Re:How I faced my fears and learned to be good at math
by epsylon on Thursday November 14, 2013 @09:28AM
(#6732436)
Good maths proofs proceed step by step, with intermediate goals written in clear English (or French, for me). And to go from step to step, you don't need explicitly long names, just like you don't name your index loops "index_over_collection" but just i. Because your function will only be a few lines long.
I actually really like mathematical notation. Once you get used to it, the terseness can make things a lot clearer than natural language.
(If you've ever tried to read old mathematical articles / books that are a few centuries old, you'll understand the power of mathematical notation. Check out "God Created The Integers" or "On the Shoulders Of Giants" by Stephen Hawking if you're curious: these are two books that provide excerpts of highly influential works from earlier mathematicians and physicists, respectively)
Re:How I faced my fears and learned to be good at math
by Dn_Ab on Wednesday November 13, 2013 @11:44PM
(#6730574)
> In a programming context if you today reduce all your variable names to single latin letters and all your function names to single greek letters, you will be widely mocked and reviled.
Serious question. What do you think is the general impression of APL programmers? =)
Re:How I faced my fears and learned to be good at math
by jacques_chester on Wednesday November 13, 2013 @11:50PM
(#6730591)
I thought about mentioning APL, but sometimes the correctness of an argument is best served by inexactitude.
I already compromised by adding "today" and "almost all" as qualifiers.
The first problem is that the notation is usually "the first symbol that popped into some random genius's head 200 years ago". And once the notation is set, it's set, no matter how poor it is, or how many other places it's already in use etc etc. Then, as you note, sometimes there are multiple notations. Ugh.
The second problem is closely related to the first. Mathematical notation is write-optimised. This makes sense because of the long history. But that doesn't change that write-optimised languages are harder to read and understand, even for experts, than read-optimised languages.
In a programming context if you today reduce all your variable names to single latin letters and all your function names to single greek letters, you will be widely mocked and reviled. In maths it's Just How Things Are Done.
I guess what I'm saying is: the curse of mathematical notation is pen and paper. The boundaries of QWERTY liberated (almost all) programming languages from the curse.