Um, japhy, I think I know the math quite well.

My point is that people don't think in terms of the logic behind it all. They don't. They really, really don't. People learn rather chaotically and only later (if ever) do they organize their world into something coherent that they can explain.

The problem is that programmers have to do that. And if you have been programming for a while, it becomes natural to start to think and understand in very different terms from the general public. It would be a serious mistake to confuse this difference for stupidity on the part of the general public. There are a lot of smart people who don't care to develop that skill. And when people first have to, it takes quite a bit of work.

Let me offer a few examples to drive this home.

The first is simple. Can you give a written description of how to tie your shoes? You (hopefully) have no problem doing it. Can you describe it?

The second involves your example. You throw around the word "modulo". Does your concept of modulo naturally include such concepts as taking polynomials over the integers and mapping them onto fields of algebraic numbers? Mine does! Are we talking about the same concept when we each say "modulo"?

The third will let you start some really good fights. It is part of a pair of questions I ran across once - and the fights will come from the knowledge that there is a verbal question that women find as easy as men find the question that I (a man of course) can remember. Here goes. Take a piece of paper and draw a cup. Draw a second cup tipped by 30 degrees. (Precision is not necessary.) Hand the picture to another person, and ask them to draw the water line if the cup is half-full of water (precision is not necessary).

Most adult men get this question right. Find it trivial. Find it unbelievable that anyone would have problems with it. The probability of success does not depend on education level.

Most adult women get this wrong. Will understand what the right answer is when they see it, but literally cannot see it. Again the probability of success does not depend on education level.

Until puberty there is no significant difference between the genders. Your ability to solve the problem (you are a mature male so I assume you will get it right) seems to be genetically determined. If you can do it it is simply astonishing that another would find it hard.

I ran across this nearly a dozen years ago now, and as I say it was one of a pair of questions. The other (which I got wrong) is a verbal question that women find easy and men fail to get, again the ability to solve it comes with puberty.

Before you make any more assertions about how people learn and think, please ask this question of several people of both genders. Ask, and think very hard about what you see.

Request:

Other than the fact it was a magazine I have no idea where this problem comes from or what the pair is. I have looked for it off and on for about a decade and have drawn blanks. If anybody knows of a reference or the paired problem, please tell me.

As I recall I read the magazine in some office, couldn't get the female problem, thought it was BS, found the male problem trivial. It was only a month or so later that I asked my gf of the time the problem as a joke and was astonished that she got it wrong. My mother did likewise. It has bugged me ever since.