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. 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.