Inside My Head

Like many other autistics, I can do an unusual amount of math in my head. My abilities here are nowhere near those of Rain Man or Albert Einstein, and they might not even be above those of the average neurologically-typical PhD in math or physics, but they're above the average of the entire human population. Unlike some other autistics, I was never able to cultivate much of an interest in math. After the 10th grade and geometry, I was not required to take any more math, and it was a great relief to be allowed to concentrate more fully on subjects I liked -- literature, history: verbal subjects. (Including philosophy. Imagine my horror upon learning that some of Western civilization's leading philosophers have also been some of its leading mathematicians. Yaaargh! No escape!) My life up until now might have been very different if I had been able to become really fascinated by numbers in the way that mathematicians and physicists often are. Just recently I experienced an exception, an encounter with a five-digit number which I find interesting. The encounter, not the number per se, and so perhaps it's not really an exception. And actually, perhaps I am finally beginning, at age 51, to feel some of the fascination that mathematicians feel for numbers, specifically for factoring. Except that I'm not actually interested in factoring for its own sake, as someone who loves numbers would be, but I've begun to wonder whether there are practical applications to physical shapes which can be arrived at by factoring.

The five-digit number is 17,153. Several days ago someone I know saw this number this number on her odometer and immediately thought of someone else we both know, who is both a mechanical engineer with some knowledge of advanced math and a fundamentalist Christian with an interest in numerology.

Don't worry, this post has nothing to do with numerology.

So anyway, the lady who saw 17,153 on her odometer asked some others of us whether we saw anything remarkable in that number. Right away I could see that it was 17x1009. Then I thought about 1009 for a minute and began to wonder whether it, like 17, was prime. I could easily see that it couldn't be divided even by any prime up through 11. If 1009 wasn't evenly divisible by any prime up through 31 then it itself was prime, because the square of the next prime past 31, 37, was larger than 1009. After dividing 1009 in my head by 17, it started to become a little tedious, and I was going to fetch a calculator, but then it occurred to me that it might actually be easier to find a list of primes which went past 1009. It was very easy to find, as it turned out, and 1009 was in fact on the list, it is in fact prime. Maybe it would've been even easier to simply look up 1009. This is an an example of the kind of thing I would know -- where to look up prime numbers -- if I had been fascinated by math as a child and gotten a Bachelor's and a Master's and maybe a Doctorate or three in math or physics or engineering. If I'd taken that route I might be much more employable, but then again I might not know who Steven Runciman or Alfred Doeblin are. Je ne regrette rien.

Also, this morning it occurred to me that 1+7+1+5+3=17. Ta-daaa!

To be completely honest, what I actually find the most remarkable about all of this is that a group of people were discussing the number 17,153, and that the person who had seen that number asked what we saw in that number which was remarkable, and I got back to them right away with the info that 17,153 is the product of two primes, and no-one else seemed to find that remarkable! But maybe that's just my own ignorance showing again, like not knowing that I could just look up 1009, or where to look it up. The lady who saw 17,153 on her odometer has a PhD in math, and maybe she has a great amount of experience with five-digit numbers, and maybe stumbling upon a five-digit number which is the product of two primes -- or even a five-digit prime, for that matter -- is not as remarkable as I imagine. I wouldn't know, because I very rarely deal with math which involves five-digit numbers.

Anyway. Back to my accustomed, much-more-purely-verbal approach to stuff (except for the posts on chess) in my next post, much more likely than not. Excelsior!