programming is the art of being able to implement what one doesn't understand, and math is the art of being able to understand what one cannot implement
If the above article piques your curiosity about Kaprekar's constant (6174), I wrote a blog post[1] last month that goes into some depth and has some nice visualizations.
I was thinking about generating a graph of connected nodes like the one you did. But TBH, i really like the ones on Wikipedia[1], and didn't really feel like making something of equal quality hehe.
I like the content, but wish the undercutting humor was given a bit more thought before publishing.
Why the need for a competitive division of mathematics and programming?
What the op did was math, and I’m unsure why the need to think of it as something else?
> I suspect a more maths-oriented person would go through this very differently. Maybe they’d try to find an elegant analytical proof, without the aid of a dumb number-crunching machine brute-forcing its way through. Or they’d try to generalize the problem to different number of digits, or different number bases.
Why drag “brute forcing” like this? Why drag yourself like this
I meant the post to be more of a personal story. Of what i, personally, wanted to explore when learning about the Kaprekar constant, and of realizing that my interest is more on the "programming" side of things (programming languages, "readable" code, etc) than the more pure maths side.
But i can see how the tone could make it seem that was a competitive division of sorts, especially the title. I'll try to take it into account for (hopefully) future posts.
Well while I have you, the message I feel I failed to adhere to in my comment was my interest in letting you, or others who follow their passion in math and programming, know that what you are doing is in fact “real” math!
Keep it up!
Your post made me click through a bunch of links in it. Thank you, but give me back that hour! ;P
Better yet, I’ll trade you a different rabbit hole.
I appreciate the clarification, as well as the initial comment TBH. And i agree actually, that doing this kind of computer-assisted search is indeed "real" maths, or at least a part of it; a useful tool. I think a comment on Lobsters[1] expressed this sentiment better than i could:
> It is, but it’s also a bit unsatisfactory, no? A lot of the time the particular statement is less important than the way it was obtained—why or how is something works seems much more relevant to me than the binary question of whether it is true. A novel result more often than not also uses novel proof techniques, which may then be adapted to other problems. One may learn a lot more from the proof than even from the applications of the result.
> (Perhaps the author does has a point about the different mindsets :))
And thanks for the video recommendation. Added to my watchlist :)
I started with Jekyll's default, Minima[1], to get something working right away. But then i tweaked lots of stuff, copying things i liked from other blogs[2], so it no longer resembles that default look.
If the author reads this, please remember to capitalize every instance of the first person pronoun “I”, including when it does not appear at the beginning of a sentence. English is weird like that.
It's easier to think in programming than math. How incredible it must be to transform ideas purely in the mind, without aid of a compiler or tests. And then to notate it, and somehow reason on its soundness, on just paper.
My suspicion is that it's not easy for a random, untrained person to think in either. I think that a lot of folks here are programmers, trained (intentionally or just by experience) to think in programming terms, and so find that easier. I'm a mathematician by training, and so find it easier to think in that way—for example, I still sometimes find it hard to force myself to think about the fact that it might matter which of two computationally equivalent formulations of a problem one uses, just because one takes orders of magnitude longer than the other to execute.
How do you know it's correct, though? Except to check the answers, or ready access to colleagues--but now a global network, and plenty of problems to review besides. There's no excuse anymore. I could even post questions myself, and find explanations enough.
Leaning on the compiler and staring at a segfault would have been pretty discouraging before Java, for example. Folks who may have given up may have found Python learnable or more forgiving. Once past that initial hump, and writing loops, operations against a database, and we're off to the races.
But there's plenty to practice in math, with textbooks even. Maybe we needed to learn to compute, do enough exercises calculating--the same as printf() and console.log()--to get the bits before proofs, before the higher-order ideas, could stick.
