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.