weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (02/21/86)
In reading Oliver Sacks _The Man Who Mistook His Wife For a Hat_, I came across a rather vivid chapter. (I cross-posted to net.jokes.d since it reminds me quite strongly of the jail jokes.) Summarizing seems impossible. (The rest of the book is also worth reading.) It concerns John and Michael, identical twins and idiot savants. Physic- ally they are undersized, with disturbing disproportions in head and hands, high-arched palates, high-arched feet, monotonous squeaky voices, a variety of peculiar tics and mannerisms, and a very high, degenerative myopia, requiring glassses so thick that their eyes seem distorted, giving them ... a misplaced, obsessed and absurd concentration. In the early sixties, they gave frequent performances of some of their talents: You give them a date, and, almost instantly, they tell you what day of the week it would be. ... One may observe ... that their eyes move and fix in a peculiar way as they do this--as if they were unrolling ... a mental calender. ... Their memory for digits is remarkable--and possibly unlimited. They will repeat a number of three digits, of thirty digits, of three hundred digits, with equal ease. He goes on to mention that they have difficulty adding and subtracting, and apparently have no comprehension of multiplication and division. He then tells of his first discovery of further talents: A box of matches on their table fell, and discharged its contents on the floor: '111,' they both cried sumultaneously; and then, in a murmer John said '37'. Michael repeated this, John said it a third time and stopped. I counted the matches ... and there were 111. 'How could you count the matches so quickly?' I asked. 'We didn't count,' they said. 'We *saw* the 111.' ... 'And why di you murmur '37', and repeat it three times?' I asked the twins. They said in unison, '37,37,37,111.' And this, if possible, I found even more puzzling. That they should *see* 111--'111-ness'--in a flash was extraordinary.... But they had gone on to 'factor' the number 111--without having any method, without even 'knowing' (in the ordinary way) what factors meant. The author tries to understand this, and compares them with Borges' story 'Funes the Memorious'. Then comes what I found most remarkable. This second time they were seated in a corner together, with a mysterious, secret smile on their faces, a smile I had never seen before, enjoying the strange pleasure and peace they now seemed to have. ... They seemed to be locked in a singular, purely numerical, converse. John would say a number--a six-figure number. Michael would catch the number, nod, smile and seem to savour it. Then he, in turn, would say another six-figure number, and now it was John who received, and appreciated it richly. They looked, at first, like two connoisseurs wine-tasting.... *What* were they doing? ... It was perhaps a sort of game, but it had a gravity and an intensity, a sort of serene and meditative and almost holy intensity which I had never seen in any ordinary game before, and which I certainly had never seen before in the usually agitated and distracted twins. I contented myself with noting down the numbers .... Had the numbers any meaning, I wondered .... Were these 'Borgesian' or 'Funesian' numbers, or ... private number-forms ... known to the twins alone? .... I had a hunch--and now I confirmed it. *All the numbers, the six figure numbers, which the twins had exchanged, were primes.* I returned to the ward the next day, carrying the precious book of primes with me. ... I quietly joined them. They were taken aback at first, but when I made no interruption, they resumed their 'game' of six-figure primes. After a few minutes I decided to join in, and ventured a number, an eight-figure prime. They both turned towards me, then suddenly became still, with a look of intense concentration and perhaps wonder on their faces. There was a long pause--the longest I had ever known them to make, it must have lasted a half- minute or more--and then suddenly, simultaneously, they both broke into smiles. They had ... suddenly seen my own eight-digit number as a prime-- and this was manifestly a great joy, a double joy, to them: first because I had introduced a delightful new plaything, a prime of an order they had never previously encountered; and secondly, because it was evident that I had see what they were doing, that I liked it, that I admired it, and that I could join in myself. They drew apart slightly, making room for me, a new playmate, a third in their world. Then John, who always took the lead, thought for a very long time--it must have been at least five minutes, though I dared not move ...--and brought out a nine-figure number; and after a similar time his twin Michael responded with a similar one. And then I, in my turn, after a surreptitious look in my book, added my own ... a ten-figure prime .... I have no idea what to make of this, and would welcome discussion on these twins. net.philosophy seems the appropriate group, and so I have directed followups there. The chapter has a sad ending. At some point it was decided that 'for their own good' they were separated and put in halfway houses doing closely supervised manual labor. Without their constant exchange, they lost their talents and 'the chief joy and sense of their lives'. ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720
eisaman@ihlpl.UUCP (Eisaman) (02/21/86)
> They drew apart slightly, making room for me, a new playmate, a > third in their world. Then John, who always took the lead, thought > for a very long time--it must have been at least five minutes, > though I dared not move ...--and brought out a nine-figure number; > and after a similar time his twin Michael responded with a similar > one. And then I, in my turn, after a surreptitious look in my book, > added my own ... a ten-figure prime .... > I was dissapointed with the end of this, all along I was expecting a punch line at the end. As soon as they started thinking long and hard to come up with a nine-figure prime and then put to the test of a ten-figure prime. I visioned, calculator tape coming out of thier mouths, smoke and sparks coming from the ears, and finally thier heads blowing up, with springs and resistors flying about the room. And then the guy says, "Damn, blew another fuse." I like my ending better.
weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (02/27/86)
In article <621@ihlpl.UUCP> eisaman@ihlpl.UUCP (Eisaman) writes: >> They drew apart slightly, making room for me, a new playmate, a >> third in their world. Then John, who always took the lead, thought >> for a very long time--it must have been at least five minutes, >> though I dared not move ...--and brought out a nine-figure number; >> and after a similar time his twin Michael responded with a similar >> one. And then I, in my turn, after a surreptitious look in my book, >> added my own ... a ten-figure prime .... >> > >I was dissapointed with the end of this, all along I was expecting a >punch line at the end. As soon as they started thinking long and hard >to come up with a nine-figure prime and then put to the test of a >ten-figure prime. I visioned, calculator tape coming out of thier >mouths, smoke and sparks coming from the ears, and finally thier >heads blowing up, with springs and resistors flying about the room. >And then the guy says, "Damn, blew another fuse." > >I like my ending better. I don't. When reading the account, I was expecting Dr. Sacks to experiment and offer them a large composite. Would they start screaming or go catatonic (or not notice)? We'll never know. ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720
eisaman@ihlpl.UUCP (Eisaman) (03/06/86)
> > [...] > >I like my ending better. > > I don't. > Too bad.