An Abstract Art of Memory

Surgeon General’s Warning

I’m leaving this work up as a spectacular example of my barking up the wrong tree.

Some time centuries past, it was fashionable as a sort of rite of passage to create your “own art of memory,” as there were other times when it was fashionable to produce a new proof to a particular well-known theorem (the Pythagorean theorem). And this marks a spectacular effort to resurrect that dead fashion, even if I’m not sure it’s learnable enough to be useful. It also represents, to my knowledge, the first art of memory specifically optimized to work gracefully with abstractions, a point on which I have found little competition.

It also falls entirely into Barlaam’s domain, where in one defining moment for the Orthodox Church, the champion of Orthodox hesychasm St. Gregory Palamas engaged the champion of Renaissance man secular learning Barlaam, and the Orthodox Church decisively recognized that the hesychastic or silent tradition still living in the East was its norm, and the Western book learning that puts logic behind the wheel has no place in living Orthodoxy.

I am leaving this up as an example of my being wrong, and as a point of hope that someone wrong may still be brought to saving grace.

Read it on Kindle: for $2.99

Abstract. Author briefly describes classic mnemotechnics, indicates a possible weakness in their ability to deal with abstractions, and suggests a parallel development of related principles designed to work well with abstractions.

Frances Yates opens The Art of Memory with a tale from ancient Greece[1]:

At a banquet given by a nobleman of Thessaly named Scopas, the poet Simonides of Ceos chanted a lyric poem in honor of his post but including a passage in praise of Castor and Pollux. Scopas meanly told the poet that he would only pay him half the sum agreed upon for the panegyric and that he must obtain the balance from the twin gods to whom he had devoted half the poem. A little later, a message was brought in to Simonides that two young men were waiting outside who wished to see him. He rose from the banquet and went out but could find no one. During his absence the roof of the banqueting hall fell in, crushing Scopas and all the guests beneath the ruins; the corpses were so mangled that the relatives who came to take them away for burial were unable to identify them. But Simonides remembered the places at which they had been sitting at the table and was therefore able to indicate to the relatives which were their dead.

After his spatial memory in this event, Simonides is credited with having created an art of memory: start with a building full of distinct places. If you want to remember something, imagine a striking image with a token of what you wish to remember at the place. To recall something naval, you might imagine a giant nail driven into your front door, with an anchor hanging from it; if you visualize this intensely, then when in your mind’s eye you go through your house and imagine your front door, then the anchor will come to mind and you will remember the boats. Imagining a striking image on a remembered place is called pegging: when you do this, you fasten a piece of information on a given peg, and can pick it up later. Yates uses the terms art of memory and artificial memory as essentially interchangeable with mnemotechnics, and I will follow a similar usage.

There is a little more than this to the technique, and it allows people to do things that seem staggering to someone not familiar with the phenomenon[2]. Being able to look at a list of twenty items and recite it forwards and backwards is more than a party trick. The technique is phenomenally well-adapted to language acquisition. It is possible for a person skilled in the technique to learn to read a language in weeks. It is the foundation to some people learning an amount of folklore so that today they would be considered walking encyclopedias. This art of memory was an important part of the ancient Greek rhetorical tradition[3], drawn by medieval Europe into the cardinal virtue of wisdom[4], and then transformed into an occult art by the Renaissance[5]. Medieval and renaissance variations put the technique to vastly different use, and understood it to signify greatly different things, but outside of Lullism[6] and Ramism[7], the essential technique was the same.

In my own efforts to learn the classical form of the art of memory, I have noticed something curious. I’m better at remembering people’s names, and I no longer need to write call numbers down when I go to the library. I was able, without difficulty, to deliver an hour-long speech from memory. Learning vocabulary for foreign languages has come much more quickly; it only took me about a month to learn to read the Latin Vulgate. My weaknesses in memory are not nearly so great as they were, and I know other people have been much better at the art than I am. At the same time, I’ve found one surprise, something different from the all-around better memory I suspected the art would give me. What is it? If there is a problem, it is most likely subtle: the system has obvious benefits. To tease it out, I’d like to recall a famous passage from Plato’s Phaedrus[8]:

Socrates: At the Egyptian city of Naucratis, there was a famous old god, whose name was Theuth; the bird which is called the Ibis was sacred to him, and he was the inventor of many arts, such as arithmetic and calculation and geometry and astronomy and draughts and dice, but his great discovery was the use of letters. Now in those days Thamus was the king of the whole of Upper Egypt, which is in the district surrounding that great city which is called by the Hellenes Egyptian Thebes, and they call the god himself Ammon. To him came Theuth and showed his inventions, desiring that the other Egyptians might be allowed to have the benefit of them; he went through them, and Thamus inquired about their several uses, and praised some of them and censured others, as he approved or disapproved of them. There would be no use in repeating all that Thamus said to Theuth in praise or blame of the various arts. But when they came to letters, This, said Theuth, will make the Egyptians wiser and give them better memories; for this is the cure of forgetfulness and folly. Thamus replied: O most ingenious Theuth, he who has the gift of invention is not always the best judge of the utility or inutility of his own inventions to the users of them. And in this instance a paternal love of your own child has led you to say what is not the fact: for this invention of yours will create forgetfulness in the learners’ souls, because they will not use their memories; they will trust to the external written characters. You have found a specific, not for memory but for reminiscence, and you give your disciples only the pretence of wisdom; they will be hearers of many things and will have learned nothing; they will appear to be omniscient and will generally know nothing; they will be tiresome, having the reputation of knowledge without the reality.

There is clear concern that writing is not what it appears, and it will endanger or destroy the knowledge people keep in memory; a case can be made that the phenomenon of Renaissance artificial memory as an occult practice occurred because only someone involved in the occult would have occasion to keep such memory after books were so easily available.

What kind of things might one wish to have in memory? Let me quote one classic example: the argument by which Cantor proved that there are more real numbers between 0 and 1 than there are counting numbers (1, 2, 3…). I paraphrase the basic argument here:

  1. Two sets are said to have the same number of elements if you can always pair them up, with nothing left over on either side. If one set always has something left over after the matching up, it has more elements.
  2. Suppose, for the sake of argument, that there are at least as many counting numbers as real numbers between 0 and 1. Then you can make a list of the numbers between 0 and 1:
    1:  .012343289889...
    2:  .328932198323...
    3:  .438724328743...
    4:  .988733287923...
    5:  .324432003442...
    6:  .213443765001...
    7:  .321010320030...
    8:  .323983213298...
    9:  .982133982198...
    10: .321932198904...
    11: .000321321278...
    12: .032103217832...
  3. Now, take the first decimal place of the first number, the second of the second number, and so on and so forth, and make them into a number:
    1:  .012343289889...
    2:  .328932198323...
    3:  .438724328743...
    4:  .988733287923...
    5:  .324432003442...
    6:  .213443765001...
    7:  .321010320030...
    8:  .323983213298...
    9:  .982133982198...
    10: .321932198904...
    11: .000321321278...
    12: .032103217832...


  4. Now make another number between 0 and 1 that is different at every decimal place from the number just computed:
  5. Now, remember that we assumed that the list has all the numbers between 0 and 1: every single one, without exception. Therefore, if this assumption is true, then the latter number we constructed must be on the list. But where?The number can’t be the first number on the list, because it was constructed to be different at the first decimal place from the first number on the list. It can’t be the second number on the list, because it was constructed to be different at the second decimal place from the second number on the list. Nor can it be the third, fourth, fifth… in fact, it can’t be anywhere on the list because it was constructed to be different. So we have one number left over. (Can we put that number on the list? Certainly, but the argument shows that the new list will leave out another number.)
  6. The list of numbers between 0 and 1 doesn’t have all the numbers between 0 and 1.
  7. We have a contradiction.
  8. We started by assuming that you can make a list that contains all the numbers between 0 and 1, but there’s a contradiction: any list leaves numbers left over. Therefore, our assumption must be wrong. Therefore, there must be too many real numbers between 0 and 1 to assign a separate counting number to each of them.

Let’s say we want to commit this argument to memory. A mathematician with artificial memory might say, “That’s easy! You just imagine a chessboard with distorted mirrors along its diagonal.” That is indeed a good image if you are a mathematician who already understands the concept. If you find the argument hard to follow, it is at best a difficult thing to store via the artificial memory. Even if it can be done, storing this argument in artificial memory is probably much more trouble than learning it as a mathematician would.

Let me repeat the quotation from the Phaedrus, while changing a few words:

Jefferson: At the Greek region of Thessaly, there was a famous old poet, whose name was Simonides; totems seen with the inner eye were devoted to him, and he was the inventor of a great art, greater than arithmetic and calculation and geometry and astronomy and draughts. Now in those days Rousseau was a sage revered throughout the West, and they called the god himself Rationis. To him came Simonides and showed his invention, desiring that the rest of the world might be allowed to have the benefit of it; he went through it, and Rousseau inquired about its several uses, and praised some of them and censured others, as he approved or disapproved of them. There would be no use in repeating all that Rousseau said to Simonides in praise or blame of various facets. But when they came to inner writing, This, said Simonides, will make the West wiser and give it better memory; for this is the cure of forgetfulness and of folly. Rousseau replied: O most ingenious Simonides, he who has the gift of invention is not always the best judge of utility or inutility of his own inventions to the users of them. And in this instance a paternal love of your own child has led you to say what is not the fact; for this invention will create forgetfulness in the learner’s souls, because they will not remember abstract things; they will trust to mere mnemonic symbols and not remember things of depth. You have found a specific, not for memory but for reminiscence, and you give your disciples only the pretence of wisdom; they will be hearers of many things and will have learned nothing; they will appear to be omniscient and will generally know nothing; they will be tiresome, having the reputation and outer shell of knowledge without the reality of deep thought.

It is clear that if we follow Thomas Aquinas’s instructions on memory to visualize a woman for wisdom, we may recall wisdom. What is less clear is that this inner writing particularly helps an abstract recollection of wisdom. It may be able to recall an understanding of wisdom acquired without the help of artificial memory, but this art which allows at times stunning performance in the memorization of concrete data is of more debatable merit in learning abstraction. It has been my own experience that abstractions can be forced through the gate of concreteness in artificial memory, but it is like forcing a sponge through a funnel. While I admittedly don’t have a medieval practitioner’s inner vocabulary to deal with abstractions, using the artificial memory to deal with abstractions seems awkward in much the same way that storing individual letters through artificial memory[9] is awkward. The standard artificial memory is a tool for being reminded of abstractions, but not for remembering them. It offers the abstract thinker a seductive way to recall a great many concrete facts instead of learning deep thought.

The overall impression I receive of the artificial memory is not so much a failed attempt at a tool to store abstractions as a successful attempt at a concrete tool which was not intended to store abstractions. It is my belief that some of its principles, in modified form, suggest the beginnings of an art of memory well-fitted to dealing with abstractions. The mature form of such an endeavor will not simply be an abstract mirror image of a concrete artificial memory, but it is appropriate enough for the first steps I might hazard.

Consider the following four paragraphs:

  1. Physics is like music. Both owe something of substance to the Pythagoreans. Both are aesthetic endeavors that in some way represent nature in highly abstracted form. Both are interested in mechanical waves. Many good physicists are closet musicians, and all musical instruments operate on physical principle.
  2. Physics is like literature. Both are written in books that vary from moderately easy to very hard. Both deal with a distinction between action and what is acted on, be it plot and character or force and particle, and both allow complex entities to be built of simpler ones. Practitioners of both want to be thought of as insightful people who understand reality.
  3. Physics is like an adventure. Both involve a venture into the unknown, where the protagonist tries to discover what is happening. Both have a mystique that exists despite most people’s fear to experience such things themselves. To succeed in either, one is expected to have impressive strengths.
  4. Physics is like magic. Both flourished in the West, at the same time, out of the same desire: a desire to understand nature so as to control it. Both attract abstract thinkers, are practiced in part through the manipulation of arcane symbols, and may be found in the same person, from Newton to Feynman[10]. Magical theory claims matter to be composed of earth, air, fire, and water, while physics finds matter to be composed of solid, liquid, gas, and plasma.

What is the merit of these comparisons? They recall a story in which a literature professor asked Feynman if he thought physics was like literature. Feynman led him on with an elaborate analogy of how physics was like literature, and then said, “But it seems to me you can make such an analogy between any two subjects, so I don’t find such analogies helpful.” He observed that one can make a reasonably compelling analogy even if there’s no philosophically substantial connection.

The laws of logic and philosophy are not the laws of memory. What is a liability to Feynman’s implicit philosophical method is a strength to memory. The philosophical merit of the above comparisons is debatable. The benefit to memory is different: it appears to me that this is an abstract analogue to pegging. A connection, real or spurious, aids the memory even if it doesn’t aid a rigorous philosophical understanding. In pegging, it is considered an advantage to visualize a ludicrously illogical scene: it is much more memorable than something routine and sensible. Early psychological experiments in memory involved memorization of nonsense syllables. The experimenters intentionally chose meaningless material to memorize. Why? Well, if the subject perceived meaning, that would provide a spurious way for the subject to remember the data, and so proper Ebbinghausian memory study meant investigating how people investigate memory material which was as meaningless as possible. Without pausing to develop an obvious critique, I’d suggest that this spurious route to memory is of great interest to us. Meaningful data is more memorable than meaningless, and this is true whether the meaning perceived is philosophically sound or obviously contrived. I might suggest that interesting meaning provides a direct abstract parallel to the striking, special-effect appearance of effective images in pegging.

I intentionally chose not to compare physics to astronomy, chemistry, computer science, engineering, mathematics, metaphysics, or statistics, because I wanted to show how a different concept can be used to establish connections to a new one. Or, more properly, different concepts. Having a new concept connected to three very different ones will capture different facets than one anchor point, and possibly cancel out some of each other’s biases. A multiplicity of perspectives lends balance and depth. This isn’t to say similar concepts can’t be used, only that searching for a partial or full isomorphism to a known concept is easier than encoding from scratch. If memorable connections can be made between physics and adventure, music, English, and magic, what might be obtained from comparison with mathematics, chemistry, and engineering? A comparison between physics and these last three disciplines is left as an exercise to the reader, and one that may be quite fruitful.

Is this a desirable way to remember things? I would make two different comments on this score. First, when learning Latin words, I would first peg it to an English word with a vivid image, then later recall the image and reconstruct the English equivalent, then recall the image and remember the English, then the image would drop out so I would directly remember the English, and finally the English word would drop out too, leaving me with a Latin usage often different from the English equivalent used. Artificial memory does not circumvent natural memory; instead it streamlines the process and short-circuits many of the disruptive trips to the dictionary. Pegs vanish with use; they are not an alternate final product but a more efficient route for concepts more frequently used, and a cache of reference material. Therefore, even if remembered comparisons between physics and adventure/music/English/magic fall short of how one would desire to understand the concept, a similar flattening of the learning curve is possible. Second, I would say that even if you fail to peg something, you may succeed. How? In trying to peg a person’s name, I hold that name and face in an intense focus—quite the opposite how I once reacted: “I’ll never remember that,” a belief which chased other people’s names out of my mind in seconds. That focus is relevant to memory, and it has happened more than once that I completely failed to create a peg, but my failure used enough mental energy that I still remembered. If you search through your memory and fail to make even forced connections between a new concept and existing concepts, the mental focus given to the concept will leave you much better off than if you had thrown up your hands and thought the self-fulfilling prophecy: “I will never remember that!”

Certain kinds of emotional intelligence are part of the discipline. Learning to cultivate presence has to do with an emotional side, and I have written elsewhere about activities that can help to cultivate such presence[11]. We learn material better if we are interested in it; therefore consciously cultivating an interest in the material and seeing how it can be fascinating is another edge. Cultivating and guarding your inner emotional state can have substantial impact on memory and learning abstractions. Much of it has to do with keeping a state of presence. Shutting out abstractions is one obvious way to do this; another, perhaps less obvious, is to avoid cramming and simply ploughing through material unless it’s something you don’t really need to learn. Why?

If there is a sprinkler that disperses a fine mist, it will slowly moisten the ground. What if there’s a high-volume sprinkler that shoots big, heavy drops of water high up in the air? With all that water pounding on the ground, it looks like the ground is quickly saturated. The appearance is deceptive. What has happened is that the heavy drops have pounded the surface of the ground into a beaten shield, so there really is water rolling off of a very wet surface, but go an inch down and the soil is as parched as ever. This sort of thing happens in studying, when people think that the more force they use, the better the results. Up to a point, definitely, and perseverance counts—but I have found myself to learn much more when I paid attention to my mental and emotional state and backed off if I sensed that I was leaving that optimal zone. I learn something if I say “This is important, so I’ll plough through as much as I can as quickly as I can,” but it’s not as much, and keeping on task needs to be balanced with getting off task when that is helpful.

Consider the following problem:[12]

In the inns of certain Himalayan villages is practiced a most civilized and refined tea ceremony. The ceremony involves a host and exactly two guests, neither more nor less. When his guests have arrived and have seated themselves at his table, the host performs five services for them. These services are listed in order of the nobility which the Himalayan attribute to them: (1) Stoking the Fire, (2) Fanning the Flames, (3) Passing the Rice Cakes, (4) Pouring the Tea, and (5) Reciting Poetry. During the ceremony, any of those present may ask another, “Honored Sir, may I perform this onerous task for you?” However, a person may request of another only the least noble of the tasks which the other is performing. Further, if a person is performing any tasks, then he may not request a task which is nobler than the least noble task he is already performing. Custom requires that by the time the tea ceremony is over, all the tasks will have been transferred from the host to the most senior of the guests. How may this be accomplished?

Incomprehensible appearances notwithstanding, this is a very simple problem, the Towers of Hanoi. Someone who has learned the Towers of Hanoi may still solve the tea ceremony formulation as slowly as someone who’s never seen any form of the problem[13]. A failure to recognize isomorphisms provides one of the more interesting passages in Feynman’s memoirs[14]:

I often liked to play tricks on people when I was at MIT. One time, in a mechanical drawing class, some joker picked up a French curve (a piece of plastic for drawing smooth curves—a curly, funny-looking thing) and said, “I wonder if the curves on this thing have some special formula?”

I thought for a moment and said, “Sure they do. The curves are very special curves. Lemme show ya,” and I picked up my French curve and began to turn it slowly. “The French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal.”

All the guys in the class were holding their French curve up at different angles, holding their pencil up to it at the lowest point and laying it along, and discovering that, sure enough, the tangent is horizontal. They were all excited by this “discovery”—even though they had already gone through a certain amount of calculus and had already “learned” that the derivative (tangent) of the minimum (lowest point) of any curve is zero (horizontal). They didn’t put two and two together. They didn’t even know what they “knew.”

What is going on here is that Feynman perceives an isomorphism where the others do not. There may be a natural bent to or away from perceiving isomorphisms, and cognitive science suggests most people have a bent away. The finding, as best I can tell, is not so much that people can’t look for isomorphisms, as that they don’t. The practice of looking for and finding isomorphisms has something to give, because something can be treated as already known instead of learned from scratch. I might wonder in passing if the ultra-high-IQ rapid learning and interdisciplinary proclivities stem in part from the perception and application of isomorphisms, which may reduce the amount of material actually learned in picking up a new skill.

The classical art of memory derives strength from a mind that works visually; a background in abstract thought will help one learn abstractions. It has been thought[15] that people can more effectively encode and remember material in a given domain if it’s one they have worked with; I would suggest that this abstract pegging also creates a way to encode material with background from other domains. An elaborate, intense, and distinct encoding is believed to help recall[16]. Heightening of memorable features, in what is striking or humorous[17], should help, and mimetics seems likely to contain jewels in its accounts of how a meme makes itself striking.

Someone familiar with artificial memory may ask, “What about places (loci)?” Part of the art of memory, be it ancient, medieval, or renaissance, involved having an inner building of sorts that one could imagine going through in order and recalling items. I have two basic comments here. First, a connection could use traditional artificial memory techniques as an index: imagine a muscular man with a tremendous physique running onto the scene, grabbing an adventurer’s sword, shield, and pack, sitting down at a pipe organ which has a large illuminated manuscript on top, and clumsily playing music until a giant gold ring engraved with fiery letters falls on the scene and turns it to dust. You have pegged physics to adventure, music, literature, and magic; if you wanted to reconstruct an understanding of physics, you could see what it was pegged to, and then try to recall the given similarities. Second and more deeply, I believe that a person’s entire edifice of previously acquired concepts may serve as an immense memory palace. It is not spatial in the traditional sense, and I am not here concerned with the senses in which it might be considered a topological space, but it is a deeply qualitative place, and accessible if one uses traditional artificial memory for an index: these adaptations are intended to expand the repertoire of what disciplined artificial memory can do, not abolish the traditional discipline.

Symbols are the last unexplored facet. Earlier I suggested that a chessboard with mirrors along its diagonal may be a good token to represent Cantor’s diagonal argument, but does not bring memory of the whole proof. Now I would like to give the other side: an abstraction may not be fully captured by a symbol, but a good symbol helps. A sign/symbol distinction has been made, where a sign represents while a symbol represents and embodies. In this sense I suggest that tokens be as symbolic as possible.

Why use a token? Aren’t the deepest thoughts beyond words? Yes, but recall depends on being able to encode. I have found my deepest thoughts to not be worded and often difficult to translate to words, but I have also found that I lose them if I cannot put them in words. As such, thinking and choosing a good, mentally manipulable symbol for an abstraction is both difficult and desirable. My own discipline of formation, mathematics, chooses names for variables like ‘x’, ‘y’, and ‘z’ which software engineers are taught not to use because they impede comprehension: a computer program with variable names like ‘x’ and ‘y’ is harder to understand or even write to completion than one which with names like ‘trucks_remaining’ or ‘customers_last_name’. The authors of Design Patterns[18] comment that naming a pattern is one of the hardest parts of writing it down. The art of creating a manipulable symbol for an abstraction is hard, but worth the trouble. This, too, may also help you to probe an abstraction in a way that will aid recall.

To test these principles, I decided to spend a week[19] seeing what I could learn of a physics text[20] and Kant’s Critique of Pure Reason[21]. I considered myself to have understood a portion of the physics text after being able to solve the last of the list of questions. I had originally decided to see how quickly I could absorb material. After working through 10% of the physics text in one day, I decided to shift emphasis and pursue depth more than speed. In reading Kant, the tendency to barely grasp a difficult concept forgotten in grasping the next difficult concept gave way, with artificial memory, to understanding the concepts better and grasping them in a way that had a more permanent effect. I read through page 108 of 607 in the physics text and 144 of 669 in Kant’s Critique of Pure Reason.

The first day’s physics ventures saw two interesting ways of storing concepts, and one comment worth mentioning. There is a classic skit, in which two rescuers are performing two-person CPR on a patient. Then one of the rescuers says, “I’m getting tired. Let’s switch,” and the patient gets up, the tired rescuer lies down, and the other two perform CPR on him. This was used to store the interchangeability of point of effort, point of resistance, and fulcrum on a lever, based on an isomorphism to the skit’s humor element.

The rule given later, that along any axis the sum of forces for a body in equilibrium is always zero, was symbolized by an image of a knife cutting a circle through the center: no matter what angle of cutting there was, the cut leaves two equal halves.

These both involved images, but the images differed from pegging images as a schematic diagram differs from a computer animated advertisement. They seemed a combination of an isomorphism and a symbol, and in both cases the power stemmed not only from the resultant image but the process of creation. The images functioned in a sense related to pegging, but most of the images so far developed have been abstract images unlike anything I’ve read about in historical or how-to discussion of the art of memory.

The following was logged that night. The problem referred to is a somewhat complex lever problem given in three parts:

In reviewing the day’s thoughts at night, I recognized that the problems seem to admit a shortcut solution that does not rigorously apply the principles but obtains the correct answer: problem 12 on page 31 gives two weights and other information, and all three subproblems can be answered by assuming that there are two parts in the same ratio [as] the weights, and applying a little horse sense as to which goes where. It’s a bit like general relativity, which condenses to “Everything changes by a factor of the square root of (1 – (v^2/c^2)).” I am not sure whether this is a property of physics itself or a socially emergent property of problems used in physics texts.

I believe this suggests that I was interacting with the material deeply and quite probably in a fashion not anticipated by the authors.

In reading Kant, I can’t as easily say “I solved the last exercises in each section” and don’t simply want to just say, “I read these pages.” I would like to demonstrate interaction with the material with excerpts from my log:

…I am now in the introduction to the second edition, and there are two images in reference to Kant’s treatment of subjective and objective. One is of a disc which has been cut in half, sliced again along a perpendicular axis and brought together along the first axis so that the direction of the cut has been changed. The other is of a sphere being turned out by [topologically] compactifying R3 [Euclidean three-space] by the addition of a single point, and then shifting so the vast outside has become the cramped inside and the cramped inside has become the vast outside. Both images are inadequate to the text, indicating at best what sort of thing may be thought about in what sort of shift Kant tries to introduce, and I want to reread the last couple of pages. Closer to the mark is a story about three umpires who say, in turn, “I calls them as they are,” “I calls them as I see them,” and “They may be strikes, they may be balls, but they ain’t nothing until I calls them!”

Having reread, I believe that the topological example is truer than I realized. I made it on almost superficial grounds, after reading a footnote which gave as example scientific progress after Copernicus proposed, rather than that the observer be fixed and the heavens rotate, the heavens are fixed and the observer rotate. The deeper significance is this: prior accounts had apparently not given sufficient account to subjective factors, treating subjective differences as practically unimportant—what mattered for investigation was the things in themselves. Thus the subjective was the unexamined inside of the sphere. Then, after the transformation, the objective was the unexaminable inside of the new sphere: we may investigate what is now outside, our subjective states and the appearances conformed to them, but things in themselves are more sealed than our filters before: before, we didn’t look; after, we can’t look. What is stated [in Kant] so far is a gross overextension of a profound observation.

The below passages refer to pp. 68-70:

Kant’s arguments that space is an a priori concept can be framed as showing that there exists a chicken-and-egg or bootstrapping gap between them and sense data.

What is a chicken-and-egg/bootstrapping gap? In assisting with English as a Second Language instruction, I was faced with a difficulty in explanation. Assuming certain background, it is possible for a person not to know something while there is a straightforward way of explaining—perhaps a very long way of explaining, but it’s obvious enough how to explain it in terms of communicable concepts. Then there is the case where there is no direct way to explain something: one example is how to explain to a small child what air is. One can point to water, wood, metal, stone, food, and a great many other things, but the same procedure may not yield understanding of air. It may be possible with a Zen-like cleverness to circumvent it—in saying, for example, that air is what presses on your skin on a windy day—but it is not as straightforward as even an involved and difficult explanation where you know how to use the other person’s concepts to build the one you want.

In English as a Second Language instruction, this kind of gap is a significant phenomenon in dealing with students who have no beginning English knowledge, and in dealing with concepts that cannot obviously be demonstrated: ‘sister’ and ‘woman’, when both terms refer to an adult, differ in a way that is almost certainly understood in the student’s native tongue but is nonetheless extremely difficult to explain. When I first made the musing, I envisioned a Zen-like solution. Koans immortalize incidents in which Zen masters bypassed chicken-and-egg gaps in trying to convey enlightenment that cannot be straightforwardly explained, and therefore show a powerful kind of communication. That is what I envisioned, but it is not how English is taught to speakers of other languages. What happens in ESL classes, and with younger children, is a gradual emergence that is difficult to account for in the terms of analytic philosophy—a straightforward explanation sounds like hand-waving and sloppy thinking—but with enough repetition, material is picked up. It may have something to do with a mechanism of learning outlined in Polanyi’s Personal Knowledge, which talks about how i.e. swimmers learn from coaches to inhale more air and exhale less completely so that their lungs act more as a flotation device than a non-swimmers, even though neither swimmer nor coach is likely aware of what is going on on any conscious level. People pick things up through at least one route besides grasping a concept consciously synthesized from sense data.

Kant’s proof that a given concept is a priori essentially consists of argument that the concept that cannot be synthesized from sense data through the obvious means of central route processing. He is probably right in that the concepts he classifies as a priori, and presumably others as well, cannot just be synthesized from sense data through central route processing. It does not follow that a concept must be a priori: there are other possibilities besides the route Kant investigates that one can acquire a belief. I do believe, though, that we come with some kind of innate or a priori knowledge: the difficulties experienced in visualizing four dimensional objects suggest that our dealing with three-dimensional space is not simply the result of a completely amorphous central nervous system which we happen to condition to deal with three dimensions; there is something of substance, comparable in character to a psychologist’s broader understanding of memory, that we are born to. An investigation of that would take me too far afield.

P. 87. “Now a thing in itself cannot be known throu[g]h mere relations; and we may therefore conclude that since outer science gives us nothing but mere relations, this sense can contain in its representation only the relation of an object to the subject, and not the inner properties of the object in itself.”

There is a near-compatibility between this and realist philosophy of science. How?

Recall my observation about chicken-and-egg gaps and how they may be surmounted (here I think of Zenlike short-circuiting of the gap rather than the vaguely indicated gradual emergence of concepts which haven’t been subject to a detailed and understood explanation). What goes on in a physics experiment? The truly famous ones since 1900—I think of the Millikin oil-drop experiment—include a very clever hack that tricks nature into revealing herself. People, not even experimental physicists, can grab a handful of household items and prove that electric charge is quantized.[22] Perhaps that was possible in Galileo’s day, but a groundbreaking experiment involves a brilliant, clever, unexpected trickery of nature that is isomorphic to a Zen short-circuiting in a chicken-and-egg gap, or a clever hack, and so on and so forth. Even a routine classroom experiment uses technology that is the fruit of this kind of resourcefulness. People do something they “shouldn’t” be able to do. This is possibly how we might learn intuitions Kant classifies as a priori, and how experimental scientists cleverly circumvent the roadblock Kant describes here. It might be said that understanding this basic problem is prerequisite to a good realist philosophy of science.

‘Hack’, in this context, refers to the programming cleverness described in Programming Pearls[23]. I analyzed that fundamental mode of problem solving and compared it with its counterpart in “Of Technology, Magic, and Channels”[24]. There are other observations and interactions with the text, but I believe these should adequately make the point.

I chose Kant because of his reputation as an impenetrable analytic philosopher. With the aid of a good translation and these principles, I was at times surprised at how easy it was to read. By the end of the week, I had another surprise when I decided to reread George MacDonald’s Phantastes[25], a work which I have greatly enjoyed. This time, my experience was different. I felt my mind working differently despite a high degree of mental fatigue. The evocative metaphor fell dead, and I found myself reading the text as I would read Kant, thinking in a manner deeply influenced by reading Kant, and in the end setting it down because my mind had shifted deeply into a mode quite different from what allows me to enjoy Phantastes. I was surprised at how deeply using abstract memory to read Kant had affected not only conscious recall of ideas but also ways of thought itself.

I do not consider my recorded observations to be in any sense a rigorous experiment, but I believe the experience suggests it’s interesting enough to be worth a good experiment.

Here are twelve proposed principles, or rules of thumb, of abstract memory:

  1. Be wholly present. Want to know the material. Make it emotionally relevant and connected to something that concerns you. Don’t take notes[26].
  2. Encode material in multiple ways. Some different ways to encode are: analogies to different abstractions, list distinctions from similar abstractions, paraphrase, search for isomorphisms, use the concepts, and create visual symbols.[27]
  3. At least in the beginning, mix a little bit of reading material with a lot of processing. Don’t plough through anything you want to remember. Work on drawing a lot of mist in, not pounding with heavy drops that will create a beaten shield.
  4. Don’t read out of a desire to finish reading a text. Read to draw the materials through processed thought.
  5. Process in a way that is striking, stunning, novel, and counter-intuitive: in a word, memorable.
  6. Process material on as deep a level as you can.[28]
  7. Search for subtle distinctions between a concept under study and its near neighbors.
  8. Converse, interact with, and respond to the abstractions. What would you say if an acquaintance said that in a discussion? What questions would you ask? Write it down.
  9. Know how much mental energy you have, and choose battles wisely. Given a limited amount of energy, it is better to fully remember a smaller number of critical abstractions than to have diffuse knowledge of many random ideas.
  10. Guard your emotions. Be aware of what emotional states you learn well in, and put being in those states before passing your eyes over such-and-such many pages of reading material.
  11. Review material after study, seeking to find a different way of putting it.
  12. Metacogitate. Be your own coach.

Committing these principles to memory is left as an exercise to the reader.

What can I say to conclude this monograph? I can think of one or two brief addenda, such as the programmer’s virtue of laziness[29], but in a very real sense I can’t conclude now. I can sketch out a couple of critiques that may be of interest. Jerry Mander[30] critiques the artificial unusuality of television and especially advertising, in a way that has direct bearing on traditional mnemotechnics. He suggests that giving otherwise uninteresting sensation a strained and artificial unusuality has undesirable impact on how people perceive life as seen outside of TV, and the angle of his critique is the main reason why I was hesitant to learn artificial memory. There may be room for similar critiques about why making ridiculous comparisons to remember ideas creates a bad habit for someone who wishes to think rigorously. There is also the cognitive critique that the search for isomorphisms will introduce unnoted distortion. One thinks of the person who says, “All the religions in the world say the same thing.” There is a common and problematic tendency to be astute in perceiving substantial similarities among world religions and all but blind in perceiving even more substantial differences. That is why I suggest comparing with multiple and different familiar concepts, rather than one. I could give other thoughts about critiques, but I’m trying to explain an art of memory, not especially to defend it.My intention here is not to settle all questions, but open the biggest one and suggest a direction of inquiry by which an emerging investigation may find a more powerful way to learn abstractions.[31]


    1. Yates, Frances A., The Art of Memory, hereafter AM, Chicago: University of Chicago Press, 1966, pp. 1-2. The text is a treasure trove on the development of mnemotechnics, also referred to here as artificial memory or the art of memory. Back
    2. Trudeau, Kevin, Kevin Trudeau’s Mega Memory, hereafter KTMM, New York: William Morrow & Co., 1995 is one of several practical manuals for someone who thinks the classical art of memory interesting and would like to be able to use it. Back
    3. AM, pp. 27ff. Back
    4. Ibid., pp. 50ff. Back
    5. Ibid., pp. 129ff. Back
    6. Ibid., pp. 173ff. Back
    7. Ibid., pp. 231ff. Back
    8. Jowett, B., The Dialogues of Plato, Vol. III, hereafter DP, New York: National Library Company, pp. 442-443. Back
    9. AM, pp. 112ff describes one popularizer whose somewhat debased form advocated memorizing individual letters. This practice is awkward, much as it would be awkward to record the appearance of a room by taking a notepad and writing one letter on each sheet of paper. Back
    10. Feynman, Richard, Surely You’re Joking, Mr. Feynman, hereafter SYJMF, New York: W. W. Norton & Company, 1985, pp. 338ff and other places in the text. He began his famous “Cargo Cult Science” address by talking about his occult diversions from scientific endeavors, and it is arguable that Newton’s groundbreaking work in physics and optics was a scientific diversion from his main occult endeavors. I find it revealing that, even with Feynman’s occult forays left in the book, the index shows curious lacunae for “ESP”, “Hallicunation”, “New Age”, “Reflexology”, “Sensory deprivation”, etc. Back
    11. 100 Ways of Kything, hereafter 1WK, by CJS Hayward, at describes a number of activities which can embody presence and focus. Back
  • Hayes, J.R., and Simon, H.A., “Understanding Written Problem Instructions”, 1974, in Gregg, L.W. ed., Knowledge and Cognition, hereafter KC, Hillsdale: Erlbaum. Quoted in Posner, Michael I. ed., Foundations of Cognitive Science, hereafterFCS, Cambridge: The MIT Press, 1989, pp. 534-535. Back
  • FCS, pp. 559-560. Back
  • SYJMF, pp. 36-37. A more scholarly, if more pedestrian, mention of the phenomenon is provided in FCS, pp. 559-560. Back
  • FCS, p. 690. The authors do not necessarily subscribe to this view, but acknowledge influence among many in the field. Back
  • Ibid., p. 691. Back
  • “A picture of evil”, hereafter APE, by CJS Hayward, at provides an example of communication which is striking in this manner. Back
  • Gamma, Erich; Helm, Richard; Johnson, Ralph; Vlissides, John, Design Patterns: Elements of Reusable Object-Oriented Software, hereafter DP, Reading: Addison-Wesley, p. 3. The book describes recurring good practices that are known to many expert practitioners, but often only on a tacit level—and tries to explain how this tacit knowledge can be made explicit. The book is commonly called ‘GoF’ (“Gang of Four”) by software developers. Thanks to Ron Miles for locating the page number. Back
  • February 9-15 2002. Testing abstract artificial and honing this article were juggled with other responsibilities. Back
  • Black, Newton Henry; Davis, Harvey Nathaniel, New Practical Physics: Fundamental Principles and Applications to Daily Life, hereafter NPP, New York: Macmillan, 1929. Given to me as a whimsical Christmas gift in 2001. At the time of beginning, I was significantly out of practice in both physics and mathematics. Back
  • Smith, Norman Kemp tr., Immanuel Kant’s Critique of Pure Reason, hereafter IKCPR, London: Macmillan, 1929. I had not previously read Kant. Back
  • I knew that science doesn’t deal in proof; experiments may corroborate a theory, but not establish it as something to never again doubt. I was thinking at that point along another dimension, to convey a quality of physics experiments today. Back
  • Bentley, Jon Louis, Programming Pearls, hereafter PP, Reading: Addison-Wesley, 1986. Back
  • Hayward, Jonathan, “Of Technology, Magic, and Channels”, in Gift of Fire, June 2001, number 126. Back
  • MacDonald, George, Phantastes, hereafter P, reprinted Grand Rapids: Wm. B. Eerdmans, 1999. Back
  • Despite widespread endorsement of this practice, taking notes taxes limited mental energy that can better be used to understand the material, and acts to the mind as a signal of, “This can safely be forgotten.” KTMM, very early on, makes a point of telling readers not to take notes (p. 5). The purpose of attending a lecture or reading a book is to make internal comprehension rather than external reference materials. Back
  • Tulving, Endel; Craik, Fergus I.M., The Oxford Handbook of Memory, hereafter OHM, Oxford: Oxford University Press, 2000, refers on p. 98 to the picture superiority effect, which states that pictures are better remembered because of a dual coding where they are encoded as image and words and therefore have two chances at being stored rather than the one chance when material is presented only as words. Back
  • OHM mentions on p. 94 the “levels of processing” view, a significant perspective which states that material is retained better the more deeply it is processed. Back
  • Wall, Larry; Christiansen, Tom; Schwartz, Randal L., Programming Perl, Second Edition, hereafter PP2, Sebastopol: O’Reilly, pp. 217ff and other places throughout the book. Known by the affectionate nickname of “the camel book” among software developers. (This book is distinct from PP). Back
  • Mander, Jerry, Four Arguments for the Elimination of Television, hereafter FAET, New York: Morrow Quill, 1978, pp. 299ff. Back
  • I would like to thank Robin Munn for giving me my first serious introduction to the art of memory, Linda Washington and Martin Harris for looking at my manuscript, William Struthers for valuable comments about source material, and Chris Tessone, Angela Zielinski, Kent and Theo Nebergall, and people from Wheaton College and International Christian Mensa for prayer. I would also like to thank those who read this article, apply it, perhaps extend it, and perhaps tell others about them. Back