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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)

#81

Post by username90 »

ddxxdd wrote: post #76
username90 wrote: post #72

Earlier quoted context omitted.

You could say that math is the part of laws of physics which humans can't imagine being different. You can pretty easily imagine a world where newtons laws are different, but I'd argue it is impossible to imagine a world where 1 + 1 is not 2. However being impossible for us to imagine doesn't mean that such worlds can't exist, it would just have completely ridiculous consequences we can't imagine, so those rules are…

A universe where 1 + 1 != 2 is a universe filled with self-contradictions and so cannot exist. It's like imagining a universe where True == False. It's not a hypothetical, it's a logical impossibility.

1 + 1 = 2 is based on conservation of particles. You put a marble in a bowl, then another marble in the bowl, you now have two marbles in the bowl. If you remove conservation then there is no reason why 1 + 1 should equal 2. 1 + 1 being equal to anything could just be nonsense in that universe, such a construct wouldn't exist and there would be no way to reason about quantities. That isn't a logical inconsistency, so such a universe could exist.

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

#82

Post by mkl »

ddxxdd wrote: post #76
username90 wrote: post #72

Earlier quoted context omitted.

You could say that math is the part of laws of physics which humans can't imagine being different. You can pretty easily imagine a world where newtons laws are different, but I'd argue it is impossible to imagine a world where 1 + 1 is not 2. However being impossible for us to imagine doesn't mean that such worlds can't exist, it would just have completely ridiculous consequences we can't imagine, so those rules are…

A universe where 1 + 1 != 2 is a universe filled with self-contradictions and so cannot exist. It's like imagining a universe where True == False. It's not a hypothetical, it's a logical impossibility.

In modulo arithmetic, 1+1 != 2 can work just fine. We're not talking about the literal universe, but the space of possibilities that opens up when you change the rules. E.g. all the amazing power and complexity that comes from imagining the existence of a number i with the property that i^2 = -1. This was initially thought to be a logical impossibility.

True == False does seem pretty broken though. Not sure that can go anywhere.

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

#83

Post by tenaciousDaniel »

_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…

That kinda describes my experience. I was never formally trained in computer science; I fell into it in my late twenties and taught myself. I never took math at the collegiate level, so I don't really understand the fundamentals. However, I am able to get by for about 95% of the things I've needed to do. But the last 5% is always the most interesting, and I hate it when I hit those walls.

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

#84

Post by kovac »

mkl wrote: post #60
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.

I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. But nature or applications to it are the primary focus in many other fields of maths. In still others, nature would be a source of analogies, or applications of a few special cases, etc. Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "disc…

Whatever people may think what mathematicians think, this comment describes the real situation best as I've experienced it.

Most pure mathematicians I've met/worked with actually look down (in a jocular way) on applied mathematics/physics. When Lagrange reformulated Newtonian physics, he was very proud of the fact that he didn't use any diagrams and arrows showing forces in his paper. In fact, of all the Physics I've seen, I found Lagrange's work to be the most beautiful and elegant.

I love how the commenter put it as "Nature is of no consideration whatsoever in some fields of maths". I'd restate it as "Nature is of no consideration whatsoever in pure mathematics" and I'm quite sure that the pure mathematicians would agree.

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

#85

Post by BillyTheKing »

tenaciousDaniel wrote: post #83
_void wrote: post #64

Earlier quoted context omitted.

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…

That kinda describes my experience. I was never formally trained in computer science; I fell into it in my late twenties and taught myself. I never took math at the collegiate level, so I don't really understand the fundamentals. However, I am able to get by for about 95% of the things I've needed to do. But the last 5% is always the most interesting, and I hate it when I hit those walls.

well I hope there will always be that 5% left that you can't answer yet, and that you find interesting enough to learn more about. At the end of the day, that's probably the best way to learn more maths and get a deeper understanding of how computer programs work, at least that was the case for me who's, so far, been pretty bad at learning theory without having applied it first.

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

#86

Post by js8 »

ccortes wrote: post #74
js8 wrote: post #47

Earlier quoted context omitted.

I understand what you're saying, but disagree. In calculus, uncountable sets are just the theater, the real actors are sequences. As long as the theater is a complete metric space, we don't really care about its structure. Hence the name, it signifies that we are unconcerned with cardinality above aleph 0. The finite/countable/uncountable distinction IMHO shows where the focus is. Analogically, in CS, you use infinit…

> As long as the theater is a complete metric space, we don't really care about its structure. I agree with that, but I fail to see how that means that traditional math studies primarily infinite countable structures.

Perhaps better would be to say that traditional math studies structures constructed from countable building blocks (and we don't care so much whether the result is countable or uncountable).

In contrast with CS, where the building blocks are finite, and the resulting structures can be large finite or infinite, which in practice only matters a little.

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

#87

Post by mkl »

username90 wrote: post #80
mkl wrote: post #75

Earlier quoted context omitted.

> I'd argue it is impossible to imagine a world where 1 + 1 is not 2. Actually, you've probably done that yourself, in a programming setting: integers modulo 2, where 1+1 = 0. It's useful in places and the consequences aren't too ridiculous in this case. Following through figuring out the consequences of rule changes is a key thing mathematicians do. E.g. do we need this rule? What if this was weaker? What if this wa…

That is a number system where 1 + 1 isn't 2, not a universe. At least I can't imagine a universe where the concept of 1 + 1 equals 2 doesn't exist.

Numbers don't exist in any real sense, so we're clearly not talking about the actual physical universe. The universes we're talking about are the spaces of possibilities that arise from sets of rules. Examples include number systems and physics models built on them. Newtonian physics, built on Euclidean space; Einsteinian physics, built on space distorted by mass; quantum circuits, where modular arithmetic can show up.

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

#88

Post by username90 »

mkl wrote: post #87
username90 wrote: post #80

Earlier quoted context omitted.

That is a number system where 1 + 1 isn't 2, not a universe. At least I can't imagine a universe where the concept of 1 + 1 equals 2 doesn't exist.

Numbers don't exist in any real sense, so we're clearly not talking about the actual physical universe. The universes we're talking about are the spaces of possibilities that arise from sets of rules. Examples include number systems and physics models built on them. Newtonian physics, built on Euclidean space; Einsteinian physics, built on space distorted by mass; quantum circuits, where modular arithmetic can show u…

> Numbers don't exist in any real sense

I'd argue they do, numbers arise when counting and counting is definitely a part of our reality. It is pretty hard to imagine a universe where you can't count things.

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

#89

Post by dstola »

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

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

#90

Post by dmak »

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?
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