Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Poll: What level of math is programming roughly analogous to?

news.ycombinator.com

Post reply on HN
Print view View original

121–130 of 165 posts

Re: Poll: What level of math is programming roughly analogous to?

#121

Post by rickhanlonii »

zachrose wrote: post #51
rickhanlonii wrote: post #38

Earlier quoted context omitted.

Then the answer is "it depends". You can program at a level with a cognitive demand on par with Algebra (however defined), and you can program at the level of Complex Analysis. There's no one-to-one map between the two. Just like math, you can go as deep into a programming language or concept as your mind will carry you so there's no equivalence relation.

Yes, but I'm also skeptical of the idea that some math subjects are cognitively more intense than others. The "cognitive load" or whatever is really just a function of how much you've practiced and internalized that area of math. Calculus builds on algebra, sure, but once you've internalized algebra you don't have to "think real hard about algebra" _while_ you "think real hard about calculus." Running a 10k for the f…

As someone who studied math as an undergrad, I completely agree. As far as I can remember, Learning the Fundamental Theorem of Galois Theory was no more difficult to me than learning the Mean Value Theorem.

But I guess my point is that programming at an "Algebra" level means you have very little knowledge the language, while programming at a "Calculus" level means that you have much more knowledge.

Re: Poll: What level of math is programming roughly analogous to?

#122

Post by pavelrub »

algorias wrote: post #119
pavelrub wrote: post #97

Earlier quoted context omitted.

This is philosophical mumbo-jumbo. When people program, they (usually) don't do math. And that's it. The fact that you can view a programming language as a formal system, and the fact that computer programs can be viewed as mathematical proofs of mostly totally uninteresting propositions, doesn't magically turn programmers into mathematicians, just as the fact that the brain can be viewed as a chemical and physical s…

> When people program, they (usually) don't do math. And that's it. I disagree. Whenever you implement an algorithm, you build a proof of correctness in your mind. If you reasoned about your program and are convinced that it handles all corner cases properly, then it would only be a formality to write this proof down. If you can't easily do that, then you can't possibly be certain that your program has no bugs. In pr…

If you don't usually bother with this kind of thing, it means that you don't usually do this kind of math when you program.

Re: Poll: What level of math is programming roughly analogous to?

#123

Post by codemonkeymike »

Most programming languages were made by mathematicians, because of that you will see a lot of terms and concepts analogous to terms and concepts in advanced mathematics. Thus it can only help having more of a math education. Personally I think the vast majority people would be fine with Calculus 1, and Discrete Mathematics (which is a 200 level class in my uni while Calc 2 is 300 level). That's because Linear algebra and Multivariable Calculus are concepts that are only used by the smallest percentage of programmers and knowledge in such fields wont make you any more money in the job field.

Re: Poll: What level of math is programming roughly analogous to?

#124

Post by drewblay »

pavelrub wrote: post #97
tikhonj wrote: post #92

Earlier quoted context omitted.

No, the relationship between programming and mathematics is much deeper than that. In particular, it's not a relationship to the sort of mathematics you are thinking of--not the sort that you would use to solve a concrete problem or apply to physics or cooking. Rather, the relationship is between what a program is and the very foundations of mathematics--formal logic. In particular, a programming language is a formal…

This is philosophical mumbo-jumbo. When people program, they (usually) don't do math. And that's it. The fact that you can view a programming language as a formal system, and the fact that computer programs can be viewed as mathematical proofs of mostly totally uninteresting propositions, doesn't magically turn programmers into mathematicians, just as the fact that the brain can be viewed as a chemical and physical s…

I would like to jump in here and agree you. You can program some really cool stuff with a very minimal knowledge of math.

Anything beyond understanding some basic Algebra and Geometry concepts isn't required in order to program.

Most of the stuff (at least that I have run into) is just organizing data into a visual (like a report or graph) that will allow someone to make informed decisions. This only requires basic math (averages, percentages). If you can filter data, perform basic math functions on that data, spit it back out onto a report or graph then you can program for the majority of business needs.

The only time advance mathematics would be needed is if you are coding for scientists/mathematicians that want to apply advanced math to their data.

Re: Poll: What level of math is programming roughly analogous to?

#126

Post by the_cat_kittles »

tedsanders wrote: post #54

Math doesn't come in levels. It only seems linear because it's taught that way. You can teach kids group theory before calculus without a hitch.

That is a little bit of a stretch- I think it generally makes more sense to people to move from discrete to abstract. But I agree that it's much less linear than how its currently taught.

Re: Poll: What level of math is programming roughly analogous to?

#127

Post by shawndumas »

OP here: Wow! I did not expect such a response.

I want to offer a few clarifying points: We homeschool. My son likes math but does not like the 'busy work' associated. Mom was wondering if my son just didn't get long division, ratios, and fractions. I was thinking that if he can program js, awk, lua, and objective-c then he can do anything that arithmetic might demand of him.

In other words I intuited a character issue not a cognition issue and wanted other opinions.

Also, I really do understand that programming cannot strictly be equated with math. I purposefully used the word analogy because they are not 'fungible' things. In fact the term analogy connotes that I understand that there is a resemblance in some particulars between things that are otherwise unlike.

I posit that the resemblance is effort of cognition (though, of course, some might disagree that there is even that point of connection).

Another common misunderstanding was that I was asking how much math does my son need to know/learn to be a programmer (or otherwise). We will explore the very limits of his education (sane, practical, healthy limits); that's the whole point of us homeschooling him. Once he hits mom's limit in any given realm we will out source. I hope his current love of math/science/writing will know no parental impediment.

Re: Poll: What level of math is programming roughly analogous to?

#128

Post by Iftheshoefits »

algorias wrote: post #119
pavelrub wrote: post #97

Earlier quoted context omitted.

This is philosophical mumbo-jumbo. When people program, they (usually) don't do math. And that's it. The fact that you can view a programming language as a formal system, and the fact that computer programs can be viewed as mathematical proofs of mostly totally uninteresting propositions, doesn't magically turn programmers into mathematicians, just as the fact that the brain can be viewed as a chemical and physical s…

> When people program, they (usually) don't do math. And that's it. I disagree. Whenever you implement an algorithm, you build a proof of correctness in your mind. If you reasoned about your program and are convinced that it handles all corner cases properly, then it would only be a formality to write this proof down. If you can't easily do that, then you can't possibly be certain that your program has no bugs. In pr…

Algorithms researchers may be employing the mathematics of computing depending upon the particular subject and scope of study. That body of non-CS academics (mathematicians, physical scientists, and engineers) who use mathematics daily as a primary component of their research are doing math when they write programs--but not necessarily the mathematics of computing.

Almost everybody else who writes programs isn't thinking in terms of mathematics, be it of computing or any other thing. Asking "what level of mathematics is this equivalent to" is therefore kind of a nonsense question--it has no real answer, because it implies there's a legitimate comparison to be made when there isn't.

Re: Poll: What level of math is programming roughly analogous to?

#130

Post by chriswarbo »

On your scale, I'd put programming somewhere around Aleph0.

Programming is completely equivalent to constructive Maths (see http://en.wikipedia.org/wiki/Constructivism_(mathematics) ). Constructive Maths is basically regular (classical) Maths, with the acknowlegement that the halting problem is undecidable. One major consequence of this is that we can't use the Law of the Excluded Middle (ie. "for all P, P or not P").

There's some really interesting research going on here that's far outstrips 'advanced calculus', for example take a look at Homotopy Type Theory.

Post reply on HN