How much math you need for programming (2014) • Hacker News Board

Re: How much math you need for programming (2014)

#101

Post by nobodyandproud » Sat, Dec 26, 2020, 4:12 PM UTC

TheOtherHobbes wrote: post #53

TeMPOraL wrote: post #50

Earlier quoted context omitted.

In that sense, though, programming would be a branch of physics that's concerned with making brute-force experiments cheap (thus saving the mathematical work needed to find clever tricks to do that same experiment by manipulating a small bunch of symbols).

Well - that's engineering. Physics is experimental model building of phenomena which are not yet understood and are being explored. Engineering is experimental model building of phenomena which are mostly understood, albeit sometimes with some quirks and unexpected edge cases. Applied math is the toolset used in both physics and engineering. Pure math is the abstract and philosophical exploration of symbolic relation…

There’s a difference between applied physics and theoretic physics as well.

Every discipline has its ivory tower and “plebeian” branches.

No need to give physics a free pass :)

Re: How much math you need for programming (2014)

#102

Post by enriquto » Sat, Dec 26, 2020, 4:17 PM UTC

prionassembly wrote: post #100

enriquto wrote: post #48

Earlier quoted context omitted.

> I would argue that this is wrong. That's what physicists do, not mathematicians. Notice that many mathematicians would not agree with you, here (but probably, a majority would). As the mathematician V.I.Arnold famously said, "mathematics is a branch of physics where experiments are cheap". So, yes, in the minds of lots of mathematicians, what they do is precisely to study and understand nature.

Then, Arnold also says that mechanics is geometry in phase space (which subsumes physics in mathematics, like in the later “mathematical universe hypothesis” metaphysicians).

you know, as they say, "(...) consistency is the hobgoblin of little minds (...)"

Re: How much math you need for programming (2014)

#103

Post by alephnil » Sat, Dec 26, 2020, 4:18 PM UTC

How much math you need for programming does not have a single right answer. Often you can get away with very little math, but if you know math, you may be able to see patterns in the domain you are working in that allows you to come up with a much better and more elegant solution than you would otherwise. Or you can attack problems that the people around you consider too hard or go beyond the standard library used in your domain.

Then, if you don't know the math that applies, you may never even see the opportunity, and be convinced that math does not applies to what you do, and that you never needed it in the first place.

And often, it makes you the most natural person to work on the most interesting and challenging problems.

Re: How much math you need for programming (2014)

#104

Post by carapace » Sat, Dec 26, 2020, 4:24 PM UTC

Reminds me of one of my favorite jokes, I have forgotten who said it, maybe Dijkstra?

"Computer science could be called the post-Turing decline in the study of formal systems."

Re: How much math you need for programming (2014)

#105

Post by prionassembly » Sat, Dec 26, 2020, 4:27 PM UTC

enriquto wrote: post #102

prionassembly wrote: post #100

Earlier quoted context omitted.

Then, Arnold also says that mechanics is geometry in phase space (which subsumes physics in mathematics, like in the later “mathematical universe hypothesis” metaphysicians).

you know, as they say, "(...) consistency is the hobgoblin of little minds (...)"

It’s middlebrow but I still love Whitman where he goes “Do I contradict myself? Very well, I contradict myself. I am large, I contain multitudes”.

Re: How much math you need for programming (2014)

#106

Post by wendello » Sat, Dec 26, 2020, 4:41 PM UTC

Agingcoder wrote: post #23

There are two different problems actually : what you write, and the quantitative aspects of your code. What you write may or may not have a strong maths component ( game engine vs crud app say, or PDE solver vs typical 'plumbing' app). However, the moment you start having performance issues (and this is everywhere), maths comes in very handy : big o, back of the envelope calculations, orders of magnitude, etc. You ma…

I'm self-taught with minimal maths and this is something I've used. I started re-learning some basic math for fun and now I find it helpful now to visualize mathematical models of some basic runtime characteristics of my programs. A simple example is that I will visualize X number of users firing Y number of requests, and I'll actually imagine this as a live system with various statistical properties (% of errors and the like). It's not typically strictly mathematical—I don't write down many (if any) numbers or symbols—but I'm creating a quantitative model in my mind to think through the behavior of my program when actually in use as opposed to a sequence of logical commands like I usually do.

Re: How much math you need for programming (2014)

#107

Post by sethammons » Sat, Dec 26, 2020, 4:47 PM UTC

MeinBlutIstBlau wrote: post #62

alkonaut wrote: post #24

You need all the math for the domain. If you are in engineering, games, DSP, ML, then that can be a lot . At the same time some developers can go a whole career without ever (knowingly) using a floating point number. They work with web sites/services/databases/apis etc. But developers should at least know basic calculus, logic, and what what you need to grok basic algorithms and data structures. That part of math isn…

I still fail to see how calculus relates to programming for what most people do. Web or not.

Simple example: monitoring your systems when data only increases, like number of hits to your site or queries to the db. That graph is always up and to the right. However, if you look at the rate of change (cough, derivative/calculus), the graph now tells you interesting things. Granted, the calculus understanding there is superficial, but it is there!

Re: How much math you need for programming (2014)

#108

Post by wendello » Sat, Dec 26, 2020, 4:50 PM UTC

jamil7 wrote: post #55

A lot more than people make out, at least in my experience. There’s a lot of talk about how you don’t need maths or cs theory but to me this only seems true for certain areas or levels. For me its been especially true with performance, cs theory and maths can help you to know what and where to optimise and give you ideas on the how.

Jonathan Blow has a good talk about this. He says when he interviews he wants somebody that will default to a naive implementation (because most code is not performance-sensitive and you should optimize for development time in those cases), but he expects people to have a wide knowledge of tricks and techniques for the ~10% that is performance sensitive. That seems fair to me, as somebody who probably wouldn't pass his standards and needs to develop my algorithmic knowledge to handle that 10% better.

Re: How much math you need for programming (2014)

#109

Post by GnarfGnarf » Sat, Dec 26, 2020, 5:03 PM UTC

dmak wrote: post #90

dstola wrote: post #89

There is a joke/saying/anecdote I heard a long time ago that may or may not be relevant "Programmers are mathematicians that solve all their problems by Induction" After being a software engineer for over half a decade now, that still rings strangely true to me

I don’t understand this. Could you elaborate on it?

"Induction" means you prove it's true for 1, then you prove that if it's true for 'N', then it's true for N+1.

Re: How much math you need for programming (2014)

#110

Post by thevardanian » Sat, Dec 26, 2020, 5:10 PM UTC

enriquto wrote: post #48

mattbit wrote: post #28

> Now what does does a mathematician do? He tries to understand nature and uses mathematics as a language to do that. I would argue that this is wrong. That's what physicists do, not mathematicians. Mathematics is about abstract ideas, which can live regardless of nature or application. Physics instead is about understanding nature. Most physicists use mathematics to do that, but that's just for practical reasons. Th…

> I would argue that this is wrong. That's what physicists do, not mathematicians. Notice that many mathematicians would not agree with you, here (but probably, a majority would). As the mathematician V.I.Arnold famously said, "mathematics is a branch of physics where experiments are cheap". So, yes, in the minds of lots of mathematicians, what they do is precisely to study and understand nature.

Math, like philosophy, is only interested in using concepts, structures, or otherwise rigorous ideas to pry into other ideas. Like philosophy it is in some senses self referential, and not really interested in discovering some idea of "truth", but rather exploring the avenues by which truth itself is defined.