Robin van Spaandonk wrote: I suspect rather that the written symbols function as a form of external > memory, > allowing one to build a larger construct than one could build in the mind > alone. >
That is true too. It is not a case of "rather" but "also." The original purpose of symbols was to communicate the idea to others, and to shape ideas that are too large and complicated to be held in the mind. However, once symbols were invented, the art of physics, programming, architecture and so on became, in a real sense, something you do with your hands with a pencil and paper. (Or on a computer screen nowadays.) Of course you are also doing mental work, assembling and moving the symbols in your mind. There are various other mental processes at work. A computer programmer is imagining himself to be the machine in a sense. When a group of programmers are in a meeting, you may hear one say something like: "Okay, I take your input, check it against Table A, and hand it on to Mary" meaning that's what his section of the program does. If mind-reading computers are improved in the future, and come into general use, it will be interesting to see whether they improve the arts and sciences, or make them worse. (Such computers have been invented and are being developed to help paraplegic patients.) Sometimes the mental skill migrates to the hand and then migrates back to something closer to a pure mental ability. For example, some people in Japan used to be very good at arithmetic with an abacus (soroban). In the 1940s the top people could do arithmetic faster than a skilled American using a Comptometer mechanical calculator. Some were so skilled they could do the calculations with their eyes closed, moving their fingers, with no actual abacus at hand. They had a mental image of the columns and bead positions. That's typically 21 columns (divided into registers) with 6 beads per column. The top bead is a binary 2, and the total is 5 * 2 = 10 per column, with 2 or 3 registers per abacus. As many as you need for the level of precision you select. So you are talking about a mental image keeping track of 126 bits, which are changing at high speed, sometimes in complex patterns for things like table-based long division. - Jed
