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How much math you need for programming (2014)

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

#161

Post by FabHK »

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.

> As the mathematician V.I.Arnold famously said, "mathematics is a branch of physics where experiments are cheap".

I think that is not so much subsuming mathematics under physics as a cheeky way of avowing mathematical Platonism, where eternal mathematical truths reside in some Platonic realm of ideas and wait to be discovered (not invented or proven) by mathematicians.

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

#162

Post by mhh__ »

dehrmann wrote: post #145
guenthert wrote: post #140

Earlier quoted context omitted.

Reminds me of a buddy of mine working on a computer game. Gravity needed to be simulated -- easy enough, the formula is as basic as it gets. Results looked wrong to him though and he ended up using some trigonometric function instead ;-}

Most games don't use 9.8 for g. There's also the bit about how Mario violates Newton's First Law when he changes direction mid-air, but don't let physics get in the way of fun.

Bunny hopping (https://youtu.be/SNvDUO42Hys?t=47) is reliant on the player being able to play with their momentum without touching the ground

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

#163

Post by mhh__ »

_void wrote: post #64
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…

Sometimes I feel like software developers don't actually know the fundamentals of how the programs run, not taking into account all the math behind the algorithms, etc. Being good developer IMO is first understanding the system from ground up, second - understanding the domain and if it requires math, yes, you need to know that as well. Otherwise you can go on your whole career copy/pasting and using APIs/language fe…

Most developers don't work in domains where there is any math as per se.

I do however feel a little sorry for the some /r/programmerhumor post-ers, who are obviously students who think that everyone just copies stackoverflow - I understand what my code does, I look at the assembly etc. etc. I wrote my first interpreter at 14/15 though so I may not be the best example, but you get the idea.

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

#164

Post by enriquto »

FabHK wrote: post #161
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.

> As the mathematician V.I.Arnold famously said, "mathematics is a branch of physics where experiments are cheap". I think that is not so much subsuming mathematics under physics as a cheeky way of avowing mathematical Platonism, where eternal mathematical truths reside in some Platonic realm of ideas and wait to be discovered (not invented or proven) by mathematicians.

You can read the whole text that starts with that quote here:

https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html

As you say, it is written in a playful and cheeky manner, but it is just a rhetorical device; the meaning is certainly very deep. Even deeper and longer, but in a similar spirit, you have this text:

http://math.ucr.edu/home/baez/Polymath.pdf

It starts with a famous quote, replicating Caesar's gallic war:

All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).

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

#165

Post by AnimalMuppet »

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'm not sure I agree with that outside of functional programming.

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

#166

Post by ajarmst »

JadeNB wrote: post #160
ajarmst wrote: post #131

Earlier quoted context omitted.

It’s possible that the sample set of anecdotes I base this on is a bit skewed, as I teach undergraduate maths. In my limited experience I had to put a lot more effort into keeping basic differential calculus in the required freshman curriculum than my colleagues from the English department had to keep the %#^* five-paragraph essay. (Full disclosure, I’ve also taught our “Communications” course because of a misspent y…

I am also an undergraduate math professor. In our faculty governing body, I had an argument with colleagues in English who, while urging the importance of the written-communication core requirement, since everyone needs to be able to communicate clearly (a claim with which I agree!), also urged removing the quantitative-reasoning core requirement, since that skill is not important to people in the humanities. I can s…

Exactly. Or, for that matter, might make one think that those basic literacies might enhance each other. I clearly remember participating in an Honours Philosophy seminar where we did close studies of works by Russell and Leibniz, and I was literally the only person in the room who had any formal training in Set Theory or Calculus, and one of perhaps three (including the professor) with Symbolic Logic beyond the freshman intro. The idea that such exposure would be valuable in studying “The Philosophy of Logical Atomism” or “The Monadology” wasn’t one we were equipped to contemplate, much less address. I also recall that my jokes about imaginary numbers during lectures on Descartes fell pretty flat, but that was probably for the best.

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

#167

Post by contravariant »

throw6537 wrote: post #59
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…

Meh, disagree. A bunch of developers I know don't know the Pythagorean theorem but they are crazy good (developers). It completely depends on what your job requires you to do. For some developers to be great, they don't need even middle school math.

Not knowing some part of mathematics doesn't preclude them from doing something mathematical.

The fact that middle school mathematics is often disconnected from what most people would find useful is a big problem.

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

#168

Post by contravariant »

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.

It crops up when you start to do statistics usually. That said programming itself is usually more about discrete things, so knowing about calculus is more helpful in figuring out what to use programming for than programming in general.

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

#169

Post by WalterBright »

ajarmst wrote: post #124

As usual, the answer to the eternal question of “how much formal math training do you need for X” turns out to be “right around the amount the author of the argument has had.” Why is it that we always have to prove the instrumental value of maths education? You’re a lot more likely to “need” your maths in the “real world” than your Shakespeare, but few have much energy for fighting the idea that literature should be…

> few have much energy for fighting the idea that literature should be studied for it’s own sake

I agree with your post, except that statement is a bit of personal choice. From my perspective, knowing how airplanes work and how they fly makes my life richer, but I doubt lit majors would feel the same way.

(For example, when my house was built, I noticed a weak spot in the structure holding the house up, and had it reinforced. Without engineering training, I never would have noticed. Does this matter? In my previous house, some of the doors wouldn't close properly, and in the crawl space I noticed the main loads were not supported directly by a column on a concrete pad. The structure there had been gradually sinking. Jacking up that section of the house, installing a pad and a column, fixed that and the doors all worked again. I missed another structural fault until one day a window just shattered from the stress of the distorting wall.)

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

#170

Post by newen »

AnimalMuppet wrote: post #165
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'm not sure I agree with that outside of functional programming.

For loops, while loops, and recursion are all induction. Functional programming is just a style of programming, as in, algorithms which are designed and proven using induction can be implemented in imperative or functional styles.
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