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Varon
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Do you believe that in Quantum Gravity, quantization of gravity is only a small part and it is really Quantum Spacetime or the unification of Matter, Space and Time that is the general feature or attraction?
Varon said:Do you believe that in Quantum Gravity, quantization of gravity is only a small part and it is really Quantum Spacetime or the unification of Matter, Space and Time that is the general feature or attraction?
Varon said:Is there a possibility that quantum mechanics and general relativity are classical limits of a third theory that can no longer be described by any known mathematics? For example, an idea or thought or dream can't be described by mathematics. What if the Final Theory involves ingredient similar to it that can no longer be modeled by mathematics? Is this possible?
Varon said:Is there a possibility that quantum mechanics and general relativity are classical limits of a third theory that can no longer be described by any known mathematics? For example, an idea or thought or dream can't be described by mathematics. What if the Final Theory involves ingredient similar to it that can no longer be modeled by mathematics? Is this possible?
marcus said:Varon there is a difficulty with the question itself. The difficulty is that mathematics is a self-creating language which is constantly growing. It has no fixed borders. So you might have something that is not readily described by "any known mathematics"---and 20 years later the language might have evolved so that it can express the idea, describe the data, derive the prediction or whatever it needs to do.
So it is risky to try to say what is NOT possible. I mean in the evolution of physics as a mathematical science in the Empirical tradition. Physics is not especially hampered or limited or constrained by the fact that it is a mathematical science, because math language is always growing.
To illustrate, this week Muxin Han gave this talk at the Loops 2011 conference. 100 years ago these concepts were not part of mathematics. The spinfoam is a concept of something that is not spacetime but is the underlying degrees of freedom which describe or give rise to spacetime. The Feynman diagram (a way of describing particle field behavior) also did not exist 100 years ago, and was not part of mathematics. Muxin Han is finding that at some level the spinfoam and the Feynman diagram are the same thing, or part of the same thing. This was not mathematics a few decades ago, and now it is mathematics:
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Spinfoam Fermions.
Muxin Han
M. Ambientales Room. Tuesday, May, 24th, 14:45 - 15:05.
Abstract:
We discuss fermion coupling in the framework of spinfoam quantum gravity. We analyze the gravity-fermion spinfoam model and its fermion correlation functions. We show that there is a spinfoam analog of PCT symmetry for the fermion fields on spinfoam model, where a PCT theorem is proved for spinfoam fermion correlation functions. We compute the determinant of the Dirac operator for the fermions, where two presentations of the Dirac determinant are given in terms of diagram expansions. We compute the fermion correlation functions and show that they can be given by Feynman diagrams on the spinfoams, where the Feynman propagators can be represented by a discretized path integral of a world-line action along the edges of the underlying 2-complex.
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What limits physics ultimately not its mathematical language, but rather it is the guiding rules of the 4 centuries old Empirical tradition founded by Francis Bacon (a Londoner contemporary of William Shakespeare).
The Baconian tradition says that any theory must make predictions that one can check, so one can have a chance of shooting it down if it is wrong. A theory is not Empirical (in the Baonian tradition) unless it is testable.
One motive physicists have for formulating their theories in math language is that it let's you express the theory in model from which you can derive definite predictions, suitable for testing. And there are gray areas and provisional borderline concepts too, that are not testable theories but are used in a tentative or heuristic way to arrive at models. But ultimately it comes down to experiments, or astronomical observations, to check something to see if it is right.
Varon said:So everything can be modeled by math. How about subjective conscious experience like watching a sunset and feeling awed by it. Can this be modeled by math? If not. Why? How do you distinguish between things that can be modeled by it and things that can't?
marcus said:You misrepresent what I said. I don't use math to describe everything. What you are suggesting is silly. I have lots of channels of expression and experience. I sing choral music, I write poems, I walk up the hill and watch the clouds or the sunset. I am awed mornings when I go out into our garden where evolution of plants and insects and birds is taking place, driven by the sunlight which warms my back, as I eat a sandwich full of solar energy that has been transformed by living things into my food. As far as I'm concerned nature and the universe are awesome and both physics and biology help me appreciate that and i don't need math to describe the awe. I can sing it to music if I want, or dance it if I'm feeling spry, or whatever.
You are not contradicting, or challenging anything AFAICS.
I will repeat what I said:
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Your original question did not make sense to me because it treated math as a limited fixed language. Could physics evolve to something math can't handle?
The question is hard to answer because math does not have a fixed essence, it can expand creatively, so 100 years from now it will be able to describe stuff it can't describe now, and we cannot predict how it will develop.
Basically what keeps physicists using math models is not that they have an algebra compulsion or hidebound obsession with calculus---what keeps them at it is the Baconian tradition.
Empiricism. Math models have definite unambiguous consequences, that nobody can deny follow from the model, and that you can test conclusively. Songs and other pieces of music do not. Poems do not. Mystical religious visions do not. They can describe aspects of the world, often very well, or one's subjective experience---but you don't get to derive undeniable consequences that destroy the poem or the song or the religion if the predicted thing doesn't happen.
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Please don't misconstrue what I'm saying. This is not to say that Empirical science is better than Poetry. It just means they are different, with different standards, different paths of evolution, and survival fitness criteria. Tradition matters in both cases. I feel protective about both traditions---the 400 year old Baconian code of science ethics and the 4000 year old tradition of poetry going back, say, to the Sumerian city of Ur where some Old Testament legends may have originated.
We need both traditions and it is the job of each generation to keep them both vital.
tom.stoer said:But according to the Platonist view math is just the realm of ideas.
You should read
http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis
http://arxiv.org/abs/0704.0646
I'd say that's God's problem, not mine ;)Varon said:Bad choice of words. I just want to say what if the universe were an idea or dream of say God.
Fra said:I'd say that's God's problem, not mine ;)
I'll describe my "dreams" and leave others the pleasure of worrying about theirs.
I don't quite see the rationale in the question. Mathematics in physics is really just a language for quantifying things, in particular observations and predictions. Such as quantifying the odds of something. Mathematics is a human thing, but quantification can be physical encoded by physical states.
Something that human scientists can't quantify (describe by mathematics) are probably not something that influences our decision making anyway.
/Fredrik
Varon said:Steven Weinberg mentioned the Final Theory would be purely mathematical. So I guess you all agree it would still be describable by mathematics. Good if it is. But further beyond the Final Theory.. i guess that's when you can no longer describe it by math. My question is what if the non-math realm is even projected down to say Quantum Gravity. Supposed QM and GR are classical limits of a third theory that is directly descended from beyond the Final Theory. Then there is a possibility that even quantum gravity is no longer mathematical?
Lost in Space said:It's strange in a way that mathematics predicts (and proves) that there are things that can't be solved using mathematics.
marcus said:That works for a specific version or type of mathematics. Like axiomatic set theory, or the construction of the system of real numbers based on axiomatic set theory. That is a great basis for mathematics. And it can describe its own limitations! (An admirable achievement.)
But I am skeptical of the assumption that the extension of human language called mathematics will always be based on axiomatic set theory.
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I would rather change what you said to read "known mathematics as it is today predicts (and proves) that there are things that can't be solved using known mathematics as it is today."
I don't feel that I can make statements about 22nd century mathematics, because I can't foresee well enough what it will be like. Nor can I anticipate the mathematics of an alien civilization (if any exist and if any of them have something we would call math.) These things are fun to speculate about but it is risky to make grand universal pronouncements about them when one really doesn't know the boundaries.
I could be wrong. Maybe Tom has a better grasp. Maybe one can make universal statements valid for all time about this kind of thing, but I feel reluctant to at present.
marcus said:Tom's post suggests that a "Final Theory" might very well not exist----just, at best, a progression of better and better theories.
Theories are human artifacts, we cannot know our future and we may continue to improve our theories without ever reaching a final one.
If there is no Final, then there is nothing "beyond" Final. The words "beyond Final" are meaningless.
And why do you say "beyond Final" would be "no longer describable by math"?
What is mathematics? You cannot say what it is or what it may become in future. You cannot specify its limits.
Math is one possible extension of human language. It happens to be adapted to formulating empirical models and it keeps on evolving and growing.
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As far as we know, mathematics has a purely human significance. It is a human creation, just like spoken languages: like Greek, or French, or Chinese.
It has no universal significance, any more than, say English does. It would be foolish to try to base a theology on considerations of a human artifact, or so I think anyway.
It seems to me that you Varon are ill-advisedly "groping for gaps". We frequently encounter people searching for a Gap where their idea of God can sit. They try this or that Gap as a temporary place to situate a gap-god idea. It seems to me a futile and inept exercise.
So you Varon seem to fall into this pattern: currently exploring the imagined Gap which is "beyond" the nebulous idea of the "Final Theory". The latter might very well not exist and would in any case be a human artifact formulated in some future extension of human language.
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I find it more interesting to speculate about the existence of aliens.
Could there be other living organisms which have for instance...
...well, might some of them, say, if they exist, have discovered Planck's constant?
Does Planck's constant have a kind of rough approximate cross-cultural universality? In the sense that something like it eventually gets discovered a lot of times by various other forms of life (if there are any.)
Varon said:you said it's categorically and 100% certain that all can be explained by math, including Penrose idea of brain and consciousness and everything...
Roger Penrose who said the brain processes was noncomputable.. that is.. consciousness is beyond math (and can never be modeled by math)
marcus said:Where do you think I said that? Could you quote the exact sentence? I'm curious how you got that idea.
What I thought I said was that math has no fixed essence. It is an evolving growing human language. We cannot know our future, so in particular we cannot know the limits of what can and cannot be described.
I wouldn't be apt to say what you attribute to me because a categorical statement would presume knowledge of the future evolution of the language and what will or will not be expressible/explainable.
My attitude here is skeptical agnostic about capabilities of human language and its symbolic extensions. As I said, I don't think your original question made sense.
It does not follow that if some process is noncomputable (say by a Turing machine) it is "beyond math" and cannot be modeled.
Modern math deals with lots of stuff which is technically not computable, say by a finite automaton in a finite time. That's part of the fun, these days.
Indeed quantum mechanics itself models processes which are not deterministic and as far as we know are not computable.
You had better quote the exact words of Penrose. You may be confused about what he's saying, or over-interpreting. Popular books often mislead people.
Or Penrose could have been wrong. Many people think his book about consciousness was below par, not up to his usual standards. I haven't read it. So I would need a quote. Maybe you can find a link to the passage in question in google books.
Varon said:... indeterministic is many magnitudes worse than QM, and integers and numbers don't even have precedence or logic. But from this emerge quantum mechanics and general relativity because of symmetry breaking of this mathless unreal no ontology beyond the beyond realm of pure chaos.
marcus said:This sounds like poetry to me. It is an intense vision of fertile illogical turmoil.
If I were you I would simply admit that this is your own vision and stop pretending you can support it with Penrose.
At this point I would say don't bother to look in your attic for Penrose consciousness book.
This is just my two cents worth of advice. Save yourself the trouble. I don't see how there is any chance that Penrose ideas would support such extreme regard for utter chaos.
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Lee Smolin, as I recall, or someone in his circle, has toyed with a scheme where both geometry and quantum mechanics arise out of total connectivity (or if you like total chaos) by evolution according to some rules which in effect favor breaking connections and smoothing things out.
QM arises in this scheme from "disordered locality", the residue of connectivity that didnt get smoothed out.
Varon said:And this can still be modeled by math. Ok. So if we discovered the theory of Quantum Gravity. They say it can tell what happens 1/10^10^100000 seconds after the Big Bang. But I guess quantum gravity won't help us understand what occurred prior to the Big Bang, isn't it when you have to admit that math may lose its predictive power or even usages at T=0 when Space, Time and Matter don't even exist.
isn't it when you have to admit that math may lose...
But I guess quantum gravity won't help us understand what occurred prior to the Big Bang, isn't it when you have to admit that math may lose its predictive power or even usages at T=0 when Space, Time and Matter don't even exist.
petm1 said:... Trying to visualize prior to big bang is not predictive power it is prior conditions.
Quantum spacetime is a theoretical framework that combines the principles of quantum mechanics and general relativity to describe the fundamental nature of space and time at the smallest scales.
In quantum spacetime, matter, space, and time are no longer treated as separate entities, but rather as interconnected aspects of a single unified system. This framework allows for a deeper understanding of how matter and energy interact with the fabric of spacetime.
Exploring quantum spacetime is crucial for developing a deeper understanding of the fundamental laws of the universe. It has the potential to provide us with new insights into the nature of gravity, the origins of the universe, and the behavior of matter at the smallest scales.
There are several theoretical and experimental approaches to studying quantum spacetime. Some scientists use mathematical models and equations to explore the theoretical implications of this framework, while others conduct experiments using high-energy particle accelerators and telescopes to gather data and test hypotheses.
Although quantum spacetime is still a theoretical concept, it has the potential to revolutionize our understanding of the universe and have practical applications in fields such as quantum computing, space travel, and energy production. It could also lead to the development of new technologies and materials based on the properties of spacetime at the quantum level.