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An Abstract Art of Memory
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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.
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An Abstract Art of Memory
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