, does the publisher try to do? The publisher is not the author, but publishers have specific aims and goals. It would seem to require explanation to say that a company indiscriminately publishes yielding and unyielding analysis because both resonate equally well with its editorial climate.

There will be a decided imbalance between attention paid to Keener and O'Brien. Part of this is due to external constraints, and part is due to a difference between O'Brien and Keener. With one major exception, described shortly, O'Brien's analysis doesn't run afoul of the concern I am exploring. If I were writing cultural commentary for my texts as Keener and O'Brien write cultural commentary for their texts, I would ideally spend as much time explaining the backgrounds to what Keener and O'Brien said. I believe they are both thinkers who were shaped by, draw on, and are critical of their cultures and subcultures. Explaining what they said, as illuminated by their context, would require parity in treatment. However, I do not elaborate their teachings set in context, but explore a problem that is far more present in Keener than in O'Brien or Thurston. I have more of substance to say about how Keener exhibits a problem than how O'Brien doesn't. As such, after describing a problem, I might give a footnote reference to a passage in O'Brien which shows someanalogy without seeming to exhibit the problem under discussion, but I will not systematically attempt to make references to O'Brien's yielding analysis as wordy as explanations of Keener's unyielding analysis.

The one significant example of unyielding analysis noted in O'Brien is in the comment on 5:21: O'Brien notes that reciprocal submission is not enjoined elsewhere in the Bible, points out that 'allelous' occurs in some contexts that do not lend themselves to reciprocal reading ('so that men should slay one another'[5]), and concludes that 'Believers, submit to one another,' means only that lower-status Christians should submit to those placed above them. This is as problematic as other instances of unyielding analysis, and arguably more disturbing as it lacks some of the common indicators alerting the careful reader to be suspicious. There is a point of contact between this treatment and Keener's: both assume that 5:21 and 5:22-6:9 are not merely connected but are saying the same thing, and it is one thing only. It is assumed that the text cannot enjoin of us both symmetrical and asymmetrical submission, so one must be the real commandment, and the other is explained away. Both Keener and O'Brien end up claiming that something is commanded in 5:21 with clarificatory examples following, without asserting that either 5:21 or 5:22-6:9 says something substantively different from the other about submission. I will not further analyse this passage beyond this mention: I consider it a clear example of unyielding analysis. This is the one part of O'Brien I have read of which I would not say, '...and this is an example of analogous concerns addressed by yielding scholarship.'

The introductions to O'Brien and Keener provided valuable cues as to the tone subsequently taken by the texts. Both are written to persuade a claim that some of their audience rejects, but the divergence in how they seek to persuade is significant. Keener's introduction is written to persuade the reader of Biblical Egalitarianism: in other words, of a position on one of today's current issues. The beginning of O'Brien's introduction tries to persuade the reader of Pauline authorship for Ephesians, which they acknowledge to be an unusual position among scholars today; the introduction is not in any direct sense about today's issues. O'Brien's introduction is written both to persuade and introduce the reader to scholarly perspectives on background; while nontechnical, it is factually dense and heavy with footnotes. Keener's introduction seems to be written purely to persuade: he give statistics[6] concerning recent treatment of women which are highly emotionally charged, no attempt being made to connect them to the text or setting of the Pauline letters. Keener's introduction uses emotion to bypass rationality, using loaded language and various other forms of questionable persuasion explored below; a naive reader first encountering this debate in Keener's introduction could well wonder how any compassionate person could be in the other camp. O'Brien works to paint a balanced picture, and gives a fair account of the opposing view before explaining why he considers it inadequate. O'Brien seeks to persuade through logical argument, and his book's pages persuade (or fail to persuade) as the reader finds his arguments to be sufficient (or insufficient) reason to accept its conclusions.

Emotional Disinformation

Among the potential indicators found in Keener, the first broad heading I found could be described as factual disinformation and emotional disinformation. 'Disinformation', as used in military intelligence ordinarily denotes deception through careful presentation of true details; I distinguish 'factual disinformation' (close to 'disinformation' traditionally understood) from 'emotional disinformation', which is disinformation that acts on emotional and compassionate judgment as factual disinformation acts on factual judgment. While conceptually distinct, they seem tightly woven in the text, and I do not attempt to separate them.

An Emotional Plea

One distinguishing feature of Keener's introduction is that it closes off straightforward rebuttal. Unlike O'Brien, he tries to establish not only the content of debate but the terms of debate itself, and once Keener has established the terms of debate, it is difficult or impossible to argue the opposing view from within those terms. Rebuttal is possible, of course, but here it would seem to require pushing the discussion back one notch in the meta-level hierarchy and arguing at much greater length. O'Brien seems more than fair in his style of argument; Keener loads the dice before his reader knows what is going on.

One passage is worth citing for close study [7]:

There are issues where most Biblically conservative Christians, including myself, disagree with prominent elements of the feminist movement... But there are other concerns which nearly all Christians, including myself, and nearly the whole women's movement plainly share....

[Approximately two pages of alarming claims and statistics, including:] ...Although "bride-burning" is now illegal in India, it still happens frequently; a bride whose dowry is insufficient may be burned to death so that her husband can find a new partner. There is no investigation, of course, because it is said that she simply poured cooking oil over herself and set herself on fire accidentally.... A Rhode Island Rape Crisis Center study of 1700 teenagers, cited in a 1990 InterVarsity magazine, reported that 65% of the boys and 47% of the girls in sixth through ninth grades say that a man may force a woman to have sex with him if they've been dating for more than six months.... Wife-beating seems to have been a well-established practice in many patriarchal families of the 1800's....

But while some Christians may once have been content to cite proof-texts about women's subordination to justify ignoring this sort of oppression, virtually all of us would today recognise that oppression and exploitation of any sort are sinful violations of Jesus's commandment to love our neighbour as ourselves and to love fellow-Christians as Christ loved us. [Keener goes on to later conclude that we must choose between a feminist conception of equality and an un-Christian version of subordination.]

The text starts by presenting Keener as Biblically conservative, moves to a heart-wrenching list of wrongs against women, implicitly conflates nonfeminist Christians with those who condone rape and murder, and presents a choice crystallising the fallacy of the excluded middle that had been lurking in prior words. It has more than one attribute of emotional disinformation.

Keener both identifies himself as Biblically conservative and says that, among some Christians, the egalitarian position is the conservative one (contrast chapter 4, where 'conservative' means a reactionary misogynist). Why? People are more likely to listen to someone who is perceivedly of the same camp, and falsely claiming membership in your target's camp is a tool of deceptive persuasion.

The recitation of statistics is interesting for several reasons.

On a strictly logical level, it is a non sequitur. It has no direct logical bearing on either camp; even its rhetorical position assumes that conservative, as well as liberal, members of his audience believe that rape and murder are atrocities. This is a logical non sequitur, chosen for its emotional force and what impact that emotional recoil will have on susceptibility. The trusting reader will recoil from the oppression listed and be less guarded when Keener provides his way to oppose such oppression. The natural response to such a revolting account is to say, 'I'm not that! I'm the opposite!' and embrace what is offered when the fallacy of the excluded middle is made explicit, in the choice Keener later presents.

Once a presentation of injustice has aroused compassion to indignation, most people do not use their full critical faculties: they want to right a wrong, not sit and analyse. This means that a powerful account of injustice (with your claims presented as a way to fight the injustice) is a powerful way to get people to accept claims that would be rejected if presented on their logical merits. Keener's 'of course' is particularly significant; he builds the reader's sense of outrage by adding 'of course' with a (carefully studied but) seemingly casual manner. It is not obvious to a Western reader that a bride's murder would be left uninvestigated; adding 'of course' gives nothing to Keener's logical case but adds significantly to the emotional effect Keener seeks, more effectively and more manipulatively than were he to visibly write those words from outrage.

The sentence about proof-texts and loving one's neighbour is of particular interest. On a logical level, it is restrained and cannot really be attacked. The persuasive and emotional force—distinct from what is logically present—is closer to, 'Accepting those proof-texts is equivalent to supporting such oppression; following the Law of Love contradicts both.'

This is one instance of a broader phenomenon: a gap between what the author entails and implicates. Both 'entail' and 'implicate' are similar in meaning to 'imply', but illustrate opposite sides of a distinction. What a text entails is what is implied by the text in a strictly logical sense; what a text implicates is what is implied in the sense of what it leads the reader to believe. What is implicated includes what is entailed, and may often include other things. The entailed content of 'But while some Christians...' is modest and does not particularly advance a discussion of egalitarianism. The implicated content is much more significant; it takes a logically tight reading to recognise that the text does not entail a conflation claiming that nonfeminist Christians condone rape and murder. The text implicates much more than it entails, and I believe that this combination of restricted entailment with far-reaching implication is a valuable cue. It can be highly informative to read a text with an eye to the gap between what is entailed and what is implicated. The gap between entailment and implicature seemed noticeably more pronounced in Keener than in yielding materials I have read, including O'Brien. Another example of a gap between entailment and implicature is found close[8], '...the secular generalization that Christians (both men and women) who respect the Bible oppose women's rights is an inaccurate caricature of these Christians' admits a similar analysis: the entailment is almost unassailable, while the implicature establishes in the reader's mind that the conservative position is excisable from respect for the Bible, and that the nonfeminist position denies something basic to women that they should have. The term 'women's rights' is by entailment the sort of thing one would not want to oppose, and by implicature a shorthand for 'women's rights as understood and interpreted along feminist lines'. As well as showing a significant difference between entailment and implicature, this provides an example of a text which closes off the most obvious means of rebuttal, another rhetorical trait which may be produced by the same mindset as produces unyielding analysis.

What is left out of the cited text is also significant. The statistics given are incomplete (they focus on profound ways in which women suffer so the reader will not think of profound ways in which men suffer) but as far as describing principles to discriminate yielding versus unyielding analysis, this seems to be privileged information. I don't see a way to let a reader compare the text as if there were a complementary account written in the margin. Also, a careful reading of the text may reveal a Biblical nonfeminist position as the middle fallaciously excluded earlier, in which sexual distinction exists on some basis other than violence. All texts we are interested in—yielding or unyielding—must stop somewhere, but it is possible to exclude data that should have been included and try to conceal its absence. Lacunae that seem to have been chosen for persuasion rather than limitation of scope may signal unyielding analysis.

Further Examples

In a discussion[9] of the haustafel's (Ephesians 5:21 and following [10] injunction that the husband love his wife based on Christ's love for the Church, Keener says, 'Indeed, Christ's love is explicitly defined in this passage in terms of self-sacrificial service, not in terms of his authority.' The passage does not mention that self-sacrificial service is a defining feature of Christ's model of authority, and in these pages the impression is created that the belief in servant love is a Biblical Egalitarian distinctive, so that the reader might be surprised to find the conservative O'Brien saying[11]:

...Paul does not here, or anywhere else for that matter, exhort husbands to rule over their wives. They are nowhere told, 'Exercise your headship!' Instead, they are urged repeatedly to love their wives (vv. 25, 28, and 33). This will involve each husband showing unceasing care and loving service for his wife's entire well-being...

O'Brien is emphatic that husbands must love their wives; examples could easily be multiplied. Keener argues for loving servanthood as if it were a claim which his opponents rejected. The trusting reader will believe that nonfeminists believe in submission and egalitarians alone recognise that Paul calls husbands to servant love. I believe that this selective fact-telling is one of the more foundational indicators: some factual claims will be out of a given reader's competence to evaluate, but so far as a reader can evaluate whether a fair picture is presented, the presence or absence of selective fact-telling may help.

Chapter 4 is interesting in that there are several thoughts that are very effectively conveyed without being explicitly stated. The account of 'conservatives' (i.e. misogynistic reactionaries) is never explicitly stated to apply to Christians who disagree with Keener, but works in a similar fashion (and for similar reasons) to the 'Green Book' which introduces the first major argument in The Abolition of Man.[12] By the same mechanism as the Green Book leads the reader to believe that claims about the outer world are in fact only claims about ourselves, not the slightest obstacle is placed to the reader believing that Keener exposes the true nature of 'conservatism', and that the picture of Graeco-Roman conservatism portrayed is a picture of conservatism, period, as true of conservatism today as ever.

A smaller signal may be found in that Keener investigates inconvenient verses in a way that never occurs for convenient ones. Keener explores the text, meaning, and setting to 5:22-33 in a way that never occurs for 5:21; a careless reader may get the impression that 5:21 doesn't have a cultural setting.

Drawing on Privileged Information

I would next like to outline a difference between men's and women's communication, state what Keener's Roman conservatives did with this, and state what Keener did with the Roman conservatives. One apparent gender difference in communication is that when a woman makes a claim, it is relatively likely to mean, 'I am in the process of thinking and here is where I am now,' while a man's claim is more likely to mean, 'I have thought. I have come to a conclusion. Here is my conclusion.' Without mentioning caveats, there is room for considerable friction when men assume that women are stating conclusions and women assume that men are giving the current state of a developing thought. The conservatives described by Keener seem frustrated by this friction; Keener quotes Josephus [13]:

Put not trust in a single witness, but let there be three or at least two, whose evidence shall be accredited by their past lives. From women let no evidence be accepted, because of the levity and temerity of their sex; neither let slaves bear witness, because of the baseness of their soul.

This passage is introduced, "...regards the prohibition of women's testimony as part of God's law, based in the moral inferiority inherent in their gender." The reader is not likely to question whether it's purely misogyny for a man (frustrated by women apparently showing levity by changing their minds frequently) to find this perceived mutability a real reason why these people should not be relied on as witnesses when someone's life may be at stake. Keener has been working to portray conservatives as misogynistic. Two pages earlier[14], he tells us,

An early Jewish teacher whose work was undoubtedly known to Paul advised men not to sit among women, because evil comes from them like a moth emerging from clothes. A man's evil, this teacher went on to complain, is better than a woman's good, for she brings only shame and reproach.

This, and other examples which could be multiplied, deal with something crystallised on the previous page[15]. Keener writes,

Earlier philosophers were credited with a prayer of gratitude that they were not born women, and a century after Paul a Stoic emperor could differentiate a women's soul from that of a man.

The moral of this story is that believing in nonphysical differences between men and women is tantamount to misogyny. This is a highly significant claim, given that the questions of women's ordination and headship in marriage are largely epiphenomenal to the question of whether we are created masculine and feminine at every level of our being, or ontologically neuter spirits in reproductively differentiated bodies. Keener produces a conclusion (i.e. that the human spirit is neuter) without ever stating it or drawing the reader to consciously consider whether this claim should be believed. In a text that is consistently polite, the opposing view is not merely negated but vilified: to hold this view (it is portrayed) is tantamount to taking a view of women which is extraordinarily reprehensible. Either of these traits may signal unyielding analysis; I believe the combination is particularly significant.

Tacit and Overt Communication

Although the full import of tacit versus overt communication is well beyond my competency to address, I would like to suggest something that merits further study.[16] Keener seemed, to a significant degree, to:

Tacitly convey most of his important points, without stating them explicitly.
Present claims so the opposing view is never considered.
Build up background assumptions which will produce the desired conclusions, more than give explicit arguments.
Work by manipulating background assumptions, often provided by the reader's culture.

As an example of this kind of tacit communication, I would indicate two myths worked with in the introduction and subsequently implied. By 'myth' I do not specifically mean 'widespread misconception', but am using a semiotic term comparable in meaning to 'paradigm': '[M]yths act as scanning devices of a society's 'possibles' and 'pensables' [17]. The two myths are:

- Men are powerful and violent aggressors, whilst women are powerless and innocent victims. The alarming claims and statistics[18] mention aggression against men only in the most incidental fashion.
- The accurate spokesperson for women's interests is the feminist movement. Keener diminishes this myth's force by disclaiming support for abortion (and presenting a pro-choice stance as separable from other feminist claims), but (even when decrying prenatal discrimination in sex-selective abortion[19]) Keener refers to the feminist movement interchangeably as 'the feminist movement'[20] and 'the women's movement'[21], and does not lead the reader to consider that one could speak for women's interests by contradicting feminism, or question the a priori identification of womens' interests with the content of feminist claims.As well as the emotional disinformation explored in many of the examples above, there are several points where the nature of the argument is of interest. Five argument-like features are explored:
  - Verses which help our position are principles that apply across all time; verses which contradict our position were written to address specific issues in a specific historical context.
  - X had beneficial effect Y; X was therefore purely instrumental to Y, and we may remove X if we no longer require X as an instrument to Y.
  - The absolute position taken in this passage addresses a specific historical idiosyncrasy, but the relative difference between this passage and its surroundings is a timeless principle across all times.
  - If X resonates with a passage's cultural context, then X need not be seen as part of the Bible's revelation.
  - We draw the lines of equivalence in the following manner...
  'Verses which help our position are principles that apply across all time; verses which contradict our position were written to address specific issues in a specific historical context' is less an argument than an emergent property. It's not argued; the text just turns out that way. Keener gives a diplomatically stated reason why Paul wrote the parts of 5:22-6:9 he focuses on: 'Paul was very smart.'[22] The subsequent argument states that Paul wrote in a context where Christians behaving conservatively would diminish he perceived threat to social conservatives. Keener writes[23], 'Paul is responding to a specific cultural issue for the sake of the Gospel, and his words should not be taken at face value in all cultures.' There is a fallacy which seems to be behind this argument in Keener: being timeless principles and being historically prompted are non-overlapping categories, so finding a historical prompt suffices to demonstrate that material in question does not display a timeless principle.'The absolute position taken in this passage addresses a specific historical idiosyncrasy, but the relative difference between this passage and its surroundings is a timeless principle across all times.' A text embodies both an absolute position in se, and a relative difference by how it is similar to and different from its surrounding cultural mainstream. 5:22-33 requires submission of wives and love of husbands; that absolute position can be understood with little study of context, while the relative difference showed both a continuity with Aristotelian haustafels and a difference by according women a high place that was unusual in its setting. The direction of Keener's argument is to say explicitly[25] that the verses should not be taken at face value, and to implicitly clarify that the absolute position should not be taken at face value, but part of the relative position, namely the sense in which Paul was much more feminist-like than his setting ('[A quote from Plutarch] is one of the most "progressive" social models in Paul's day... It is most natural to read Paul as making a much more radical statement than Plutarch, both because of what Paul says and because of what he does not say,'[26]) is a timeless principle that should apply in our day as well as Paul's. Without proper explanation of why the relative difference should be seen as absolute, given that the absolute position is idiosyncratic, the impression is strongly conveyed that respecting Paul's spirit means transposing his absolute position so that a similar relative difference exists with relation to our setting.'We draw equivalences in the following manner...' This is not a single argument so much as an attribute of arguments; I believe that what is presented as equivalent can be significant. In the autobiographical comments in the introduction, Keener writes[27]:What Keener has been arguing is not just the relevance of culture but the implicit necessity of a piecemeal hermeneutic. The implication (beyond an excluded middle) is that using culture to argue a piecemeal, feminist modification to Paul is the same sort of thing as not literally practicing the holy kiss.[28] The sixth of seven chapters, after emotionally railing against slavery, argues that retaining the institution of marriage while excising one dimension is the same sort of thing as abolishing the institution of slavery; 'The Obedience of Children: A Better Model?'[29] explicitly rejects the claim that marriage is more like parenthood than owning slaves. While no comparison is perfect, I believe that these are examples of comparisons where it is illuminating to see what the author portrays as equivalent.In my own experience at least, this kind of argument is not purely the idiosyncrasy of one book. The idea this thesis is based on occurred to me after certain kinds of arguments recurred. Certain dark patterns, or anti-patterns, came up in different contexts like a broken record that kept on making its sound. I'm not sure how many times I had seen instances of 'X had beneficial effect Y; X was therefore purely instrumental to Y, and we may remove X if we no longer require X as an instrument to Y,' but I did not first meet that argument in Keener. These arguments represent fallacies of a more specialised nature than post hoc, ergo propter hoc ("after the fact, therefore because of the fact") or argumentum ad ignorantiam ("appeal to ignorance"). I believe that they allow a persuasive, rational-seeming argument of a conclusion not yet justified on logical terms. The experience that led to the formation of my thesis was partly from repeatedly encountering such fallacies in surprising cultural find arguments.I have tried to provide a pilot study identifying indicators of unyielding analysis. These indicators are not logically tied in the sense of 'Here's something which, on logical terms, can only indicate unyielding analysis.' The unyielding analysis I have met, before and in Keener, has been constructed with enough care to logic that I don't start by looking at logic. There are other things which are not of logical necessity required by unyielding analysis, but which seem to be produced by the same mindset. I have encountered these things both in the chosen text and in repeated previous experiences which first set me thinking along these lines.It is unfortunate that my control text made little use of emotion. I believe my case study would have been better rounded, had I been able to contrast emotion subverting logic in Keener with emotion complementing logic in the control text. As it is, the case study lends itself to an unfortunate reading of "logic is good and emotion is bad", and gives the impression that I consider the bounds of legitimate persuasion to simply be those of logic.
  
  Directions for Further Inquiry
  
  There were other indicators which I believe could be documented from this text with greater inquiry, but which I have not investigated due to constraints. Among these may be mentioned:
  - Misrepresentation of material. Recognising this would seem to require privileged information, and work better for an area where the reader knows something rather than nothing, but I believe that a reader who knows part of the covered domain stands to benefit from seeing if it is covered fairly.
  - Doing more than a text presents itself as doing. A certain kind of deceit, in which the speaker works hard to preserve literal truth, has a complex quality caused by more going on than is presented. I believe an exploration of this quality, and its tie to unyielding analysis, may be fruitful.
  - Shared attributes with a test case. A small and distinctive minority of cases qualify to become test cases in American legal practice; they possess a distinct emotional signature, and portions of Keener's argument (i.e. 'Would [Paul] have ignored her personal needs in favour of the church's witness?'[31]) are reminiscent in both argument and emotional appeal of test cases.
  - An Amusement Park Ride with a Spellbinding Showman. Especially in their introductions, O'Brien seems to go out of his way to let the reader know the full background to the debate; Keener seems more like a fascinating showman who directs the reader's attention to certain things and away from others; knowing the other side to statistics cited[32]—or even knowing that there is another side—destroys the effect. A careful description of this difference in rhetoric may be helpful, and I believe may be tied to disinformation in that there is a difference in working style; yielding persuasion suffers far less from the reader knowing the other side than does unyielding persuasion.Lastly, I would suggest that a study of sharpening and leveling would be fruitful.[34] 'Sharpening' and 'leveling' refer to a phenomenon where people remembering a text tend to sharpen its main points while leveling out attenuating factors. For many texts, sharpening and leveling are an unintended effect of their publication, while Keener seems at times to write to produce a specific result after sharpening and leveling have taken effect. What he writes in itself is more carefully restrained than what a reader would walk away thinking, and the latter appears to be closer to what Keener wants to persuade the reader of. Combining narrow entailment with broad implicature is a way for an author to write a text that creates a strong impression (sharpening and leveling produce an impression from what is implicated more than what is entailed) while being relatively immune to direct criticism: when a critic rereads a text closely, it turns out that the author didn't really say the questionable things the critic remembers the author to have said.[1] I.e. the 'Gang of Four': Gamma, Erich; Helm, Richard; Johnson, Ralph; Vlissides, John, Design Patterns: Elements of Reusable Object-Oriented Software, Boston: Addison-Wesley, 1994.[4] Peabody: Hendrickson, 1992.[7] Ibid., pp. 6-9; compare almost any of O'Brien pp. 4-47.[10] A haustafel is a household code such as the one found in Ephesians; for my purposes, the Ephesians haustafel stretches from 5:21 to 6:9.[13] Keener, p. 163; O'Brien in pp. 405-438 does not cite a non-Biblical primary source likely to be similarly repellent, and portrays opposing secondary sources as mistaken without setting them in a disturbing light, i.e. in footnote 211, page 413.[16] My attempts to find material discussing how these things work, academic or popular, have had mixed success. If I were to write a thesis around this issue, I would initially explore works such as Michael I. Polanyi's Personal Knowledge: Towards a Post-Critical Philosophy, Chicago: University of Chicago Press, 1958, and anthropological treatments of the high-context/low-context and direct/indirect axes of human communication (which suggest relevant lines of inquiry). C.S. Lewis's account of the Un-man's dialogue with the Lady in Perelandra (chapters 8-11, pp. 274-311 in Out of the Silent Planet / Perelandra, Surrey: Voyager Classics, 1938 / 1943), seems to represent a very perceptive grappling with the issue of tacit communication in relation to deceit.[19] Ibid., p. 7.[22] Ibid., p. 141. Contrast O'Brien's comments on 6:5-9 in 447-456, seemingly the most obvious place to portray at least some of the text as parochial; O'Brien disclaims that Paul was making any social comment on slavery (p. 448), but unpacks the verses without obviously approaching the text from the same mindset as Keener.[25] Keener, p. 170.[28] Remember that Keener is an American. The suggestion he makes is more significant in U.S. than English culture. U.S. culture has a place for giving kisses to one's romantic partner, to family, and to small children, but not ordinarily to friends. Because of this, culture shock affects almost any attempt to consider ecclesiastical usage. 'Greet one another with a holy kiss.' serves in U.S. Evangelical conversation as the standard example of a New Testament injunction which cannot be taken seriously as a commandment to follow. It seem to be often assumed as an example of cultural noise in the Bible.[31] Keener, p. 148.[34] Comments from Asher Koriat, Morris Goldsmith, and Ainat Pansky in 'Toward a Psychology of Memory Accuracy (in the 2000 Annual Review of Psychology as seen in 2003 at http://www.findarticles.com/cf_0/m0961/2000_Annual/61855635/p7/article.jhtml?term=) provide a summary, with footnotes, suggesting the basic psychological mechanism. An accessible treatment of a related, if not identical, application to what I suggest here is found on pp. 91-94 in Thomas Gilovich's How We Know What Isn't So, New York: The Free Press, 1993.

- [33] I.e. the 'Gang of Four': Gamma, Erich; Helm, Richard; Johnson, Ralph; Vlissides, John, Design Patterns: Elements of Reusable Object-Oriented Software, Boston: Addison-Wesley, 1994.
- [32] Ibid. pp. 7-8.
- [30] Oxford: Oxford University Press, 1979.
- [29] Keener, pp. 186-188; contrast O'Brien, pp. 409-438, where he elaborates the text's analogy with Christ and the Church as a model for understanding marriage, rather than comparing to slavery (which Keener not only does but works to give the reader a reservoir of anger at slavery which may transfer when he argues that marital submission is like slavery).
- [27] Ibid., p. 4; contrast the series preface before O'Brien: 'God stands over against us; we do not stand in judgment of him. When God speaks to us through his Word, those who profess to know him must respond in an appropriate way...' (page viii).
- [26] Ibid., p. 170.
- [24] Ibid., pp. 174-8. O'Brien covers some of the same basic facts without obviously presenting argument in this vein (pp. 405-409).
- [23] Keener, p. 170.
- [21] Ibid., p. 9.
- [20] Ibid., p. 6.
- [18] Keener, pp. 7-9.
- [17] Maranda, Pierre, 'Elusive Semiosis', The Semiotic Review of Books, Volume 3, Issue 1, seen in 2003 at http://www.bdk.rug.nl/onderzoek/castor/srb/srb/elusive.html.
- [15] Ibid., p. 160.
- [14] Keener, p. 161.
- [12] Lewis, C.S., chapter 1, pp. 1-26, San Francisco: Harper SanFrancisco, 1943, 2001.
- [11] O'Brien, p. 419.
- [9] Ibid., p. 167.
- [8] Keener, p. 9.
- [6] Keener, pp. 7-9.
- [5] Rev. 6:8, RSV.
- [3] Macon: Smyth & Helwys, 1999.
- [2] Leicester: Apollos, 1999.
- Footnotes
- More broadly, I believe there is room for inquiry into the relation between this use of patterns and that in other disciplines. The application I have made is not a straight transposition; in architecture and computer science patterns are a tool to help people communicate about best practices to follow, not identify questionable practice to criticise as I have done here. What becomes of the Quality Without a Name may be interesting. This thesis only suggests two patterns; GoF[33] describes twenty-three computer programming patterns broken into three groups, so that they provide a taxonomy of recurring solutions and not merely a list. A taxonomy of Biblical studies patterns could be a valuable achievement.
On a broader scale, it is my hope that this may serve not only as a pilot study regarding unyielding analysis but a tentative introduction of a modified concept of 'pattern', or rather 'dark pattern' or 'anti-pattern' in theology. The concept of pattern was introduced by the architect Christopher Alexander and is sufficiently flexible to be recognised as powerful in computer science. I believe there are other patterns that can be helpful, and I would suggest that books like Alexander's The Timeless Way of Building[30] are accessible to people in a number of disciplines.
At a fairly basic level, the case study is a study of a cultural dimension of communication. I believe that portions of this pilot study may be deepened by the insights of scholars from humanities which study human culture and communication. I believe that some of my remarks would be improved by a serious attempt to connect them with high-context and low-context communication as studied in anthropology. If I am doing a pilot study that cannot provide much of any firm answers, I do hope to suggest fruitful lines of inquiry and identify deep questions which for which interdisciplinary study could be quite fruitful.
Conclusion
In some cases, the argument types I have described are not things which must be wrong, but things which lack justification. The claim that an absolute position is parochial but the relative difference is timeless is not a claim I consider to be unjustifiable, but it is a claim which I believe requires justification, a justification which is not necessarily provided.
"But it's part of the Bible!" I protested. "If you throw this part out, you have to throw everything else out, too." I cannot recall anyone having a good response to my objection, but even as a freshman I knew very well that if I were consistent in my stance against using culture to interpret the Bible, I would have to advocate women's head coverings in church, the practice of holy kisses, and parentally arranged marriages.
'If X resonates with a passage's cultural context, then X need not be seen as part of the Bible's revelation.' This is often interwoven with the previous two arguments. Apart from showing a feminist-like relative difference, Keener works to establish that Paul used a haustafel in a way that reduced Christianity's perceived threat to conservatives. This is presented as establishing that therefore wives are not divinely commanded to submit.
'X had beneficial effect Y; X was therefore purely instrumental to Y, and we may remove X if we no longer require X as an instrument to Y.' Keener argues[24] that the haustafel mitigated prejudice against Christianity, which is presented as a reason why we need not observe the haustafel if we do not perceive need for that apologetic concern.
Argument Structure

Does Augustine Return to the Interpersonal Image of Love as Representing the Trinity, or Does He Abandon This in Favour of the Psychological Image?

I. Mindset considerations

Does Augustine Return to the Interpersonal Image of Love as Representing the Trinity, or Does He Abandon This in Favour of the Psychological Image? Behind this question may lurk another question that is both connected and distinct from it: 'Does Augustine have a relational understanding of the image, or is his understanding ultimately solipsistic?' I take Rowan Williams[1] as an example of a scholar writing from a mindset which fails to adequately distinguish the two questions. He opens with quotes that read Augustine as almost Sabellian, and ends his opening paragraph with a spectacular strawman:

Augustine stands accused of collaborating in the construction of the modern consciousness that has wrought such havoc in the North Atlantic cultural world, and is busy exporting its sickness to the rest of the globe, while occluding the vision of the whole planet's future in its delusions of technocratic mastery — a hugely inflated self-regard, fed by the history of introspection.[2]

Williams is building up to a rescue operation. He offers a careful study which either counterbalances Augustine's apparent meaning or replaces it. He brings up quotations like, 'In the West, especially since the time of Augustine, the unity of the divine being served as the starting point of Trinitarian theology'[3], as examples of the reading he doesn't like. Williams's presentation of Augustine's text does not bring up Augustine's claim that all three persons of the Trinity speak in Old Testament theophanies. This claim is significant because Augustine rejects the Patristic claim that Old Testament theophanies are specially made through the immanent Son.[4] Williams seems to be fighting an obvious reading so he can rescue relationality in Augustine. I would argue that the psychological image is relational from the beginning, and that Augustine's image is psychological.

We're looking for relationality in the wrong place if we look for it in where Augustine stood in the controversies of his day. The deepest relationality does not lie in i.e. his writing against Arianism, but something that was so deeply ingrained in the Church that he would never have thought it necessary to explain. The very individualism he is accused of helping construct had not come together. In the Reformation-era Anabaptist/Zwinglian controversy over infant baptism, the issue was not whether faith precedes baptism. Both sides believed that much. The issue was whether that faith was reckoned along proto-individualist lines, or whether the faith of a community could sanctify members too young to embrace faith on terms an individualist would recognise. Augustine lived over a thousand years before that controversy. His tacit theory of boundaries was that of a community's bishop, not a counselor imparting the 'value-free' boundaries that flow from atomist individualism. I mention these examples to underscore that Augustine's understanding of where one person ends and another begins is much less articulate, much less thorough, much less basic, much less sealed, and in the end much less focal than ours. The difference is like the qualitative difference between Father, Son, and Holy Spirit in the Bible, and what either Arian or a Trinitarian did with what is present in the Bible. One is tacitly present, something you can't explain ('That's just the way things are!'), and the other is articulate, the sort of thing you can at least begin to explain and give reason for. In the end Augustine's understanding of how one person can meet another arises from a very different mindset from a setting where scholars argue that communication is impossible. This means that combining passages with individualist assumptions gives a very different meaning from combining the same passages with Augustine's patristic assumptions. It is the latter which represents Augustine's thought. I believe that Augustine did plant proto-modernist seeds. These seeds became a vital ingredient of modernism with many thinkers' successive modifications. However, the fact that they have become modernism today with the influence of a millenium and a half of change does not make Augustine an early modernist. His beliefs were quite different from atomist individualist modernism.

What is most important in Augustine's thought, and what he believed most deeply, includes some of what would never occur to him to think needed saying. These things that leave less obvious traces than his explicit claims. With that in mind, I would like to look more closely at Augustine's interiority:

But it [the mind] is also in the things that it thinks about with love, and it has got used to loving sensible, that is bodily things; so it is unable to be in itself without their images. Hence arises its shameful mistake [errus dedecus ], that it cannot make itself out among the images of things it has perceived with the senses, and see itself alone...[5]

What is interesting is what Augustine doesn't say here. A materialist would see bodily things as including other people, but Augustine did not think from that starting point. Would he have included people? That's a little less clear-cut. People are equal to oneself, and purely sensible objects are inferior. One is trying to go upwards, and Augustine does not seem to include equal people with inferior objects. Perhaps he does not raise this question. Augustine does go on to give a primacy to 'Know thyself,' but this is a matter of means,not of final end. Augustine is telling us to start with what is near at hand[6]. The distinction between what Augustine called 'interior' and what we would call 'private' is significant. It contains not only phantasms (sense impressions) but the res ipsa (the realities themselves) of intelligible things, and is where the soul meets intelligible truth. God is in the interior, and is shared between people. Furthermore, when we unite with God, we are united with others united with God. Where there is privacy, this is darkness caused by the Fall.[7]

II. Is the psychological image relational?

I would suggest that the psychological image is relational. Furthermore, I would suggest that the deepest relationality comes before making God the object of the vestigia (divine shadows or traces in Creation) of memory, understanding, and will. Augustine comments:

Even in this case [I Cor. 8:2], you notice, he [Paul] did not say "knows him", which would be a dangerous piece of presumption, but "is known by him." It is like another place where as soon as he said, But now knowing God, he corrected himself and said,Or rather being known by God...[8]

Before we worry if God is the object of our love, he must be the Subject behind it. And that does not mean we need to worry about orienting the vestigia (traces of God imprinted in Creation) so we add relationality as something external; relationality is there in the beginning, as God knowing us.

Is remembering, understanding, and willing oneself a relational activity? If it's sought on the right terms, it is. That means that it is not the pre-eminent goal , but a means, the bridge that must be crossed to gain access to other places.[9] That means that remembering, understanding, and willing have God as their goal even before he is their object. Augustine comments in another draft of the psychological image:

This word is conceived in love of either the creature or the creator, that is of changeable nature or unchangeable truth; which means either in covetousness or in charity. Not that the creature is not to be loved, but if that love is related to the creator it will no longer be covetousness but charity. It is only covetousness when the creature is loved on its own account.[10]

Augustine's discussion of use and enjoyment forbids the psyche to enjoy itself: regardless of immediate object, God is the goal or goal of 'Know thyself.'

In regard to the rest of Creation, it is much easier to read a psychological image as non-relational. His enjoyment/use distinction is not utilitarian but helped make utilitarianism[11]. Whilst he chose Christianity over Manicheanism and Platonism, these other beliefs left a lasting imprint[12]; Augustine rejected their claims that matter was evil, but his conversion to believing in the goodness of created matter was less thorough than one could desire. At one point Augustine considered sex a major to reject marriage; later he acknowledged sex an instrumental good when it propagates the people of God[13]. Augustine's much-criticised views on sex were in continuity with his understanding of creation, especially material creation. The created order that is neither called evil nor fully embraced as good, even fallen good: 'Cleansed from all infection of corruption, they are established in tranquil abodes until they get their bodies back—but incorruptible bodies now, which will be their guerdon [beneficial help], not their burden.'[14] This negative view of our (current) bodies is not a view of something one would want to be in relation with, and that is part of who we are created to be. From these, one could argue a continuity, if perhaps not parity, with a mindset that would support an individualistic psychological image. The argument has some plausibility, but I believe it is not ultimately true.

The biggest difference between a person and mere matter is that a person has spirit. Augustine can say, 'Now let us remove from our consideration of this matter all the many other things of which man consists, and to find what we are looking for with as much clarity as possible in these matters, let us only discuss the mind,' and abstract away a person's body to see the mind. I did not find a parallel passage abstracting away a person's mind to see body alone. Even if we assume he remained fully Manichean or fully Platonist, both Manicheanism and Platonism find some people to be above the level of matter. Augustine was free enough of Platonism to forcefully defend the resurrection of the body in De Civitate Dei[15] (The City of God). His belief in community is strong enough to make the interpersonal image important in his discussion. As argued in 'Mindset Considerations', he was quite far from individualism to begin with.

If community is important, why have a psychological image? Let me give one line of speculation. Augustine may be trying to put community on a proper ground. The Trinity turns outwards, not in an attempt to remedy any kind of defect, to try to get the creation to fill some need that it can't fill itself. The Trinity turns outwards out of abundance and fulness. Augustine may not want half persons seeking other half persons to try and create fulness. I believe he wants whole persons turning outwards out of the fulness within. In other words, a psychological image lays the ground for robust interpersonal relationship. Leaving this speculation aside, community was deeply ingrained in the patristic mindset, so that it didn't need saying. A psychological image could be explored without Augustine needing to add constant footnotes saying, 'But I still believe in community.'

III. What understanding does Augustine hold in the end?

Augustine explores a number of possible images of the Trinity before settling on one. He starts with an interpersonal image of lover, beloved, and love representing Father, Son, and Spirit respectively. Then he explores a 'psychological' image of mind, mental word, and will, which he revises into memory, understanding, and will. [16] Besides these images there are others not explored in this essay, such as thing seen, sense impression formed, and will. I would like to show which image Augustine chooses.

I would also like to make a distinction which makes sense of his choosing one image from several candidates. The distinction is the distinction between images that are 'built in' and 'after the fact'.[17] The difference between an image that is 'after the fact' and one that is 'built in' is the difference between a portrait which resembles a person, and a cloud in which a resemblance is found. Is the image something prior to anything observable, something around which other things are shaped, or is the image what we can find when we find things that look like a trinity?

This is arguably latent in Augustine's discussion of enigmas[18], and in remarks like 'It is true of all of his creatures, both spiritual and corporeal, that he does not know them because they are, but that they are because he knows them.'[19] The discussion of enigmas discusses things mysteriously hidden and then brought forth: Augustine mentions the story of Hagar and Sarah and then Paul drawing out their hidden symbolism. He wrote, 'As far as I can see then, by the word "mirror" he wanted us to understand an image, and by the word "enigma" he was indicating that although it is a likeness, it is an obscure one and difficult to penetrate.'[20] Augustine has looked through any number of images 'after the fact.' Now Augustine is trying to find out which of these plausible 'after the fact' candidates holds its plausibility precisely because it is the image 'built in'. He wants to know which of the resemblances to the Trinity is there precisely because the Trinity created it to be 'after our likeness'.[21]

What, at heart, is the distance between an image 'built in' and 'after the fact'? An 'after the fact' image is an 'after the fact image' because the behaviour and properties it shows, whilst a 'built in' image is such by its internal logic. An early draft of the psychological image compares the mind to the Father, its word to the Son, and the will joining them together to the Holy Spirit. Augustine, conscious of Arianism, says that a human mental word is equal to the mind that begot it. Even if he did not say this, and the word was described as inferior to the mind, there would be reason to see the mind/word/will psychological image as a 'built in' image. A person looking for an 'after the fact' image would look for the property that word and mind are equal because Father and Son are equal; if we look at 'built in' logic it is possible that uncreated God can beget a Word equal to himself, but a creaturely mind lacks the stature to beget a word that is its equal. Then the image would lack the property of equality, but it would have the internal logic of begetting what word one can beget, and reflect the Trinity at a deeper level. [22] This is like the difference between a literal translation and a dynamic equivalent. A literal translation tries to faithfully represent the text word for word; a dynamic equivalent tries to faithfully represent the text's impact, and it may give the text much more breathing room than a literal translator feels is respectful. A literal translation preserves details, but only a dynamic equivalent can render a poem into something that breathes as poetry. This may be part of why Williams writes, 'Growing into the image of God, then, is not a matter of perfecting our possession of certain qualities held in common with God... It is for us to be at home with our created selves...'[23] Growing into the image of God is not to look as if we had not been created, a literal rendering of God's attributes, but a creaturely dynamic equivalent in which a glimpse of the Trinity is rendered in creaturely idiom. This is inadequate; the creaturely idiom isn't powerful enough to capture the divine original, regardless of how it is rendered. Yet Augustine does settle on one image, one translation, not just as bearing 'after the fact' resemblance, but as having been constructed to have a 'built in' resemblance.

At the end of XV.3, Augustine quotes Wisdom 13:1-5 on recognising creation as the work of the Creator, and comments:

I quote this passage from the book of Wisdom in case any of the faithful should reckon I have been wasting time for nothing in first searching creation for signs of that supreme trinity we are looking for when we are looking for God, going step by step through various trinities of different sorts until we arrive at the mind of man.

This sets the programme for much of book XV. This program has subtleties of various sorts, and Augustine says far more than merely settling on the psychological image. The mind is the genuine image of the Trinity in that God has projected his own likeness downwards, but if we try to project anything in creation upwards—even the image God himself has fashioned—it must fall immeasurably short. The most faithful photograph captures at best a glimpse of the living person it portrays. So while Augustine settles with the psychological image, he is careful to portray its fundamental incompleteness. The psychological image may hold a unique privelege. Of all the 'after the fact' images surveyed, it alone bears apparent 'after the fact' resemblance because it was built to be image. In the end, this privelege of place underscores the book's apophasis all the more powerfully. Not only do the various apparent 'after the fact' images which we see fail to accurately convey the Trinity, but theimage which the Trinity itself has built into us, itself falls fundamentally short of God's transcendence. This is a far greater testimony to the divine transcendence: if an 'after the fact' image breaks down on closer observation, that only says that one specific 'after the fact' image breaks down on closer inspection. When the one 'built in' image, created by the Trinity itself, also breaks down, this says that the Trinity utterly transcends anything the creation can contain. The bigger it is, the immeasurably harder it falls, and the more we can learn from its failure.

But is this a failure of the created image?

Let's look more specifically at Augustine settling on the psychological image. In book X, Augustine writes:

These three, then, memory, understanding, and will, are not three lives but one life, not three minds but one mind.... Are we already then in a position to rise with all our powers of concentration to that supreme and most high being of which the human mind is the unequal image, but image nonetheless?[24] [emphasis added]

This is an important distinction. Augustine is not looking for a perfect and uncreated image of the Trinity, as the Son is the perfect and uncreated image of the Father. This is stated here, but I am not sure that this is a basic insight which informed his thought. He writes,

Again, there is this enormous difference, that whether we talk about mind in man and its knowledge and love, or whether about memory, understanding, and will, we remember nothing of the mind except through memory, and understand nothing except through understanding, and love nothing except through will. But who would presume to say that the Father does not understand either himself or the Son or the Holy Spirit except through the Son...[25]

This is an observation that the 'built in' image he has chosen does not have what one would seek in a 'after the fact' image. In the surrounding text[26], Augustine doesn't explicitly state that the differences are failings. However the long discussion of how much of the Trinity is not captured in this image does not seem a verbose way of saying that this image functions along 'built in' rather than 'after the fact' lines. It seems to be criticising the 'built in' image for failing to demonstrate 'after the fact' properties. If so, Augustine made something like a category error. This would suggest that the meticulous Augustine, so careful in accounting for the details of Bible verses, didn't conceive this as something to be meticulous about. The impression I receive from reading Augustine is that Augustine probably had thoughts like the 'built in'/'after the fact' distinction I drew, but they were probably tacit, much less developed and much less prominent, and in particular not an organising principle or winnowing tool Augustine used in deciding which of many trinities he would rest with.

And there are other texts which show a psychological image:

So the trinity as a thing in itself is quite different from the image of the trinity in another thing. It is on account of this image that the thing in which these three [memory, understanding, and love] are found is simultaneously called image...[27]

IV. Directions for further enquiry

The distinction between 'built in' and 'after the fact' appears to be significant. It would be interesting to study more specifically what is the relation between Augustine and this concept. There are quotations one could piece together to argue that Augustine thought in these terms, but other passages make this somewhat less clear. I have raised a question, but I believe more work needs to be done. My comments about that distinction in regard to Augustine's choice of image may be treated more as a question than an answer.

People who read Augustine as overly unitarian seem to find a psychological image, and people who read him as a balanced Trinitarian seem to find an interpersonal image. Reading the psychological image as relational may suggest an alternative placement with regard to these basic positions.

V. Conclusion

The earliest Church Fathers, writing more or less systematic theological treatises, generally didn't write about the Church. Was this because it was not important or not believed? To the contrary, it was air they breathed so deeply that they would never have thought of that as needing saying. Augustine was a Church Father and had the mindset of a Church Father. He chose a psychological image and did not try too hard to make it relational because he never thought it was the sort of thing that needed to have relationship added.

I have chosen an obvious reading which people may give people pause because it appears individualistic and not relational; this reading is that Augustine chose memory, understanding, and will as the 'built in' image of the Trinity. Of things raised in this essay that could merit further study, the most interesting is probably the concept of 'built in' images as contrasted with 'after the fact' images.

Bibliography

Ayres, Lewis, 'The Discipline of Self-Knowledge in Augustine's De Trinitate Book X', in ed. Ayres, Lewis, The Passionate Intellect, Rutgers University Studies in the Classical Humanities, vol. 7, Brunswick: Transaction, 1995, pp. 261-96

Bourassa, F., 'Théologie trinitaire chez s. Augustin', Gregorianum 58, 1997

Brown, Peter, Augustine of Hippo (revised edition), London: Faber and Faber Ltd., 1967, 2000

Cavadini, John, 'The Structure and Intention of Augustine's De Trinitate,' Augustinian Studies 23, 1992

Fitzgerald, Allan D. (ed.), Augustine through the Ages: An Encyclopedia, Eerdmans: Grand Rapids, 1999

Hill, Edmund (tr.), The Trinity, New City Press: Hyde Park, 1991.

MAXIMOS O PLANOUDHS, AUGUSTONOU PERI TRIADOS BIBLIA PENTEKAILEKA APER EK TES LATINON DIALEKTOU EIS THN ELLADA METENEGKE, AQENAI: KENTRON EKDOSEWS ERGWN ELLHNON SUGGRAFEWN, 1995 (Maximus the Traveler, Augustine's On the Trinity, Fifteen Books From the Latin Translated to [medieval] Greek Brought Together [in parallel translation], Athens: Center For Giving Greek Work and Collaborative Writing, 1995)

Meyendorff, John, Byzantine Theology. Historical Trends and Doctrinal Themes, London, 1975

Williams, Rowan, 'Sapientia and the Trinity: Reflections on the De Trinitate', Augustiniana, 1990.

Yates, Frances, The Art of Memory, London: Routledge and Kegan Paul Ltd., 1966, pp. 1-49

Footnotes

[1] Williams 1990, 317-332

[2] Williams 1990, 317

[3] Meyendorff 1974 (page number not specified), as quoted in Williams 1990, 317

[4] II.19-22; Williams 1990, 317-332. Unless otherwise noted, all references to Augustine are from De Trinitate, and all English quotations from De Trinitate are from Hill's translation.

[5] X.11

[6] 'The mind you see is not told Know thyself in the same way as it might be told "Know the cherubim and seraphim"; of them, as absent beings, we believe what they are declared to be, that they are certain heavenly powers.' (X.12)

[7] These latter observations in the same paragraph are taken from Fitzgerald 1999, 454-5.

[8] IX.1

[9] X.12 presents 'thyself' as more immediately knowable than (higher) 'cherubim and seraphim'.

[10] IX.13.

[11] Hill 1991, 283-4.

[12] Fitzgerald 1999, 341, 591.

[13] Ibid., 535-6.

[14] XV.45.

[15] Fitzgerald 1999, 653.

[16]'Memory', 'understanding', 'will', and (mental) 'word' are all understood very differently in Augustine from their meanings today. I can give a bare hint at the nature of difference by saying will is not a Neitzchian Übermensch's power to domineer, crush, and persevere in lonely selfishness, but something whose nature is to incline towards the other in love, and something that holds things together even inside a person. Beyond that, it would be at least another essay to try to explain these different concepts. I'm going to have to content myself with saying there are significant cultural differences that I can't fairly explain. A good understanding of Augustine's memory, for instance, is suggested by reading Confessions X, complemented by Yates' (1966, 1-49) treatment of memory in relation to ancient rhetoric.

[17] I have thought of this distinction out of discussion of universalia ante rem and universalia post rem that I had read, and I had originally used the more precise, if less vivid, terminology of 'ante rem' and 'post rem' for 'built-in' and 'after the fact' respectively. So far as I know, this usage is original to me.

[18] XV.15-16

[19] XV.22

[20] XV.15

[21] Gen 1:26, RSV

[22] This distinction applies to other images Augustine looks at; I chose and modified this example to highlight something also present in other parts of the text.

[23] Williams 1990, 321

[24] X.18,19

[25] XV.12

[26] XV.11-13

[27] XV.42

AI as an Arena for Magical Thinking Among Skeptics

Surgeon General's Warning

This piece represents my first serious study as an Orthodox Christian. The gist of it, by which I mean a critique of the artificial intelligence and cognitive science movement whose members are convinced of its progress for reasons unrelated to any real achievement of its core goal, is one I would still maintain. Artificial intelligence, over a decade after the thesis was written, remains "just around the corner since 1950". The core pioneer John von Neumann's The Computer and the Brain's core assertion that the basis of human thought is "add, subtract, multiply, and divide" remains astonishingly naïve to the point of being crass.

With that much stated, there are things that don't belong. The "I-Thou" existentialism is not of Orthodox origin and its study of occult aspects is simply inappropriate. I do not say inaccurate, only wrong. I believe there is probably some truth to some suggestion that the artificial intelligence endeavor represents a recurrence of age-old occult dreams dressed in the clothing of computer science and secular rationality. Such things should still not have been studied, or at very least not by me.

For those still interested, my dissertation is below.

Cog, portrayed as 'Robo Sapiens'

AI as an Arena for Magical Thinking Among Skeptics
Artificial intelligence, cognitive science, and Eastern Orthodox views on personhood

M.Phil. Dissertation

CJS Hayward
christos.jonathan.hayward@gmail.com
CJSHayward.com

15 June 2004

Abstract

Introduction

Artificial Intelligence

The Optimality Assumption

Just Around the Corner Since 1950

The Ghost in the Machine

Occult Foundations of Modern Science

Renaissance and Early Modern Magic

Science, Psychology, and Behaviourism

I-Thou and Humanness

Orthodox Anthropology in Maximus Confessor's Mystagogia

Intellect and Reason

Intellect, Principles, and Cosmology

The Intelligible and the Sensible

Knowledge of the Immanent

Intentionality and Teleology

Conclusion

Epilogue

Bibliography

Abstract

I explore artificial intelligence as failing in a way that is characteristic of a faulty anthropology. Artificial intelligence has had excellent funding, brilliant minds, and exponentially faster computers, which suggests that any failures present may not be due to lack of resources, but arise from an error that is manifest in anthropology and may even be cosmological. Maximus Confessor provides a genuinely different background to criticise artificial intelligence, a background which shares far fewer assumptions with the artificial intelligence movement than figures like John Searle. Throughout this dissertation, I will be looking at topics which seem to offer something interesting, even if cultural factors today often obscure their relevance. I discuss Maximus's use of the patristic distinction between 'reason' and spiritual 'intellect' as providing an interesting alternative to 'cognitive faculties.' My approach is meant to be distinctive both by reference to Greek Fathers and by studying artificial intelligence in light of the occult foundations of modern science, an important datum omitted in the broader scientific movement's self-presentation. The occult serves as a bridge easing the transition between Maximus Confessor's worldview and that of artificial intelligence. The broader goal is to make three suggestions: first, that artificial intelligence provides an experimental test of scientific materialism's picture of the human mind; second, that the outcome of the experiment suggests we might reconsider scientific materialism's I-It relationship to the world; and third, that figures like Maximus Confessor, working within an I-Thou relationship, offer more wisdom to us today than is sometimes assumed. I do not attempt to compare Maximus Confessor's Orthodoxy with other religious traditions, however I do suggest that Orthodoxy has relevant insights into personhood which the artificial intelligence community still lacks.

Introduction

Some decades ago, one could imagine a science fiction writer asking, 'What would happen if billions of dollars, dedicated laboratories with some of the world's most advanced equipment, indeed an important academic discipline with decades of work from some of the world's most brilliant minds—what if all of these were poured into an attempt to make an artificial mind based on an understanding of personhood that came out of a framework of false assumptions?' We could wince at the waste, or wonder that after all the failures the researchers still had faith in their project. And yet exactly this philosophical experiment has been carried out, in full, and has been expanded. This philosophical experiment is the artificial intelligence movement.

What relevance does AI have to theology? Artificial intelligence assumes a particular anthropology, and failures by artificial intelligence may reflect something of interest to theological anthropology. It appears that the artificial intelligence project has failed in a substantial and characteristic way, and furthermore that it has failed as if its assumptions were false—in a way that makes sense given some form of Christian theological anthropology. I will therefore be using the failure of artificial intelligence as a point of departure for the study of theological anthropology. Beyond a negative critique, I will be exploring a positive alternative. The structure of this dissertation will open with critiques, then trace historical development from an interesting alternative to the present problematic state, and then explore that older alternative. I will thus move in the opposite of the usual direction.

For the purposes of this dissertation, artificial intelligence (AI) denotes the endeavour to create computer software that will be humanly intelligent, and cognitive science the interdisciplinary field which seeks to understand the mind on computational terms so it can be re-implemented on a computer. Artificial intelligence is more focused on programming, whilst cognitive science includes other disciplines such as philosophy of mind, cognitive psychology, and linguistics. Strong AI is the classical approach which has generated chess players and theorem provers, and tries to create a disembodied mind. Other areas of artificial intelligence include the connectionist school, which works with neural nets,[1] and embodied AI, which tries to take our mind's embodiment seriously. The picture on the cover[2] is from an embodied AI website and is interesting for reasons which I will discuss below under the heading of 'Artificial Intelligence.'

Fraser Watts (2002) and John Puddefoot (1996) offer similar and straightforward pictures of AI. I will depart from them in being less optimistic about the present state of AI, and more willing to find something lurking beneath appearances. I owe my brief remarks about AI and its eschatology, under the heading of 'Artificial Intelligence' below, to a line of Watts' argument.[3]

Other critics[4] argue that artificial intelligence neglects the body as mere packaging for the mind, pointing out ways in which our intelligence is embodied. They share many of the basic assumptions of artificial intelligence but understand our minds as biologically emergent and therefore tied to the body.

There are two basic points I accept in their critiques:

First, they argue that our intelligence is an embodied intelligence, often with specific arguments that are worth attention.

Second, they often capture a quality, or flavour, to thought that beautifully illustrates what sort of thing human thought might be besides digital symbol manipulation on biological hardware.

There are two basic points where I will be departing from their line of argument:

First, they think outside the box, but may not go far enough. They are playing on the opposite team to cognitive science researchers, but they are playing the same game, by the same rules. The disagreement between proponents and critics is not whether mind may be explained in purely materialist terms, but only whether that assumption entails that minds can be re-implemented on computers.

Second, they see the mind's ties to the body, but not to the spirit, which means that they miss out on half of a spectrum of interesting critiques. I will seek to explore what, in particular, some of the other half of the spectrum might look like. As their critiques explore what it might mean to say that the mind is embodied, the discussion of reason and intellect under the heading 'Intellect and Reason' below may give some sense of what it might mean to say that the mind is spiritual. In particular, the conception of the intellects offers an interesting base characterisation of human thought that competes with cognitive faculties. Rather than saying that the critics offer false critiques, I suggest that they are too narrow and miss important arguments that are worth exploring.

I will explore failures of artificial intelligence in connection with the Greek Fathers. More specifically, I will look at the seventh century Maximus Confessor's Mystagogia. I will investigate the occult as a conduit between the (quasi-Patristic) medieval West and the West today. The use of Orthodox sources could be a particularly helpful light, and one that is not explored elsewhere. Artificial intelligence seems to fail along lines predictable to the patristic understanding of a spirit-soul-body unity, essentially connected with God and other creatures. The discussion becomes more interesting when one looks at the implications of the patristic distinction between 'reason' and the spiritual 'intellect.' I suggest that connections with the Orthodox doctrine of divinisation may make an interesting a direction for future enquiry. I will only make a two-way comparison between Orthodox theological anthropology and one particular quasi-theological anthropology. This dissertation is in particular not an attempt to compare Orthodoxy with other religious traditions.

One wag said that the best book on computer programming for the layperson was Alice's Adventures in Wonderland, but that's just because the best book on anything for the layperson was Alice's Adventures in Wonderland. One lesson learned by a beginning scholar is that many things that 'everybody knows' are mistaken or half-truths, as 'everybody knows' the truth about Galileo, the Crusades, the Spanish Inquisition, and other select historical topics which we learn about by rumour. There are some things we will have trouble understanding unless we can question what 'everybody knows.' This dissertation will be challenging certain things that 'everybody knows,' such as that we're making progress towards achieving artificial intelligence, that seventh century theology belongs in a separate mental compartment from AI, or that science is a different kind of thing from magic. The result is bound to resemble a tour of Wonderland, not because I am pursuing strangeness for its own sake, but because my attempt to understand artificial intelligence has taken me to strange places. Renaissance and early modern magic is a place artificial intelligence has been, and patristic theology represents what we had to leave to get to artificial intelligence.

The artificial intelligence project as we know it has existed for perhaps half a century, but its roots reach much further back. This picture attests to something that has been a human desire for much longer than we've had digital computers. In exploring the roots of artificial intelligence, there may be reason to look at a topic that may seem strange to mention in connection with science: the Renaissance and early modern occult enterprise.

Why bring the occult into a discussion of artificial intelligence? It doesn't make sense if you accept science's own self-portrayal and look at the past through its eyes. Yet this shows bias and insensitivity to another culture's inner logic, almost a cultural imperialism—not between two cultures today but between the present and the past. A part of what I will be trying to do in this thesis is look at things that have genuine relevance to this question, but whose relevance is obscured by cultural factors today. Our sense of a deep divide between science and magic is more cultural prejudice than considered historical judgment. We judge by the concept of scientific progress, and treating prior cultures' endeavours as more or less successful attempts to establish a scientific enterprise properly measured by our terms.

We miss how the occult turn taken by some of Western culture in the Renaissance and early modern period established lines of development that remain foundational to science today. Many chasms exist between the mediaeval perspective and our own, and there is good reason to place the decisive break between the mediaeval way of life and the Renaissance/early modern occult development, not placing mediaeval times and magic together with an exceptionalism for our science. I suggest that our main differences with the occult project are disagreements as to means, not ends—and that distinguishes the post-mediaeval West from the mediaevals. If so, there is a kinship between the occult project and our own time: we provide a variant answer to the same question as the Renaissance magus, whilst patristic and mediaeval Christians were exploring another question altogether. The occult vision has fragmented, with its dominion over the natural world becoming scientific technology, its vision for a better world becoming political ideology, and its spiritual practices becoming a private fantasy.

One way to look at historical data in a way that shows the kind of sensitivity I'm interested in, is explored by Mary Midgley in Science as Salvation (1992); she doesn't dwell on the occult as such, but she perceptively argues that science is far more continuous with religion than its self-understanding would suggest. Her approach pays a certain kind of attention to things which science leads us to ignore. She looks at ways science is doing far more than falsifying hypotheses, and in so doing observes some things which are important. I hope to develop a similar argument in a different direction, arguing that science is far more continuous with the occult than its self-understanding would suggest. This thesis is intended neither to be a correction nor a refinement of her position, but development of a parallel line of enquiry.

It is as if a great island, called Magic, began to drift away from the cultural mainland. It had plans for what the mainland should be converted into, but had no wish to be associated with the mainland. As time passed, the island fragmented into smaller islands, and on all of these new islands the features hardened and became more sharply defined. One of the islands is named Ideology. The one we are interested in is Science, which is not interchangeable with the original Magic, but is even less independent: in some ways Science differs from Magic by being more like Magic than Magic itself. Science is further from the mainland than Magic was, even if its influence on the mainland is if anything greater than what Magic once held. I am interested in a scientific endeavour, and in particular a basic relationship behind scientific enquiry, which are to a substantial degree continuous with a magical endeavour and a basic relationship behind magic. These are foundationally important, and even if it is not yet clear what they may mean, I will try to substantiate these as the thesis develops. I propose the idea of Magic breaking off from a societal mainland, and sharpening and hardening into Science, as more helpful than the idea of science and magic as opposites.

There is in fact historical precedent for such a phenomenon. I suggest that a parallel with Eucharistic doctrine might illuminate the interrelationship between Orthodoxy, Renaissance and early modern magic, and science (including artificial intelligence). When Aquinas made the Christian-Aristotelian synthesis, he changed the doctrine of the Eucharist. The Eucharist had previously been understood on Orthodox terms that used a Platonic conception of bread and wine participating in the body and blood of Christ, so that bread remained bread whilst becoming the body of Christ. One substance had two natures. Aristotelian philosophy had little room for one substance which had two natures, so one thing cannot simultaneously be bread and the body of Christ. When Aquinas subsumed real presence doctrine under an Aristotelian framework, he managed a delicate balancing act, in which bread ceased to be bread when it became the body of Christ, and it was a miracle that the accidents of bread held together after the substance had changed. I suggest that when Zwingli expunged real presence doctrine completely, he was not abolishing the Aristotelian impulse, but carrying it to its proper end. In like fashion, the scientific movement is not a repudiation of the magical impulse, but a development of it according to its own inner logic. It expunges the supernatural as Zwingli expunged the real presence, because that is where one gravitates once the journey has begun. What Aquinas and the Renaissance magus had was composed of things that did not fit together. As I will explore below under the heading 'Renaissance and Early Modern Magic,' the Renaissance magus ceased relating to society as to one's mother and began treating it as raw material; this foundational change to a depersonalised relationship would later secularise the occult and transform it into science. The parallel between medieval Christianity/magic/science and Orthodoxy/Aquinas/Zwingli seems to be fertile: real presence doctrine can be placed under an Aristotelian framework, and a sense of the supernatural can be held by someone who is stepping out of a personal kind of relationship, but in both cases it doesn't sit well, and after two or so centuries people finished the job by subtracting the supernatural.

Without discussing the principles in Thomas Dixon's 1999 delineation of theology, anti-theology, and atheology that can be un-theological or quasi-theological, regarding when one is justified in claiming that theology is present, I adopt the following rule:

A claim is considered quasi-theological if it can conflict with theological claims.

Given this rule, patristic theology, Renaissance and early modern magic (hereafter 'magic' or 'the occult'), and artificial intelligence claims are all considered to be theological or quasi-theological.

I will not properly trace an historical development so much as show the distinctions between archetypal scientific, occult, and Orthodox worldviews as seen at different times, and briefly discuss their relationships with some historical remarks. Not only are there surprisingly persistent tendencies, but Lee repeats Weber's suggestion that there is real value to understand ideal types.[5]

I will be attempting to bring together pieces of a puzzle—pieces scattered across disciplines and across centuries, often hidden by today's cultural assumptions about what is and is not connected—to show their interconnections and the picture that emerges from their fit. I will be looking at features including intentionality,[6] teleology,[7] cognitive faculties,[8] the spiritual intellect,[9] cosmology, and a strange figure who wields a magic sword with which to slice through society's Gordian knots. Why? In a word, all of this connected. Cosmology is relevant if there is a cosmological error behind artificial intelligence. There are both an organic connection and a distinction between teleology and intentionality, and the shift from teleology to intentionality is an important shift; when one shifts from teleology to intentionality one becomes partly blind to what the artificial intelligence picture is missing. Someone brought up on cognitive faculties may have trouble answering, 'How else could it be?'; the patristic understanding of the spiritual intellect gives a very interesting answer, and offers a completely different way to understand thought. And the figure with the magic sword? I'll let this figure remain mysterious for the moment, but I'll hint that without that metaphorical magic sword we would never have a literal artificial intelligence project. I do not believe I am forging new connections among these things, so much as uncovering something that was already there, overlooked but worth investigating.

This is an attempt to connect some very diverse sources, even if the different sections are meant primarily as philosophy of religion. This brings problems of coherence and disciplinary consistency, but the greater risk is tied to the possibility of greater reward. It will take more work to show connections than in a more externally focused enquiry, but if I can give a believable case for those interconnections, this will ipso facto be a more interesting enquiry.

All translations from French, German, Latin, and Greek are my own.

Artificial Intelligence

Artificial intelligence is not just one scientific project among others. It is a cultural manifestation of a timeless dream. It does not represent the repudiation of the occult impulse, but letting that impulse work out according to its own inner logic. Artificial intelligence is connected with a transhumanist vision for the future[10] which tries to create a science-fiction-like future of an engineered society of superior beings.[11] This artificial intelligence vision for the future is similar to the occult visions for the future we will see below. Very few members of the artificial intelligence movement embrace the full vision—but I may suggeste that its spectre is rarely absent, and that that spectre shows itself by a perennial sense of, 'We're making real breakthroughs today, and full AI is just around the corner.' Both those who embrace the fuller enthusiasm and those who are more modestly excited by current project have a hope that we are making progress towards creating something fundamentally new under the sun, of bequeathing humanity with something that has never before been available, machines that genuinely think. Indeed, this kind of hope is one of magic's most salient features. The exact content and features vary, but the sometimes heady excitement and the hope to bestow something powerful and new mark a significant point contact between the artificial intelligence and the magic that enshrouded science's birth.

There is something timeless and archetypal about the desire to create humans through artifice instead of procreation. Jewish legend tells of a rabbi who used the Kaballah to create a clay golem to defend a city against anti-semites in 1581.[12] Frankenstein has so marked the popular imagination that genetically modified foods are referred to as 'Frankenfoods,' and there are many (fictional) stories of scientists creating androids who rebel against and possibly destroy their creators. Robots who have artificial bodies but think and act enough like humans never to cause culture shock are a staple of science fiction. [13] There is a timeless and archetypal desire to create humans by artifice rather than procreation. Indeed, this desire has more than a little occult resonance.

We should draw a distinction between what may be called 'pretentious AI' and 'un-pretentious AI.' The artificial intelligence project has managed technical feats that are sometimes staggering, and from a computer scientist's perspective, the state of computer science is richer and more mature than if there had been no artificial intelligence project. Without making any general claim that artificial intelligence achieves nothing or achieves nothing significant, I will explore a more specific and weaker claim that artificial intelligence does not and cannot duplicate human intelligence.

A paradigm example of un-pretentious AI is the United States Postal Service handwriting recognition system. It succeeds in reading the addresses on 85% of postal items, and the USPS annual report is justifiably proud of this achievement.[14] However, there is nothing mythic claimed for it: the USPS does not claim a major breakthrough in emulating human thought, nor does it give people the impression that artificial mail carriers are just around the corner. The handwriting recognition system is a tool—admittedly, quite an impressive tool—but it is nothing more than a tool, and no one pretends it is anything more than a tool.

For a paradigm example of pretentious AI, I will look at something different. The robot Cog represents equally impressive feats in artificial hand-eye coordination and motor control, but its creators claim something deeper, something archetypal and mythic:

The robot Cog, portrayed as Robo sapiens
Fig. 2: Cog, portrayed as Robo sapiens[15]

The scholar places his hand on the robots' shoulder as if they had a longstanding friendship. At almost every semiotic level, this picture constitutes an implicit claim that the researcher has a deep friendship with what must be a deep being. The unfortunately blurred caption reads, '©2000 Peter Menzel / Robo sapiens.' On the Cog main website area, every picture with Cog and a person theatrically shows the person treating the robot as quite lifelike—giving the impression that the robot must be essentially human.

But how close is Cog to being human? Watts writes,

The weakness of Cog at present seems to be that it cannot actually do very much. Even its insect-like computer forebears do not seem to have had the intelligence of insects, and Cog is clearly nowhere near having human intelligence.[16]

The somewhat light-hearted frequently-asked-questions list acknowledges that the robot 'has no idea what it did two minutes ago,' answers 'Can Cog pass the Turing test?' by saying, 'No... but neither could an infant,' and interestingly answers 'Is Cog conscious?' by saying, 'We try to avoid using the c-word in our lab. For the record, no. Off the record, we have no idea what that question even means. And still, no.' The response to a very basic question is ambiguous, but it seems to joke that 'consciousness' is obscene language, and gives the impression that this is not an appropriate question to ask: a mature adult, when evaluating our AI, does not childishly frame the question in terms of consciousness. Apparently, we should accept the optimistic impression of Cog, whilst recognising that it's not fair to the robot to ask about features of human personhood that the robot can't exhibit. This smells of begging the question.

Un-pretentious AI makes an impressive technical achievement, but recognises and acknowledges that they've created a tool and not something virtually human. Pretentious AI can make equally impressive technical achievements, and it recognises that what it's created is not equivalent to human, but it does not acknowledge this. The answer to 'Is Cog conscious?' is a refusal to acknowledge something the researchers have to recognise: that Cog has no analogue to human consciousness. Is it a light-hearted way of making a serious claim of strong agnosticism about Cog's consciousness? It doesn't read much like a mature statement that 'We could never know if Cog were conscious.' The researcher in Figure 2 wrote an abstract on how to give robots a theory of other minds[17], which reads more like psychology than computer science.

There's something going on here that also goes on in the occult. In neo-paganism, practitioners find their magic to work, not exactly as an outsider would expect, by making incantations and hoping that something will happen that a skeptic would recognise as supernatural, but by doing what they can and then interpreting reality as if the magic had worked. They create an illusion and subconsciously embrace it. This mechanism works well enough, in fact, that large segments of today's neo-paganism started as jokes and then became real, something their practitioners took quite seriously.[18] There's power in trying to place a magical incantation or a computer program (or, in programmer slang, 'incantation') to fill a transcendent hope: one finds ways that it appears to work, regardless of what an outsider's interpretation may be. This basic technique appears to be at work in magic as early as the Renaissance, and it appears to be exactly what's going on in pretentious AI. The basic factor of stepping into an illusion after you do what you can makes sense of the rhetoric quoted above and why Cog is portrayed not merely as a successful experiment in coordination but as Robo sapiens, the successful creation of a living golem. Of course we don't interpret it as magic because we assume that artificial and intelligence and magic are very different things, but the researchers' self-deception falls into a quite venerable magical tradition.

Computers seem quite logical. Are they really that far from human rationality? Computers are logical without being rational. Programming a computer is like explaining a task to someone who follows directions very well but has no judgment and no ability to recognise broader intentions in a request. It follows a list of instructions without any recognition or a sense of what is being attempted. The ability to understand a conversation, or recognise another person's intent—even with mistakes—or any of a number of things humans take for granted, belongs to rationality. A computer's behaviour is built up from logical rules that do certain precise manipulations of symbols without any sense of meaning whatsoever: it is logical without being rational. The discipline of usability is about how to write well-designed computer programs; these programs usually let the user forget that computers aren't rational. For instance, a user can undo something when the computer logically and literally follows an instruction, and the user rationally realises that that isn't really what was intended. But even the best of this design doesn't let the computer understand what one meant to say. One frustration people have with computers stems from the fact that there is a gist to what humans say, and other people pick up that gist. Computers do not have even the most rudimentary sense of gist, only the ability to logically follow instructions. This means that the experience of bugs and debugging in programming is extremely frustrating to those learning how to program; the computer's response to what seems a correct program goes beyond nitpicking. This logicality without rationality is deceptive, for it presents something that looks very much like rationality at first glance, but produces unpleasant surprises when you treat it as rational. There's something interesting going on here. When we read rationality into a computer's logicality, we are in part creating the illusion of artificial intelligence. 'Don't anthropomorphise computers,' one tells novice programmers. 'They hate that.' A computer is logical enough that we tend to treat it as rational, and in fact if you want to believe that you've achieved artificial intelligence, you have an excellent basis to use in forming a magician's self-deception.

Artificial intelligence is a mythic attempt to create an artificial person, and it does so in a revealing way. Thought is assumed to be a private manipulation of mental representations, not something that works in terms of spirit. Embodied AI excluded, the body is assumed to be packaging, and the attempt is not just to duplicate the 'mind' in a complete sense, but our more computer-like rationality: this assumes a highly significant division of what is essential, what is packaging, and what comes along for free if you duplicate the essential bits. None of this is simply how humans have always thought, nor is it neutral. Maximus Confessor's assumptions are different enough from AI's that a comparison makes it easier to see some of AI's assumptions, and furthermore what sort of coherent picture could deny them. I will explore how exactly he does so below under the heading 'Orthodox Anthropology in Maximus Confessor's Mystagogia,' More immediately, I wish to discuss a basic type of assumption shared by artificial intelligence and the occult.

The Optimality Assumption

One commonality that much of magic and science share is that broad visions often include the assumption that what they don't understand must be simple, and be easy to modify or improve. Midgley discusses Bernal's exceedingly optimistic hope for society to transform itself into a simplistically conceived scientific Utopia (if perhaps lacking most of what we value in human society);[19] I will discuss later, under various headings, how society simply works better in Thomas More's and B.F. Skinner's Utopias if only it is re-engineered according to their simple models.[20] Aren't Utopian visions satires, not prescriptions? I would argue that the satire itself has a strong prescriptive element, even if it's not literal. The connection between Utopia and AI is that the same sort of thinking feeds into what, exactly, is needed to duplicate a human mind. For instance, let us examine a sample of dialogue which Turing imagined going on in a Turing test:

Q: Please write me a sonnet on the subject of the Forth Bridge.

A: Count me out on this one. I never could write poetry.

Q: Add 34957 to 70764.

A: (Pause about 30 seconds and then give as answer) 105621.

Q: Do you play chess?

A: Yes.

Q: I have K at my K1, and no other pieces. You have only K at K6 and R at R1. It is your move. What do you play?

A: (After a pause of 15 seconds) R-R8 mate.[21]

Turing seems to assume that if you duplicate his favoured tasks of arithmetic and chess, the task of understanding natural language comes along, more or less for free. The subsequent history of artificial intelligence has not been kind to this assumption. Setting aside the fact that most people do not strike up a conversation by strangely requesting the other person to solve a chess problem and add five-digit numbers, Turing is showing an occult way of thinking by assuming there's nothing really obscure, or deep, about the human person, and that the range of cognitive tasks needed to do AI is the range of tasks that immediately present themselves to him. This optimism may be damped by subsequent setbacks which the artificial intelligence movement has experienced, but it's still present. It's hard to see an artificial intelligence researcher saying, 'The obvious problem looks hard to solve, but there are probably hidden problems which are much harder,' let alone consider whether human thought might be non-computational.

Given the difficulties they acknowledge, artificial intelligence researchers seem to assume that the problem is as easy as possible to solve. As I will discuss later, this kind of assumption has profound occult resonance. I will call this assumption the optimality assumption: with allowances and caveats, the optimality assumption states that artificial intelligence is an optimally easy problem to solve. This doesn't mean an optimally easy problem to solve given the easiest possible world, but rather, taking into the difficulties and nuances recognised by the practitioner, the problem is then assumed to be optimally easy, and thenit could be said that we live in the (believable) possible world where artificial intelligence would be easiest to implement. Anything that doesn't work like a computer is assumedly easy, or a matter of unnecessary packaging. There are variations on the theme of begging the question. One basic strategy of ensuring that computers can reach the bar of human intelligence is to lower the bar until it is already met. Another strategy is to try to duplicate human intelligence on computer-like tasks. Remember the Turing test which Turing imagined, which seemed to recognise only the cognitive tasks of writing a poem, doing arithmetic, and solving a chess problem: Turing apparently assumed that natural language understanding would come along for free by the time computers could do both arithmetic and chess. Now we have computer calculators and chess players that can beat humans, whilst natural language understanding tasks which are simple to humans represent an unscaled Everest to artificial intelligence.

We have a situation very much like the attempt to make a robot that can imitate human locomotion—if the attempt is tested by having a robot race a human athlete on a racetrack ergonomically designed for robots. Chess is about as computer-like a human skill as one could find.

Turing's script for an imagined Turing test is one manifestation of a tendency to assume that the problem is optimally easy: the optimality assumption. Furthermore, Turing sees only three tasks of composing a sonnet, adding two numbers, and making a move in chess. But in fact this leaves out a task of almost unassailable difficulty for AI: understanding and appropriately acting on natural language requests. This is part of human rationality that cannot simply be assumed to come with a computer's logicality.

Four decades after Turing imagined the above dialogue, Kurt VanLehn describes a study of problem solving that used a standard story problem.[22] The ensuing discussion is telling. Two subjects' interpretations are treated as problems to be resolved, apparently chosen for their departure from how a human 'should' think about these things. One is a nine year old girl, Cathy: '...It is apparent from [her] protocol that Cathy solves this problem by imagining the physical situation and the actions taken in it, as opposed to, say, converting the puzzle to a directed graph then finding a traversal of the graph.' The purpose of the experiment was to understand how humans solve problems, but it was approached with a tunnel vision that gave a classic kind of computer science 'graph theory' problem, wrapped up in words, and treated any other interpretation of those words as an interesting abnormality. It seems that it is not the theory's duty to approach the subject matter, but the subject matter's duty to approach the theory—a signature trait of occult projects. Is this merely VanLehn's tunnel vision? He goes on to describe the state of cognitive science itself:

For instance, one can ask a subject to draw a pretty picture... [such] Problems whose understanding is not readily represented as a problem space are called ill-defined. Sketching pretty pictures is an example of an ill-defined problem... There have only been a few studies of ill-defined problem solving.[23]

Foerst summarises a tradition of feminist critique:[24] AI was started by men who chose a particular kind of abstract task as the hallmark of intelligence; women might value disembodied abstraction less and might choose something like social skills. The critique may be pushed one step further than that: beyond any claim that AI researchers, when looking for a basis for computer intelligence, tacitly crystallised intelligence out of men's activities rather than women's, it seems that their minds were so steeped in mathematics and computers that they crystallised intelligence out of human performance more in computer-like activities than anything essentially human, even in a masculine way. Turing didn't talk about making artificial car mechanics or deer hunters any more than he had plans for artificial hostesses or childminders.

Harman's 1989 account of functionalism, for instance, provides a more polished-looking version of an optimality assumption: 'According to functionalism, it does not matter what mental states and processes are made of any more than it matters what a carburetor or heart or a chess king is made of.' (832). Another suggestion may be made, not as an axiom but as an answer to the question, 'How else could it be?' This other suggestion might be called the tip of the iceberg conception.

A 'tip of the iceberg' conception might reply, 'Suppose for the sake of argument that it doesn't matter what an iceberg is made of, so long as it sticks up above the surface and is hard enough to sink a ship. The task is then to make an artificial iceberg. One can hire engineers to construct a hard shell to function as a surrogate iceberg. What has been left out is that these properties of something observable from the surface rest on something that lies much, much deeper than the surface. (A mere scrape with an iceberg sunk the Titanic, not only because the iceberg was hard, but because it had an iceberg's monumental inertia behind that hardness.) One can't make a functional tip of the iceberg that way, because a functional tip of an iceberg requires a functional iceberg, and we have very little idea of how to duplicate those parts of an iceberg that aren't visible from a ship. You are merely assuming that one can try hard enough to duplicate what you can see from a ship, and if you duplicate those observables, everything else will follow.' This is not a fatal objection, but it is intended to suggest what the truth could be besides the repeated assumption that intelligence is as easy as possible to duplicate in a computer. Here again is the optimality assumption, and it is a specific example of a broader optimality assumption which will appear in occult sources discussed under the 'Renaissance and Early Modern Magic' heading below. The 'tip of the iceberg' conception is notoriously absent in occult and artificial intelligence sources alike. In occult sources, the endeavour is to create a magically sharp sword that will slice all of the Gordian knots of society's problems; in artificial intelligence the Gordian knots are not societal problems but obstacles to creating a thinking machine, and researchers may only be attempting to use razor blades to cut tangled shoelaces, but researchers are still trying to get as close to that magic sword as they believe possible.

Just Around the Corner Since 1950

The artificial intelligence movement has a number of reasonably stable features, including an abiding sense of 'Today's discoveries are a real breakthrough; artificial minds are just around the corner.' This mood may even be older than digital computers; Dreyfus writes,

In the period between the invention of the telephone relay and its apotheosis in the digital computer, the brain, always understood in terms of the latest technological inventions, was understood as a large telephone switchboard, or more recently, as an electronic computer.[25]

The discoveries and the details of the claim may change, and experience has battered some of strong AI's optimism, but in pioneers and today's embodied AI advocates alike there is a similar mood: 'What we've developed now is effacing the boundary between machine and human.' This mood is quite stable. There is a striking similarity between the statements,

These emotions [discomfort and shock at something so human-like] might arise because in our interactions with Cog, little distinguishes us from the robot, and the differences between a machine and its human counterparts fade.[26]

and:

The reader must accept it as a fact that digital computers can be constructed, and indeed have been constructed, according to the principles we have described, and that they can in fact mimic the actions of a human computer very closely.[27]

What is interesting here is that the second was made by Turing in 1950, and the first by Foerst in 1998. As regards Turing, no one now believes 1950 computers could perform any but the most menial of mathematicians' tasks, and some of Cog's weaknesses have been discussed above ("Cog... cannot actually very much. Even its insect-like forebears do not seem to have had the intelligence of insects..."). The more artificial intelligence changes, the more it seems to stay the same. The overall impression one receives is that for all the surface progress of the artificial intelligence, the underlying philosophy and spirit remain the same—and part of this underlying spirit is the conviction, 'We're making real breakthroughs now, and full artificial intelligence is just around the corner.' This self-deception is sustained in classically magical fashion. Artificial intelligence's self-presentation exudes novelty, a sense that today's breakthroughs are decisive—whilst its actual rate of change is much slower. The 'It's just around the corner.' rhetoric is a longstanding feature. For all the changes in processor power and greater consistency in a materialist doctrine of mind, there are salient features which seem to repeat in 1950's and today's cognitive science. In both, the strategy to ensure that computers could jump the bar of human intelligence is by lowering the bar until it had already been jumped.

The Ghost in the Machine

It has been suggested in connection with Polanyi's understanding of tacit knowledge that behaviourists did not teach, 'There is no soul.' Rather, they draw students into a mode of enquiry where the possibility of a soul is never considered.

Modern psychology takes completely for granted that behavior and neural function are perfectly correlated, that one is completely caused by the other. There is no separate soul or lifeforce to stick a finger into the brain now and then and make neural cells do what they would not otherwise. Actually, of course, this is a working assumption only....It is quite conceivable that someday the assumption will have to be rejected. But it is important also to see that we have not reached that day yet: the working assumption is a necessary one and there is no real evidence opposed to it. Our failure to solve a problem so far does not make it insoluble. One cannot logically be a determinist in physics and biology, and a mystic in psychology.[28]

This is a balder and more provocative way of stating what writers like Turing lead the reader to never think of questioning. The assumption is that the soul, if there is one, is by nature external and separate from the body, so that any interaction between the two is a violation of the body's usual way of functioning. Thus what is denied is a 'separate soul or lifeforce to stick a finger into the brain now and then and make neural cells do what they would not do otherwise.' The Orthodox and others' doctrine of unified personhood is very different from an affirmation of a ghost in the machine. To affirm a ghost in the machine is to assume the soul's basic externality to the body: the basic inability of a soul to interact with a body creates the problem of the ghost in the machine. By the time one attempts to solve the problem of the ghost in the machine, one is already outside of an Orthodox doctrine of personhood in which spirit, soul, and body are united and the whole unit is not an atom.

The objective here is not mainly to criticise AI, but to see what can be learned: AI seems to fail in a way that is characteristic. It does not fail because of insufficient funding or lack of technical progress, but on another plane: it is built on an erroneous quasi-theological anthropology, and its failures may suggest something about being human. The main goal is to answer the question, 'How else could it be?' in a way that is missed by critics working in materialist confines.

What can we say in summary?

First, artificial intelligence work may be divided into un-pretentious and pretentious AI. Un-pretentious AI makes tools that no one presents as anything more than tools. Pretentious AI is presented as more human than is properly warranted.

Second, there are stable features to the artificial intelligence movement, including a claim of, 'We have something essentially human. With today's discoveries, full artificial intelligence is just around the corner.' The exact form of this assertion may change, but the basic claim does not.

Third, artificial intelligence research posits a multifarious 'optimality assumption,' namely that, given the caveats recognised by the researcher, artificial intelligence is an optimally easy assumption to solve. The human mind is assumed to be the sort of thing that is optimally easy to re-create on a computer.

Fourth, artificial intelligence comes from the same kind of thinking as the ghost in the machine problem.

There is more going on in the artificial intelligence project than an attempt to produce scientific results. The persistent rhetoric of 'It's just around the corner.' is not because artificial intelligence scientists have held that sober judgment since the project began, but because there's something else going on. For reasons that I hope will become clearer in the next section, this is beginning to look like an occult project—a secularised occult project, perhaps, but 'secularised occult' is not an empty term in that you take all of the occult away if you take away spellbooks. There is much more to the occult than crystal balls, and a good deal of this 'much more' is at play even if artificial intelligence doesn't do things the Skeptical Enquirer would frown on.

Occult Foundations of Modern Science

With acknowledgment of the relevance of the Reformation, the wake of Aristotelianism, and the via moderna of nominalism,[29] I will be looking at a surprising candidate for discussion on this topic: magic. Magic was a large part of what shaped modernity, a much larger factor than one would expect from modernity's own self-portrayal, and it has been neglected for reasons besides than the disinterested pursuit of truth. It is more attractive to our culture to say that our science exists in the wake of Renaissance learning or brave Reformers than to say that science has roots in it decries as superstition. For reasons that I will discuss below under the next heading, I suggest that what we now classify as the artificial intelligence movement is a further development of some of magic's major features.

There is a major qualitative shift between Newton's development of physics being considered by some to be a diversion from his alchemical and other occult endeavours, and 'spooky' topics today being taboo for scientific research. Yet it is still incomplete to enter a serious philosophical discussion of science without understanding the occult, as as it incomplete to enter a serious discussion of Christianity without understanding Judaism. Lewis points out that the popular understanding of modern science displacing the magic of the middle ages is at least misleading; there was very little magic in the middle ages, and then science and magic flourished at the same time, for the same reason, often in the same people: the reason science became stronger than magic is purely Darwinian: it worked better.[30] One may say that medieval religion is the matrix from which Renaissance magic departed, and early modern magic is the matrix from which science departed.

What is the relationship between the mediaeval West and patristic Christianity? In this context, the practical difference is not yet a great one. The essential difference is that certain seeds have been sown—such as nominalism and the rediscovered Aristotelianism—which in the mediaeval West would grow into something significant, but had not in much of any practical sense affected the fabric of society. People still believed that the heavens told the glory of God; people lived a life oriented towards contemplation rather than consumption; monasteries and saints were assumed so strongly that they were present even—especially—as they retreated from society. Certain seeds had been sown in the mediaeval West, but they had not grown to any significant stature. For this discussion, I will treat mediaeval and patristic Christianity as more alike than different.

Renaissance and Early Modern Magic

Magic in this context is much more than a means of casting spells or otherwise manipulating supernatural powers to obtain results. That practice is the token of an entire worldview and enterprise, something that defines life's meaning and what one ought to seek. To illustrate this, I will look at some details of work by a characteristic figure, Leibniz. Then I will look at the distinctive way the Renaissance magus related to the world and the legacy this relationship has today. Alongside this I will look at a shift from understanding this life as a contemplative apprenticeship to Heaven, to understanding this life as something for us to make more pleasurable.

Leibniz, a 17^th century mathematician and scientist who co-discovered calculus, appears to have been more than conversant with the occult memory tradition,[31] and his understanding of calculus was not, as today, a tool used by engineers to calculate volumes. Rather, it was part of an entire Utopian vision, which could encompass all knowledge and all thoughts, an apparently transcendent tool that would obviate the need for philosophical disagreements:

If we had this [calculus], there would be no more reason for disputes between philosophers than between accountants. It would be enough for them to take their quills and say, 'Let us calculate!'

Leibniz's 1690 Ars Combinatoria contains some material that is immediately accessible to a modern mathematician. It also contains material that is less accessible. Much of the second chapter (9-48) discusses combinations of the letters U, P, J, S, A, and N; these letters are tied to concepts ranging from philosophy to theology, jurisprudence and mathematics: another table links philosophical concepts with numbers (42-3). The apparent goal was to validly manipulate concepts through mechanical manipulations of words, but I was unable to readily tell what (mathematico-logical?) principle was supposed to make this work. (The principle is apparently unfamiliar to me.) This may reflect the influence of Ramon Lull, thirteenth century magician and doctor of the Catholic Church who adapted a baptised Kaballah which involved manipulating combinations of (Latin) letters. Leibniz makes repeated reference to Lull (28, 31, 34, 46), and specifically mentions his occult ars magna (28). Like Lull, Leibniz is interested in the occult, and seeks to pioneer some new tool that will obviate the need for this world's troubles. He was an important figure in the creation of science, and his notation is still used for calculus today. Leibniz is not trying to be just another member of society, or to contribute to society's good the way members have always contributed to society's good: he stands above it, and his intended contribution is to reorder the fabric of society according to his endowed vision. Leibniz provides a characteristic glimpse of how early modern magic has left a lasting imprint.

If the person one should be in Orthodoxy is the member of Church and society, the figure in magic is the magus, a singular character who stands outside of the fabric of society and seeks to transform it. What is the difference? The member of the faithful is an integrated part of society, and lives in submission and organic connection to it. The magus, by contrast, stands above society, superior to it, having a relation to society as one whose right and perhaps duty is to tear apart and reconstruct society along better lines. We have a difference between humility and pride, between relating to society as to one's mother and treating society as raw material for one to transform. The magus is cut off from the common herd by two closely related endowments: a magic sword to cut through society's Gordian knots, and a messianic fantasy.[32] In Leibniz's case the magic sword is an artificial language which will make philosophical disagreements simply obsolete. For the artificial intelligence movement, the magic sword is artificial intelligence itself. The exact character of the sword, knot, and fantasy may differ, but their presence does not.

The character of the Renaissance magus may be seen as as hinging on despair with the natural world. This mood seems to be woven into Hermetic texts that were held in such esteem in the Renaissance and were connected at the opening of pre-eminent Renaissance neo-Platonist Pico della Mirandola's Oration on the Dignity of Man.[33] If there is good to be had, it is not met in the mundane world of the hoi polloi. It must be very different from their reality, something hidden that is only accessible to an elite. The sense in which this spells out an interest in the occult means far more than carrying around a rabbit's foot. The specific supernatural contact was valued because the occult was far hidden from appearances and the unwashed masses. (The Christian claim that one can simply pray to God and be heard is thus profoundly uninteresting. Supernatural as it may be, it is ordinary, humble, and accessible in a way that the magus is trying to push past.) This desire for what is hidden or very different from the ordinary means that the ideal future must be very different from the present. Therefore Thomas More, Renaissance author, canonised saint, and strong devotee of Mirandola's writing, himself writes Utopia. In this work, the philosophic sailor Raphael establishes his own reason as judge over the appropriateness of executing thieves,[34] and describes a Utopia where society simply works better: there seem to be no unpleasant surprises or unintended consequences. [35] There is little sense of a complex inner logic to society that needs to be respected, or any kind of authority to submit to. Indeed, Raphael abhors authority and responds to the suggestion that he attach himself to a king's court by saying, 'Happier! Is that to follow a path that my soul abhors?' This Utopian vision, even if it is from a canonised Roman saint, captures something deep of the occult currents that would later feed into the development of political ideology. The content of an occult vision for constructing a better tomorrow may vary, but it is a vision that seeks to tear up the world as we now know it and reconstructs it along different lines.

Magic and science alike relate to what they are interested in via an I-It rather than an I-Thou relationship. Relating to society as to one's mother is an I-Thou relationship; treating society as raw material is an I-It relationship. An I-Thou relationship is receptive to quality. It can gain wisdom and insight. It can connect out of the whole person. The particular kind of I-It relationship that undergirds science has a powerful and narrow tool that deals in what can be mathematically represented. The difference between those two is misunderstood if one stops after saying, 'I-It can make technology available much better than I-Thou.' That is how things look through I-It eyes. But I-Thou allows a quality of relationship that does not exist with I-It. 'The fundamental word I-Thou can only be spoken with one's whole being. The fundamental word I-It can never be spoken with one's whole being.' I-Thou allows a quality-rich relationship that always has another layer of meaning. In the Romance languages there are two different words for knowledge: in French,connaissance and savoir. They both mean 'knowledge,' but in different ways: savoir is knowledge of fact (or know-how); one can sait que ('know that') something is true. Connaissance is the kind of knowledge of a person, a 'knowledge of' rather than a 'knowledge that' or 'knowledge how.' It can never be a complete knowledge, and one cannot connait que ('know-of that') something is true. It is personal in character. An I-It relationship is not just true of magic; as I will discuss below under the heading of 'Science, Psychology, and Behaviourism,' psychology seeks a baseline savoir of people where it might seek a connaissance , and its theories are meant to be abstracted from relationships with specific people. Like magic, the powers that are based on science are epiphenomenal to the relationship science is based on. Relating in an I-Thou rather than I-It fashion is not simply less like magic and science; it is richer, fuller, and more human.

In the patristic and medieval eras, the goal of living had been contemplation and the goal of moral instruction was to conform people to reality. Now there was a shift from conforming people to reality, towards conforming reality to people.[36] This set the stage, centuries later, for a major and resource-intensive effort to create an artificial mind, a goal that would not have fit well with a society oriented to contemplation. This is not to say that there is no faith today, nor that there was no technology in the middle ages, nor that there has been no shift between the early modern period and today. Rather, it is to say that a basic trajectory was established in magic that significantly shapes science today.

The difference between the Renaissance magus and the mediaeval member of the Church casts a significant shadow today. The scientist seems to live more in the shadow of the Renaissance magus than of the member of mediaeval society. This is not to say that scientists cannot be humble and moral, nor that they cannot hold wonder at what they study. But it is to say that there are a number of points of contact between the Renaissance magus's way of relating to the world and that of a scientist and those who live in science's shadow. Governments today consult social scientists before making policy decisions: the relationship seems to be how to best deal with material rather than a relationship as to one's mother. We have more than a hint of secularised magic in which substantial fragments of Renaissance and early modern magic have long outlived some magical practices.

Under the patristic and medieval conception, this life was an apprenticeship to the life in Heaven, the beginning of an eternal glory contemplating God. Magic retained a sense of supernatural reality and a larger world, but its goal was to improve this life, understood as largely self-contained and not as beginning of the next. That was the new chief end of humanity. That shift is a shift towards the secular, magical as its beginning may be. Magic contains the seeds of its own secularisation, in other words of its becoming scientific. The shift from contemplation of the next world to power in this world is why the occult was associated with all sorts of Utopian visions to transform the world, a legacy reflected in our political ideologies. One of the tools developed in that magical milieu was science: a tool that, for Darwinian reasons, was to eclipse all the rest. The real magic that has emerged is science.

Science, Psychology, and Behaviourism

What is the niche science has carved out for itself? I'd like to look at an academic discipline that is working hard to be a science, psychology. I will more specifically look at behaviourism, as symptomatic within the history of psychology. Is it fair to look at behaviourism, which psychology itself rejected? It seems that behaviourism offers a valuable case study by demonstrating what is more subtly present elsewhere in psychology. Behaviourism makes some basic observations about reward and punishment and people repeating behaviours, and portrays this as a comprehensive psychological theory: behaviourism does not acknowledge beliefs, for instance. Nonetheless, I suggest that behaviourism is a conceivable development in modern psychology which would have been impossible in other settings. Behaviourism may be unusual in the extreme simplicity of its vision and its refusal to recognise internal states, but not in desiring a Newton who will make psychology a full-fledged science and let psychology know its material with the same kind of knowing as physics has for its material.

Newton and his kin provided a completely de-anthropomorphised account of natural phenomena, and behaviourism provided a de-anthropomorphised account of humans. In leading behaviourist B.F. Skinner's Walden Two (1948), we have a Utopian vision where every part of society seems to work better: artists raised under Skinner's conditioning produce work which is 'extraordinarily good,' the women are more beautiful,[37] and Skinner's alter ego expresses the hope of controlling the weather,[38] and compares himself with God.[39] Skinner resemble seems to resemble a Renaissance magus more than a mediaeval member: society is raw material for him to transform. Skinner is, in a real sense, a Renaissance magus whose magic has become secularised. Quite a lot of the magus survives the secularisation of Skinner's magic.

Even without these more grandiose aspirations, psychology is symptomatic of something that is difficult to discern by looking at the hard sciences. Psychological experiments try to find ways in which the human person responds in terms comparable to a physics experiment—and by nature do not relate to their subjects as human agents. These experiments study one aspect of human personhood, good literature another, and literature offers a different kind of knowing from a psychological experiment. If we assume that psychology is the best way to understand people—and that the mind is a mechanism-driven thing—then the assumed burden of proof falls on anyone saying, 'But a human mind isn't the sort of thing you can duplicate on a computer.' The cultural place of science constitutes a powerful influence on how people conceive the question of artificial intelligence.

Behaviourism offers a very simple and very sharp magic sword to cut the Gordian knot of unscientific teleology, a knot that will be discussed under the heading of 'Intentionality and Teleology' below. It removes suspicion of the reason being attached to a spiritual intellect by refusing to acknowledge reason. It removes the suspicion of emotions having a spiritual dimension by refusing to acknowledge emotions. He denies enough of the human person that even psychologists who share those goals would want to distance themselves from him. And yet Skinner does more than entertain messianic fantasies: Walden Two is a Utopia, and when Skinner's alter ego compares himself with God, God ends up second best.[40] I suggest that this is no a contradiction at all, or more properly it is a blatant contradiction as far as common sense is concerned, but as far as human human phenomena go, we have two sides of the same coin. The magic sword and the messianic fantasy belong to one and the same magus.

There is in fact an intermediate step between the full-fledged magus and the mortal herd. One can be a magician's assistant, clearing away debris and performing menial tasks to support the real magi. [41] The proportion of the Western population who are scientists is enormous compared to science's founding, and the vast majority of the increase is in magician's assistants. If one meets a scientist at a social gathering, the science is in all probability not a full-fledged magus, but a magician's assistant, set midway between the magus and the commoner. The common scientist is below the magus in knowledge of science but well above most commoners. In place of a personal messianic fantasy is a more communal tendency to assume that the scientific enterprise is our best hope for the betterment of society. (Commoners may share this belief.) There is a significant difference between the magus and most assistants today. Nonetheless, the figure of the magus is alive today—secularised, in most cases, but alive and well. Paul Johnson's Augustinian account ofIntellectuals includes such eminent twentieth century scientific figures as Bertrand Russell, Noam Chompsky, and Albert Einstein;[42] the figures one encounters in his pages are steeped in the relationship to society as to raw material instead as to one's mother, the magic sword, and the messianic fantasy.

I-Thou and Humanness

I suggest that the most interesting critiques of artificial intelligence are not obtained by looking through I-It eyes in another direction, but in using other eyes to begin with, looking through I-Thou eyes. Let us consider Turing's 'Arguments from Various Disabilities'.[43]Perhaps the people who furnished Turing with these objections were speaking out of something deeper than they could explain:

Be kind, resourceful, beautiful, friendly, have initiative, have a sense of humour, tell right from wrong, make mistakes, fall in love, enjoy strawberries and cream, make some one fall in love with it, learn from experience, use words properly, be the subject of its own thought, have as much diversity of behaviour as a man, do something really new.

Be kind:
Kindness is listed by Paul as the fruit of the Spirit (Gal. 5:22) in other words, an outflow of a person living in the Spirit. Disregarding the question of whether all kindness is the fruit of the Spirit, in humans kindness is not merely following rules, but the outflow of a concern for the other person. Even counterfeit kindness is a counterfeit from someone who knows the genuine article. It thus uses some faculty of humanity other than the reasoning ability, which classical AI tries to duplicate and which is assumed to be the one thing necessary to duplicate human cognition.

Be resourceful:
The artificial intelligence assumption is that if something is non-deterministic, it is random, because deterministic and pseudo-random are the only options one can use in programming a computer. This leaves out a third possibility, that by non-computational faculties someone may think, not merely 'outside the box,' in a random direction, but above it. The creative spark comes neither from continuing a systematic approach, nor simply picking something random ('because I can't get my computer to turn on, I'll pour coffee on it and see if that helps'), but something that we don't know how to give a computer.

Be beautiful:
Beauty is a spiritual quality that is not perceived by scientific enquiry and, given our time's interpretation of scientific enquiry, is in principle not recognised. Why not? If we push materialist assumptions to the extreme, it is almost a category error to look at a woman and say, 'She is beautiful.' What is really being said—if one is not making a category error—is, 'I have certain emotions when I look at her.' Even if there is not a connection between physical beauty and intelligence, there seems to be some peasant shrewdness involved. It is a genuine, if misapplied, appeal to look at something that has been overlooked.

Be friendly:
True as opposed to counterfeit friendliness is a manifestation of love, which has its home in the will, especially if the will is not understood as a quasi-muscular power of domination, but part of the spirit which lets us turn towards another in love.

Remarks could easily be multiplied. What is meant to come through all this is that science is not magic, but science works in magic's wake. Among relevant features may be mentioned relating as a magus would (in many ways distilling an I-It relationship further), and seeking power over the world in this life rather living an apprenticeship to the next.

Orthodox Anthropology in Maximus Confessor's Mystagogia

I will begin detailed enquiry in the Greek Fathers by considering an author who is foundational to Eastern Orthodoxy, the seventh century Greek Father Maximus Confessor. Out of the existing body of literature, I will focus on one work, his Mystagogia,[44] with some reference to the Capita Gnosticae. Maximus Confessor is a synthetic thinker, and the Mystagogia is an anthropological work; its discussion of Church mystagogy is dense in theological anthropology as the training for a medical doctor is dense in human biology.

Orthodox Christians have a different cosmology from the Protestant division of nature, sin, and grace. Nature is never un-graced, and the grace that restores from sin is the same grace that provides continued existence and that created nature in the first place. That is to say, grace flows from God's generosity, and is never alien to nature. The one God inhabits the whole creation: granted, in a more special and concentrated way in a person than in a rock, but the same God is really present in both.

Already, without having seriously engaged theological anthropology, we have differences with how AI looks at things. Not only are the answers different, but the questions themselves are posed in a different way. 'Cold matter,' such as is assumed by scientific materialism, doesn't exist, not because matter is denied in Berkeleyan fashion but because it is part of a spiritual cosmology and affirmed to be something more. It is mistaken to think of cold matter, just as it is mistaken to think of tepid fire. Even matter has spiritual attributes and is graced. Everything that exists, from God and the spiritual creation to the material creation, from seraphim to stone, is the sort of thing one connects to in an I-Thou relationship. An I-It relationship is out of place, and from this perspective magic and science look almost the same, different signposts in the process of establishing a progressively purer I-It relationship.

Intellect and Reason

Maximus' anthropology is threefold: the person is divided into soul and body, and the soul itself is divided into a higher part, the intellect, and a lower part, the reason:[45]

[Pseudo-Dionysius] used to teach that the whole person is a synthesis of soul and body joined together, and furthermore the soul itself can be examined by reason. (The person is an image which reflects teaching about the Holy Church.) Thus he said that the soul had an intellectual and living faculty that were essentially united, and described the moving, intellectual, authoritative power—with the living part described according its will-less nature. And again, the whole mind deals with intelligible things, with the intelligible power being called intellect, whilst the sensible power is called reason.

This passage shows a one-word translation difficulty which is symptomatic of a difference between his theology and the quasi-theological assumptions of the artificial intelligence project. The word in question, which I have rendered as 'authoritative power,' is 'exousiastikws,' with root word 'exousia.' The root and its associated forms could be misconstrued today as having a double meaning of 'power' and 'authority,' with 'authority' as the basic sense. In both classical and patristic usage, it seems debatable whether 'exousia' is tied to any concept of power divorced from authority. In particular this passage's 'exousiastikws' is most immediately translated as power rather than any kind of authority that is separate from power. Yet Maximus Confessor's whole sense of power here is one that arises from a divine authorisation to know the truth. This sense of power is teleologically oriented and has intrinsic meaning. This is not to say that Maximus could only conceive of power in terms of authority. He repeatedly uses 'dunamis,' (proem.15-6, 26, 28, etc), a word for power without significant connotations of authority. However, he could conceive of power in terms of authority, and that is exactly what he does when describing the intellect's power.

What is the relationship between 'intellect'/'reason' and cognitive faculties? Which, if either, has cognitive faculties a computer can't duplicate? Here we run into another difficulty. It is hard to say that Maximus Confessor traded in cognitive faculties. For Maximus Confessor the core sense of 'cognitive faculties' is inadequate, as it is inadequate to define an eye as something that provides nerve impulses which the brain uses to generate other nerve impulses. What is missing from this picture? This definition does not provide any sense that the eye interacts with the external world, so that under normal circumstances its nerve impulses are sent because photons strike photoreceptors in an organ resembling a camera. Even this description hides most teleology and evaluative judgment. It does not say that an eye is an organ for perceiving the external world through an image reconstructed in the brain, and may be called 'good' if it sees clearly and 'bad' if it doesn't. This may be used as a point of departure to comment on Maximus Confessor and the conception of cognitive faculties.

Maximus Confessor does not, in an amoral or self-contained fashion, see faculties that operate on mental representations. He sees an intellect that is where one meets God, and where one encounters a Truth that is no more private than the world one sees with the eye is private.

Intellect and reason compete with today's cognitive faculties, but Maximus Confessor understands the intellect in particular as something fundamentally moral, spiritual, and connected to spiritual realities. His conception of morality is itself different from today's private choice of ethical code; morality had more public and more encompassing boundaries, and included such things as Jesus' admonition not to take the place of highest honour so as not to receive public humiliation (Luke 14:7-10): it embraced practical advice for social conduct, because the moral and spiritual were not separated from the practical. It is difficult to Maximus Confessor conceiving of practicality as hampered by morality. In Maximus Confessor's day what we separate into cognitive, moral, spiritual, and practical domains were woven into a seamless tapestry.

Intellect, Principles, and Cosmology

Chapter twenty-three opens by emphasising that contemplation is more than looking at appearances (23.1-10), and discusses the Principles of things. The concept of a Principle is important to his cosmology. There is a foundational difference between the assumed cosmologies of artificial intelligence and Maximus Confessor. Maximus Confessor's cosmology is not the artificial intelligence cosmology with a spiritual dimension added, as a living organism is not a machine modified to use foodstuffs as fuel.

Why do I speak of the 'artificial intelligence cosmology'? Surely one can have a long debate about artificial intelligence without adding cosmology to the discussion. This is true, but it is true because cosmology has become invisible, part of the assumed backdrop of discussion. In America, one cultural assumption is that 'culture' and 'customs' are for faroff and exotic people, not for 'us'—'we' are just being human. It doesn't occur to most Americans to think of eating Turkey on Thanksgiving Day or removing one's hat inside a building as customs, because 'custom' is a concept that only applies to exotic people. I suggest that Maximus Confessor has an interesting cosmology, not because he's exotic, but because he's human.

Artificial intelligence proponents and (most) critics do not differ on cosmology, but because that is because it is an important assumption which is not questioned even by most people who deny the possibility of artificial intelligence. Searle may disagree with Fodor about what is implied by a materialist cosmology, but not whether one should accept materialism. I suggest that some artificial intelligence critics miss the most interesting critiques of artificial intelligence because they share that project's cosmology. If AI is based on a cosmological error, then no amount of fine-tuning within the system will rectify the error. We need to consider cosmology if we are to have any hope of correcting an error that basic. (Bad metaphysics does not create good physics.) I will describe Maximus Confessor's cosmology in this section, not because he has cosmology and AI doesn't, but because his cosmology seems to suggest a correction to the artificial intelligence cosmology.

At the base of Maximus's cosmology is God. God holds the Principles in his heart, and they share something of his reality. Concrete beings (including us) are created through the Principles, and we share something of their reality and of God. The Principles are a more concrete realisation of God, and we are a more concrete realisation of the Principles. Thought (nohsis) means beholding God and the Principles ( logoi) through the eye of the intellect. Thinking of a tree means connecting with something that is more tree-like than the tree itself.

It may be easier to see what the important Principles in Maximus Confessor's cosmology if we see how they are being dismantled today. Without saying that Church Fathers simply grafted in Platonism, I believe it safe to say that Plato resembled some of Church doctrine, and at any rate Plato's one finger pointing up to God offers a closer approximation to Christianity than Aristotle's fingers pointing down. I would suggest further that looking at Plato can suggest how Christianity differs from Aristotelianism's materialistic tendencies, tendencies that are still unfolding today. Edelman describes the assumptions accompanying Darwin's evolution as the 'death blow' to the essentialism, the doctrine that there are fixed kinds of things, as taught by Plato and other idealists.[46] Edelman seems not to appreciate why so many biologists assent to punctuated equilibrium.[47] However, if we assume that there is solid evidence establishing that all life gradually evolved from a common ancestor, then this remark is both apropos and perceptive.

When we look around, we see organisms that fit neatly into different classes: human, housefly, oak. Beginning philosophy students may find it quaint to hear of Plato's Ideas, and the Ideal horse that is copied in all physical horses, but we tend to assume Platonism at least in that horses are similar 'as if' there were an Ideal horse: we don't believe in the Ideal horse any more, but we still treat its shadow as if it were the Ideal horse's shadowy copy.

Darwin's theory of evolution suggests that all organisms are connected via slow, continuous change to a common ancestor and therefore to each other. If this is true, there are dire implications for Platonism. It is as if we had pictures of wet clay pottery, and posited a sharp divide between discrete classes of plates, cups, and bowls. Then someone showed a movie of a potter deforming one and the same clay from one shape to another, so that the divisions are now shown to be arbitrary. There are no discrete classes of vessels, just one lump of clay being shaped into different things. Here we are pushing a picture to the other end of a spectrum, further away from Platonism. It is a push from tacitly assuming there is a shadow, to expunging the remnant of belief in the horse and its shadow.

But this doesn't mean we're perfect Platonists, or can effortlessly appreciate the Platonic mindset. There are things we have to understand before we can travel in the other direction. If anything, there is more work involved. We act as if the Ideas' shadows are real things, but we don't genuinely believe in the shadows qua shadows, let alone the Ideas. We've simply inherited the habit of treating shadows as a convenient fiction. But Maximus Confessor believed the Principles (Ideas) represented something fuller and deeper than concrete things.

This is foundational to why Maximus Confessor would not have understood thought as manipulating mental representations in the inescapable privacy of one's mind. Contemplation is not a matter of closing one's eyes and fantasising, but of opening one's eyes and beholding something deeper and more real than reality itself. The sensible reason can perceive the external physical world through the senses, but this takes a very different light from Kant's view.

Maximus Confessor offers a genuinely interesting suggestion that we know things not only because of our power-to-know, but because of their power-to-be-known, an approach that I will explore later under the heading 'Knowledge of the Immanent.' The world is not purely transcendent, but immanent. For Kant the mind is a box that is hermetically sealed on top but has a few frustratingly small holes on the bottom: the senses. Maximus Confessor doesn't view the senses very differently, but the top of the box is open.

This means that the intellect is most basically where one meets God. Its powerful ability to know truth is connected to this, and it connects with the Principles of things, as the senses connect with mere things. Is it fair to the senses to compare the intellect's connection with Principles with the senses' experience of physical things? The real question is not that, but whether it is fair to the intellect, and the answer is 'no.' The Principles are deeper, richer, and fuller than the mere visible things, as a horse is richer than its shadow. The knowledge we have through the intellect's connection with the Principles is of a deeper and richer sort than what is merely inferred from the senses.

The Intelligible and the Sensible

Maximus Confessor lists, and connects, several linked pairs, which I have incorporated into a schema below. The first column of this schema relates to the second column along lines just illustrated: the first member of each pair is transcendent and eminent to the second, but also immanent to it.

Head	Body
Heaven	earth (3.1-6)
holy of holies	sanctuary (2.8-9)
intelligible	sensible (7.5-10)
contemplative	active (5.8-9)
intellect	reason (5.9-10)
spiritual wisdom	practical wisdom (5.13-15)
knowledge	virtue (5.58)
unforgettable knowledge	faith (5.58-60)
truth	goodness (5.58-9)
archetype	image (5.79-80)
New Testament	Old Testament (6.4-6)
spiritual meaning of a text	literal meaning of a text (6.14-5)
bishop's seating on throne	bishop's entrance into Church (8.5-6, 20-21)
Christ's return in glory	Christ's first coming, glory veiled (8.6-7, 18)

Maximus Confessor's cosmology sees neither a disparate collection of unconnected things, nor an undistinguished monism that denies differences. Instead, he sees a unity that sees natures (1.16-17) in which God not only limits differences, as a circle limits its radii (1.62-67), but transcends all differences. Things may be distinguished, but they are not divided. This is key to understanding both doctrine and method. He identifies the world with a person, and connects the Church with the image of God. Doctrine and method are alike synthetic, which suggests that passages about his cosmology and ecclesiology illuminate anthropology.

One recurring theme shows in his treatment of heaven and earth, the soul and the body, the intelligible (spiritual) and the sensible (material). The intelligible both transcends the sensible, and is immanent to it, present in it. The intelligible is what can be apprehended by the part of us that meets God; the sensible is what presents itself to the world of senses. (The senses are not our only connection with the world.) This is a different way of thinking about matter and spirit from the Cartesian model, which gives rise to the ghost in the machine problem. Maximus Confessor's understanding of spirit and matter does not make much room for this dilemma. Matter and spirit interpenetrate. This is true not just in us but in the cosmos, which is itself 'human': he considers '...the three people: the cosmos (let us say), the Holy Scriptures, and this is true with us' (7.40-1). The attempt to connect spirit and matter might have struck him like an attempt to forge a link between fire and heat, two things already linked.

Knowledge of the Immanent

The word which I here render 'thought' is 'nohsis', cognate to 'intellect' ('nous') which has been discussed as that which is inseparably the home of thought and of meeting God. We already have a hint of a conceptual cast in which thought will be understood in terms of connection and contemplation.

In contrast to understanding thought as a process within a mind, Maximus describes thought in terms of a relationship: a thought can exist because there is a power to think of in the one thinking, and a power to be thought of in what is thought of.[48] We could no more know an absolutely transcendent creature than we could know an absolutely transcendent Creator. Even imperfect thought exists because we are dealing with something that 'holds power to be apprehended by the intellect' (I.82). We say something is purple because its manifest purpleness meets our ability to perceive purple. What about the claim that purple is a mental experience arising from a certain wavelength of light striking our retinas? One answer that might be given is that those are the mechanisms by which purple is delivered, not the nature of what purple is.[49] The distinction is important.

We may ask, what about capacity for fantasy and errors? The first response I would suggest is cultural. The birth of modernity was a major shift, and its abstraction introduced new things into the Western mind, including much of what supports our concept of fantasy (in literature, etc.). The category of fantasy is a basic category to our mindset but not to the patristic or medieval mind. Therefore, instead of speculating how Maximus Confessor would have replied to these objections, we can point out that they aren't the sort of thing that he would ever think of, or perhaps even understand.

But in fact a more positive reply can be taken. It can be said of good and evil that good is the only real substance. Evil is not its own substance, but a blemish in good substance. This parallels error. Error is not something fundamentally new, but a blurred or distorted form of truth. Fantasy does not represent another fundamentally independent, if hypothetical, reality; it is a funhouse mirror refracting this world. We do not have a representation that exists in one's mind alone, but a dual relationship that arises both from apprehending intellect and an immanent thing. The possibility of errors and speculation make for a longer explanation but need not make us discard this basic picture.

Intentionality and Teleology

One of the basic differences in cosmology between Maximus Confessor and our own day relates to intentionality. As it is described in cognitive science's philosophy of mind, 'intentionality' refers to an 'about-ness' of human mental states, such as beliefs and emotions. The word 'tree' is about an object outside the mind, and even the word 'pegasus' evokes something that one could imagine existing outside of the mind, even if it does not. Intentionality does not exist in computer programs: a computer chess program manipulates symbols in an entirely self-enclosed system, so 'queen' cannot refer to any external person or carry the web of associations we assume. Intentionality presents a philosophical problem for artificial intelligence. Human mental states and symbol manipulation are about something that reach out to the external world, whilst computer symbol manipulation is purely internal. A computer may manipulate symbols that are meaningful to humans using it, but the computer has no more sense of what a webpage means than a physical book has a sense that its pages contain good or bad writing. Intentionality is a special feature of living minds, and does not exist outside of them. Something significant will be achieved if ever a computer program first embodies intentionality outside of a living mind.

Maximus Confessor would likely have had difficulty understanding this perspective as he would have had difficulty understanding the problem of the ghost in the machine: this perspective makes intentionality a special exception as the ghost in the machine made our minds' interaction with our bodies a special exception, and to him both 'exceptions' are in fact the crowning jewel of something which permeates the cosmos.

The theory of evolution is symptomatic of a difference between the post-Enlightenment West and the patristic era. This theory is on analytic grounds not a true answer to the question, 'Why is there life as we know it?' because it does not address the question, 'Why is there life as we know it?' At best it is a true answer to the question, 'How is there life as we know it?' which people often fail to distinguish from the very different question, 'Why is there life as we know it?' The Enlightenment contributed to an effort to expunge all trace of teleology from causality, all trace of 'Why?' from 'How?' Of Aristotle's four causes, only the efficient cause[50] is familiar; a beginning philosophy student is liable to misconstrue Aristotle's final cause[51] as being an efficient cause whose effect curiously precedes the cause. The heavy teleological scent to final causation is liable to be missed at first by a student in the wake of reducing 'why' to 'how'; in Maximus Confessor, causation is not simply mechanical, but tells what purpose something serves, what it embodies, what meaning and relationships define it, and why it exists.

Strictly speaking, one should speak of 'scientific mechanisms' rather than 'scientific explanations.' Why? 'Scientific proof' is an oxymoron: science does not deal in positive proof any more than mathematics deals in experiment, so talk of 'scientific proof' ordinarily signals a speaker who has more faith in science than understanding of what science really does. 'Scientific explanation' is a less blatant contradiction in terms, but it reflects a misunderstanding, perhaps one that is more widespread, as it often present among people who would never speak of 'scientific proof.' Talk of 'scientific explanation' is not simply careless speech; there needs to be a widespread category error before there is any reason to write a book like Mary Midgley's Science as Salvation (1992). Science is an enterprise which provides mechanisms and has been given the cultural place of providing explanations. This discrepancy has the effect that people searching for explanations turn to scientific mechanisms, and may not be receptive when a genuine explanation is provided, because 'explanation' to them means 'something like what science gives.' This may not be the only factor, but it casts a long shadow. The burden of proof is born by anyone who would present a non-scientific explanation as being as real as a scientific explanation. An even heavier burden of proof falls on the person who would claim that a non-scientific explanation—not just as social construction, but a real claim about the external world—offers something that science does not.

The distinction between mechanism and explanation is also relevant because the ways in which artificial intelligence has failed may reflect mechanisms made to do the work of explanations. In other words, the question of 'What is the nature of a human?' is answered by, 'We are able to discern these mental mechanisms in a human.' If this is true, the failure to duplicate a human mind in computers may be connected to researchers answering the wrong question in the first place. These are different, as the question, 'What literary devices can you find in The Merchant of Venice[52]?' is different from 'Why is The Merchant of Venice powerful drama?' The devices aren't irrelevant, but neither are they the whole picture.

Of the once great and beautiful land of teleology, a land once brimming in explanations, all has been conquered, all has been levelled, all has been razed and transformed by the power of I-It. All except two stubborn, embattled holdouts. The first holdout is intentionality: if it is a category error to project things in the human mind onto the outer world, nonetheless we recognise that intentionality exists in the mind—but about-ness of intentionality is far less than the about-ness once believed to fill the cosmos. The second and last holdout is evolution: if there is to be no mythic story of origins that gives shape and meaning to human existence, if there cannot be an answer to 'Why is there life as we know it?' because there is no reason at all for life, because housefly, horse, and human are alike the by-product of mindless forces that did not have us in mind, nonetheless there is still an emaciated spectre, an evolutionary mechanism that does just enough work to keep away a teleological approach to origins questions. The land of teleology has been razed, but there is a similarity between these two remnants, placeholders which are granted special permission to do what even the I-It approach recognises it cannot completely remove of teleology. That is the official picture, at least. Midgley is liable to pester us with counterexamples of a teleology that is far more persistent than the official picture gives credit for: she looks at evolution doing the work of a myth instead of a placeholder that keeps myths away, for instance.[53] Let's ignore her for the moment and stick with the official version. Then looking at both intentionality and evolution can be instructive in seeing what has happened to teleology, and appreciating what teleology was and could be. Now Midgley offers us reasons why it may not be productive to pretend we can excise teleology: the examples of teleology she discusses do not seem to be improved by being driven underground and presented as non-teleological.

Maximus's picture, as well as being teleological, is moral and spiritual. As well as having intentions, we are living manifestations of a teleological, moral and spiritual Intention in God's heart. Maximus Confessor held a cosmology, and therefore an anthropology, that did not see the world in terms of disconnected and meaningless things. He exhibited a number of traits that the Enlightenment stripped out: in particular, a pervasive teleology in both cosmology and anthropology. He believed in a threefold anthropology of intellect/spirit, reason/soul, and body, all intimately tied together. What cognitive science accounts for through cognitive faculties, manipulating mental representations, were accounted for quite differently by an intellect that sees God and the Principles of beings, and a reason that works with the truths apprehended by intellect. The differences between the respective cosmologies and anthropologies are not the differences between two alternate answers to the same question, but answers to two different questions, differently conceived. They are alike in that they can collide because they are wrestling with the same thing: where they disagree, at least one of them must be wrong. They are different in that they are looking at the same aspect of personhood from two different cultures, and Maximus Confessor seems to have enough distance to provide a genuinely interesting critique.

Conclusion

Maximus Confessor was a synthetic thinker, and I suggest that his writings, which are synthetic both in method and in doctrine, are valuable not only because he was brilliant but because synthetic enquiry can be itself valuable. I have pursued a synthetic enquiry, not out of an attempt to be like Maximus Confessor, but because I think an approach that is sensitive to connections could be productive here. I'm not the only critic who has the resources to interpret AI as floundering in a way that may be symptomatic of a cosmological error. It's not hard to see that many religious cosmologies offer inhospitable climates to machines that think: Foerst's reinterpretation of the image of God[54] seems part of an effort to avoid seeing exactly this point. The interesting task is understanding and conveying an interconnected web. So I have connected science with magic, for instance, because although the official version is that they're completely unrelated, there is a strong historic link between them, and cultural factors today obscure the difference, and for that matter obscure several other things that interest us.

This dissertation falls under the heading of boundary issues between religion and science, and some readers may perceive me to approach boundary issues in a slightly different fashion. That perception is correct. One of the main ways that boundary issues are framed seems to be for Christian theologians to show the compatibility of their timeless doctrines with that minority of scientific theories which have already been accepted by the scientific community and which have not yet been rejected by that same community. With the question of origins, there has been a lot of work done to show that Christianity is far more compatible with evolutionary theory than a literal reading of Genesis 1 would suggest. It seems to have only been recently that gadflies within the intelligent design movement have suggested both that the scientific case for evolution is weaker that it has been made out to be, and there seems to be good reason to believe that Christianity and evolution are incompatible at a deep enough level that the literal details of Genesis 1 are almost superfluous. Nobody conceives the boundary issues to mean that theologians should demonstrate the compatibility of Christianity with that silent majority of scientific theories which have either been both accepted and discredited (like spontaneous generation) or not yet accepted (like the cognitive-theoretic model of the universe). The minority is different, but not as different as people often assume.

One of the questions which is debated is whether it is best to understand subject-matter from within or without. I am an M.Phil. student in theology with a master's and an adjunct professorship in the sciences. I have worked to understand the sciences from within, and from that base look and understand science from without as well as within. Someone who only sees science from without may lack appreciation of certain things that come with experience of science, whilst someone who only sees science from within may not be able to question enough of science's self-portrayal. This composite view may not be available to all, nor is it needed, but I believe it has helped me in another basic röle from showing religion's compatibility with current science: namely, serving as a critical observer and raising important questions that science is itself unlikely to raise, sometimes turning a scientific assumption on its head. Theology may have other things to offer in its discussion with science than simply offering assent: instead of solely being the recipient of claims from science, it should be an agent which adds to the conversation.

Are there reasons why the position I propose is to be preferred? Science's interpretation of the matter is deeply entrenched, enough so that it seems strange to connect science with the occult. One response is that this perspective should at least be listened to, because it is challenging a now entrenched cultural force, and it may be a cue to how we could avoid some of our own blind spots. Even if it is wrong, it could be wrong in an interesting way. A more positive response would be to say that this is by my own admission far from a complete picture, but it makes sense of part of the historical record that is meaningless if one says that modern science just happened to be born whilst a magical movement waxed strong, and some of science's founders just happened to be magicians. A more robust picture would see the early modern era as an interlocking whole that encompassed a continuing Reformation, Descartes, magic, nascent science, and the wake of the Renaissance polymath. They all interconnect, even if none is fully determined. Lack of time and space preclude me from more than mentioning what that broader picture might be. There is also another reason to question the validity of science's basic picture:

Artificial intelligence doesn't work, at least not for a working copy of human intelligence.

Billions of dollars have been expended in the pursuit of artificial intelligence, so it is difficult to say the artificial intelligence project has failed through lack of funding. The project has attracted many of the world's most brilliant minds, so it is difficult to say that the project has failed through lack of talent. Technology has improved a thousandfold or a millionfold since a giant like Turing thought computer technology was powerful enough for artificial intelligence, so it is difficult to say that today's computers are too underpowered for artificial intelligence. Computer science has matured considerably, so it's hard to say that artificial intelligence hasn't had a chance to mature. In 1950, one could have posited a number of reasons for the lack of success then, but subsequent experience has made many of these possibilities difficult to maintain. This leaves open the possibility that artificial intelligence has failed because the whole enterprise is based on a false assumption, perhaps an error so deep as to be cosmological.

The power of science-based technology is a side effect of learning something significant about the natural world, and both scientific knowledge and technology are impressive cultural achievements. Yet science is not a complete picture—and I do not mean simply that we can have our own private fantasies—and science does not capture the spiritual qualities of matter, let alone a human being. The question of whether science understands mechanical properties of physical things has been put to the test, and the outcome is a resounding yes. The question of whether science understands enough about humans to duplicate human thought is also being put to the test, and when the rubber meets the road, the answer to that question looks a lot like, 'No.' It's not definitive (it couldn't be), but the picture so far is that science is trying something that can't work. It can't work because of spiritual principles, as a perpetual motion machine can't work because of physical principles. It's not a matter of insufficient resources available so far, or still needing to find the right approach. It doesn't seem to be the sort of thing which could work.

We miss something about the artificial intelligence project if we frame it as something that began after computer scientists saw that computers can manipulate symbols. People have been trying to make intelligent computers for half a century, but artificial intelligence is a phenomenon that has been centuries in the making. The fact that people saw the brain as a telephone switchboard, when that was the new technology, is more a symptom than a beginning. There's more than artificial intelligence's surface resemblance to alchemists' artificial person ('homunculus'). A repeated feature of the occult enterprise is that you do not have people giving to society in the ways that people have always given to society; you have exceptional figures trying to delve into unexplored recesses and forge some new creation, some new power—some new technology or method—to achieve something mythic that has simply not been achieved before. The magus is endowed with a magic sword to powerfully slice through his day's Gordian knots, and with a messianic fantasy. This is true of Leibniz's Ars Combinatoria and it is true of more than a little of artificial intelligence. To the reader who suggests, 'But magic doesn't really work!' I would point out that artificial intelligence also doesn't really work—although its researchers find it to work, like Renaissance magi and modern neo-pagans. The vast gap between magic and science that exists in our imagination is a cultural prejudice rather than a historical conclusion. Some puzzles which emerge from an non-historical picture of science—in particular, why a discipline with modest claims about falsifying hypotheses is held in such awe—seem to make a lot more sense if science is investigated as a historical phenomenon partly stemming from magic.

If there is one unexpected theme running through this enquiry, it is what has emerged about relationships. The question of whether one relates to society (or the natural world) as to one's mother or as to raw material, in I-Thou or I-It fashion, first crept in as a minor clarification. The more I have thought about it, the more significant it seems. The Renaissance magus distinguished himself from his medieval predecessors by converting I-Thou relationships into I-It. How is modern science different? To start with, it is much more consistent in pursuing I-It relationships. The fact that science gives mechanisms instead of explanations is connected; an explanation is an I-Thou thing, whilst a bare mechanism is I-It: if you are going to relate to the world in I-It fashion, there is every reason to replace explanations with mechanisms. An I-Thou relationship understands in a holistic, teleological fashion: if you are going to push an I-It relationship far enough, the obvious approach is to try to expunge teleology as the Enlightenment tried. A great many things about magus and scientist alike hinge on the rejection of Orthodoxy's I-Thou relationship.

In Arthurian legend, the figure of Merlin is a figure who holds magical powers, not by spells and incantations, but by something deeper and fundamental. Merlin does not need spells and incantations because he relates to the natural world in a way that almost goes beyond I-Thou; he relates to nature as if it were human. I suggest that science provides a figure of an anti-Merlin who holds anti-magical powers, not by spells and incantations, but by something deeper and fundamental. Science does not need spells and incantations because it relates to the natural world and humans in a way that almost goes beyond I-It; it relates to even the human as if it were inanimate. In both cases, the power hinges on a relationship, and the power is epiphenomenal to that relationship.

If this is a problem, what all is to be done? Let me say what is not to be done. What is not to be done is to engineer a programme to enlist people in an I-Thou ideology. Why not? 'I-Thou ideology' is a contradiction in terms. The standard response of starting a political programme treats society as raw material to be transformed according to one's vision—and I am not just disputing the specific content of some visions, but saying that's the wrong way to start. Many of the obvious ways of 'making a difference' that present themselves to the modern mind work through an I-It relationship, calculating how to obtain a response from people, and are therefore tainted from the start. Does that mean that nothing is to be done? No; there are many things, from a walk of faith as transforming communion with God, to learning to relate to God, people, and the entire cosmos in I-Thou fashion, to using forms of persuasion that appeal to a whole person acting in freedom. But that is another thesis to explore.

Epilogue, 2010

I look back at this piece six years later, and see both real strengths and things I wince at. This was one of my first major works after being chrismated Orthodox, and while I am enthusiastic for Orthodoxy there are misunderstandings. My focus on cosmology is just one step away from Western, and in particular scientific, roots, and such pressure to get cosmology right is not found in any good Orthodox theologian I know. That was one of several areas where I had a pretty Western way of trying to be Orthodox, and I do not blame people who raise eyebrows at my heavy use of existentialist distinction between I-Thou and I-It relationship. And the amount of time and energy spent discussing magic almost deterred me from posting it from my website; for that reason alone, I spent time debating whether the piece was fit for human consumption. And it is possibly theology in the academic sense, but not so much the Orthodox sense: lots of ideas, cleverly put together, with little invitation to worship.

But for all this, I am still posting it. The basic points it raises, and much of the terrain, are interesting. There may be fewer true believers among scientists who still chase an artificial intelligence pot o' gold, but it remain an element of the popular imagination and belief even as people's interests turn more and more to finding a magic sword that will slice through society's Gordian knots—which is to say that there may be something relevant in this thesis besides the artificial intelligence critique.

I am posting it because I believe it is interesting and adds something to the convesation. I am also posting it in the hope that it might serve as a sort of gateway drug to some of my more recent works, and provide a contrast: this is how I approached theology just after being received into Holy Orthodoxy, and other works show what I would present as theology having had more time to steep in Orthodoxy, such as The Arena.

I pray that God will bless you.

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Footnotes

[1] These neural nets are modelled after biological neural nets but are organised differently and seem to take the concept of a neuron on something of a tangent from its organisation and function in a natural brain, be it insect or human.

[2] Cog, http://www.ai.mit.edu/projects/humanoid-robotics-group/cog/images/cog-rod-slinky.gif, as seen on 11 June 2004 (enlarged).

[3] 2002, 50-1.

[4] Searle 1998, Edelman 1992, etc., including some of Dreyfus 1992. Edelman lists Jerome Brunner, Alan Gauld, Claes von Hofsten, George Lakoff, Ronald Langaker, Ruth Garrett Millikan, Hilary Putnam, John Searle, and Benny Shannon as convergent members of a realist camp (1992, 220).

[5] Lee 1987, 6.

[6] 'Intentionality' is a philosophy of mind term for the 'about-ness' of mental states.

[7] By 'teleology' I understand in a somewhat inclusive sense that branch of theology and philosophy that deals with goals, ends, and ultimate meanings.

[8] 'Cognitive faculty' is a philosophy of mind conception of a feature of the human mind that operates on mental representations to perform a specific function.

[9] The spiritual 'intellect' is a patristic concept that embraces thought, conceived on different terms from 'cognitive science,' and is inseparably the place where a person meets God. Augustine locates the image of God in the intellect (In Euangelium Ioannis Tractatus, III.4), and compares the intellect to Christ as illuminating both itself and everything else (In Euangelium Ioannis Tractatus, XLVII, 3).

[10] Watts 2002, 57-8. See the World Transhumanist Association website at http://www.transhumanist.org for further information on transhumanism.

[11] C.S. Lewis critiques this project in The Abolition of Man (1943) and That Hideous Strength (1965). He does not address the question of whether this is a possible goal, but argues that it is not a desirable goal: the glorious future it heralds is in fact a horror compared to the present it so disparages.

[12] Encyclopedia Mythica, 'Rabbi Loeb,' http://www.pantheon.org/articles/r/rabbi_loeb.html, as seen on 26 Mar 04.

[13] Foerst 1998, 109 also brings up this archetypal tendency in her conclusion.

[14] United States Postal Service 2003 annual report, http://www.usps.com/history/anrpt03/html/realkind.htm, as seen on 6 May 2004.

[15] Cog, as seen on http://www.ai.mit.edu/projects/humanoid-robotics-group/cog/images/scaz-cog.gif, on 6 May 2004 (enlarged).

[16] 2002, 57.

[17] Cog, 'Theory of Mind for a Humanoid Robots,' http://www.ai.mit.edu/projects/humanoid-robotics/group/cog/Abstracts2000/scaz.pdf, as seen on 6 May 2004.

[18] Adler 1986, 319-321.

[19] 1992, 161-4.

[20] Utopias are often a satire more than a prescription literally conceived, but they are also far more prescriptive than one would gather from a simple statement that they are satire.

[21] Turing 1950.

[22] VanLehn 1989, in Posner 1989, 532.

[23] Ibid. in Posner 1989, 534.

[24] 1998, 101.

[25] 1992, 159.

[26] Foerst 1998, 103.

[27] Turing 1950.

[28] Hebb 1949, as quoted in the Linux 'fortune' program.

[29] Nominalism said that general categories are something in the mind drawn from real things, and not something things themselves arise from. This has profoundly shaped the course of Western culture.

[30] Lewis 1943, 46.

[31] Yates 1966, 380-382.

[32] Without submitting to the Church in the usual way, the magus is equal to its highest members (Webster 1982, 57).

[33] George Mason University's Modern & Classical Languages, 'Pico della Mirandola: Oratio de hominis dignitate,' http://www.gmu.edu/departments/fld/CLASSICS/mirandola.oratio.html, as seen on 18 May 2004. See Poim 27-9, CH7 1-2 in Bentley 1987 for texts reflecting an understanding of the world as evil and associated contempt for the hoi polloi.

[34] Thomas More: Utopia, Digitale Rekonstruktion, http://www.ub.uni-bielefeld.de/cgi-bin/button.cgi?pfad=/diglib/more/utopia/jpeg/&seite=00000017.jpg&jump=1, http://www.ub.uni-bielefeld.de/cgi-bin/button.cgi?pfad=/diglib/more/utopia/jpeg/&seite=00000018.jpg&jump=1, etc. (pp. 35-6), as seen on 2 June 2004.

[35] Thomas More: Utopia, Digitale Rekonstruktion, http://www.ub.uni-bielefeld.de/cgi-bin/button.cgi?pfad=/diglib/more/utopia/jpeg/&seite=00000039.jpg&jump=1, http://www.ub.uni-bielefeld.de/cgi-bin/button.cgi?pfad=/diglib/more/utopia/jpeg/&seite=00000040.jpg&jump=1, etc., (pp. 79-86), as seen on 2 June 2004. This runs through most of the book.

[36] Lewis 1943, 46.

[37] Ibid., 33-35.

[38] Ibid., 23-24.

[39] Ibid., 295-299.

[40] Ibid.

[41] See Midgley, 1992, 80.

[42] 1990, 195, 197-224,337-41.

[43] 1950.

[44] References will be to the online Greek version at Thesaurus Linguae Graecae, http://stephanus.tlg.uci.edu/inst/wsearch?wtitle=2892+049&uid=&GreekFont=Unicode&mode=c_search, according to chapter and line. Unless otherwise specified, references in this section will be to the Mystagogia.

[45] 5.1-10. 'Intellect' in particular is used as a scholarly rendering of the Greek 'nous,' and is not equivalent to the layman's use of 'intellect,' particularly not as cognate to 'intelligence.' The 'reason' ('logos') is closer to today's use of the term, but not as close as you might think. This basic conceptualisation is common to other patristic and medieval authors, such as Augustine.

[46] 1992, 239.

[47] 'Punctuated equilibrium' is a variant on Darwin's theory of (gradual) evolution. It tries to retain an essentially Darwinian mechanism whilst acknowledging a fossil record and other evidence which indicate long periods of stability interrupted by the abrupt appearance and disappearance of life forms. It is called 'punk eek' by the irreverent.

[48] I.82. Material from the Capita Gnosticae, not available in Thesaurus Linguae Graecae, will be referenced by century and chapter number, i.e. I.82 abbreviates Century I, Chapter 82.

[49] See Lewis 2001, 522.

[50] What we usually mean by 'cause' today: something which mechanically brings about its effect, as time and favourable conditions cause an acorn to grow into an oak.

[51] The 'final cause' is the goal something is progressing towards: thus a mature oak is the final cause of the acorn that would one day grow into it.

[52] As seen on the Project Gutenberg archive at http://www.gutenberg.net/etext97/1ws1810.txt on 15 June 2004.

[53] 1992, 147-165.

[54] 1998, 104-7.