More From Inside My Head

In a previous post I noted that 17,153 is the product of two prime numbers, 17 and 1009. This morning I thought about some numbers near 1009, and calculated that 1007 is 19x53, 1003 is 17x59, 1001 is 7x11x13, 997 and 991 are prime numbers and 989 is 23x43. I calculated all this with the help of a pocket calculator I bought around 1992, which was not at all an advanced calculator even by 1992 standards. I got it because it looks cool and I find it very user-friendly. I divided each 4- or 3-digit number by bigger and bigger primes until I got a dividend which was either a whole number or a fraction smaller than the square root of the 4- or 3-digit number. Then I remembered that lists of prime numbers are readily available, and stopped calculating, and wondered, as I had many times previously, what possible purpose such calculations could serve.

Then I put that pocket calculator away and got out the other of the 2 pocket calculators I own. I don't remember exactly when I bought this one. I think it was closer to the present than to 1992. This other calculator is made by the same manufacturer. [PS, 8 Feb 2018: That manufacturer is Casio, a company for whom I have more respect now, after having heard about their legendary G-Shock watches.] It doesn't look nearly as cool to me. And it does much more. I don't understand what all of its functions are. I know what things like sine, cosine and tangent are, which the newer calculator features and the older one, the one I like better, which has bigger keys and a bigger screen and folds in half with the keyboard on one half and the screen on the other, does not. But I don't know, for example, what the "modes" are which are described above the keyboard of the newer calculator. Not a clue.

As far as I can remember, the only key I have ever used which the newer calculator has and the older one does not, is the X to the power of Y key. And as far as I can remember I only used that one to see whether I understood how it was to be used. I guessed that if you hit X, then the key, then Y, then =, the screen would display X to the power of Y. For example, if you hit 3, then the key, then 4, then =, the screen would display 81. My guess was correct.

So I'm looking at the newer calculator now, and I'm looking at an instrument whose purposes I am largely ignorant of, and I'm wondering how much less mysterious to me the instrument might be if I had not stopped taking math courses as soon as I was allowed to stop, after geometry in the 10th grade. I'm also wondering whether and to what extent fancy -- I'm sure it's not at all fancy to some people. I remember it wasn't the most expensive pocket calculator in the store -- to what extent fancy calculators like this one might have been rendered redundant because smart phones can do everything they do. My phone is not smart. It has a calculator on it, which I used once, but I found it excruciatingly difficult both to find and to use and I don't plan to use it again soon.

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!