God and Mathematics

But those conservation laws are already maths/physics. The inter-relationship must exist to even have conservation laws. And why do we have those conservation laws? I understand why, but only in mathematical terms as local symmetries of the tangent plane. I have no physical understanding of why we should have them, other than as postulates.

Ok, can you explain any of the consequences of GR physically? Good questions... I cannot conceive a universe built on Newtonian mechanics, with classical mechanics. I don't think such a universe can exist. It is built of unrelated concepts bolted together in a hope that the whole will work. It is mathematical in seperate parts, but there is no encompassing theory. Our universe is revealing itself to be one integrated whole. The closer we get to what that is, the more we see that it is essentially mathematical in nature.

Conservation needn't be expressed as a mathematical law. It can be simply stated as "can't be created or destroyed only transfered".

What can't be destroyed? What can't be created? And why? What is "transfered"? (edit - clarification: what does "transfered" mean?)These are great classical concepts but don't survive our modern notions of reality at the large and the small. It's only in the middle that these concepts have some approximate meaning, like velocity, time, matter, etc. And these approximations are modelled very well by mathematics. To me, this is not surprising because the ultimate reality is mathematical... or even mathematics itself, whatever that means This message has been edited by cavediver, 07-13-2005 08:45 AM

Has anybody read a book called "Quantum Philosophy"? I don't recall it very well, and did not understand all of it to begin with, but I think the gist of it is that what the author calls "formalism" (mathematical conclusions) always wins out over other ways of looking at the world, no matter how none-commonsensical or bizarre the mathematical conclusions are. The world operates mathematically.

Yaro, I guess I should have stressed that more recently I have to come to think that physical reality IS the Platonic realm... it's just that at our level of observation, all we ever see are crude reflections and copies of the mathematical truths which build up reality. We talk of physical reality being an emergent concept within mathematics.There's a great parallel here with string theory, when it is viewed in its most geometric (and least discussed) form: there is no multi-dimensional universe-only a 2-dimensional world-sheet of the strings. What we think of as dimensions are actually fields (or degrees of freedom) carried by the strings. The universe we see is merely a realisation or projection of these degrees of freedom. This is precisely how string theory developed, but because it was developed by particle physicists (Green and Schwarz in its modern context), this view was never really picked up. The graviton of string theory is not an n-dimensional field but a 2-dimensional coupling constant between the fields. Arrgghhh, I can't explain this by typing... give me a lecture room anyday Anyway, my point is that reality is an emergent property of mathematics. Anyone buy that

Sorry Taro, missed your last point. [qs]Besides, dosn't maths tight bond with reality itself beg a bigger question? Namely why does anything exist at all?
[\qs]Of course it does, that's why it's such fun IMO this is far more coherent entry point into philosophy/theology/meta-physics than any talk of "what came before the big bang" or "what made the big bang happen" or "if the uiniverse had no beginning how could someone create it".

I do. But metaphysically what does that view fall into? Materialism, dualism, idealism?

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Ok, can you explain any of the consequences of GR physically?

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Well you have to remember that my education in physics stopped with Special Relativity and some QM (both VERY rusty). But I don't see what you are getting at. Can you explain your point ?

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Good questions... I cannot conceive a universe built on Newtonian mechanics, with classical mechanics. I don't think such a universe can exist...

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THat's an interesting response. Is it possible that any universe that could concievably exist must be describable by mathematics - must have a ToE ? If so then doesn't it follow that the "unreasonable" effecitveness of mathematics is a necessary truth and thus not unreasonable at all ?

Why did I start this thread when I have over 200 A-level maths papers to mark by the weekend Sorry Paul, let me get a few done then I'll come back... promise!

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...It's not perfect, because we can't possibly ever account for all the variables.

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Hi, arachnophilia.Personally, I think that it's not perfect because reality is what it is and the universe behaves in the way it does, and all of our mathematical theories are and will always be just approximations to how the universe actually acts. This isn't a scientific theory, just my personal unproven, perhaps unprovable, philosophy.

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The more fundemental we have pushed physics (outwards and inwards), nature has demonstrated itself as more mathematical, not less.

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Hi, cavediver.Again, I have to respectfully disagree. Nature has not demonstrated itself more mathematical -- better mathematical models have been developed. There is a selection process going on here: if a mathematical theory does not quite match up with reality, a better one is developed. If the new mathematical theory doesn't do a better job at describing reality then it is thrown out -- or at least put ont the back burner where it might be improved.Remember one of the first mathematical models of the universe, the ptolemaic system where the planets went around the earth in perfect circles, was actually quite terrible at describing reality. Each advance in theory was a better, more accurate description of the motion of the planets, but that is because they would not have been accepted had they not been more accurate.

That's a shame, but explains your position (if that doesn't sound too condescending )Undergrad QM will lead you to precisely the opposite view and SR is very very rarely presented well at undergrad level, with a distinct emphasis on the physics even when taught in maths degree classes.My request wasn't very clear. Take space-time. What is it? It has curvature, it has a topology. As a mathematician I have a very good idea of what space-time is, but what can a physicist say? Rubber-sheet is the best I've ever seen anyone come up with At the large and small scales, the "physics" has no analogues... there is now way of explaining what is going on in terms of other physics. Everything is talked about in terms of mathematics. I have no definitions of space-time, matter, energy, etc, etc that don't end with... well, it's a solution of... or... it's just an irrep of SU(3). Well, that is a question... I would say that to have a self-sustaining existence, you need a self-consistent framework upon which to build it. But I certainly agree with your last statement. To me, there is nothing unreasonable about the effectiveness of mathematics... it's blatently obvious when it is the stuff from which the universe is created

Hi Chiroptera,I agree totally with your view up to the end of the 19th century. But then something revolutionary happend, and we had a paradigm shift. Admittedly, as I've just said above, this isn't obvious unless you work within GR, quantum gravity, theroretical QFT, string theory, etc, etc. Outside of these areas, maths and physics have pretty much been doing what they've always been doing. The number of physicists I know for whom maths is and always will be a toolbox...The more fundemental we push physics, the more simple the mathematical picture becomes. Distinct areas are unified, using mathematics that no-one ever dared imagine would be used in the real-world. Physcial descriptions of reality break down and all we are left with is explanation purely in terms of mathematics. To me, we are seeing a converegence: that the fundemental structure of physics is mathematics.This message has been edited by cavediver, 07-13-2005 01:37 PM

Hey Cavediver,I don't wan't to sound mean, but what are you getting at? Are you proposing that math can lead us to a conclusion about god and/or his existence?I allways get warry when someone toes the line between physics, objective reality, and metaphysics. It begins to sound like Quantum psychobable.You are obviously a very well read, inteligent person. Heck it sounds like you may even have a Phd under your belt. I am not calling your academic capacity into question at all, I simply am interested in where are you going with this discussion.