Programming as a Way of Thinking • Hacker News Board

Re: Programming as a Way of Thinking

#131

Post by osoba » Tue, May 02, 2017, 8:35 PM UTC

qznc wrote: post #127

osoba wrote: post #79

Earlier quoted context omitted.

Proofs by picture arent proofs though. And how would you even convey by picture that two line segments are of the same length. Or that if you drew C and D as separate points they turn out to be the same point?

Oliver Byrne's edition of Euclid is a nice proof-by-picture example: https://www.math.ubc.ca/~cass/euclid/byrne.html

Those look more like proofs with pictures, than proofs by picture, but I'm too lazy to get involved into the obscure notation of that book and check whether a random proof from the book would be equivalent to a modern proof from a standard textbook.

Altough, judging by the old timey language of the book, it's possible the book predates Hilbert's axiomatization of Euclidean geometry and the proofs in it were good enough for the standards of its time.

In modern mathematics proof by picture generally means you've drawn / pointed out a single example, possibly wrongly or in a way that doesn't generalize, and because you've shown that one example holds you assume all possible examples hold. That, obviously, needs not be the case.

Re: Programming as a Way of Thinking

#132

Post by jodooshi » Wed, May 03, 2017, 5:26 AM UTC

misingnoglic wrote: post #3

I had a math teacher at my high school who used python and SAGE to teach us pre-calculus as well as programming, computational thinking and some mathematical logic. He was an absolute genius and I wouldn't be where I was if it wasn't for him - unfortunately the school saw him as a threat to the standard model of teaching and drove him insane before he just quit. I hope he's doing ok.

> People laughed at Seymour Papert in the 1960s, more than half a century ago, when he vividly talked about children using computers as instruments for learning and for enhancing creativity, innovation, and "concretizing" computational thinking.[1]

[1] http://papert.org/

Re: Programming as a Way of Thinking

#133

Post by dragandj » Wed, May 03, 2017, 10:25 PM UTC

tarlinian wrote: post #118

dragandj wrote: post #92

Earlier quoted context omitted.

Doesn't any language that support Unicode allow that? Java for example. But, it's rather impractical to use, since greek letters are not that easy to type with English keyboard.

Julia's REPL allows for LaTeX like notation (e.g,. you can type \alpha to get the matching Greek letter), which makes it quite natural to use the Greek letters in places that make sense.

If the intended result is some kind of scientific presentation then kinda yes. If I am writing a classic software code, then I do not see how \alpha is better or more readable than, well - alpha.