Why is physics described using real numbers as a mathematical abstraction?

[zezima1]

Probably a silly question. But here it is anyways:

Why can you descibe physics, i.e. nature, with the real numbers, i.e. a mathematical abstraction?

 

[Jano L.]

Hi zezima,
I like your question, and I can give you my view. I think of physics as of the endeavour of people to understand the natural phenomena and the world (a bit like in religion). This requires observing and experimenting on one hand, and thinking on the other hand. It happens that even the thinking part is not always easy; thus people developed their thinking into more perfect and accurate forms. Mathematics with its numbers and other abstract notions can be partially viewed as the evolving result of this process. Why, from all other possible notions, the numbers are so useful? I do not know. I see numbers as constructs that do not exist as a part of Nature, but exist as our creations. So they are just thoughts. Then, the usefulness of numbers for describing the world is perhaps not that mysterious - they are our thoughts invented for that particular purpose...

Jano

 

[JHamm]

As far as I know mathematics was born out of a desire to describe the world, with numbers often representing "lengths" of sticks, things like divisibility and common factors were imagined by which lengths of sticks could be used to measure others and so forth. So mathematics seems to have been born out of the physical world first, then abstracted beyond it afterwards.

 

[Philip Wood]

Pythagoras (perhaps a mythical figure) reckoned all was number. An early discovery giving this plausibility was that string lengths for the octave, fifth etc. are in nice easy ratios. We now have laws ranging from those of reflection to those of quantum mechanics. Difficult to believe that mathematics isn't at the core of the physical world. And yet there's a nasty sneaky feeling that we're only seeing what we're able to see, and thereby gaining a hopelessly distorted picture. Let's just carry on enjoying the beauty and perhaps not worrying unduly how much is man-made...

 

[zoobyshoe]

Probably a silly question. But here it is anyways:

Why can you descibe physics, i.e. nature, with the real numbers, i.e. a mathematical abstraction?

Numbers are incredibly versatile and people are incredibly persistent in turning natural phenomena over and over until they find some aspect of it that yields itself to expression in numbers. Once they find something for which that approach works, it is set apart in a category of knowledge called "physics". I think Phillip Wood might possibly agree that physics seems more successful than it may actually be because its mostly a collection of the cherry picked stuff, the stuff that describes well with numbers.

 

[Philip Wood]

Yes indeed. If I had the intellect of a Wittgenstein, I'd be able to take the argument further but, as it is, I grunt assent.

 

[Nabeshin]

Probably a silly question. But here it is anyways:

Why can you descibe physics, i.e. nature, with the real numbers, i.e. a mathematical abstraction?

I think it's important to remember, as others have noted, that early mathematics was driven in large part to understand and solve problems about the real world. So the mathematics they developed was naturally related to physics. But as their inquiries went on, mathematicians have developed tons of mathematics which has no relation to the physical world (at least as far as we know).