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An Abstract Art of Memory
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Giftedness, and Profound Giftedness
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:
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.
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...
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...
Result:
.028733312972...
Now make another number between 0 and 1 that is different at every decimal place from the number just computed:
.139844423083...
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.)
The list of numbers between 0 and 1 doesn't have all the numbers between 0 and 1.
We have a contradiction.
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.
Jonathan's Corner
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An Abstract Art of Memory
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