Moderator's Comments:

The thread as a whole (at least my following post) might be suited better to the Lounge part of the forum. Depending on which direction the following takes i might transfer it to there eventually but withhold my decision for now.

In programming only one half (and probably even the less significant half, for that matter) is about coding techniques. Much more important is to understand what you do and to understand the "structure" of the problem you are working on:

Now, this will work as expected and of course produce the correct result. Who could argue with that?

Let me tell you a story: the young Friedrich Gauss was attending grammar school (as far as i know the story he is purported to be 7 years old) and one day the teacher didn't feel like teaching, so he assigned the class this task: calculate the sum of all integers 1-100. He expected that the pupils will be busy all day doing all the additions. But 10 minutes after the assignment Gauss turned in his work - and earned a solid slap in the face for obviously not doing what the teacher told him to do.

Anyway, the slate (they wrote with chalk on slates) was put on the teachers desk face down and the other pupils were for a long time busy adding and adding. After some time one after the others were turning in their results and the slates were stacked face down. Finally the teacher controlled the results, taking one slate after the other and all were written all over with intermediate results - some wrong, some correct, but that is not really the point.

Finally he got to Gauss' slate there were no intermediate calculations, just a result: 5050. Bewildered he asked Gauss how he came to this result (which is correct, btw.) and in the little time he spent. Gauss answered:

Let us take the first number (1) and the last number (100) and add them: we get 101. Now take the second and the penultimate number and the sum is also 101. And so on, we get fifty pairs (1+100, 2+99, ... 50+51) each adding up to 101. We multiply therefore 101x50, which is easy to do in the head and arrive at 5050 - q.e.d.

You see, programming is about identifying such properties. I once had to correct such a "i have no idea what i am doing"-way of implementing something. The solution there was obviously "outwardly" absolutely correct but equally obviously neglected basic properties of the ways things work.

If you don't understand applied mathematics at least to some degree you simply don't have what it takes to do programming, regardless of which language you try. I always wonders how "computer science" can be a science at all. A computer is a tool and you have to learn how to use it properly, but that is not a science, it is a trade. As there is no "hammerology" but simply blacksmithing there is no "computer science". There is, though, a number of sciences related to it (mathematics being one of these, language theory being another) and as i see it the problems in modern software development come from gravely ignoring this aspect of writing programs.

bakunin