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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)

#91

Post by mkl »

username90 wrote: post #88
mkl wrote: post #87

Earlier quoted context omitted.

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.

We can count things, because we use the concept of numbers. Numbers aren't a physical thing, they are all imagined. How I see it is that physics models can be described using number systems, but the numbers aren't part of what's being described. E.g. the numbers describing properties of particles are categorically different from the particles themselves, and only the particles can interact with other physical objects. An electron can never bang into a 7.

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

#93

Post by camjw »

mkl wrote: post #75
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…

> 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…

To me this is a non-example though because in this context 2 = 0. So 1 + 1 = 2 = 0.

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

#94

Post by gjm11 »

mkl wrote: post #75
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…

> 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 isn't a situation where 1+1 isn't 2. It's a situation where 1+1=2 but also 2=0.

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

#95

Post by nobodyandproud »

coldtea wrote: post #79
mkl wrote: post #73

Earlier quoted context omitted.

Yes, that's what my comment says (but maybe you read it before I edited it to be clearer): >> Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "discovered", for example.

Yes, that. Though I wouldn't necessarily consider it "muddying the waters", but taking another criterium as important in the distinction of physics-like or not. Namely, not whether it concerns the study of the material universe, but whether it involves experimentation/discovery of in place structures, and other such physics-like processes (which they think it does).

This is muddying the waters though, though I think you’re in good company.

I’m not sure if mathematics belongs in the sciences or art; it really has hallmarks of both.

It a modeling language that can be used to describe the universe. You don’t have science today, without the math.

Yet some of the proofs and mental exercises in pure math are almost divine; inspired in a way that resonates like a beautiful work of music.

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

#96

Post by enriquto »

kovac wrote: post #84
mkl wrote: post #60

Earlier quoted context omitted.

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…

> "Nature is of no consideration whatsoever in pure mathematics" and I'm quite sure that the pure mathematicians would agree.

Only if you have the audacity to call Arnold "not a true pure mathematician"... He mockingly said that the parts of "so-called" mathematics that have no connection to nature are useless mental masturbation.

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

#98

Post by mbeex »

coldtea wrote: post #67
mkl wrote: post #60

Earlier quoted context omitted.

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…

> I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. It's not about actual nature (the universe etc) being into consideration. It's about many mathematicians coming to see maths as exploration (physics-style) of a mathematical universe, so to speak, rather than a simple constructive process. So, they come to see mathematics as a kind of physics in this regard, no in the sense that…

The controversy between assuming a point of view of "creating" vs "discovering" things is as old as mathematics.

> rather than a simple constructive process.

This requires some more distinction. 'constructive' can mean very different things. Some non-intuitionists would consider their counterparts definition of 'constructive' as possibly OK, but simple - and held other cases still for construction. Anecdotally, Ramanujan received his results as an inspiration from his household deity. Thinking about it probably brings up 5 different opinions among two people.

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

#99

Post by mirko22 »

Just a random opinion:

You don't need math at all to make a computer program. All you need is a computer with some kind of language that is easy to run installed and a tutorial for hello world for it.

But what about programming a program that does some math calculations? Seem like it would be good to know those math calculations that you need to implement...

Or lets take accounting software for example? You need basic math most of the time but it turns out it is quite valuable to know about accounting. Yes, you can write an accounting software without knowing any accounting and just depend on what product manager tells you. But it is much easier to understand what he is saying if you know a lot about accounting... It is also much easier and faster to make decisions without going to product for each tiny detail.

You can expand this to the problem of building teams. You can read few tutorials on agile development and what not, however knowing psychology and having enough empathy to understand people you work with in depth will bring much better results then any so called management book that is taken literally.

And so it goes... The more you know about how world works the better decisions you can make that eventually might lead you to better solutions to the problem at hand.

This is a general thing in life in my experience, but also one that seems to be looked over quite often... The more you know about problem domain the better you will be at problem solving inside that domain. Coding that solution into a computer program at that point is just a matter of knowing how to use that tool (which is a specific problem domain in of it self.)

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

#100

Post by prionassembly »

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.

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