[HN Gopher] Programming vs. Mathematical Curiosity
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       Programming vs. Mathematical Curiosity
        
       Author : todsacerdoti
       Score  : 17 points
       Date   : 2024-04-20 13:27 UTC (9 hours ago)
        
 (HTM) web link (demian.ferrei.ro)
 (TXT) w3m dump (demian.ferrei.ro)
        
       | turtleyacht wrote:
       | 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.
        
         | JadeNB wrote:
         | > It's easier to think in programming than math.
         | 
         | I think that it depends a lot on background.
         | 
         | 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.
        
           | turtleyacht wrote:
           | 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.
        
       | gremgoth wrote:
       | 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
        
       | ashton314 wrote:
       | 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.
        
       | olooney wrote:
       | 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.
       | 
       | [1]: https://www.oranlooney.com/post/kaprekar/
        
       | jrhvmt wrote:
       | 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 don't really know.
       | 
       | Exactly, so why imagine a divisive assumption?
        
         | epidemian wrote:
         | Thanks for the feedback!
         | 
         | 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.
        
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