Programming as a Way of Thinking

Post by Jill_the_Pill » Mon, May 01, 2017, 9:20 PM UTC

School-Cotton wrote: post #83

blktiger wrote: post #73

Earlier quoted context omitted.

True, much of math is relegated to experts. This is _exactly_ the problem. Why do you think so many adults have such little understanding of math and will proudly proclaim that they haven't used algebra or geometry in their adult life? Yes, there are are some areas of mathematics that are extremely specific and do require experts but a lot of math is useful to people in general and anything we do to make it easier fo…

Making mathematics accessible to the general public isn't part of mathematicians' jobs, nor is it something most of them care about. If you want to write some articles that make mathematics more accessible to the general public, and you want to use longer variable names in order to do that, nobody is going to stop you. It's unreasonable, however, to expect mathematicians to try to do this at the same time they're doi…

Post by Jill_the_Pill » Mon, May 01, 2017, 9:25 PM UTC

eldavido wrote: post #30

ccleve wrote: post #22

This article starts to get at an idea that I've had for a while now -- that mathematicians are doing it wrong. In the software business we learned a long time ago to name our variables properly, name our functions logically, and to control complexity by breaking ideas into modules and then hiding the details inside. If you can't name something, then you don't know what it is, and that tells you that you should rethin…

It's more standard than people realize. Offhand: x: "some real-valued variable" n: "a countable quantity, usually a total" i: "an index" k: "some kind of constant", often an integer, whose value doesn't change, "c" is also used for this e: almost never used as a variable, it's Euler's number p: some kind of probability, or a prime number, along with p and q t: some kind of parameter, often goes from [0,1] or (0,1) z:…

Post by tnecniv » Mon, May 01, 2017, 9:39 PM UTC

vlasev wrote: post #64

tnecniv wrote: post #56

Earlier quoted context omitted.

I used to think this way, but as I learned more math, I realized that the way mathematicians do things isn't an issue in practice. I do wish notation was more standardized, but that's a nitpick (i.e. whether/how scalars and vectors are distinguished). When it comes to proofs, you can only keep so much information in your head at once. In most cases, if you have a ton of variables floating around, you are probably try…

> whether/how scalars and vectors are distinguished This becomes less of an issue once you go through some abstract algebra. But typically, constants would come from the start of the English alphabet, and vectors, from the end. > I will note the worst code I've ever read was written by a control theorist that used only single letter variables. I later found out the variable names were the same as a paper, but the pap…

Post by tnecniv » Mon, May 01, 2017, 9:58 PM UTC

School-Cotton wrote: post #86

ccleve wrote: post #31

Earlier quoted context omitted.

There may be occasions when a single letter makes sense, but this should be the exception, not the rule. If you've got a ton of "anything" variables in your code, then that means there's probably a better, more understandable design for your system which expresses what the variables represent with more precision.

> If you've got a ton of "anything" variables in your code > design for your system We're not talking about programming; we're talking about math; that's the whole point.

Post by ethn » Mon, May 01, 2017, 10:20 PM UTC