Math and Reality. What is the deep connection?


by rogerl
Tags: connection, deep, math, reality
nismaratwork
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#19
Mar24-11, 07:35 PM
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Quote Quote by rogerl View Post
I think we can never arrive at the TOE if we don't have answers to it first. For example. SU(5) is very elegant and should work. How come SU(3)xSU(2)xU(1) works and not SU(5).. that is.. Protons don't decay. In the case of #1. Maybe we can to integrate the
3D projection scalar field to explain a sub-broken symmetry or sora. In case #2 where we are inside a computer program, perhaps SU(5) doesn't work because of certain programming algorithm use. In the case of #3. Perhaps the will aspect that hold in maintainance the values of the constants of nature are not included in the calculations. So it's possible we will never arrive at any Final Unification without taking this into account. Just for example Superstring Theory. Lee Smolin said we don't even know what is the basic principle of it and zero experimental confirmation of any kinds of its dozens of predictions. A phycisist even describe our current physics as "Recreational Mathematical Theology". Now knowing the mechanisms of how it all occur whether one of the 3 cases or others can give us guiding principle that can make us nail the TOE.
I'm reminded of the 'Hitchiker's Guide To The Galaxy', That you want the answer before you know the question. I don't think that this is a place where the cart can be placed before the horse. I doubt we'll ever find a TOE, but certainly we won't have spontaneous answers before we have questions... or rather, when we do we require even more time and effort to formulate the questions that make the answers sensible.
apeiron
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#20
Mar24-11, 07:38 PM
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Quote Quote by rogerl View Post
If GR, QM can only be united by treating the planck scale as the pixel of reality, then perhaps there comes a point when we can no longer go beyond it and call it quits. Right?
It could be that some aspects of a TOE remain arbitrary - such as a handful of constants needed to define coupling strengths, the planck scale, or other essential parameters.

In that case, either some aspects of reality are irreduciably random, a matter of chance which way the symmetry broke. Or it could instead be anthropic. Every choice was made "somewhere" and so there is an infinity of universes out there.

But what would be really nice is if even the constants are fixed by some kind of self-organising logic. Like they could be emergent ratios in the way that pi, e and other mathematical constants are.

So perhaps answering my own question earlier in the thread, maths models the symmetries, and what maths has to say about constants could be central to the story of how symmetries get broken.

Constants arise in maths as the limits of processes. Limits of complex processes in fact.

Anyway, getting back to your going beyond the final pixel, there is a way to do this based on a logic of vagueness. Because instead of just dissolving smallness, you are also dissolving any largeness. As you zero in on the pixel, it dissolves, and you dissolve, so nothing definite now can lie beyond (as finding anything smaller would demand that you as the observer are still around to see it).

This is the quantum foam story of course. The HUP principle. Except that now we have a better name to describe what "lies beyond" - vague potential.
apeiron
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#21
Mar24-11, 07:52 PM
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Quote Quote by rogerl View Post
You are saying it is possible that the 4 forces can't be unified at all?
Personally I'm not sure whether they should or shouldn't. But I see gravity as a global symmetry rather than a local or gauge one, so that is one reason to think that it is not going to end up as a "fourth force" unified with a gauge symmetry.

The reason for expecting EW and strong to be unified is definitely because of the way the couplings run and look to become vanilla at the GUT scale. That is a strong motivation. And gravity would also run, suggesting a planck scale unification of some sort

Or instead, in my view, a planck scale dissolution into vagueness. That is gravity would have the vanilla force strength, but it would no longer be coherently directed so as to be pulling in a clear direction. The 3D space would have dissolved into foam by that stage.
rogerl
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#22
Mar24-11, 08:37 PM
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Guys. Is there a possibility that the TOE would involve no math at all... since physics involves math.. and TOE is beyond math. Then it's the end of physics? What I mean to say is. What if beyond the Planck is a realm that is no longer describable by math. Is this possible? Or would physics evolve to other systems of modelling that don't use math anymore? If so, Symmetry may be the final concept that is still math connected. Beyond Symmetries may lie mathless facts... for example, what if in the planck realm where spacetime breaks down and quantum fluctuations ruin any continuous manifold lie something that is no longer modelable by math?
apeiron
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#23
Mar24-11, 08:54 PM
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Quote Quote by rogerl View Post
Guys. Is there a possibility that the TOE would involve no math at all... since physics involves math.. and TOE is beyond math. Then it's the end of physics? What I mean to say is. What if beyond the Planck is a realm that is no longer describable by math. Is this possible? Or would physics evolve to other systems of modelling that don't use math anymore? If so, Symmetry may be the final concept that is still math connected. Beyond Symmetries may lie mathless facts... for example, what if in the planck realm where spacetime breaks down and quantum fluctuations ruin any continuous manifold lie something that is no longer modelable by math?
Most would say the problem lies in observable maths - scientific models that are framed as formal statements with measurable consequences (rather than unmeasurable ones).

Science involves both models and measurements in interaction. So for a TOE to be scientific, it has to be testable.

If a TOE is just a formally stated hypothesis that is ultimately untestable, then it becomes metaphysics.

So I would say it is looking like the maths will stretch beyond the eventual reach of science. Instead of mathless fact, it is more likely we will end up with factless maths!

Which is good news for the future career prospects of metaphysicians.
rogerl
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#24
Mar24-11, 09:20 PM
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Quote Quote by apeiron View Post
Most would say the problem lies in observable maths - scientific models that are framed as formal statements with measurable consequences (rather than unmeasurable ones).

Science involves both models and measurements in interaction. So for a TOE to be scientific, it has to be testable.

If a TOE is just a formally stated hypothesis that is ultimately untestable, then it becomes metaphysics.

So I would say it is looking like the maths will stretch beyond the eventual reach of science. Instead of mathless fact, it is more likely we will end up with factless maths!

Which is good news for the future career prospects of metaphysicians.

So even if it were true that the constants of nature were fine tuned into values compatible with life by a Universal Mind. It still can be modelled by math? It's like this. Big Bang might occur to seed life and mind. Now this can explain how our mind can tap the Mind of the universe and even make us possess the power to create/uncreate reality (nothing that Miracles occured down the centuries where Saints can bilocate (be in 2 places at once) and even levitate as well as numerous phenomena documented by many sources). So you mean all these can be modelled by math? If so, then it is part of physcis and not metaphysics (which can't be modelled by math). In other words, any measurable effects can be modelled by math, is this what you are saying?

"There are more things in Heaven and Earth, Horatio than are dreamt off in your philosophy".
nismaratwork
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#25
Mar24-11, 09:21 PM
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Quote Quote by rogerl View Post
So even if it were true that the constants of nature were fine tuned into values compatible with life by a Universal Mind. It still can be modelled by math? It's like this. Big Bang might occur to seed life and mind. Now this can explain how our mind can tap the Mind of the universe and even make us possess the power to create/uncreate reality (nothing that Miracles occured down the centuries where Saints can bilocate (be in 2 places at once) and even levitate as well as numerous phenomena documented by many sources). So you mean all these can be modelled by math? If so, then it is part of physcis and not metaphysics (which can't be modelled by math). In other words, any measurable effects can be modelled by math, is this what you are saying?

"There are more things in Heaven and Earth, Horatio than are dreamt off in your philosophy".
I'd tell Billy that he's in the wrong forum for metaphysics.
apeiron
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#26
Mar24-11, 09:40 PM
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Quote Quote by rogerl View Post
So even if it were true that the constants of nature were fine tuned into values compatible with life by a Universal Mind. It still can be modelled by math? It's like this. Big Bang might occur to seed life and mind. Now this can explain how our mind can tap the Mind of the universe and even make us possess the power to create/uncreate reality (nothing that Miracles occured down the centuries where Saints can bilocate (be in 2 places at once) and even levitate as well as numerous phenomena documented by many sources). So you mean all these can be modelled by math? If so, then it is part of physcis and not metaphysics (which can't be modelled by math). In other words, any measurable effects can be modelled by math, is this what you are saying?

"There are more things in Heaven and Earth, Horatio than are dreamt off in your philosophy".
OK, so now you want to make me regret taking your questions seriously .

Miracles would have to count as observables to fall within the realms of scientific discussion. So you say these things happened, but if there is no good evidence so far as the rest of us are concerned, then there is no real interest in debating the implications for theory.

And the universal mind seems to me a vacuous concept unless it can be pinned down as a formalism that is at least potentially measurable. If you can provide a source that does that for you, please do.

Peircean semiotics is for example a kind of "universal mind" approach - but nothing like what you probably mean here.

So time to source your model of the universal mind, citing some mainstream philosophical approach. But it is unlikely I would have much to say about it.
rogerl
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#27
Mar24-11, 09:47 PM
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Quote Quote by apeiron View Post
OK, so now you want to make me regret taking your questions seriously .

Miracles would have to count as observables to fall within the realms of scientific discussion. So you say these things happened, but if there is no good evidence so far as the rest of us are concerned, then there is no real interest in debating the implications for theory.

And the universal mind seems to me a vacuous concept unless it can be pinned down as a formalism that is at least potentially measurable. If you can provide a source that does that for you, please do.

Peircean semiotics is for example a kind of "universal mind" approach - but nothing like what you probably mean here.

So time to source your model of the universal mind, citing some mainstream philosophical approach. But it is unlikely I would have much to say about it.
Ok. Miracles can be observable too and can be modelled by math. Now let's not discuss further on this lest this thread be locked. Let's go back to GR, SR QM and be within just its small circle. Anyway. I just found out about Brian Greene new book "The Hidden Universe
... I'm listening to MP3 now about chapter 10 called "Computers, Universes and Mathematical Reality". It sounds interesting.
nismaratwork
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#28
Mar24-11, 09:49 PM
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Quote Quote by rogerl View Post
Ok. Miracles can be observable too and can be modelled by math. Now let's not discuss further on this lest this thread be locked. Let's go back to GR, SR QM and be within just its small circle. Anyway. I just found out about Brian Greene new book "The Hidden Universe
... I'm listening to MP3 now about chapter 10 called "Computers, Universes and Mathematical Reality". It sounds interesting.
No rogerl, you don't throw out "mathematically modeled miracles" and walk away. You should be worried about your fate, not the thread's.

Please, do explain in accordance with PF guidelines or retract your claim. And roger... I'm in a mood to hurt someone, so lets not make this emotionally painful.
rogerl
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#29
Mar24-11, 10:02 PM
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Quote Quote by nismaratwork View Post
No rogerl, you don't throw out "mathematically modeled miracles" and walk away. You should be worried about your fate, not the thread's.

Please, do explain in accordance with PF guidelines or retract your claim. And roger... I'm in a mood to hurt someone, so lets not make this emotionally painful.

Ok. I'll retract it. Mind has nothing to do with the Big Bang or the Constants of Nature. General Relativity, Special Relativity and Quantum Mechanics are the final words and we are bound to them. Our brain is just emergence of biochemistry. And the world is just pure physical, with no possibility of anything higher. If I need to delete the threads.. just let me know as one can only delete them within 2 hours.
nismaratwork
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#30
Mar24-11, 10:04 PM
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Quote Quote by rogerl View Post
Ok. I'll retract it. Mind has nothing to do with the Big Bang or the Constants of Nature. General Relativity, Special Relativity and Quantum Mechanics are the final words and we are bound to them. Our brain is just emergence of biochemistry. And the world is just pure physical, with no possibility of anything higher. If I need to delete the threads.. just let me know as one can only delete them within 2 hours.
No, this works for me.
rogerl
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#31
Mar24-11, 10:19 PM
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Brian Green new book is very interesting... so relevant to many of the topics we discuss like Mathematical Reality. I wonder what would happen if superstrings and branes are just figment of the imagination. Lee Smolin believes in "Trouble with Physics" that they may not be real.. instead of 20 constants of nature.. we now have over 250 constants of nature if Superstrings are real.. so maybe some other Ultimate Symmetry can bind all that can explains the constants? He who discovers it can win 2 Nobel at the same time.. lol
apeiron
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#32
Mar24-11, 10:31 PM
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Quote Quote by rogerl View Post
Brian Green new book is very interesting... so relevant to many of the topics we discuss like Mathematical Reality. I wonder what would happen if superstrings and branes are just figment of the imagination. Lee Smolin believes in "Trouble with Physics" that they may not be real.. instead of 20 constants of nature.. we now have over 250 constants of nature if Superstrings are real.. so maybe some other Ultimate Symmetry can bind all that can explains the constants? He who discovers it can win 2 Nobel at the same time.. lol
So long as you realise these guys are beating each other up over the 2% they don't agree on rather than the 98% that they do.

The 2% is of course where they make a career for themselves.
Ken G
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#33
Mar24-11, 10:59 PM
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Quote Quote by apeiron View Post
The key question may be whether we are imagining the symmetries as something we are breaking away from, or headed towards. Are they in the universe's past, or in its future?
Another duality. Perhaps it could never be one without the other-- the symmetries from our past that are breaking gives meaning to the concept of past, and the symmetries we are breaking toward give meaning to the concept of future. The duality gives meaning to the concept of time.
I think we can say the universe is a highly broken symmetry from the point of view that it is a long way from the infinite dimensional space it could be. Being 3D is a highly reduced state of affairs - very asymmetric when you compare 3 to infinity. But then a complete breaking of that infinite symmetry would be to arrive at a 0D point.

However, a point or singularity is again a highly symmetric state itself - infinity of another kind as you point out.
Yes, probably the near-symmetry is that the potentially infinite dimensional universe is "modded out" by the four dimensions of spacetime, much like the integers mod 4. The other dimensions are probably not completely gone-- there would be a hierarchy of these nearly unbroken symmetries, the nearly unbroken symmetry between time and space, and the nearly unbroken symmetry of the 11 dimensions of M-theory (if it is a valid theory). So we cannot completely mod out the dimensions above 4, but we nearly can, and most likely we could not completely mod out the dimensions above 11, but we nearly can, etc. ad infinitum. We live in the world of the most broken symmetry, the symmetry between space and time and the mod 4 symmetry of spacetime, with only ghostly hints of the higher-order much more nearly unbroken symmetries. Since we see what we understand, our minds automatically collapse those nearly unbroken symmetries into obscurity, until very careful and high energy observations resurrect them.
There are in fact two extremes of order in an ideal gas. One pole of order is where all the particles are trapped in the same small corner (and so will want to spread out randomly). The other is where all the particles are trapped in an exact lattice configuration, completely regular in their placing (the situation covered by the third law of thermodynamics).
Yes-- delta functions in the two complementary variables of "x" and "k" space. Another duality-- one gives us constructive interference with location, the other constructive interference with motion. Neither by themselves has any meaning-- location means nothing without motion to connect locations, and motion means nothing without locations to connect. Since neither can trigger recognition in us without the other, what we see as reality must involve a blend of both, a blend that is not a pure state of either. Equilibrium between the poles.

So there could be a good reason why reality ends up poised between infinite dimensionality and zero dimensionality here. There could be a logical reason for the nearly broken state (as it is in fact a fully broken or entropic state once you recognise that the extremes of symmetry or order are dichotomous and being maximally broken falls somewhere between the two states as an equilibrium balance).
Yes, and I think that reason must have to do with what we count as important, worth noting. Our intelligence has evolved to notice an incredibly tiny fraction of "what is really going on", and label it as "important", because that's how we get power over our environment, and that's how we survive. It's as much about us, about how we think about reality, as it is about reality itself (another duality-- neither would mean anything without the other).
Another quick point is that your translational symmetry argument holds true I believe only for flat space (of any number of dimensions).
Yes, symmetries in GR are local, they have differential generators rather than global ones. Not that I'm any GR expert.
rogerl
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#34
Mar24-11, 11:13 PM
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Quote Quote by apeiron View Post
So long as you realise these guys are beating each other up over the 2% they don't agree on rather than the 98% that they do.

The 2% is of course where they make a career for themselves.
Have you read Smolin's "Trouble with Physics"? He wants us to go back to fundamentals and try to understand for example what made QM ticks. He even thinks the entire Superstring theory is false.. so I wonder what 98% are you talking about. I know he digs for Loop Quantum Gravity.. but he is saying quantum mechanics needs to be reinvestigated because the unification may not be along the superstring programme. Anyway. After rereading the book. I realized that there are two kinds of physicists, the realist and the other one. Einstein, Schroedinger's are realists.. like Smolin, in that they want to look for a physical side to the theory. But the other parties like Feynman, Julian, 't Hoofe... mathematical beauty is enough without regards to any physical basis or mechanism. This is why I wonder what math has to do with reality because it can give us insight if Smolin has basis of the need to look for the physical side of it or just pure mathematical investigations in the case of the others without regards for what form of structure or nature reality have take.
rogerl
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#35
Mar24-11, 11:29 PM
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Lee Smolin wrote about the following in Trouble with Physics (just brief quotes):

"In the approach of particle physics developed and taught by Richard Feynman, Freeman Dyson, and others, reflections on foundational problems had no place in research"

"However, as I will argue in detail in the pages to come, the lesson of the last thirty years is that the problems we're up against today cannot be solved by this pragmatic way of doing science. To continue the progress of science, we have to again confront deep questions about space and time, quantum theory, and cosmology"


Do you guys believe in Smolin approach? If Smolin is right and we don't do re-investigation of foundational problems, we will never have any TOE. So it's NOT like we have to find the TOE first and then contemplate on the insight later. I still can't decide if Smolin is right or wrong.. and this is why I asked the initial questions in the thread.
nismaratwork
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#36
Mar24-11, 11:31 PM
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Quote Quote by rogerl View Post
Lee Smolin wrote about the following in Trouble with Physics (just brief quotes):

"In the approach of particle physics developed and taught by Richard Feynman, Freeman Dyson, and others, reflections on foundational problems had no place in research"

"However, as I will argue in detail in the pages to come, the lesson of the last thirty years is that the problems we're up against today cannot be solved by this pragmatic way of doing science. To continue the progress of science, we have to again confront deep questions about space and time, quantum theory, and cosmology"


Do you guys believe in Smolin approach? If Smolin is right and we don't do re-investigation of foundational problems, we will never have any TOE. So it's NOT like we have to find the TOE first and then contemplate on the insight later. I still can't decide if Smolin is right or wrong.. and this is why I asked the initial questions in the thread.
I think you should look at what QM has correctly predicted, despite detractors and want of a single Interpretation. Then, you draw your own conclusions, I'm not sure there is a right one.


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