Savantism
Another great Wired article. This one’s on autism and prodigious savants. Interesting observations on the link between music and maths, and between tonal languages and perfect pitch (what they call “absolute pitch”). A friend back in high school had perfect pitch – he also got his piano LMus in Year 11 or so. We’d hum notes to him and he’d immediately tell us what note we were humming. He was also an incredible thespian and debater who could come up with intricately structured speeches at the drop of a hat without ever needing palm cards or notes of any kind. There was one occasion, I am told, where, during a play, he had finished reciting a few lines that were in verse/rhyme. There was a mishap backstage, which resulted in a delay in the next actor appearing… so to stall for time and without skipping a beat, he ad libbed a few more lines in verse so much so that the audience didn’t realise that he was actually improvising. Scary stuff. How much normality would you trade for a “dash” of autism?
12:33am (GMT +11.00) tomorrow 
All of it.
Well, music IS math. For example, a concert C pitch is 440 cycles per minute (if I remember correctly) while a C one octave higher is 880. Notes in harmony are divisible when looking at cycles per minute (ex, 440 (C) and 660 (F??) are harmonic….
When you get into music theory and look at it mathematically, there is all inds of neat stuff. :)
The difference, though, is that many, many people who have trouble adding up prices in a shopping list in their head can easily listen to two notes and tell you whether they’re harmonic. Without knowing that one of them is 440 Hz and the other is 660 Hz and finding the GCD of 440 and 660 or whatever. And this is quite apart from the fact that the sound we hear can be quite a complex waveform that would take quite a lot of complicated analysis to even work out in the first place that it’s vibrating at 440 Hz, let alone a combination of two notes at 440 and 660.
So we all, apparently, have an innate ability to do very complicated mathematics entirely by intuition. Maybe savantism is just the ability to apply that intuition consciously to areas other than music.
Read “The Long Dark Tea Time of the Soul” by (the late) Douglas Adams. It’s humour but it’s very intelligent humour.
It’s a well known fact that the human brain does complex mathematical calculations extremely quickly. Anyone who did 3U maths or any physics in high school will remember how long it took them to work out what angle to shoot the cannon at in order to hit a point a certain distance away. Yet if you were aiming the cannon you could hit it in maybe 2 or 3 attempts without using a protractor. Similarly, when someone throws you a ball and you catch it, there is immensely complicated maths going on. Anyone who’s ever been on a cricket team and had to do the ‘soft hands’ egg-throwing exercise will know that it doesn’t take long before you can see an incoming egg, instantly work out where it will be when it gets to you, and the velocity it’s travelling at so you can move your hands back in the right way to slow it down without breaking it (to avoid an impact which would break the egg the 3rd derivative of the egg’s displacement must be a continuous function, which is the principle upon which they build train tracks, but most cricketers probably don’t know that – it doesn’t stop them catching the eggs successfully).
When you drive your car, and change lanes while automatically adjusting your speed so you don’t hit the car in front of you or slow down traffic, you are solving maybe half a dozen simultaneous differential equations … anyone who’s encountered differential equations at uni knows they are all painful, and the majority are not actually possible to solve analytically with current maths theory.
Of course because the brain is a black box we don’t know whether it does all this the same way we would program a computer to do it (high-speed number crunching) and can simply crunch numbers at a mind-boggling rate, or if there’s some amazingly clever elegant algorithm hidden in there we’ve yet to come up with.
In savants the areas of the brain are simply allocated differently – the maths part gets more cubic cm (which is apparently what counts with brains) and the other parts get less, or are omitted completely … it’s probably an evolutionary step and in a few thousand years all humans will no doubt be able to factorise 11231234 digit numbers into their prime factors in their head, at the cost of not understanding social conventions which will by then have ceased to exist. Probably savants are just random steps in evolution that happened ahead of their time, and that line of evolution doesn’t continue because they are considered abnormal by current society. But an interesting question is – is there any difference between savants and, say, people with Tourette’s syndrome? People with Tourette’s make excellent drivers despite uncontrollable convulsive spasms because their reaction time is on average 6 times faster than normal people – is this another form of savantism, a ‘physical savantism’? Will someone who has this exagerrated to a higher level be able to dodge bullets?
Anyway I’m done raving … I’ve never met anyone who could factorise huge numbers into their 100-digit prime factors (although if you meet such a person, hold onto them because they could undermine all modern strong encryption..or maybe better yet stay away so you aren’t killed along with them ;p) nor anyone who could tell me instantly what day of the week the 13th of October will be in 2118, but one of our teachers at school spoke 14 (yes, fourteen) languages almost fluently and could tell you pretty much all the info contained in a dense a4 page of 12pt typing after looking at it for 30 seconds.. He claimed, through training … but … yeah, right.