Why does maths describe nature?

[themos]

Systems shake down into their simplest state

I think they shake down to their most complicated state, if you take the amount of information needed to specify their microstate as the measure. The classic experiment is letting air out of a bottle in a vacuum filled room. You need more information to specify the positions and velocities of the molecules after you've opened the bottle than before.

[brianb]

Mathematics, perhaps as its greatest assumption, considers the universe we perceive to be the only one that warrants study.

NO! That's physics you're talking about ... mathematics has no connection to this universe or any other except in so far as it needs "intelligence" to formulate theorems.

The absolutely amazing this is that, whichever totally obscure branch of pure mathematics you look at, there is always some way in which it can be found propping the physical universe up ... like the relationship of the zeros of the Riemann zeta function (and therefore the distribution of prime numbers) in modelling the stability of heavy atomic nuclei ...

[arad85]

I think they shake down to their most complicated state, if you take the amount of information needed to specify their microstate as the measure. The classic experiment is letting air out of a bottle in a vacuum filled room. You need more information to specify the positions and velocities of the molecules after you've opened the bottle than before.

It depends on how you view this. Is the quiescent state of 2 objects at different pressures and densities simpler or more complex to model than a single object at the average pressure of the two

Thinking on the grand scalem, when people do the maths of galaxies interacting at long distances, they just model them as a point source and don't worry about the individual placement/masses of the stars/planets within them.

Generally, the maths that does the "global" picture is relatively straightforward (i.e. if you have your head screwed on, you can understand it). Personally, I think that's because the interactions between objects have to be - on the larger scale - relatively simple which leads us to maths being able to describe most of what we can see.

[themos]

eads us to maths being able to describe most of what we can see.

The interactions of proteins are not simple though, even though the underlying laws are known to be simple (or have a simple formulation : quantum electrodynamics).

I still say that it's wrong-headed to view maths as "out there" and then wonder that it's good at describing experience. Maths is experience, formalised and abstracted.

It's like thinking that there is a "Grammar" out there and then wondering why it's so good at describing language.

[astoc]

NO! That's physics you're talking about ... mathematics has no connection to this universe or any other except in so far as it needs "intelligence" to formulate theorems.

Utter rubbish! (Putting it as nicely as I can )

The axioms upon which the entire precipice of Mathematics is built are assumptions based on our experience of the universe we occupy. Further, we process deductions from these axioms using our own intrinsic logical understanding.

Perhaps we're mixing our definitions of 'universe'. Mathematics has nothing to do with physical observations, as I think I hinted at in my original post. It does however, have everything to do with the underlying properties of the universe as perceived by its occupants. As an example, there is no reason why there might not be a 'realm' of this universe completely beyond our understanding, occupied by creatures with a maths very different to our own. The point is however that since this 'realm' is completely beyond the limits of our perceived universe, it simply isn't part of our universe.

Mathematics is as much a part of the universe as physics is, it's just built from the foundations up as opposed to the pinnacle downward.

John

[arad85]

By "see" I meant with our eyes (and with telescopes). The maths that describe how stellar objects move and interact with each other are, in the grand scheme, relatively simple. You model the planets interacting with the sun as two massive point sources. The maths is simple (comparatively) and has allowed us to detect many larger planets orbiting other stars. In fact, here, the simplest explanation (i.e. simplest maths) has worked and continues to work as we are able to measure things more accurately. In fact, it was only when we got the model correct of what was going on the the maths fitted so well...

I for one wouldn't like to start to try and understand the maths of the large Hadron collider - but then that's on a different scale entirely - and is using forces that are completely different.

[kniclander]

Utter rubbish! (Putting it as nicely as I can )

The axioms upon which the entire precipice of Mathematics is built are assumptions based on our experience of the universe we occupy. Further, we process deductions from these axioms using our own intrinsic logical understanding.

Perhaps we're mixing our definitions of 'universe'. Mathematics has nothing to do with physical observations, as I think I hinted at in my original post. It does however, have everything to do with the underlying properties of the universe as perceived by its occupants. As an example, there is no reason why there might not be a 'realm' of this universe completely beyond our understanding, occupied by creatures with a maths very different to our own. The point is however that since this 'realm' is completely beyond the limits of our perceived universe, it simply isn't part of our universe.

Mathematics is as much a part of the universe as physics is, it's just built from the foundations up as opposed to the pinnacle downward.

John

hmm - being rude and then posting a smiley does not make it any less rude. especially if you're completely wrong and talking out of your ****. if by "a maths very different to our own" you mean, somthing like, 1+1=3 then, no, there couldn't. it is a logical property of oneness that if you have another "one" you have "two" - if you don't then your "one" is not the same as my "one" (or anyone else's). Your post is also (appears to be ) contradictory - you say that the axioms of maths are based on our experience of the universe; then you say, maths has nothing to do with physical observations... well then, how are we "experiencing" the universe if not through physical observations?

maths is a series of tautologies (necessary truths) whereas the universe is a series of contingencies - therefore, maths is independent of the universe (ie whatever the universe was like, the maths would be the same).

[astoc]

hmm - being rude and then posting a smiley does not make it any less rude.

I was being jestful. It was no less 'rude' than the initial 'NO!' i responded to. Sorry if you were unable to appreciate that, I meant no harm.

especially if you're completely wrong and talking out of your ****. if by "a maths very different to our own" you mean, somthing like, 1+1=3 then, no, there couldn't. it is a logical property of oneness that if you have another "one" you have "two" - if you don't then your "one" is not the same as my "one" (or anyone else's).

That's not what I mean at all. Properties of this universe that we would be unable to understand would be beyond the reach of thought experiment. You're using our-world ideas to try to explain 'other-world' impossibilities.

Your post is also (appears to be ) contradictory - you say that the axioms of maths are based on our experience of the universe; then you say, maths has nothing to do with physical observations... well then, how are we "experiencing" the universe if not through physical observations?

Perhaps my language wasn't clear enough, although in the context of the exchange between myself and brianb I would have thought it fairly obvious that 'nothing to do with physical observations' referred to the experiment-observe-theorise-refine methodology of physics (and indeed all sciences). I challenge you to show me that mathematics is NOT built upon observations (logical or otherwise) of our universe.

maths is a series of tautologies (necessary truths) whereas the universe is a series of contingencies - therefore, maths is independent of the universe (ie whatever the universe was like, the maths would be the same).

The 'necessary truths' are necessary for our conceptualisation and understanding of the universe we occupy. Existence is a subjective matter and in assuming our understanding of the universe says something about what lies beyond it you are taking the step from science/mathematics into mere speculation and theology.

John

[themos]

maths is a series of tautologies (necessary truths)

Maths does not buy us truth. It buys us clarity.

[part timer]

See! I told you there would be an argument over this!!!

[Glasspusher]

I would prefer to say that Nature describes Maths.

John

[astoc]

See! I told you there would be an argument over this!!!

I really did make my comment to brianb in jest Hopefully brianb himself will see that!

John

[astoc]

Maths does not buy us truth. It buys us clarity.

I agree with the sentiment here, though I think it would be more accurate to say that mathematics is a series of necessary truths if we are to consider our initial assumptions as intrinsic properties of 'nature'.

John

[George Jones]

I have worked extensively with maths and physics for more than two decades, and I don't know why they are related so closely.

After all this time, I still am astonished and delighted by this close relationship.

[ollypenrice]

I have worked extensively with maths and physics for more than two decades, and I don't know why they are related so closely.

After all this time, I still am stonished and delighted by this close relationship.

Aha! Exactly. I haven't worked at all closely in this field - my background is in liiterature - but I'm deligted to hear that you think the relationshi[p surprizing. I really do think the question worthy of deep thought. Perhaps we could write to Melvyn Bragg and ask him to get John Barrow back!

Ollly

[kniclander]

I was being jestful. It was no less 'rude' than the initial 'NO!' i responded to. Sorry if you were unable to appreciate that, I meant no harm.

That's not what I mean at all. Properties of this universe that we would be unable to understand would be beyond the reach of thought experiment. You're using our-world ideas to try to explain 'other-world' impossibilities.

Perhaps my language wasn't clear enough, although in the context of the exchange between myself and brianb I would have thought it fairly obvious that 'nothing to do with physical observations' referred to the experiment-observe-theorise-refine methodology of physics (and indeed all sciences). I challenge you to show me that mathematics is NOT built upon observations (logical or otherwise) of our universe.

The 'necessary truths' are necessary for our conceptualisation and understanding of the universe we occupy. Existence is a subjective matter and in assuming our understanding of the universe says something about what lies beyond it you are taking the step from science/mathematics into mere speculation and theology.

John

John, I think I must have been in a bad mood yesterday ( or someone from another universe took over my body...) - there wasn't any excuse for my comments.

i don't agree with what you say; tbh (without being rude;)) i think that it is lacking in "rigour" but I don't have time now (damn this pesky job...) to go into it - the problem with this sort of discussion is often that the principles are lost in the semantics and when poeple don't agree, it's often because they're not discussing the same thing.

But, anyway, unreserved apologies. I'm not usually such a ****.

[astoc]

Ah don't worry about it! A misunderstanding is all, just hope brianb didn't take my tone as you did! haha

Wrt the maths, i've not been particularly concise in what i've been trying to convey. Perhaps a large part of the problem is differing ideas of what the word 'universe' means. Personally, I take the philosophical approach and deem the universe to be all that we can perceive and conceive of - anything external to that just isn't worth consideration in my eyes. But its far too early to be thinking about stuff like this today, haha.

Cheers,

John

[part timer]

I think the most interesting thing about this discussion for me, is the huge variance in where people draw the line between Mathematics and Physics.

I've wanted to argue a few points in this thread but, after carefully reading the posts in question, I don't think any one person is discussing exactly the same point as anyone else.

As an example, I view the remarkable Mathematical patterns found in nature to be physical phenomena. Our understanding of the 'rules' by which Physics happens is very young and so rather jumbled and incomplete. Also, I always like to point out that I've never read a single paper which has even attempted to explain why thing are this way. We are still very much engaged in the description of nature rather than truly understanding it (I view this as the main reason for Mathematical complexity).

Mathematics is,to me, the language of description. The key to understanding everything is Physics. That maths describes Physics is completely unremarkable from this point of view as it could never do anything else.

I also think that these things are difficult to discuss over the internet as some of the meaning of each post is always misunderstood.

Anyway, it's a fascinating thread, not least for the deeper understanding gained of the human mindset!

[themos]

why thing are this way.

That's not science, science asks "how": how does this experience relate to that.

[acey]

The quadrivium of Archytas (4th cent. BC)

Shape at rest: geometry

Shape in motion: astronomy

Number at rest: arithmetic

Number in motion: music

[part timer]

That's not science, science asks "how": how does this experience relate to that.

The perfect example of what I mean. Neither of us has understood the other.

As a slight aside I totally disagree with you on that, science exists solely to find out why. It does so by investigating how in the hope of eventually getting to answer.

But that's a whole different argument.

[George Jones]

Perhaps we could write to Melvyn Bragg and ask him to get John Barrow back!

Ollly

Or we could read (or reread) the last chapter from Barrow's book Pi in the Sky: Counting Thinking and Being,

Amazon.com: PI in the Sky: Counting, Thinking, and Being (9780316082594): John D. Barrow: Books

The UK amazon site doesn't seem to have new copies, and doesn't seem to have the LOOK INSIDE! feature that amazom.com does. Use this to view the Table of Contents.

I can't find my copy. Its 1) in a box at my place waiting to be unpacked from my last move almost four years ago; 2) in a box in storage at wife's parent's place more than 1000 km distant from me; or 3) lost in one of my many moves.

[astoc]

Or we could read (or reread) the last chapter from Barrow's book Pi in the Sky: Counting Thinking and Being,

Amazon.com: PI in the Sky: Counting, Thinking, and Being (9780316082594): John D. Barrow: Books

This looks like it might be a good read - cheers.

John

[themos]

science exists solely to find out why.

Have you ever played that game with a child that has figured out how to keep a conversation going by asking "but, why?" after every answer?

[part timer]

Erm, no