Tegmark's Mathematical Universe

Theories involving the idea of spacetime as a continuum are indeed rather naive in that such theories ignore the qualitative difference between the ideas of space and time. The idea of the curved space is really quite naive and the idea of spacetime relativity is so confused.

There are clear differences between the classical Galilean/Newtonian/Maxwelian ideas of the transformations of motions (velocity or motion transformations) and the Einsteinian idea of transformations of space and time (spacetime transformations).

The classical view assumed the space dimension as an absolute/unchanging background container of the corporeal substance of existence in which motion transformations are wrought, and the classical assumed the time dimension as an absolute/unchanging background container of the abstract instance of existence in which duration transformations are wrought. The substance of existence was considered ethereal (Maxwell's ether) and that the instance of existence was considered ephemeral.

Einstein's idea that the ethereal substance of existence does not exist advanced the idea that the space dimension itself is that which is subject to the transformations, and his assertion that time is a continuum with space also advanced the idea that time dimension itself is also subject to the transformations. Thus, essentially the modern assertion is that the substance of existence is the space dimension itself and the instance of existence is the time dimension itself. Hence, the idea of spacetime transformations - which apparently means that space is ascribed the motions and time is ascribed the motions with the idea of duration being explained away or done away with according to the destruction of the idea of simultaneity. These ideas were of a new kinematics that abandoned the classical assumptions and the common sense perspectives. Einstein's weird kinematics is a departure from the classical kinematics.

The classical views of the corporeal motion transformations (or curvature of motions) wrought on the substance of existence within the space dimension and of the abstract duration transformation (or passage of instants) wrought on the instance of existence within the time dimension remain very much in the common sense perspective. However, the popular interpretations of the mathematical formulations persist in an abject salaam to the Einsteinian ideas of mixed-up spacetime transformations, which is why our science cannot seem to get its act together.

Most of the mathematical formulations in our physics can readily be interpreted as descriptions of the phenomena (the corporeal) in the existence according to the idea of motion transformations and of the noumena (the abstract) in the existence according to the idea of duration transformations, which are rather classical common sense ideas. Einstein's famous formula E=mc2 for the mass-energy equivalence is actually of the idea of motion transformations. The ideas of linear motion transformations and tensor motions transformations are readily interpreted from the formulations, and relating these are apparently enough for a description of the dynamic physical universe. Establishing an understanding of how information is processed would also allow a comprehensive view involving the phenomena (the corporeal/physical reality) and the noumena (the abstract reality) in the existence, which quite covers everything there is in the existence.

It would be lovely if I had grant money to spend for the time to do the formal research and presentation of the idea of kinematic relativity, which is the more sensible idea instead of the idea of spacetime relativity. But grant money for a formal research on this sort of thing and for one who is not really a science guy is hard to obtain; and, as it is, all I can afford is my website where I have some discussions on the idea of kinematic relativity and the idea of motion transformations owing to curved motions. Perhaps one of these days I could figure out how to (a difficult thing since I am not currently connected to the academe) and finally get around to submitting a research proposal (perhaps to FQXi) that will be worthy of an ample grant for the kind of formal research and presentation that I have in mind.

If we are looking for a fundamental level, we do not stop at something that we know comes from simpler principles. Mathematics find their origin in rules of logic. Rules that are observed, followed and obeyed in all realms and theories. These are the real rules the universe follows, not our laws of physics that actually rule our observations of the universe. The observation is not the universe...

Lets look for the logic of things, not just their observational description.

Marcel,

I've posted the following at http://en.wikipedia.org/wiki/Talk:Multiverse

Its a continuation of my post above.

Some parts of Max Tegmark's theory "all structures that exist mathematically exist also physically" CAN BE TESTED by carefully designed internet routing software and patterns of information flowing through it. Some people say "universe" only includes the present, but if the universe equals the total of math, there would be no limits on what can be experienced. You could change the laws of physics because all possible laws of physics are a subset of math. Consciousness and time would also be a subset of math. The "Global Consciousness Project" has already demonstrated unexpected results from their quantum-hardware-generated random numbers.

If the universe equals all math, then we should be able to write a reasonably short Lisp program to run on the Lisputer software and verify the Lisputer is executing in the same way the "laws of physics" are executing, by verifying that the Global Consciousness Project's "random" numbers become less random at that time. The Global Consciousness Project has years of data (about patterns some times and lack of patterns other times, in their generated "random" numbers) to compare it to. We must be careful to cover all possibilities, but if the Lisputer demonstrates an ability to change those random numbers, then we should take that as evidence that Max Tegmark is right, unless later a flaw is found in the test setup or assumptions made in designing/interpreting the test.

http://noosphere.princeton.edu QUOTE: The Global Consciousness Project, also called the EGG Project, is an international, multidisciplinary collaboration of scientists, engineers, artists and others. We collect data continuously from a global network of physical random number generators located in 65 host sites around the world. The archive contains more than 10 years of random data in parallel sequences of synchronized 200-bit trials every second." Our purpose is to examine subtle correlations that may reflect the presence and activity of consciousness in the world. We predict structure in what should be random data, associated with major global events. When millions of us share intentions and emotions the GCP/EGG network data show meaningful departures from expectation. This is a powerful finding based in solid science. END QUOTE.

The following 2 softwares are still being planned and do not exist yet, but what they will do is very simple. The few lines below should be enough for you to understand why those softwares will be able to test Max Tegmarks theory, when I finish building those 2 softwares. I must make an exception on Wikipedia's "unbiased" rule, because claims have been made against Max Tegmark's theory being untestable, and I am the only one who has any idea how to test it. There is a policy against "orginal research", but this is directly based on Tegmark's theory for the purpose of testing it. If what I write here is to be removed, the claim that the theory is untestable should also be removed. Both should stay because testability (falsifiable) is an important part of every science theory.

http://sourceforge.net/projects/lisputer QUOTE: Lisputer "Don't panic". Based on Max Tegmark's theories, a high-level quantum prog-lang for solomonoff, bayesian, determinism, nondeterminism, Global Consciousness Project. Plugin for Schrodingers Network Router. Recursion controls blur/sharpen of multiverse END QUOTE.

http://sourceforge.net/projects/schrouter QUOTE: Schrodingers Network Router Research framework for interactions between UDP packets as exponential amounts of uncertainty build up in divergently branching recursions (EQ, XOR) through many computers on the Internet. Set AI goals more/less uncertainty for multiverse blur/sharpen. END QUOTE.

(repost from blog)

Science is empirical. What does it mean? It means that we recognize not knowing about the underlying reality. It means that we accept this ignorance because we have found about 200 years ago a pragmatic approach to this situation. We simply treat this universe as a black box. We ignore the content of the box and concentrate our study on our interaction or experience (empirical) with the box. By studying our experiences of the box we have come up with regularities and some possible images and ideas of what the box contains. These are our laws of physics and the models that we can infer from them. But no matters how pointed our empirical method is, no matters how sharp and detailed our models are, they are still modeled and framed on the requirements of proof within the empirical system. In other words, the empirical method was meant to study our experience of the box, never to find its content, which must be addressed in a metaphysical approach. No matter how wonderful our science may appear, it is just a small portion of what can be done and known. Without knowing the content of the box, we do not have any idea of what we are really doing. This is the limit of physics. We don't do or understand as much as we could and should.

Once we understand the Nature (substance and Cause) of the content of the box, we may resume doing physics knowing and understanding what we are really doing. We will do much better than we are now. So, this is a temporary limit. It would be very hard to argue against the need to understand the content of the box. And the content of the box is by definition outside the domain of science. The right tool for that domain is metaphysics. I do not see any other choice. This accepted ignorance or blindness by convention must stop. Everything is now in place and available to answer the question.

Marcel,

Florin,

Before we even start an argument here, there is already a good side to this exchange. If/if you are anything like me, you re-read the other essay more in depth, past the simple cursory reading. I did so and revisited the three principles. The choice of this forum is in line with both our essays.

Marcel,

Marcel,

I am glad we can discuss those issues here. Let me start with a few observations.

Observation 1: in some cases math is not only a model of reality, it is reality. Case in point: Minkowski space. It is impossible to accelerate any object faster than the speed of light "c" or to transmit information faster than c. Mass and spin are related to the representations of the Poincare group.

Observation 2: After Galileo, physics is an experimental science. This means that we validate our descriptions of nature against experiments. Beautiful self-consistent theories were discarded to the trash bin because nature said something else.

Observation 3: Math is about abstract relationships regardless of their realization. For example the rules of complex numbers can be modeled by the Argand plane or by a 2X2 matrix representation.

I hope you agree with all of the 3 observations above. Then the question becomes: can we describe scientifically reality, or is this the job of metaphysics (or God)?

I contend that if axiomatizing physics is achievable, then we can solve the nature of reality in a mathematical way. This means that there will be a mathematical proof which anybody can check about the necessity of existence of nature as we observe it. If this proof is ever going to be reached, then we no longer need to have physics as an experimental science, all we need is to see if our models of reality can be made a consequence of the axioms of nature. If yes, then we are guaranteed that they will be experimentally verified as well. Is this far fetched? Not at all. In smaller slices of reality this happens already. (Take a grounded infinite conductor plate and position an electric charge at a distance d. Compute by Maxwell's equations the attraction force the charge experiences and compare it with experiment. They agree and we do not need to doubt our mathematical calculation because we know that Maxwell's equations are valid.)

But for physics axiomatization, we are talking about whole nature and we no longer have the luxury of partial models (like Maxwell's equations above). By observation 3, can we find a grand mathematical equation which describes the whole nature? Suppose the answer is yes. Then write it down on a piece of paper, say "fly" and a new universe will start. Is this possible? Of course not, they are only marks on the paper, not another universe. So the answer is NO. Therefore we have:

Consequence 1: Starting from pure math is impossible to axiomatize physics.

Let's now use Observation 2. By observing small slices of nature, can we infer something about existence as a whole? Maybe yes, maybe no, nobody was successful so far. But the boundary of knowledge keeps advancing, and for now it is a matter of personal taste or belief of what we think the answer is ultimately going to be. But if it is a matter of belief, then we are in the realm of metaphysics already and your argument fits well in here. Lets go with it and infer:

Consequence 2: starting from experiments and models of reality is impossible to come up with a definite answer to the question "what is existence"?

Time now to use Observation 1. In some cases math is reality and being math, there should be some way this can be derived mathematically. If starting from experiments/reality is not the way to go, and if starting from pure math is not the way to go either, the only remaining option is to start from both. Here we recall the "unreasonable effectiveness" of math to describe nature. Reality and math are made out of the same building blocks, just like liquid water and ice. Maybe the place to start is to seek the similarities and differences between math and reality. Scholars already studied the similarities but ultimately got stuck in Consequence 2.

Heuristic rule: seek the differences between reality and math (see here my essay contest). Those differences act as filters selecting only a very few "unique" or "distinguished" mathematical structures from the infinite world of math. This is a work in progress and now this problem becomes a mathematical well posed problem and my essay is dedicated towards this aspect. But there is an entire different discussion from the philosophical point of view.

So assume (big assumption) for now that the math case is settled and indeed we did have achieved complete physics axiomatization and let's explore the philosophical consequences.

First question. Why did this work? Suppose you are God and want to create the world. What do you want to have? You have your building blocks (the mathematical structures which existed before time in an acausal Platonic world), but those blocks are valid only within a limited domain (their axiomatic framework). The first thing you want is to have existence independent of context (see the universal truth property). The second thing you want is to allow interaction in your world, otherwise it is only a static frozen mathematical structure like say set theory. So here comes the composability principle. By now you can create a clock, or a software program, all nice things, but it needs something else: free will, or infinite complexity (see deformability principle).

Now second question: why there is something rather than nothing. Answer: because it can be.

Third question: Why is our universe happening only once? Are there multiverses? Where they come from? For this God needs to eliminate the universal truth property. Why? Because it is this requirement that confines us to a particular universe. So what do you get when you eliminate it? Surprise: hyperbolic quantum mechanics. I speculate that the proper way of solving the birth of our universe is in a hyperbolic QM framework. In this theory, time does not exist.

Forth question: what is God? It is the platonic world of math.

Final question: what is reality? It is the platonic world of math rearranged to achieve the 3 requirements of reality: independent existence, unrestricted interaction, and infinite complexity.

Regards,

Florin

Tegmark advances the notion of a first order calculus which skirts the problem of Godel. I am not sure that Tegmark's ideas are particularly workable in physics, for I fail to see how we can empirically test it. I have similar questions about axiomatizing physics. Back in the 1980s there was a movement towards axiomatic field theory, but none of that managed to come up with anything particularly valuable for how people actually do science.

Cheers LC

Lawrence,

I think axiomatizing physics can have two outcomes: 1. prove our universe could be only in the way we observe it, 2. help open up new roads into existing puzzles like quantum gravity.

First, what does it mean to axiomatize physics? There are 2 approaches: Tegmark's which take the standard definition of axiomatization (and of course runs into head on problems with Gödel) and my approach which uses the axioms not to derive the useful mathematical structures applicable in nature, but to select them from an infinite set of available structures.

There is a subtle point to be made about proving uniqueness of nature. All mathematical structures are unique. There are no 2 Pythagoras theorems. A better term is "distinguished". We can have a Minkowski space with 1 time and 429 spatial dimensions, but the 1+3 space is distinguished by nature.

The old-fashioned axiomatization approach of the axiomatic field theory did not yield much except increased rigor. This was expected as you get out what you put in (remember bootstrap theories). The ultimate roadblock stems from Gödel and you can avoid it with Tegmark's approach for example, but I believe it will be ultimately proven as too restrictive as well. But when one uses axioms as requirements instead, Gödel's limitation no longer applies. As requirements, the axiomatization of physics is achieved in meta-mathematics.

Florin

Florin

Wow! You do not start in low gear ...!

Observation 1:

Maths are the metric extension of logic. Logic is therefore more primitive, more fundamental than mathematics.

The metric extension pertains to the multiple identities presented by the observer status i.e. our need to know in relation to our experience. It describes our relationship with the box, not its content. Mathematics are not stuff or a substance you can build something out of.

Observation 2: What nature is and what it says through our experience is very different. Our experience requires that we build space and time to position our experience. ...we validate our description of our reality against experiments, the Nature of which escapes us (black box).

Observation 3: "Math is abstract relationship " .... Is contrary to observation 1: .. " it is reality"

Here is my position on the God thing/argument:

If you truly believe in God, you know better to discuss its status under a microscope..

If you don't believe in God ... then what are you talking about exactly?

This is why I don't discuss the matter

Reality: Physics is the study of our Reality as provided by our experience. We create our reality according to our experiences. So, what is the universe like when it is not modeled by our human experience ? The Nature of something is what this thing is by itself outside the scope and modeling of our experience. The concepts of "reality" and "nature", "nature of something"..etc. are the most commonly confused concepts of all...

"can we find a grand mathematical equation which describes the whole nature". It would be a description of our experience, not that of the universe or underlying reality. A description is a complete metric sentence that does not need or even allow causality. Lets make this clear: our reality is the sum of our experiences, a binary relationship between the underlying reality and the observer, senses and mind. Our reality is this relationship that exists only with us at one end of it. So, the Nature of the underlying reality, as something "by itself", will never be described in terms of our experience of it. Our reality is not a state, but is a relationship, a relationship highly contingent on our position, size, senses and mind. In order to understand the universe, we have to see past the transformation and complexity we introduce into the data.

Natural metaphysics pertains to the study of substance and cause of the underlying reality i.e the content of the box. No belief, souls etc.

Consequence 1: As described in my essay, science is a collection of truth systems that all converge on something out of reach; the underlying reality. Because all truth system are logically incompatible with each other, the axiomatization of all of physics is, in my opinion, impossible ( i.e. no physical TOE) On the other hand, the underlying reality can be axiomatized under natural metaphysics, as the unreachable cornerstone of all our experiences.

"The first thing you want is to have existence independent of context (see the universal truth property)"

Why in the world would you want this? We make this distinction/ partition; the universe doesn't.

The three principles:

Universal truth: Logic is the rule of the universe and this is why it is equally valid inside and outside the box in

maths, science etc. It is the one common denominator in all we do and know. Pretty obvious?

Composability: A universe based on logic accepts only one substance and only one cause and is therefore

a monistic system, fully composable(?).

Deformability: Substance, cause and logic form a completely fluid system, fully deformable.

We could not have more opposite ideas! I say that the whole universe is made of an explosive process/substance that we call the passage of time. Incidently, I show in my essay the logical creation of the universe and it allows only one substance to exist; the passage of time. Just try to create the universe out of nothing without resorting to the logical rule of non-contradiction! Good luck!

Conclusion:

1) I think that in general, we have a poor semantic use of some terms carrying multiple meanings and that need constant limiting adjectives, like time, nature, reality, empirical, truth, substance, cause, etc. For example, time means many things and if unspecified, it means everything and nothing specific.

2) Natural metaphysics can be built in a bottom-up approach as I did in my essay. It doesn't require one reject anything from physics. It explains logically what is observed empirically, the cause but not the metric.

These explanations support present descriptions and can help physics to evolve beyond its intrinsic limitations; the point of view of the observer.

Marcel,

Marcel,

There are so many things I can discuss with you, but I'll pick and choose what I think are the most important differences between our views.

"Because all truth system are logically incompatible with each other, the axiomatization of all of physics is, in my opinion, impossible ( i.e. no physical TOE) On the other hand, the underlying reality can be axiomatized under natural metaphysics, as the unreachable cornerstone of all our experiences."

Indeed, all truth systems are logically incompatible with each other and this is the essence of Gödel's result about the impossibility to have a TOE of math. However, a TOE of physics is an entirely different matter. Find one logical inconsistency in nature. There is none. Order the platonic world of math in a way that avoids all contradictions and you get the necessity of time (among other consequences). Time is a necessary condition to avoid self-referencing contradictions.

"[The first thing you want is to have existence independent of context (see the universal truth property] Why in the world would you want this? We make this distinction/ partition; the universe doesn't."

There are two definitions of truth: (1) the mathematical definition: a statement is true if it can be derived from the axioms (2) the physical definition: true is something corresponds to reality. The mathematical definition is very narrow and the same statement is true or false depending on the axiomatic context. 2+2 = 4 is true in the usual arithmetic, but it is false in the addition modulo 4 for example. But in nature, truth has a much larger reach and this is remarkable. It is this larger reach which gives reality its ontological value independent of any observers.

"We could not have more opposite ideas! I say that the whole universe is made of an explosive process/substance that we call the passage of time. Incidently, I show in my essay the logical creation of the universe and it allows only one substance to exist; the passage of time. Just try to create the universe out of nothing without resorting to the logical rule of non-contradiction! Good luck!"

Not quite, I use to think in the past along your lines, but time by itself while necessary, it is not sufficient.

The key of explaining the birth of our universe is in an acausal domain and I think is linked with the multiverse idea. If the 3 principles guarantee the uniqueness of our universe, then to get to the multiverse scenario we need to break this uniqueness, meaning removing one or more of the 3 principles. And indeed there is a mathematical solution called split-complex (or hyperbolic) QM which has inequivalent representations (unlike standard QM). There are no logical contradictions, everything is consistent within a representation, and I believe this is the mathematical starting point of the multiverse investigation.

"1) I think that in general, we have a poor semantic use of some terms carrying multiple meanings and that need constant limiting adjectives, like time, nature, reality, empirical, truth, substance, cause, etc. For example, time means many things and if unspecified, it means everything and nothing specific."

This was the main point of Wittgenstein.

"2) Natural metaphysics can be built in a bottom-up approach as I did in my essay. It doesn't require one reject anything from physics. It explains logically what is observed empirically, the cause but not the metric."

As Wittgenstein put it, philosophy is mainly playing with words. What we need is unequivocal mathematical proof of our statements, in other words, we need physics axiomatization. A proof, is a proof, is a proof. When axiomatization is achieved, then anybody, even a machine can mechanically check the validity of the proof. No more fuzzy semantics.

I believe I showed the way of how to do it. Compare math and reality. Extract core characteristics of reality: (independent ontology, unrestricted interaction, and infinite complexity). Then derive mathematical consequences from them. Prove the necessity of time, quantum mechanics, space-time in 4 dimensions, electroweak symmetry. This is already done. To do: Eliminate all supporting assumptions. Attempt to prove the rest of nature: strong force, standard model, quantum gravity, cosmology. Then physics axiomatization will be complete.

What I propose is first and foremost a paradigm. The existing mathematical results were all obtained as part of various unrelated research programs with their own motivation. But together they enforce the hope that the rest of the program will be ultimately successful.

Florin

Hi all ,

That seems interesting about the axiomatization but if the referential is not good thus all is false .The road is false ,the gauge too and the math tools too .

When a theory is correct ,we see its applications and laws everywhere .

Only the physics explain the physicality .The maths at this moment imply confusions .

The metaphysics too needs a balance .If the fourth dimensions are inserted thus where are we going ,Einstein is really bad understood .It is probably the reason why the distorsions and bizares things are inserted .

The toe doesn't exist due to the evolution and thus the lack of mass.Only a GUT IN OPTIMIZATION AND EVOLUTION CAN BE ACCEPTED.The toe are like a search of credibility in the sciences community ,thus the individualism is a problem .

It exists only one axiomatization and we are youngs at the universal scale .

Dear Florin ,

you say

Then physics axiomatization will be complete.......impossible because the line time constant is a reality thus the evolution too thus our unknew too and walls ............

Regards

Steve

Marcel,

There are so many things I can discuss with you, but I'll pick and choose what I think are the most important differences between our views.

"Because all truth system are logically incompatible with each other, the axiomatization of all of physics is, in my opinion, impossible ( i.e. no physical TOE) On the other hand, the underlying reality can be axiomatized under natural metaphysics, as the unreachable cornerstone of all our experiences."

Indeed, all truth systems are logically incompatible with each other and this is the essence of Gödel's result about the impossibility to have a TOE of math. However, a TOE of physics is an entirely different matter. Find one logical inconsistency in nature. There is none. Order the platonic world of math in a way that avoids all contradictions and you get the necessity of time (among other consequences). Time is a necessary condition to avoid self-referencing contradictions.

lebel:1)"Find one logical inconsistency in nature. There is none" The universe obeys logic-is operational on logic = only one substance allowed!

2)"Time is a necessary condition to avoid self-referencing contradictions." it has to be so in all points, everywhere.

1) + 2) = universe all made of time operating on logic

"[The first thing you want is to have existence independent of context (see the universal truth property] Why in the world would you want this? We make this distinction/ partition; the universe doesn't."

There are two definitions of truth: (1) the mathematical definition: a statement is true if it can be derived from the axioms (2) the physical definition: true is something corresponds to reality. The mathematical definition is very narrow and the same statement is true or false depending on the axiomatic context. 2+2 = 4 is true in the usual arithmetic, but it is false in the addition modulo 4 for example. But in nature, truth has a much larger reach and this is remarkable. It is this larger reach which gives reality its ontological value independent of any observers.

lebel: Again, it is a matter of definition: For me a truth is an absence of choice. A most certain truth is an impossibility. My essay is based on that definition.

"We could not have more opposite ideas! I say that the whole universe is made of an explosive process/substance that we call the passage of time. Incidently, I show in my essay the logical creation of the universe and it allows only one substance to exist; the passage of time. Just try to create the universe out of nothing without resorting to the logical rule of non-contradiction! Good luck!"

Not quite, I use to think in the past along your lines, but time by itself while necessary, it is not sufficient.

The key of explaining the birth of our universe is in an acausal domain and I think is linked with the multiverse idea. If the 3 principles guarantee the uniqueness of our universe, then to get to the multiverse scenario we need to break this uniqueness, meaning removing one or more of the 3 principles. And indeed there is a mathematical solution called split-complex (or hyperbolic) QM which has inequivalent representations (unlike standard QM). There are no logical contradictions, everything is consistent within a representation, and I believe this is the mathematical starting point of the multiverse investigation.

"1) I think that in general, we have a poor semantic use of some terms carrying multiple meanings and that need constant limiting adjectives, like time, nature, reality, empirical, truth, substance, cause, etc. For example, time means many things and if unspecified, it means everything and nothing specific."

This was the main point of Wittgenstein.

"2) Natural metaphysics can be built in a bottom-up approach as I did in my essay. It doesn't require one reject anything from physics. It explains logically what is observed empirically, the cause but not the metric."

As Wittgenstein put it, philosophy is mainly playing with words. What we need is unequivocal mathematical proof of our statements, in other words, we need physics axiomatization. A proof, is a proof, is a proof. When axiomatization is achieved, then anybody, even a machine can mechanically check the validity of the proof. No more fuzzy semantics.

lebel: "philosophy is mainly playing with words" which is what gave philosophy a bad name in the first place...

I believe I showed the way of how to do it. Compare math and reality. Extract core characteristics of reality: (independent ontology, unrestricted interaction, and infinite complexity). Then derive mathematical consequences from them. Prove the necessity of time, quantum mechanics, space-time in 4 dimensions, electroweak symmetry. This is already done. To do: Eliminate all supporting assumptions. Attempt to prove the rest of nature: strong force, standard model, quantum gravity, cosmology. Then physics axiomatization will be complete.

lebel: Philosophy and science used to be one and the same (PhD). This present schizo approach leaves pieces of the puzzle in the hands of two different group of people. Science build truth systems by adding truths. Philosophy produces opinion that add up only to more opinions. This means that in metaphysics, you get it all in one shot, or you don't. It must be self sustaining and cannot use any previous work or be based on citations. This is how it works. The core question is always the same; What do you want? Create one more description or to understand the meaning of all descriptions. You look for description, I look for the real stuff; substance and cause of the universe.

What I propose is first and foremost a paradigm. The existing mathematical results were all obtained as part of various unrelated research programs with their own motivation. But together they enforce the hope that the rest of the program will be ultimately successful.

lebel: Your essay could win for summarizing well the work on the subject. But your goal is that of a physicist. You are condemned to the hopes of a physicist, hopes that share the limits of physics. The exercise of finding the limits of physics was not to find more physics but rather to find out what comes next, after physics. What is physics missing and in need of?

I wish you well, Marcel

Florin

Florin,

I tend to think that algorithim-atizing physics is preferable to axiomatization. The question to my mind of greater importance is how quantum information, eg Q-bits and Q-n-tuples, are preserved and the conservation laws they obey. In this sense the universe may preserve them according to some quantum error correction code.

I read a couple of Tegmark's papers some years ago. I am sometimes accused of being speculative and of proposing conjectures, but Tegmark's ideas are way out there. So I will confess I have trouble seeing these ideas as at all empirically verifiable, even in principle. Yet as I recall Tegmark did restrict the physics aspect of this to some first order calculus, instead of up to Lambda calculus, so that the Godellian problem does not impact his program. I

Cheers LC

Marcel,

I agree that there is a deep connection between time and logic. I do not agree that truth implies the absence of choice although it seems plausible. The problem is the fuzziness of the definition of "choice". A quantum mechanics wavefunction may have a definite (true) value in some region, and still there is a choice available as QM is probabilistic. However, if you narrow the definition of "choice", your argument becomes valid.

"Philosophy and science used to be one and the same (PhD). This present schizo approach leaves pieces of the puzzle in the hands of two different group of people. Science build truth systems by adding truths. Philosophy produces opinion that add up only to more opinions. This means that in metaphysics, you get it all in one shot, or you don't. It must be self sustaining and cannot use any previous work or be based on citations. This is how it works. The core question is always the same; What do you want? Create one more description or to understand the meaning of all descriptions. You look for description, I look for the real stuff; substance and cause of the universe."

I am certainly not a philosopher, but new ideas do not develop in a vacuum. All research programs have a fuzzy philosophical side called heuristics, a really fancy word for "gut feeling". It is this heuristics that guides us during the search in the dark, until we manage to prove new results. Sometimes this is fool's gold, sometimes it is the real deal, but we do not really know until we have the math on our side. Now I have found my heuristics and I do not feel the need to polish it at this time. It may not be at the required level of sophistication, but it is good enough for me. What I really want to do is to mathematically prove that I am right.

I wish you well too, Florin

Lawrence,

I have recently discovered the wonderful results of Bob Coecke and I think you may appreciate his approach. In short, he starts from the isomorphism between the tensor product of 2 Hilbert spaces with the vector space of linear transformation between the 2 spaces. From this he develops a high level pictorial approach to QM and finds links with a special kind of logic (which forbids information duplication and deletion), algorithmic theory, and category theory. Not quite error correction, but a high level language where certain QM theorems are given trivial proofs.

About Tegmark's approach, he runs under Godel's radar, but this is a weakness: the approach is not rich enough to model the entire nature. What comes to mind is the brain-in-the-vat argument. How can we prove that we are not for example just a computer simulation in some supercomputer somewhere in a vastly different type of reality? I believe the answer is complexity in the AIT sense. If AIT complexity is not infinite, then we are a brain-in-a-vat/computer simulation, if not, we are the real deal. Proposals that avoid Godel by postulating computability are just too simplistic to model nature.

Regards,

Florin

Hi ,

I am sorry to use this thread.I read your posts and I try to encircle your lines of reasoning .I see a kind of confusion between the computing and the universality .

In an extrapolated model (and simulations),the variables and parametrs are specifics ,correlated with the idea of the conceptor ,here the computer .The informations and the linear transformations thus are invented by humans .Thus we can change the laws .It is different I think .

Never a computer will be able to create life ,and more the biological system .Why ? bECAUSE SIMPLY THE TIME EVOLUTION MUST BE CONSIDERED with the weak polarisations near centers of gravity since the begining .

The computer in conclusion is just a tool .The mass ,the time ,...can't be invented by a computer ,physically speaking .

Thus we return about the essentials ,the referential and the topology with the universal correlations and laws must be respected in all systems.

I agree that all can be explained with maths ,but if and only if the good parameters are inserted .I have nothing against math but the physics need some limits .

Regards

Steve

Florin,

I have been looking at some of Coeckes. They are a bit on the long side. Yet they do seem to center around categorical structures (functors) with QM. I think that quantum mechanics and general relativity have a partial functor. A Schold's ladder construction has a Galois GF(4) logic, as does the structure of a spin-1/2 system in QM. I will have to study these further. He seems to work with the Naimark approach to linear spaces which leads to noncommutative systems and geometry.

I have thought that underlying all of physics might be a Godelian nest of self-referential states, which form a sort of self-referential chaos. I think this is maybe the ultimate end of physics, which might exist at the Planck scale with maybe an asymptotic "onion layering" of structures above it. String theory at ~ 10L_p is one such layer we currently have some possible understanding of and there might be layers beneath that. Maybe there is an infinite nesting of such layers as one approaches the Planck length. So Godel might be lurking underneath things in the end. I am not sure whether we can ever plumb the depths of particle physics and cosmology to reach that.

Cheers LC

Lawrence,

Category theory is useful in physics mostly because it captures well the idea of a tensor product. Personally I am inclined to investigate in depth Hopf algebras. In a 10,000 feet view, a Hopf algebra has a build-in zoom-in operator (the product) and a zoom-out operator (the co-product) and this makes them useful in many ways, including renormalization group approach and supersymmetry. And non-commutative geometry uses them extensively. By the way, non-commutative geometry has string and LQG features as well. I believe that the central question of physics today is deciding if supersymmetry truly exists in nature. If invalidated by experiments, it will simply kill string theory. One argument against it is the fact that the standard model is maximally chiral. Pure chirality appears only in simple groups; increasing the complexity can easily generate partial chiral symmetries. Combined with an anomaly cancellation argument (to include the strong force as well), all SM may arise from a simpler GUT without supersymmetry. But if superpartners are discovered, string theory would get a major boost.

I agree with the onion metaphor.

Florin

The recent findings of simulatneous arrivals of photons of widely different wave lengths puts a big nix on LQG. The discrete system near the Planck scale predicts an intrinsic dispersion that depends on frequency. The Fermi spacecraft found none of this from a burstar 4 billion light years away. Supersymmetry is also by the Coleman-Mandula theorem the spinorial extension of internal and external symmetries into a single symmetry system. If SUSY fails that would be profoundly disappointing.

Hopf algebra are though interesting. They are significant in Wilson loop or line integrals and connections to knot theory. I notice some Hopf algebra structure in Bob Coecke's papers. I have not as yet read them on a hard level yet.

Cheers LC