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While he would be too modest to toot his own horn, there's nothing stopping me from pointing out that 'mad Max' has recently put out a very interesting paper on whether all possible formal systems (and the 'physical' universes that some subset of them describe) are equally 'real'.

I like lots of things about this paper. One part that I worry about -- or perhaps misunderstand -- is the connection with Godel's theorem. Max makes an extended argument that if we exclude all human-centric 'baggage' then the universe must be mathematical, and in particular isomorphic to some formal system. He then limits this to 'Godel-complete' formal systems. But why? My feeling is that exactly what Godel proved is that there are mathematical truths that are not decidable using the formal system within which they are formulated. So the *truth or falsity* of them ('truthiness'?) is (a) baggage-free, but (b) outside of any formal system. So in his scheme is it real or not? I don't know.

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Lee Bloomquist replied on Oct. 13, 2011 @ 20:19 GMT

"Level 4: Other mathematical structures give different fundamental equations of physics" (Tegmark)

To start with our own universe--

Maybe it's close to the point where our fundamental equations of physics are supported by a chosen mathematical structure, but this chosen mathematical structure supports no fundamental equations involving dark matter or dark energy.

It is possible to search for a different mathematical structure that loses nothing gained so far with this chosen mathematical structure, and which may support new fundamental equations involving candidates for dark matter and dark energy.

Something like this has happened before. Abraham Robinson used a tool from logic called enlargements to enlarge the mathematical structure of standard analysis into the mathematical structure of nonstandard analysis. In the process, a new object appeared-- the monad.

To paraphrase p.55 (Non-standard Analysis, Robinson)-- If R is the standard model of Analysis and *R the nonstandard model of Analysis, every mathematical notion which is meaningful for R is meaningful for *R. Every mathematical statement (e.g., every fundamental equation of physics) which is meaningful and true for R is meaningful and true also for *R....

But in the nonstandard mathematical structure, one can say more. It's within the nonstandard statements where one could search for those that involve dark matter and dark energy.

For example, in a monad of spacetime there is a structure I've been calling the Born infomorphism. (The latter term comes from the book Information Flow: The Logic of Distributed Systems by Barwise and Seligman. The distributed system in this case is the monad of spacetime, within which there is as nonstandard past and a nonstandard future. Due to the Born infomorphism, at the time of "now" within the monad there exists a perfect translation from language about nonstandard past into language about nonstandard future.)

Wish I could have made that deadline for the contest about time.

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Well, if we accept the Mathematical Universe Hypothesis (which is pretty neat) then ALL mathematics is "real" -- as that's what the universe, err, is. But that can't be the last word, for a couple of reasons. First, our universe seems fairly simple, at least compared to how complicated it could be if all mathematics were manifested. Second, we run up against G??del's incompleteness theorem. I...

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Well, if we accept the Mathematical Universe Hypothesis (which is pretty neat) then ALL mathematics is "real" -- as that's what the universe, err, is. But that can't be the last word, for a couple of reasons. First, our universe seems fairly simple, at least compared to how complicated it could be if all mathematics were manifested. Second, we run up against G??del's incompleteness theorem. I suspect I know just enough about G??delian incompletenes to get into trouble (and even if I did truly know it, I wouldn't be able to prove I knew it), but I'll offer up some ideas anyway.

G??del's incompleteness theorem is the dagger through the heart of Hilbert's program to build all of mathematics from a simple logical foundation. Real mathematics (what real mathematicians (i.e. not me) do) is usually about proving things (theorems), and those things, including the proofs, can be encoded as numbers and operations between them. Hilbert hoped all true theorems in mathematics, with proofs, could be built up with logic. But G??del came up with this zinger: "This theorem is true but cannot be proven to be true." And there it sits, a theorem, which can be encoded by a G??del number, that is true but has no proof. So any sufficiently complicated formal system, in which these G??del numbers can be formulated, is incomplete since it has true statements that aren't provable.

This incompleteness wouldn't be much of a bother for physicists (who tend not to care much for proofs anyway) except the MUH proposes that mathematics, including proofs, is our long sought Theory Of Everything. So, as far as I can tell, Max Tegmark introduced the Computable Universe Hypothesis in order to dodge G??delian incompleteness. The CUH says maybe the universe consists of mathematics simple enough that G??del's theorem doesn't apply. It's a neat idea, since it also explains why the universe seems relatively comprehensible, but I sure hope it's wrong. If it's right, it implies the universe is finite, and anyone trying to build a TOE out of continuous pieces (like me or them) would have to toss the whole effort and (like him) consider something more like Legos. Now, I've always loved Legos, but they got kinda boring after age twelve or so, and I'd be sad now if that's all there was to play with. So, if we accept the MUH, how do we dodge the CUH? I can think of two options:

1) Live with G??delian incompleteness as part of our universe. This doesn't seem so bad to me, but as a physicist I'm more interested in truth than in proofs. I don't know why it's bad to have things about the universe that are true but not provable. (And it would be frustrating for mathematicians -- which is fun to see as a physicist often humbled by math papers.) I'm hoping someone else here (maybe Janna Levin?) will argue why a mathematical universe would vanish in a puff of logic if there were true things that weren't provable.

2) Limit the MUH another way (with minimal carry-on baggage). I don't know enough math to argue this well -- but I remember that naive set theory had problems with G??delish paradoxes which led to the formulation of axiomatic set theory. Maybe the universe is just a complex mathematical shape, or a geometric automata, that exists and acts in a way describable by a set of mathematical axioms that preclude G??delian self-reference? It's true that we can write down and think about G??del's theorem -- but that doesn't necessarily mean our substrate cares about the theorem, does it?

Anyway, fun stuff to think about.

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My take on why his central thesis is flawed:

http://aeolist.wordpress.com/2007/04/26/confusing-bag
gage/

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What I like most about such ideas is that it demistifies some couterintuitive aspects of arificial intelligence, the subjective aspects about our personal experiences etc. If indeed all mathematical systems are universes in their own right, then consider the (personal) universe that is defined by the formal rules that describes how someone's brain works.

Personal experiences are simply events that happen in such personal universes. We are such personal universes but we find ourselves living inside simulations performed by neural networks in a universe that is accurately decribed by the Standard Model and General Relativity. Presumably this is because very complex universes (that can onlty be specified using a large amount of data) have a small measure while simple universes that can be specified with a small amount of information have a large measure.

In case of our minds, the formal rules are not really how exactly the neurons are connected to each other, that's just the way the program is implemented in this universe. But there also exists a "source code" that describes who we are. The way one implements the program does not matter to the program itself.

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There's also another way to argue that ERH implies MUH than outlined in the paper.

If every mathematical structure exists, we can choose the mathematical structure which approximates our universe so well we could not distinguish it from our own, given that we can not distinguish it; our universe can be described by that mathematical structure and given that there is no way to distinguish it, it actually is this structure.

Now I must agree that ERH is not exactly the same as stating that every mathematical structure exists. It certainly is at least as general a proposition as ERH and it can also be considered as a form of ERH given that mathematical existence implies an external physical existence.

I also do not see how any of this is counterintuitive; given that we would simulate a given SAS (Self Aware Structure) two times in an exact way. It would be absurd for the SAS to state that he was the first or second being simulated, given there is no way to distinguish the different simulations. Only the probability measure can/will be affected. In a broader context I do not like the wording that we would be living in a simulated reality as this is again a absurd statement. Given that we accept MUH, we exist regardless of the fact if we are being simulated or not. Would it not be counterintuitive that only SAS being simulated exist and those who are not simulated do not exist ?

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William wrote: "given that mathematical existence implies an external physical existence."

That is an extremely strong "given", which if true would imply the [in my opinion absurd] consequence that every possible mathematical structure exists in some universe. I also can't think of any good arguments for it.

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Re. Ponder Stibbons, I don't see that it is absurd that every mathematical structure should exist. The hypothesis "all mathematical structures exist" is simpler than "only certain mathematical structures exist" and so is to be preferred by Occam. In fact, the MUH is the simplest possible metaphysics, having no free parameters at all.

Re. Garett Lisi: I don't see that the CUH implies a finite universe. If the computation never stops (halts), the universe will be infinite. One might posit existence as identical with proof. On this analysis the universe is a mathematical proof machine. Godel would imply that there must thus be true theorems (possible universes) that are not provable (never exist).

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Of course math can explain the universe. Even astrology has a math behind it that allows precise calculations of how the stars supposedly influence different people's lives, although they lack an adequate explanation of the physical process involved.

Understanding the universe will require looking at the issue of physical dimensions of reality in strict mathematical terms instead of relying...

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Reason:"In the strict mathematical sense a dimension is a characteristic or variable. The only information the three Euclidean dimensions provide is length, width and height. They provide the location of "points", but cannot provide any further information about the points."

But then Height is relative to a width, and width is reletive to a length?

Thus:"If reality consisted only of these three dimensions, we would see a world in black and white only. Our eyes could only determine that something was in a location or not. They could not determine other characteristics of objects because characteristics like color require additional information provided by other variables." we see a "range" of colours..because each colour is relative to another colour, ie spectrum?

We do not see just black and white, not because there are MORE dimensions, but they are part of a combination, spectrum?

There cannot be more than 3-Dimensions for our physical Universe, at this moment in time, this is not to say that the Universe will always remain 3-D. I believe the Universe to be dynamic, it changes over time, and in the future it will develop "extra" dimensions.

A simple water molocule cannot be placed within a 5-Dimensional space and remain a water molocule?..the stucture of matter within space-time is 3-D. But all of 3-D structures have "edges", these can be viewed as 2-D boundaries, thus as you state, fields or forces help gather matter into 3-D forms.

It is interesting that all of forces/fields are hard to detect..visually that is, because edges can have linearrly finite form, from this perspective, 2-D fields always "surround" 3-D structures.

You cannot find 2-D fields within a 3-D structure, but you can find a 3-D structure within a 2-D field!

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I am not a mathematician and when I happen to read or hear some complicated mathematical issues, I always feel very ignorant, but before falling in a deep depression I react imagining to be in front of a mathematical formula and asking it to show me how it interact with all other formulas to construct and regulate the reality I am living in.

When I see that the formula remain still, I feel better, and realise that, contrary to the formula, my ignorance doesn‚Äôt prevent me to act in a free and constructing way.

Perhaps I am wrong, but my vision of mathematic is that of an instrument that serve its purpose only if is used by an operator, (man, animal and down to the single element of nature)

At this point a question arise: can the single element of nature that uses the mathematical instrument, be considered o represented as a mathematical function?

I don‚Äôt believe so, and I feel backed also by G??del theorem, the operator to correctly operate the instrument, must necessarily be positioned a step higher, (whatever this step higher means)

Am I right? Hope so.

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I agree with Jonathan Colby (may 23, 2007) that the hypothesis ‚Äúall mathematical structure exist‚Äù is simpler than ‚Äúonly certain mathematical structure exist‚Äù, and therefore preferable, I am also convinced that the first would be in better position to represent our reality.

I recon also that my conviction in not a scientific proof, in fact there could be only two way of proving it:

¬? Verify one by one all structures,

¬? Introducing, according to G??del a meta-rule.

Not having a meta-rule, I would be stuck, if it weren‚Äôt for the awareness of disposing, as individual, a partial or limited meta-rule: the possibility of making a choice.

Having the possibility of a choice means that instead of a definite proof, I can propose an hypothesis, verify it, and, if not happy, propose a new and different hypothesis.

With any luck, even if I will never arrive to a definite proof, in meantime I will have proved myself to be real and alive.

Now the question: if all mathematical structure exists, would there also be a structure capable of making a choice like I do myself? In other word produce a partial or limited meta-rule to self-justify it existence? (And therefore partially satisfy the G??del theorem?)

The question is not an easy one, and might be left with many other unsolved theoretical questions, but there is a fact to consider: in this moment our scientific evolution is stuck to a similar problem: how many links can a simple element of nature install with others elements?

Take away the ‚Äúone to one‚Äù possibility, there are only two left:

¬? One to many

¬? One to all

No need to say that the first possibility has been the choice of the traditional science and, at this time, most, if not all, mathematical models respect this choice.

A choice that, due to the fact that it is impossible to give a fixed amount for the ‚Äúmany‚Äù, it is not without incongruence, an incongruence that has been ‚Äúpartially‚Äù overcome by introducing average and probability calculus.

At this point, as there are still many phenomenon of our reality (most of them related to free choice, evolution and complexity) that are difficult/impossible to be represented with traditional mathematical models, the previous question becomes relevant, could the reason be of having chosen the ‚Äúmany‚Äù instead of the ‚Äúall‚Äù?

I certainly realize that the choice of ‚Äúall‚Äù would envisage a reality different from what we are used to, and at the same time it would need adequate mathematical structures (including its‚Äô meta rule) to represent it, but if the proof between ‚Äúall‚Äù and ‚Äúmany ‚Äú is only a matter of choice, and providing hypothesis to support it, be sure that the ‚Äúall‚Äù would be my choice.

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Readers of crime fiction (or other interest-driven novels) know that a dazzling beginning ultimately leads to a disappointing end. Apparently the same happens in The MU. Staring With MUH which should dislodge ERH, it soon adds CUH. Then in VII.G Tegmark candidly admits

"that virtually all historically successful theories of physics violate the CUH, and that it is far from obvious whether a viable computable alternative exists. The main source of CUH violation comes from incorporating the continuum, usually in the form of real or complex numbers". Say goodbye to the CUH and start thinking about the continuum. It was the pride and joy of XIXth century mathematics but in the next century it produced mostly trouble, witness the 'annoying infinities' that Tegmark mentions, and of course it lead, albeit indirectly, to Godel's result.

It's been a long time since the Lowenheim-Skolem theorem told us that everything has a countable model, but nobody took it ontologically, except postmodernists who said that il n'y a pas de hors-texte, and perhaps a few others.

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Is there any theory out there that addresses either of my two main concerns about using mathematics to describe physical reality? Or are my concerns unfounded?

1) All physical theories seem to utilize the mathematical constant pi. Pi is the ratio of the circumference of a circle to its diameter, in Euclidean space. In Euclidean space it is constant and incommensurable. Since physical space is non-Euclidean, the ratio of the circumference of a circle to its diameter will depend on the local curvature of space-time. Is pi included in physical theories because there is some need to include a factor of roughly 3.14159 in the equations, thus making it a purely mathematical concept? However, if it is the geometric relation and not the factor of 3.14159 that is relevant, does it make sense to include a Euclidean geometric term in a non-Euclidean theory of space-time? If pi was not constant, but determined by General Relativity, then quantum theory would be affected by General Relativity as well?

2) Is there any reason to think that the physical continuum is the same as the mathematical continuum? Arguments for including incommensurable numbers in the mathematical continuum include the fact that the point where the in-circle of a square and the diagonal of the square intersect is incommensurable. So in order for there to be an actual intersection of this line and arc there must be an irrational number. But in physics, where such lines are merely abstractions, does there really have to be such an intersection point in space-time? Would the whole subject be simplified if these very possibly "unreal" points were excluded from the mathematical system used to describe the physical world?

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Especially having discovered quantum entanglement it could be thought that understanding a large psrt of reality is not about an explanation that describes mathematically quantified properties of a cause or its effects.

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Universe itself is a conscious phenomenon, not logical one. Mind and mathematics cannot grasp consciousness and so universe totally. For that awakening of consciousness is needed. Consciousness is a scientific research tool which is distinguishing clearly between mathematical models of the universe and universe itself.

attachments: Fundamental_Physical_Phenomena_under_Examination.pdf

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There will always be potential incompleteness because objective reality can not be known directly.It can only be known by experience and comprehension of that experience. This involves processing of input which is information. From this information subjective reality is formed.

The reality formed depends upon the information received, the quality of that information (for example has there been loss, interference, delay, deception) and how it is processed. Each individual will receive different input and has a unique biology. Therefore experiencing a different present moment and personal subjective reality.

If there is no information from a part of objective reality there can be no experience and no knowledge of that part.

Therefore any mathematical model of objective reality may be incomplete, since there can be no knowledge of what is missing from the model.

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Paul,

In my opinion Quaternion mathematics designed to encompass all 4 dimensions into mathematics is a much better tool for describing and analysing the physics of the universe at all scales. It has been neglected by most and underused.

In my opinion also Pi is related to the fundamental structure of the objective material universe.

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Anthony,

The basic ideas of Max Tegmark and Gordon McCabe are right, but I disagree with the specifics, in particular the Mathematical Universe Hypothesis and the Computable Universe Hypothesis. Also the multiverse idea is not scientific because it is not falsifiable and only hides our current inability to understand the standard model parameters’ origin. What if the reason for their values is going to be found in the future?

If Mathematical Universe Hypothesis is right, then it runs afoul of Chaitin’s algorithmic information theory and Godel’s theorems. If the real world is only a mathematical structure, then its total algorithmic information is finite. However, reality contains mathematicians who continue to discover new mathematical structures. This implies that all mathematical structures discovered by mankind must be part of the mathematical structure of the real world. But Godel already killed Hilbert’s program of axiomatizing math and hence a single super-mathematical structure isomorphic with the real world cannot exist. The Computable Universe Hypothesis is design to answer the problem with Godel’s results, but it looks artificial and still cannot solve the algorithmic information challenge. What can exist are many mathematical structures describing the real world.

Then the question becomes: why only some mathematical structures are describing the real world and not others? For example why is space 3-dimensional and time one dimensional? The solution for understanding the nature of reality and for the uniqueness of the relevant mathematical structure exists and is rooted in the belief that our universe is indeed unique, and moreover, mathematically provable to be unique. What one needs to ask is not how math and reality are similar, but how are they different. If math and reality are isomorphic concepts, then the fundamental differences between them will become the ultimate physics principles. Those principles impose severe mathematical constraints on the platonic world of math and act as very selective filters of the mathematical structure able to describe reality. Is this just a speculation? Not at all. See my essay entry: “Heuristic rule for constructing physics axiomatization” for the state-of-the-art results in proving uniqueness results. Character limitations forced me to give only a cursory introduction to those results and their extremely rich foundational implications. I am looking forward to discussing in depth any questions about those results and their foundational interpretation. In particular, the nature of time is very clear, quantum mechanics is now intuitive, and the dimensionality of the space-time is a mathematical theorem. Even the standard model parameters may be mathematically obtained in our lifetime.

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Still need to digest more of this, I agree with the general MUH idea, but the CUH, and the static bird description seem like... well, baggage.

Simply stating that spacetime is divided up into 3 spatial and 1 temporal dimensions overlooks the qualitative difference between what space and time are.

Space is a structure which defines relations within itself in a particular...

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I think I have a more consistent version of "all structures that exist mathematically exist also physically" based on small changes in the definitions of some words. Its a few paragraphs down...

People do not pay enough attention to definitions of words. For example, in USA, a law was changed simply by saying "consent" instead of "choose". Science words work the same way.

Some people...

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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...

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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.

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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...

view entire post

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.

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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,

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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...

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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.

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(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,

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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,

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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...

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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

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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

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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...

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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...

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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

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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...

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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

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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

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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

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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

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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

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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

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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

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Lawrence,

I am not so sure LQG is really dead. Physicists have this amazing ability to fine tune theories to fit experimental data. And SUSY is just one way to beat the C-M theorem. SUSY has several advantages, but there is no clear mechanism of how to break it.

Florin

PS: have a nice Christmas

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Hi to both of you ,Florin and Lawrence and Happy Christmass .

You know I have nothing against your ideas but I think simply that if you superimpose several imaginaries and pure mathematical extrapolations ,you are going to be in a big confusion about our physicality .A lot of theories in this line of reasoning thus are not possible for a verification .I agree it is so far in the extrapolations what it is difficult to verify them. The pure maths are foundamentals for the physicality if and only if the good numbers and the goog limits are utilized ,it is not a question of tools but of referential .With your capacity to play with maths inside a good referential ,your results shall be so important and thus very important for the sciences community .There the complemenatrity seems still an essential .

Best Regards and happy new year too

Steve

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I have this idea that loop variables might be a constraint system on spacetime manifold as defined in a stringy sence. The AdS ~ CFT correspondence does indicate that spacetime does have a background structure. The LQG theory is a system of constraints (based on spinorial ADM relativity and Hamilton constraints) that might work to map AdS --> dS where the de Sitter sector is the physical universe, and the AdS is more of a spacetime fiction corresponding to conformal fields. So the LQG equations seem to be one way in which this might be accomplished. My attempts at this ran into considerable difficulties.

With respect to the Tegmark many worlds idea and set theory I found the following Skolem’s Paradox, from another discussion. This seems to offer up a way of having first order logic systems which are also ZFC with arbitrary cardinalities. Again, I am not exactly on this sort of track. I think getting quantum gravity and holography worked out is a sufficient challenge. Maybe this does impact how other cosmologies can exist in a multiple outcome situation with quantum gravity. We might if we get good enough we will figure out how to detect some quantum interference between our spacetime and other spacetimes with other cosmologies. Tegmark’s ideas are much to “far out” for me to consider as potentially empirical science.

Cheers LC

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Dear Lawrence ,

Could you tell me more about the theorem of incompleteness please ?

About the works of Tegmark ,which I respect too like all works ,even if I don't agree,I have a question for the multiverses .These multiverses are in one system thus what is this uniqueness .

The Universe is purely physic ,the maths are just a tool synchronized if the referential ,physical is correct .

The multiverses idea have not limits and a real toplogy .It is just infinite in the extrapolations even for the laws and their invariances and coherences .Thus all looses its sense in the uniqueness and the specific thermodynamical link .On the other side in a human imaginary point of vue ,it is beautiful ,but is it foundamental .

If we imagine a Universe with the hubble law ,I see a big paradox about the expansion if we go behind the limits ,like the speed of the light ,the increasing of the wavelenght and the Doppler effect ,our perception is false about the expansion I think .I think it exists a lot of confusions about the real movements ,if the rotation aroud the cenetr is considered and furthermore the real movement in a specific closed system and its laws of evolution.,thus the real dynamic can be understood since the begining in the physicality.

The spherical objects don't move due to this expansion ??? The perception is different than our reality .

Regards

Steve

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Lawrence,

Skolem’s paradox in interesting in the way it discredits the realism ideal. In physics the debate about hidden variables and the proper interpretation of QM is old news, but in mathematics the naïve interpretation of set theory would lead one to believe in realism/absolute truths. Set theory is a rather hard area with many unintuitive results.

Steve,

Incompleteness theorem is rather easy and well understood. From 10,000 feet, it goes like this: Consider the liar’s paradox: “This sentence is false”. If it is true, then we take it at face value, believing what is says and it says it is false. Hence true implies false. In reverse, suppose the statement is false, meaning that the sentence is indeed false, but this is what is says itself, so it is true. Hence false implies true. In conclusion true->false and false->true. Same for any other antinomies, like the barber’s paradox: “a barber is the person who shaves precisely the people who cannot shave themselves”. Does the barber shave himself?

Now Gödel replaced truth with provability and he formed the following sentence: “This sentence is unprovable”. Now if false, it means that it is provable, meaning that there is a sequence of logical steps proving it. But wait a minute, in this case we just proved a false statement and therefore we have an inconsistent system. If the statement is false we have inconsistency. Now if the statement is true, we have incompleteness. Why? Because there is this statement which is both true and unprovable. So what Gödel showed was that one has either incompleteness or inconsistency. Now this is all a big handwaving, to make this airtight and rigorous, there is an entire mathematical construction behind it, but it can be done successfully. The key was to find a rigorous mathematical definition of provability.

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Hi dear Florin ,

Thank you very much for this explaination about the incompleteness theorem ,I understand better its meaning.I liked your line of explaination .

I am going to learn more about the works of Godel ,Tegmark ,Wheeler ...I will encircle better this necessity to have these referentials .The incompleteness seems imply a non limits in the system .

I agree it is relevant about the creativity and potential of our brain .But in the physicality ,the ultim axiomatisation seems in one universal system .The only incompleteness is the evolution and thus our step of evolution .The logic and the rationality shows us the pragmatic road even for an idea or a theory or an intuition .If an equation is coherent with its physicality ,thus all recursives axioms shall give an universal correlation .

If the superimposings are inserted in a specific definition of a system with a serie which is personal thus the incompleteness becomes a confusion and an ocean of paradoxs ,just due to the utilization of the imaginaries in the logic complexity of the referential and its laws .The incompleteness apears like an false evolutive point of vue .

On the other side in a specific system invented by humans ,like a computer ,thus the incompleteness takes all its sense in the selectivity of the codes and thus the series .This kind of superimposings imply a specificity where the physicality and its laws are different .There I can agree about some paradoxs because it is correlated with the encoded architectures .The theory of wholes and the paradise of Cantor seems a tool of pure maths which implies the pure confusion about the reality of the physicality .For all x in R or E ....all is a question of referential and synchronization with the real numbers in the physicality in fact in my opinion .Thus how can we interpret the axiomatization ,perhaps only with our evolutive limits in accepting the real whole.The human logic seems far of the universal rational logic .I say that for the physicality of course not for the computing .

The inconsistency of a theory is not a reason to accept the theory like an axiom or in the other side .

I admit it is a little confusing for me .I am going to learn more ,it is very interesting in fact .Thanks dear Florin .

Best Regards

Steve

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Hello Steve, Hello Florin,

by thinking about Zurek's Quantum Darwinism i came to an analogy i built some months ago to understand more about the dynamics with which superpositions could create reality. This analogy refers to the barber's antinomy. In its original form it was formulated by Bertrand Russell like this:

„You can define the barber as ‘one who shaves all those, and those only, who do not shave themselves.’

The question is, does the barber shave himself?”

One could "solve" this antinomy by simply assuming that both alternatives - shaving himself/not shaving himself - are somewhat superposed in the way that the candidate for the shave shaves one side of his face (this could be the barber himself) and another person is shaving the other side of his face. But that would be against the original spirit of the antinomy.

My "solution" goes a step further and says that

"the barber shaves all those and only those men, who shave the barber and only the barber."

This statement is equivalent with the situation that the barber shaves all those and only those who do not shave themselves - but without having to shave himself. I wrote a paper about why this could indeed be the case and would be happy if anyone interested in it would read it and maybe comment on it. I will attach it as pdf-file here.

I wish the entire fqxi-team, all members and participants of the current fqxi essay-contest and all commentators a happy new near and want to thank all these people for the possibility to exchange interesting ideas and viewpoints.

Best regards

Stefan Weckbach

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I am not sufficiently knowledgeable of set theory to comment on much depth. In discussions with somebody else Skolem’s paradox came up. The thought occurred to me that this “naïve” approach to set theory (or an countable cardinal interpretation that occurs “paradoxically”) might be a way in which Tegmark’s approach to his “ultra-verse,” or what ever we call it, might work in some ways that fits into deeper mathematical foundations.

My interests are more parochial I suppose. I wonder how it is that LQG and other spinorial approaches to general relativity fit into the string framework. I don’t think that dynamic triangulations or LQG are robust enough to describe foundations well on their own. However, they start from completely reasonable assumptions or bases, so I don’t think they are wrong in the sense that phlogiston theory was or pre-20th century aether theories were.

Cheers LC

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Dear Stefan,

You have quite a paper on the barber’s paradox. However, I do not really understand your solution and I feel it is mostly semantics. In my opinion, there are only 3 solutions for self-referencing paradoxes.

1. a standard antinomy is just nonsensical (like liar’s or barber’s paradox). It is similar with asking: “what is the color of the eyes of the king of USA?” Each word is well defined, but together the sentence is meaningless.

2. time evolution solution: A(t) implies ~A(t+1) implies A(t+2) …

3. QM solution via superposition. |Psi> = |A> + |~A>

Solution 1 corresponds to no-go theorems in physics like no-time travel paradoxes via either time travel is forbidden, or time travel implies lack of free will and demands “destiny” to avoid all paradoxes.

Solution 2 is realized for example in the basic electromagnetic oscillator.

Solution 3 is possible only under very strict conditions. In a theory with interactions it leads to unitarity violations.

In nature we avoid self-referencing paradoxes because of time. A universe without time (like say with the metric tensor diag (+,+,-,-)) would not be immune from those kind of paradoxes and ontology as we know it would not be possible.

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Lawrence,

Dynamic triangulation is OK, but I feel it assumes too much and achieves too little. Its roots are in very early Robb and Zeeman’s results. LQG is far richer, but I feel very uneasy with Wheeler-deWitt equation as the starting point.

Tegmark’s approach has the big merit of giving respectability to this line of research, but the major problem is extracting mathematical consequences from it. Gordon McCabe had continued his approach into the hard area of model theory, but time till tell if this would get anywhere in a reasonable amount of time.

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Dear Florin,

thank you for your important comments on my paper. Yes, i agree, many standard antinomies are in fact truly nonsensical, i agree fully with you. Also the barber antinomy is unsensical, cause a barber cannot shave those and only those who do not shave themselves. This would mean he had to shave all the people of the world! (the universe?:-), who don't shave themselves. So Russell was wrong to define his barber in that way (in my opinion)!

But my interest in such antinomies (self-referencing statements) isn't driven by the search of a specific content, but by the search of their universal form.

I am sure by mentioning the liar's paradox, you didn't refer to the original formulation but more to such sentences as "this sentence is false" etc.

The original formulation of the liar's paradox is indeed decidable ("The Cretans are always liars"). It must be false (a "lie" or whatever) cause there exists another possibility to decipher the paradox, namely the possibility that the Cretans indeed aren't always liars. So Epimenides' sentence is simply false, because if it is considered to be true, this wouldn't make sense. In this case (his famous statement), Epimenides could have been really lied. In contrast, "This sentence is false" seems to me to really being nonsensical.

But back to Russells findings. He was motivated by set-theoretic considerations. Asking, if the class of the classes that are not members of themselves, is a member of itself or not, one comes - according to Russell - indeed into difficulties. Classes that satisfy the criterion of not being a member of themselves are always formulated in explicit form. For example the class of all red cars. In this class there is no room for containing itself.

Classes that do not satisfy the criterion are always formulated in an implicit form, for example the class of all things that aren't red cars. This class is surely one of the things that aren't red cars - and therefore has to contain itself as a member. Those kinds of classes have as a property that they all contain themselves infinitely many times - due to iterations. For Russells classes that are not members of themselves, this property doesn't apply. So in my opinion the main class in question - Russells class of all these classes - cannot be a member of itself (analogically the barber in my solution cannot be a member of the class he is shaving).

My interest in such somewhat stupid things is driven by a main question that is somewhat interwoven with the manner, science comes to knowledge and to conclusions: By observing patterns and building rules out of them. My paper about the barbers antinomy could be headlined with one question that is in my opinion in deep accordance to our current essay contest:

"Has every rule an exception?" or elsewise formulated, is the following true(?):

"No rule without its exception"

Best regards

Stefan Weckbach

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Hello Stefan ,Lawrence ,Florin,

Dear Stefan,

Hope you are well ,and happy new year too .

I think you makes a very interesting point about the conscious .In a discussion with Jayakar about the intelligence and extelligence ,we see the link between the rationality which appears like relevant too.The paradox thus is not necessary for the balance between the physicality and the uknew if I can say .

The universal referential and its pure dynamic thus always will be specific with its codes .An imaginary referential ,if it is not synchronized ,will imply paradoxs and incompleteness due to the lack of limits and the lack of real topology of the chosen system .That depends always of the referential and the superimposings in my opinion .There I think it is possible to extrapolate the universal system with a synchronization of the imaginaries if the essentials are respected.

Without this kind of line of direction ,and the time and its specific periodicity,the non coherences appear and thus the confusion too.

Dear Lawrence or Florin ,could you explain me the theory of models ,please?Happy new year

Regards

Steve

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Florin,

Here is the issue as I see it. We have two types of theories. We have string/M-theory which is vast in its "theory space." There is too much structure to this to presume it is completely false. It might of course emerge in some new form, but doubtless it will remain a big "space." Then there are the small theories, such as LQG and DT. The one thing which DT has going for it is...

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Florin,

Here is the issue as I see it. We have two types of theories. We have string/M-theory which is vast in its "theory space." There is too much structure to this to presume it is completely false. It might of course emerge in some new form, but doubtless it will remain a big "space." Then there are the small theories, such as LQG and DT. The one thing which DT has going for it is it avoids some of the chaotic foam issues of LQG. The advantage these theories have is they are closer to the structure of general relativity in its pure form. I suspect these theories suffer from not having the huge domain of field theory that string theory has, which is what is leading to some of its problems, in particular the Barbero-Immirzi ambiguity. LQG does indeed stem from the Wheeler-DeWitt equation, which defines constraints NH = 0 and N^iH_i = 0, the Hamilton and momentum constraints. The quantum analogues are HΨ[g] = 0 and H^iΨ[g] = 0. These are of course not dynamical equations, but rather Lagrange multipliers which define fields on a contact manifold of solution. So far the progress with LQG has been frustrating.

So my modest (or not so modest) proposal is the following. One of the theoretical coups of string/M-theory has been the AdS-CFT correspondence. I will at this point avoid technical discussions on this, but say that this implies that on the boundary of the AdS spacetime there is defined a conformal field on the S^5 sphere. The boundary of AdS_5, with the group SO(3,2) is equivalent to a conformal field theory. The theory is then AdS_5xS^5, which can emerge from an 11 dimensional theory with the extended Anti-de Sitter group SO(4,2) ~ SU(2,2). This is a remarkable and beautiful result which Maldacena worked up 11 years ago. Susskind, Vafa and others have demonstrated that if a BTZ black hole is placed in the AdS that the conformal field theoretic information on the horizon of the BH and on the boundary of the AdS preserve that information, which has been a further recent deep development. Yet the AdS spacetime is not the physical spacetime of our universe. The universe is asymptoting to a de Sitter spacetime, with the group SO(4,1). This spacetime has a Wick rotation on the additional time-like dimension and it recovers a solution to the Einstein field equations which approximates the observable universe. Further, the BTZ black hole is replaced (by hand at this point) with physical black holes which we know exist. My proposal is to use LQG as the system which performs this map between the conformal theoretic AdS spacetime to the physical dS spacetime.

Here is what might be going on. Hyperbolic groups such as SO(m,n) have sequences of moduli points (gauge connections etc) which do not converge in a Cauchy sequence. The Wick rotation SO(3,2) - -> SO(4,1) will then impose this condition on a set of these moduli points. But a straight forwards map is a “violent procedure,” which does this in an ad hoc manner. Instead we want to preserve the conformal theoretic information of SO(3,2) when we perform the map. It is my conjecture that the constraints of loop variables might just serve this purpose. This might also provide the additional information required to work the gauge ambiguity with the Barbero-Immirzi parameter. I have tried a number starts, but so far I can’t get anywhere. I had thought, maybe still do think, that the quantions you work with might be a tool. I am not clear on just how to proceed with this. Any thoughts or suggestions would be welcome.

Cheers LC

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Dear Friends,

The key here is that simplices are the geometrical representation of Spin groups.

A simple example is Spin(4)~SO(4)xSO(4) has 12 operators - the six edges of a tetrahedron (4-simplex & FCC basis) times two directions per edge. Add in the three dimensions in which the tetrahedron exists, and you have the 15 operators of SU(4). Everything has rank-3 and dimension-3.

Similarly, Spin(3), SU(3) and G2 are related to the 2-dimensional 3-simplex (triangular lattice), and Spin(5) and SU(5) are related to the 4-dimensional 5-simplex.

As these dimensions fracture into brane structures, the Lie algebras also fracture, which is why Spin(4,2) becomes so relevant (4 dimensions of Spacetime plus 2 dimensions of AdS).

Of course, these simplices work very well within the framework of CDT.

Have Fun and Have a Happy Blue Moon of a New Decade!

Ray

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Lawrence,

I would not deny the impressive results of string theory, but I do not hold this as reason to certify its overall correctness. If for example the same amount of brain power were put in non-commutative geometry, equally impressive results would be there as well.

My interest in quantions, SO(2,4), SU(4), and SU(2,2) is from the point of view of von Neumann algebra factors and Hopf algebras. I feel that quantions may unlock “distinguished” properties which will point the correct way for SU(3) and GUT. If SUSY emerges naturally in this approach, then I will be a believer again in string theory, otherwise I fell that non-commutative geometry is the right path.

I am not sure I can really offer any meaningful guidance except to point out the problems I consider interesting myself. I would like to understand better the metaplectic group, geometrical quantization, and the link with maximal entangled states and Segre embedding. Also I would like to understand in depth the meaning of associativity and Jordan exceptional algebras. The link between quantions, Hopf algebras, and category theory is very interesting as well. The connection between quantions, von Neumann algebras, and non-commutative geometry is worth investigating combined with an in-depth understanding of the spectral triple.

Regards,

Florin

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Hi all ,

I search some explainations for the M THEORY ,If I understand weel Mr Witten utilized the bad tools .I don't critic his skills but simply the method .

The brane and strings are a false road implying confusions and unlimited non physicality .I can understand the economic strategy since this M tHEORY from Princeton buit all must be reals and pragmatics .Our sciences are not a play but a real search of the Truth .There the sale of books and ideas are just a short time.

The supergravity in 11 dimensions have no sense and rationality .It is just a mathematial false extrapolation about our physicality and its universal laws .

I think at this moment the skills focus on non rationality ,like a paradoxal dream where the imaginary part of our brain takes the main part of the method .

Impossible in this road to be in this universality and physicality .

I take the time to encircle this method and more I read or learn and more I see non coherences ,hidden unknew ,bizzare extrapolation above our 3D ,external cause of mass .I have not proofs ,I search but no I don't find them .A local proof is not a global proof .It is essential to encircle this whole I think .

Sometimes the maths and their beauty takes the main rule for some axioms ,but the physicality is the main part ,not in the other sense in fact .

Best Regards

Steve

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Florin,

I have been working quite a lot on the Jordan exceptional algebra. I think this in connection to quantum error correction codes actually underlies string/M-theory. The 27 dimensional J^3(O) with a light cone constraint reduces to the 26 dimensional bosonic string as 3 octonions plus two independent scalar degrees of freedom. The three octonions are the vector terms plus their supersymmetric pairs as spinors. So the other two additional octonions are those spinor fields and their conjugates. This reduces things to 11 dimensions, or on the light cone condition 10 dimensions. My essay paper goes into more depth on this.

Steve,

String theory is a general spacetime (with curvature) version of the S-matrix theory. The string is a parameterization of fields along a chord or loop. Even early on it was thought that one could parameterize fields in two or more dimensions. This would be the quantum sheet or quantum 3-volume, 4-volume and so forth. This did not turn out to work terribly well. What Witten did was to show how open string with their endpoints attached to a membrane would have its modes coupled to soliton waves on this brane. This permitted one string type to transform into another. I hold to the view that string and d-branes are themselves really emergent from quantum units of information --- related to what Susskind calls the D0-brane. This is a brane of zero dimensions! So in a way we are back to particles. What the d-brane does is from an S-matrix perspective to define the domain of support for the S-matrix so it can work in generalized curved spacetime of up to 11 dimensions. If you read my essay you will find some of this, and the approach with quantum information (quantum error correction codes) leads to a type of Skrymion action. This action operates for particles or quantum fields in topological knots or loops, from which I think strings emerge from --- as well as general d-branes.

Cheers LC

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Lawrence,

I am casually learning octonions, but if you already understand them, what is the physical meaning of their lack of associativity (if any)? (From the mathematical point of view the lack of associativity is related to terminating the infinite series of Lie algebras.)

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Hi dear Florin ,Lawrence ,

I thank you dear Lawrence .You know I try to be in synchro but this parameterization seems in a infinite serie more the bad tools .

The série in this logic ,never will give good results because the universal gauge between quantum and cosmological spheres are not correlated with our main laws .

You know I liked your essay because your are an exeptional mathematician .But I try still to encircle your method .

Like say Florin ,the associativity seems essential in a physical point of vue .I think when an axiomatization is correct ,it doesn't exist confusions.Just unknews .

In fact the causality is intrinsic and the evolution seems the part of the puzzle whichj builds gravitational stability and its specificities .Thus the fields ,mass ,particules and their rotations have a specific intrinsic code and even at this ultim scale ,we have the same laws with some differences ,foundamentals furthermore .

The transfert of informations is simple thus all parameterizations must be correlated with our laws .The fields too are in this proportionality .

The time and the light thus in this line of develoment can't be rational I think .

Best Regards

Steve

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Florin,

Right now I worry less about the nonassociative aspects of E_8 and am more focused on the automorphism and centralizer groups G_2 and F_4.

Nonassociativity is a bit strange. Yet all it says is that (e_ie_j)e_k – e_i(e_je_k) = C_{ijk}^le_l, where the last term is by multiplication table rules e_i(e_je_k). So you think of this as a sort of π/2 phase shift. The physical meaning I think involves the S-matrix. The S-matrix acts on a set of vertices or particles p_i

|φ) = |p_1, p_2, …, p_i, …, p_j, …p_n)

and converts this channel into an S-channel which has some overlap with

(φ| = (p_1, p_2, …, p_j, …, p_i, …p_n|,

so the expectation of the S matrix for these two ordered sets of states is

( S ) = |φ> = (p_1, p_2, …, p_j, …, p_j, …p_n|S|p_1, p_2, …, p_i, …, p_j, …p_n).

By S = 1 + 2πT this is determined by a transition matrix, which by the exchange of vertices determines the S-T-U relationships or Mandelstam variables. In this case we simply have an exchange or a commutator in a quantum group. This might be represented by (ab)---(ba) as a braid link, and for multiple exchanges the S-matrix determines a braid group. For the exchange of three elements this gives a Yang-Baxter equation which is equivalent to a Jacobi identity on the double commutator [a, [b, c]] and it is equal to zero. The channel is produced by a product of Hilbert spaces for each vertex, so

|p_1, p_2, p_3> = |p_1>|p_2>|p_3>.

Nonassociativity is an ambiguity which says that

|(p_1, p_2), p_3> = (|p_1>|p_2>)|p_3> = |p_1>(|p_2>|p_3>) + |C_{123}^4p_4>.

This is a type of Hopf algebraic system, but with a “twist.” The noncommutative system is defined by the K-linear map on the vector space V, or between V and V’, a multiplication and co-multiplication rule you get the Hopf hexagon. However, for three elements and an associative rule there is a corresponding pentagon (Stasheff polygon), the hexagon and pentagon are fused together to form a general polytope. I can delve into these detail later if you are so interested.

What would this correspond to physically? The ordering ambiguity means there are two S-matrix channels which are not commensurate with each other. For the case of a black hole a string, which is really an S-matrix element, is observed to exhibit completely different physics according to an observer who witnesses it fall towards the black hole from a distance, what Susskind calls a fiducial observer or FIFO, and an observer who falls in with the string, a freely falling observer FREFO. What Susskind has argued is how the physics observed by the two is completely different, but both are physically valid. The general polytope I mention indicates how noncommutative geometry and nonassociative algebra are related (a bit complicated), and physically this means what we think of as a proper ordering of events or trajectories must be “liberalized.”

Cheers LC

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Dear Lawrence,

You said "This is a type of Hopf algebraic system, but with a “twist.” The noncommutative system is defined by the K-linear map on the vector space V, or between V and V’, a multiplication and co-multiplication rule you get the Hopf hexagon. However, for three elements and an associative rule there is a corresponding pentagon (Stasheff polygon), the hexagon and pentagon are fused together to form a general polytope. I can delve into these detail later if you are so interested."

Actually, I am interested.

Figure 4 of my "A Case Study..." paper involves a Petrie pentagon that I purposely drew as a distorted Petrie hexagon. This makes a lot of sense if you look closely at the quantum numbers (particularly T'_G). I think this leads to a Spin(6)~Spin(4,2)->Spin(4,1) (related to the 5-simplex, Spin(5) and SU(5)) isomorphism and decomposition, which helps explain the difference between my 12-dimensional model (with 8-dimensional hyperspace - Spin(6) plus G2) and 11-dimensional M-Theory (with 7-dimensional hyperspace - Spin(4,1) plus G2). Higgs theory , the CKM matrix, and the PMNS matix may all be intertwined in G2 and this collapsed dimension.

Please review my recent tiling pattern and enlighten me.

Thanks!

Ray

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Probably a good introduction to associahedra is Root systems and generalized associahedra by Fomin and Reading. I attach two figures from the paper which illustrate the pentagonal associahedra, which involve 4 elements. The second is the rather odd Stasheff polytope for hexagonal flips. These flips can in general be maps between elements on the vertices. So I have this proposal or idea that a Hopf algebraic system can fits into a system of associahedra. This is a bit of a distant "TBD." I have just been doing background reading on noncommutative geometry and on the nature of associahedra and cyclohedra.

I have to get back to other things here pretty soon, so I might comment more on this later.

Cheers LC

attachments: associahedra.jpg, associahedra2.jpg

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Dear Lawrence,

Thank you for the article. It looks helpful. I need to read it several times and study it. Could the relationship between pentagons and hexagons be related to the Carbon-60 buckyball?

My latest ideas may be related to this 2-dimensional cyclohedron.

Have Fun!

Ray

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Dear Lawrence,

Thank you for the explanation and the archive paper, it is really helpful. I guess I am still not very clear on the physical meaning. Various properties are useful in different contexts, but can we prove for example that the special Jordan algebra cannot be the observable algebra part of a QM state space representation?

Regular Jordan algebras and spin factors can play this role, but in going from algebraic QM to state space, is associativity really required?

I would imagine that the Born rule is somehow no longer valid, but this is all fuzzy speculation. The reason I am saying this is that the Born rule is associated with the continuity of the spate space and the ability to define a distance. Is norm (or equivalently the scalar product) definable in an operator algebra space where associativity is broken? I do not know enough of operator algebra spaces to answer that but my conjecture is that it is not. If I am right, I speculate again that this would physically mean that in case of the special Jordan algebra there will be hidden (unphysical) states.

In another topic, I started listening to Susskind’s GR lecture on the web (the link you suggested for Jason). The lectures are very clear and easy to follow, even without writing anything down. But they puzzle me. For the first 4 lessons I was bored to death and the lectures did not make much sense to me. He talked about Gauss theorem and the fact that a spherical body has the same gravitational attraction as if all its mass is concentrated at the center. Now this is elementary undergraduate stuff, and how would someone interested in GR take this class before some prerequisite classes? Are those classes undergraduate classes? It looked like this, but then why someone teach GR at undergraduate level? Something is very funny here.

Regards,

Florin

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Dear Florin,

I agree about the hidden, unphysical states. Lawrence's model contains at least 3 E8's and a G2. Depending on how you arrange these, you should have more degrees-of-freedom/ states thatn my K12': (3 x 248 + 14 = 758 > 684). My K12' predicts hidden, unphysical 'scalar fermions' or 'tachyons'. I think these illogical 'particles' are related to a Higgs multiplet that is more complex the the Standard Model.

Dear Lawrence,

If we flatten out a 3-D Carbon-60 buckyball into a 2-D broken lattice and center the broken lattice around a hexagon, we could still obtain a G2 triality with some pentality symmetries. This 'G2' appears to be 2-dimensional, but contains the curvature of the third (of 3-D buckyball), apparantly invisible dimension. Now we have 12 dimensions instead of eleven.

Have Fun!

Ray

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Florin,

I will get back to technical issues tomorrow or later in the week. I am a bit tied up an the moment. When it comes to Susskind's lecture, they are very elementary at the start. In fact throughout them they rely upon pretty basic ideas, but towards the end he builds to quite a crescendo if you can make it to the 12th lecture. What intrigues me is the incredible teaching skill involved here, where with basic ideas and elementary arguments he builds a great depth of understanding. His lectures are an example of a true craftsman at work in teaching students. And if you listen to them, as I sometimes do in the background, you might find yourself intrigued by these little insights into things which occur throughout. These are like Debussy's piano music, where some pieces can sound elementary at first, but are amazingly deep in their musicology.

Cheers LC

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Lawrence,

Thanks, I look forward to it. I am currently at lesson 8 and after lesson 6 I became addicted. The first lessons were hard to watch, but I wanted to observe his teaching style. Still, I do not understand who is his audience. It is neither undergraduate, nor graduate students.

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Dear Florin ,funny is still a weak word .

If you was bored to death at lessons ,thus perhaps you can study the real sciences like biology or physicality .I have an idea ,the horticulture .

I am laughing of course ,let's laugh in this funny thread ,not relevant but funny .

Regards

Steve

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Ray,

I am not sure whether this is right or not, but these polytopes might have some relationship with the 120/600 cells ~ H_4. A pair of these compose the Weyl representation of E_8. I am not prepared to make any serious hpothesis along these lines.

Cheers LC

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Dear Steve,

I recommend you watch the lessons yourself and provide us with your feedback.

General relativity is conceptually easy (the equivalence principle) and mathematically hard. The 12 lessons are like saying: here is a course in how to build rockets to reach the Moon. Then 1/3 of the course is talking about hot air balloons, how to build them, how they work, and why they cannot reach the Moon. Now if you do not already know hot air balloons cannot reach the Moon, how can you be expected to pass a final exam on advanced rocket science?

So what I do not understand is how can anyone who is not familiar with elementary facts about Newtonian gravity is supposed to pass a final exam in general relativity if they are not a mathematical genius?

But criticism aside, the lessons are indeed crystal clear and I highly recommend them to anyone who wants to learn about the subject.

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Dear Lawrence,

That is an interesting observation. I have been wondering how Spin(6) hexagons morph into Spin(4,1) pentagons, and where does the extra dimension (#12) go?Flatenning out a buckyball came to mind because a buckyball consists of 12 pentagons and 20 hexagons in a regular lattice. It has both the triality and pentality symmetries that we need for H4 and E8. Now the question is "How does a 3-D Carbon-60 buckyball relate to a 4-D 120-cell or 600-cell?"

Have Fun!

Ray

p.s. - Maybe I should look at the lecture series as well. My specialty was HEP, not GR.

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ahahahaha oh thanks master of the maths ,the undergraduate in the imaginaries

ahahahah I insist ,the horticulture is good for health and furthermore you shall understand better the sciences and thus the maths .It is just a suggestion from a non certificated scientists .

You want to speak about maths dear Florin ,let's go .

My only condition is to use the reals and the real maths ,not an ironic system of nothing .

Good plantation .

Steve

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ps with humility of course and respect to your skills , your maths are falses and imaginaries .Your referential is false ,your limits too ,only some method are interestings and that is all .

Your axiomatization is an ocean of confusions and decoherences where the imaginaries take the main part of the physicality .The road is false ,simply .I invite you ,really and with respect to study all sciences ,really .You shall insert thus the good serie in 3D .That will permit you to have good parameterizations because there it is false in the whole .

Regards

Steve

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Sometimes I beleive you are obliged to rest in this line of reasoning .

I am frustrated with the two mavericks and you too dear Florin .Why this road really ,I am curious .

You are the 3 so competents ,why this bizare road .Is it really your choices .

Friendly

Steve

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C’mon Steve, be a good sport, join in the fun. Dive right in, take the class, it is not that hard. Physics is just like Edison said: 1% inspiration and 99% perspiration. In physics perspiration is the math. Physics without math is like hot dog without ketchup, or ping-pong without the paddle.

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Dear Spherekeeper Steve,

Buckyball = soccer ball - What part of that is imaginary? You could deflate and cut up a soccer ball if you want to see these multi-dimensional lattices represented in a somewhat simple 2-D lattice of Petrie diagrams.

The Carbon-60 buckyball was such a big deal that Sir Harry Kroto (currently at my alma mater, Florida State U.), Robert Curl, and Richard Smalley won the Nobel Prize in Chemistry for discovering Carbon-60 in soot.

The buckyball is nearly spherical, which ties into Face-Centered-Cubic close-packing lattices - similar to stacking spherical fruit at the grocery store.

The difficulty of ANY model is that there are a large number of possible paths. Your model suffers as well. I agree that spheres may be fundamental, but why is spin fundamental? Why are prime numbers fundamental? Ultimately, your arguments for spheres may not be any better than some of the 'crazy' math that I am playing with.

Have Fun!

Dr. Cosmic Ray

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Dear Spherekeeper Steve,

I have heard about your Spherical GUT for nearly a year, and yet have not seen any serious details. What direction are you taking with this research? Will you publish a 30 page journal article or a 1000 page book?

I would be glad to proof-read it for you - perhaps 10 pages at a time. I have not used anyone else's ideas without giving them proper credit. My only fear is that I might see huge similarities between our ideas: sphere-packing vs. FCC lattices, spheres vs. buckyballs, etc... You are convinced that you are working in 3 dimensions. I am convinced that you have two or three 3-branes, but you have limited your model's potential by ignoring larger branes (up to as large as an E8 octonion 8-brane) as did Garrett Lisi.

I know you do not like extra dimensions, but certainly there are extra degrees-of-freedom. For instance, an electron can be identified by its mass, charge, and intrinsic spin. Where do these extra unknown degrees-of-freedom come from? Do they miraculously jump out of the aether? I have developed a consistent multi-dimensional model for explaining these phenomena. If you would prefer to think in terms of extra degrees-of-freedom rather than extra dimensions, then that is probably a reasonable alternate approach. But do not dig a hole in the sand, bury your head, and pretend that we know everything.

Your Friend,

Dr. Cosmic Ray

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Ray,

I think if there are relationships with a hex spin(6) and the pentagon it is more that there are multiple copies of spin(6) in a hex arrangement. This is maybe a part of what I am speculating on here --- writing ideas on a whiteboard and striking them out as I figure they don't work. The pent is then some Stasheff polytope which determines an underlying nonassociative structure on the spin(6).

I think we might want to focus in on the QCD ~ AdS_3 we talked about before the holidays. That does look like workable physics at this time.

Cheers LC

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Dear Lawrence,

I agree about the multiple Spin(6) hexagons. Consider the similarities between a 2-D hexagonal tiling and a flattened out 'pseudo-2-D' buckyball tiling.

Have Fun!

Ray

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p.s. - The buckyball idea is not a tangent. It is related to your G2 trilaity and my Gravi-Weak 5-simplex.

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Dear ray ,

You know What I like you and I am nice .But I am frank and direct .That doesn't change my love about people .That said

Please the C60 is like many crystals ,it is just a idea whithout universality .

It is just a chemical architecture .Any sense in a whole point of vue .

Dear Florin ,when I studied the piano with the Hanon method ,it is the first words on the first page of the method ,1 and 99 .I have studied all sciences like that even maths but the reals maths .Not an ocean of imaginaries behind the 3D .all that is false I repeat about the limits of the series and the referential ,furthermore these kinds of confusing methods imply a non possibility for the proofs .I find that very sad for the sciences community .

Dear Ray ,I have altready explained my point of vue about E8 ,it is a joke and that is all .Why he doesn't come and Mr Witten too ,why dear Ray ,because they fear simply .I eat the pseudos sciences .

Dear Ray ,I have uderstood the play of some people ,I eat that too.If you can't understand my theory after 1 year thus never you shall undertand it .It is the same for several people ,frustrated and jalous .Simply because a young belgian has found the ultim gauge .Like I said before ,don't focus dear friends behind this gauge but let' improve inside but not with these kinds of methods ,that has no sense .

For the publication ,DO YOU THINK IT IS IMPORTANT FOR me ,I have already explained my point of vue in private ,I am already dead dear ray ,thus you can imagine my point of vue ,nothing to do in fact .With or without publication n,with or without copies or others ,my theory will rest and wikll be more foundamental than the ideas without universality and its laws .

Never I say what I know all ,I just explain my point of vue ,and when the truth is there ,some don't like that .I am laughing and that is all .

Alldays I study and complete my universal taxonomy .I class all ,and when you class all ,you see the truth ,the spherization of the universe by quantum sheres .It doesn't exist extradimensons ,just a superimposing in 3D .Higgs false too .

Limited the potential of the model and after what ....3D dear ray ,my model is too different.I can't work with you or Lawrence or Florin or Lisi or Witten ,impossible for me ,your roads are falses and without uniquness .I prefer work with pragamtic and rational people .

But for the sciences center you are welcome of course to adapt in 3D inventions for our fellow man ,I think they prefer 3D and they don't need extradimensions .The reality is the reality .

With respect for all the doctors ,professors and undergraduates ,but I suspect a very sad reality at schools ,Oh my God ,the next lessons at the university will be How to create a time machine to explore an other universe with tachyons .HUM HUM I think I prefer study in my books ,a good book is important.

Regards

Steve

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PS ,dear Ray ,I don't say you are jalous but some are like that .

I must admit I am parano due to my past ,I have lost all dear Ray ,all due to the human instinct .I can admit I am a bad economist but really here in Belgium they fall down me and not a little.I must be prudent now .

Do I must be still too nice ,no evidently ,it is important for my theory and the sciences center to be more prudent .I dislike to put the things in point but I must be like that .Be sure ,I like people ,it is my reason of life but I fear too .

I can't play with my theory ,no I must be strong .Evern if I seems arrogant .I am arrogant ,yes but I evolve .I have many things to study like all people .

Regards

Steve

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Dear Steve,

I have heard many bits and pieces of your theory, but I have not seen a complete presentation. You referred to yourself as 'dead'. I assume that you are talking about your odds of publishing in a journal, because you seem to be a person who enjoys life. I published my book online as a 'print-on-demand' book through Lulu.com and allowed distribution through Amazon.com. It does not cost much to publish a book this way, and it is accessible (in English) to nearly anyone interested.

I am listening to you, my friend. I want you to prove me wrong about multiple dimensions. Only the math makes multiple dimensions seem reasonable - common sense makes multiple dimensions seem illogical. But I suspect that you have replaced my 'pseudoscientific' hidden dimensions with equivalent 'pseudoscientific' hidden degrees-of-freedom. If so, is your model really any more fundamental than mine?

My model has 'scalar fermions'. Are these tachyons? Do they provide Higgs-like properties? I do not know. Make fun of them if you like - they are a legitimate part of these pentality symmetries. What if these 'scalar fermions' become useful in Higgs theory, the CKM matrix, and the PMNS matrix?

Don't be too serious! Have Fun!

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p.s. - A good CEO knows that he cannot do everything on his own. You must learn who can be trusted, their strengths and their weaknesses, and delegate responsibilities. A good CEO must 'watch his back', but cannot get too paranoid to ask for help. A former General gave me the following advise "Trust, but verify".

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Ray ,

You are right ,alone we are nothing in fact .

I repeat I don't critic the skills but the models .

You can do the same with mine ,between us ,you know what my Theory is correct .

Why an other logic in 3D ?It is impossible .

This reality will rest .It is not a reason it is finished for the discoveries ,no it is the begining of a real research with pragmatism about our real universe .It is more essential to study what we can study in fact and not extrapolations behind the walls ,that has no sense .The unknew is the unknew and our 3d are our 3d ,it is like that since the begining .And never that will change .

When I say that about pseudo sciences ,I insist yes all that is pseudo sciences .And the skills have others things to do I think.

It is sad all that in fact ,very sad for the sciences .

Friendly

Steve

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The real problem in fact is the referential and the correlation between the maths and the pure physicality .

The maths show us by extrapolations the limits of our perceptions with an infinity which appears due to these limits at the universal scale ,a little if I said ,we are babies of the Universe and thus it is logic to perceive an impossibility to see a limit .

It is the real answer of the relativity and the evolution point of vue inside a physical system with its specific thermodymical laws .The infinity is a confusion about our pure physical limits .That implies of course thus the confusions due to the potential of creativity of our mind .The imaginaries beleive what they has an infinity but is it logic ,I think no evidently if we accept these realities .

A physical universe is the main part of the puzzle ,the maths must be pragmatic and correlated at this harmonic road in this pure physicality with its limits and specificities.The constants due to our relativity are a reality too and must be considered ,the present takes all its sense in this logic .The maths permit to extrapolate behind these actual constants ,it is thus logic to see decoherences but all that looses its senses ,its real sense about the constants and irreversibilities .The system in the physicality always must insert the 3D and this constant implying constants ,the time .This parameter is the main piece of the relativity about the perception and thus the real datas or equations about the actual system .Only the evolution and thus the analyze of the past and the present thus to extrapolate the future ,but for that the physicality needs reals maths inside the closed system ,here the universal sphere.These tools ,the maths take only their sense about the physicality if the balance is made with the biggest harmonization .

To utilize the maths and the methods without a finite referential ,will imply always thus the confusion .

The physicality is more foundamental than maths because there only the reals exist .The imaginaries are thus humans in conclusion .

Regards

Steve

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Steve,

You said "The physicality is more foundamental than maths because there only the reals exist. The imaginaries are thus humans in conclusion."

Many of my models are based on crystalline lattices that exist in Nature. They are fundamental, not imaginary. If Nature uses a structure once, she might use it again. Is a sphere really more fundamental than a buckyball? Nature can make a buckyball with a mere 60 atoms of Carbon. In contrast, a perfect sphere is a mathematical abstraction that can never be perfectly attained in this world. Try polishing a piece of wood or marble into a perfect sphere.

Our most significant differences lie in multiple dimensions. I introduce extra degrees-of-freedom and call them new dimensions. You introduce new degrees-of-freedom and call them spin. If I am correct, then part of hyperspace is a 3-brane that mirrors 3-D space such that it is easy to confuse the two different concepts. Note that on page 10 of my book, I obtained a 3-dimensional momentum space density of states. This is a hyperspace effect, not a spacetime effect. The numbers can trick you if you mix up cause versus effect.

Have Fun and continue to evolve!

Ray

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I am going to try to get to the matter of the associator and its implications for physics by Sunday.

Cheers LC

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Hi dear Ray ,

I don't say what all your tools are imaginaries ,but you know if only one imaginary is inserted and implies decoherences thus even with one ,that implies an error .

I d like insist on the whole of my theory ,my theory of spherization says in very simple resume what the numbers of one quantic system is the same for our cosmological spheres .....the mv constant is important for the link ,the rotating spheres ,quantic or cosmologic are linked inj a pure constant .

After tyhe evolution and the time constant builds the gravity with the polarisation.And all that in a finite universal sphere probably with an evolutive volume .An other point is the existence of the center of the universe where all turns around .

Dear Dr Cosmic Ray ,please where do you see the c60 ,the crystals are just a mineral ,a physical tool .

The spherisation ,these spheres are foundamentals ,it is like that in fact with or without the ideas of humans ,even if I didn't find this theory ,an other will have found because it is evident what the universe is a sphere like all ,the physicality had need to have this universality correlated with the rotating spherisation ,that implies a specific system in evolution with its coded informations of becoming in the main central main spheres,probably the biggest volume due to the ultim fractal and its divisibility .

Like I said before ,I don't encircle these extradimensions and their rules in the physicality .The cause of the mass too is bizare for me and others things .

Your superimposings about the entanglement too implies confusions for me .I don't understand why people wants have decoherences ,reversibilities,.....the system is invariant in all localities in the 3D in my opinion .

Friendly

Steve

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Although he begins with the External Reality Hypothesis (ERH) that claims reality actually exists outside of us humans, it appears to me self-evident that Tegmark's Mathematical Universe Hypothesis (MUH) is in the realm of meta-physics. For example:

"Mathematical structures do not exist in an external space or time, are not created, or destroyed..."

can be replaced by:

"God...

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---Continuation of Klingman analysis of Tegmark's theory of reality:

Although I believe we are in the realm of religious argument, Tegmark makes a number of statements that appear to be recognition of potential problems in his argument, so we consider these next. I will list these problems below and then treat each one in detail [ER = external reality, MU = mathematical...

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---Continuation of Klingman analysis of Tegmark's theory of reality:

(C) Embarrassing Theory of Everything

Tegmark says a TOE must address Wheeler's embarrassing question:

"Why these particular equations, not others?"

My essay addresses this as follows: unless one believes, as Tegmark appears to, that math somehow exists 'outside' of space and time and yet derives...

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---Continuation of Klingman analysis of Tegmark's theory of reality:

(E) Unpredictable External Reality:

Tegmark realizes that true randomness in the laws of physics would be a severe problem for his Mathematical Universe Hypothesis.

Since Darwin, people have been looking for schemes to which everything can be reduced. The Darwinian scheme depends on randomness, which...

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---Continuation of Klingman analysis of Tegmark's theory of reality:

(H) Unsymmetrical External Reality:

Tegmark says: "...the Mathematical Universe Hypothesis implies that any symmetries in the mathematical structure correspond to physical symmetries..."

If this is the case, why are there no right-handed neutrinos? And why has QCD only approximate symmetry?

I also...

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---Continuation of Klingman analysis of Tegmark's theory of reality:

There also appears to me to be 'practical' problems in his formulation. Let us assume for a moment that Tegmark is correct --- a mathematical structure is physically real:

Which mathematical structure 'is' the hydrogen atom?

A Cartesian structure?

A cylindrical structure?

An elliptical...

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---Continuation of Klingman analysis of Tegmark's theory of reality:

If it's so simple, why do a significant (greater than zero!) number of physicists have difficulty grasping this fact?

My guess is as follows. Math, since Plato, has existed in the minds of man, and the conscious mind has been the ultimate mystery. When Newton and Leibnetz invented calculus, they increased the...

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Lawrence,

Looking forward to it. By the way, the algebra of observables is non-associative (but power associative).

Also I have just discovered this paper: http://www.dinahgroup.com/content/jglta/v2_n4_2.pdf and it seems that I was right to speculate that lack of associativity implies hidden unobservable states. This in turn means that the Born rule is broken as well. I will need some time to digest this paper.

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Hello dear Mr Klingman ,

I liked a lot reading your posts here .Thanks for this relevance .

It is well sais these words"Yet Alfred Korzybsiki's definition of sanity, in essence, is the ability to distinguish the map from the territory."

Like what the topology is essential .

Best Regards

Steve

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Florin,

I have read some papers by Vladimir Dzhunushaliev on nonassociative quantum mechanics. One can interpret equation 3.1 as an associative ordering on channels determined by an S-matrix. Since the associator returns the set of states with a sign change

[φ_i, φ_j, φ_k] = φ_i(φ_jφ_k) – (φ_iφ_j)φ_k = C_{ijk}^lφ_l = -φ_i(φ_jφ_k)

nonassociative structures imply a phase ambiguity in a Taylor expansion. So this is an indication of shadow states or something similar in the S-matrix.

He does appear to be saying that the Born rule needs to be generalized in some fashion. I will try to return to this later today, maybe after I have fully read this paper.

Cheers LC

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Dear Lawrence,

Have you seen this article? Quantum Criticality in an Ising Chain

The golden ratio 1.618 is based on the geometry of the pentagon. It is funny that speculators are proposing that this is experimental evidence for Lisi's E8 TOE when Lisi never specified the E8 pentality symmetry (that I've been talking about for months). This is the kind of experimental evidence that El Naschie could use to further his claims of E-Infinity (order of 685~(10*1.618*1.618)^2).

This gives me hope that I'm on the right path pursuing the pentagonal Spin(5)~Spin(4,1). I think a transition occurs that changes the system from a hexagonal Spin(6) tiling to a buckyball tiling composed of hexagonal Spin(6)'s and pentagonal Spin(5)'s.

Have Fun!

Ray

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Double-triple thanks for this. I heard D. A. Tennant interviewed on NPR the other day, and spent time trying to look for this. And here it is, and I am an AAAS member, but hand not checked my AAAS email.

I really am going to try to get to the nonassociator quantum mechanics, maybe tonight.

Cheers, LC

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Here is an overview of nonaxxociators and what might be called quantum homotopies.

The ordered S-matrix defines each vertex, or particle, and its neighbor. In a linear chain a general state is an S-matrix channel of the form

|φ) = |p_1,…, p_i,…, p_j ,…, p_n)

This state or S-matrix channel is related to but distinction from the channel

|φ’) = |p_1,…, p_j,…,...

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Dear Lawrence,

WOW! It will take at least a week for me to digest this information, but everything seems to be coming together.

You said "Higher homotopies exist for spaces with larger dimensions, where the ordering of homotopies determines the vertices of associahedra. A braid is a (ab) ¡ (ba) edgelink, and an associator is a(bc)¡a(bc) for fields defined on the vertices . The associators with three elements define two hexagons, which link vertices in associator by commutation of the elements in parentheses. Braid links between the commuted vertices defines the general system of associators plus commutators. The associahedra K_4 for four elements is a pentagon. In three dimensions the Stasheff polytope K_5 or associahedra. This polytope is constructed from pairs of three hexagons glued into ”tents,” which are then attached to form a solid with three squares arranged π/3 radians from each other. This polytope may also be constructed by gluing two tetrahedra together and truncating the vertices in the same plane. Similarly, to the system with three letters copies of these associator exist with commutative links between vertices."

This looks like the permutohedron of type A3. I want pentagons with a triality symmetry, so I'm thinking more like a dodecahedron (H3 - has the basic triality and pentality symmetries, but doesn't explain hexagons morphing into pentagons) or a Carbon-60 buckyball.

I've been trying to get rid of a cold for the past week. I need a clear mind to focus on these ideas.

Have Fun!

Ray

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Dear Lawrence,

Thanks for the information. It will take some time to fully digest it though.

Thanks again,

Florin

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The business of quantum homotopies might feed into the idea of E_∞, by El Naschie. I must confess at this point I don’t know what is meant by this. Yet the question did occur to me whether E_8 has some Bott periodicity structure. We might think of there being 3 SO(8)’s in there, and these have certain structure involved with Lim_{n->∞} SO(n), with Z and Z_2 homotopies and with cyclicity of 8. I studied this in depth years ago, so maybe with some review I might be able to think about this some.

Cheers LC

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Dear Lawrence,

El Naschie's E-Infinity has an order of 685.4~(26.18)^2, which is remarkably close to the K12' order of 684 that I've been playing with, and it contains the golden ratio 2.618=1.618^2 that is currently a hot topic. He and I shared some ideas a year-and-a-half ago.

My interpretation is that K12' is the first "Wigner-Seitz" primitive cell of a finite-sized lattice. If we take the limit towards an infinite lattice (in all directions) then we may need to also include fractal-sized contributions, and this may explain the differences between my discrete geometrical ideas with K12'=684 and his fractal geometrical ideas with E-Infinity=685.4.

Unfortunately, El Naschie is occupied in the lawsuit with Nature, his publications have drawn considerable critism recently, and I have been ignored by arXiv probably because of my associations with El Naschie and Lisi.

The occurance of the golden ratio 1.618 requires pentagons (I addressed this in more detail on my blog site), but does not require fractals. This is part of why I keep looking at the Carbon-60 buckyball.

Have Fun!

Ray

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Dear Physicists,

As I understand Lisi's E8 paper, he has 20 'holes' that seem to imply new particles. I claim that new particles are relevant to any search for a correct theory of physics. Since our essays were written in October 09, there have been about 12 issues of Physical Review Letters published which report on the continuing search for 'new physics'. The result is: Nothing New, but tighter constraints have been established. Of course the LHC has not yet come online, but I do wish to point out that prediction is far better than post-diction, and also to point out that my theory predicts that No New Particles will be found, Nada, Nil, Nothing. This is not based on a 'safe bet' or 'contrarian' approach. The reason for this prediction is that my theory explains ALL of the currently known particles and appears to have no mechanism for producing new fundamental particles. (The explanation for all current particles is laid out in "The Chromodynamics War".)

This means no Higgs, no axions, no right handed neutrinos, no SUSY, no WIMPs, no extra dimensions... ALL of the known particles come from my treatment of the primordial field that I assume as basic. I believe that Marcel-Marie LeBel offers a well reasoned argument for such an approach (although I differ from his interpretation of the character of this field.)

I would hope that the purveyors of other theories would clearly and distinctly state just what predictions they make. After all, it really won't be long before the LHC tells us who is correct. I believe that everyone pushing a theory should predict now, not wait until the results are known, and then attempt to 'match' these. The fact that mathematics is, for all practical purposes, infinite, says that we can always match what we know to be true. This is what Fermi meant by his 'elephant' analogy.

I can understand the excitement of new mathematical formulations, especially if one takes seriously Tegmark's Mathematical Universe hypothesis (I don't), but to a relatively unbiased observer the conversations on this thread appear to be wild thrashing and flailing, looking here, looking there, for the magic bullet that will capture "reality". Unless one has a theory that predicts what this reality will look like, what's the point? This is not to criticize those who merely find joy in exotic mathematics, but it is to ask what, as physicists, is the measure of success. If predictions no longer have significance, what does?

I hope it's not considered to be in poor taste to point out that predictions are still important in physics, and to ask physicists to state their predictions while they are still "pre"-dictions.

It's fun to state predictions, try it.

Edwin Eugene Klingman

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There are some problems with the basic E_8 theory of Lisi. One of them is that he frames the graviton with other fields in a way which is in conflict with the Coleman-Mandula theorem. The other is there are some triality conditions he imposes which are not mathematically justified. The idea is bold and as a first attempt worth its effort. I will say that the theory lacks supersymmetry, which is a consequence of the C-M violation.

Axions are a CP violating particle associated with QCD. It has been a question as to why weak intereactions have CP violations and not QCD. I am not commmitted to the idea of the axion, but there are some reasons to suppose they might exist.

Ray,

I am still not sure about E_infinity, but this seems to suggest some sort of generalization of Bott periodicity. Maybe the Bott periodicity computes the continued fraction for the golden ratio.

Cheers LC

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Dear Edwin,

You claim that your theory “explains ALL of the currently known particles and appears to have no mechanism for producing new fundamental particles.”.

Now this is a bold claim, and I took a closer look at your essay entry (assuming that this is the theory you are talking about).

On page 8 you state: “The key equations (with constants suppressed) are…” and list 4+4 equations. Now the 4 G+C equations are inconsistent.

Take curl C = dm/dt +dG/dt and div G = -m

Apply div on first equation and you get an incorrect “continuity equation” where mass is not conserved. If however the first equation is div G = +m, continuity is restored.

Now take divG = -m (or +m) and curlG = 0. It is easy to get Poisson’s equation for G with m as a source. All OK, but this is just like electrostatics and violates special relativity (just as Newtonian gravity does) because any change in the position of mass would have to be propagated with infinite velocity to the rest of the universe.

You also attack Tegmark's Mathematical Universe hypothesis. If I understood your argument correctly, it is: map is different than territory. In other words, marks on paper describing reality are not reality itself. I do not disagree with this, and I suspect neither does Tegmark.

First, math does exist outside space and time. The fact that the sum of the angles in a flat triangle is 180 is true now, was true in ancient Greece, and was true at the moment of Big Bang. Mathematical results are only waiting for mathematicians to discover them, but they do exist independent from our reality.

Then you ask: “How will Tegmark demonstrate that physical reality arises from (is) math?” Now this is a question for Tegmark, and I cannot answer it. What I can do however is present how I answer this myself in a slightly different setting, which is do not look for similarities between math and reality (like Tegmark), but look at the differences.

Regards,

Florin

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Dear Lawrence,

Bott periodicity with fractal sphere packing may be the key. I suggested something similar to this to Steve Dufourny nearly a year ago, but he didn't consider it 'foundational' enough.

I'm not trying to prove El Naschie's ideas at this point. I'm trying to discover how spacetime connects with hyperspace and supersymmetry. But it would be interesting if a minor calculation could convert my discrete geometrical K12' into El Naschie's fractal geometrical E-Infinity.

Have Fun!

Ray

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Dear Florin,

Thank you for investing the effort in my essay required for your above response.

These are of course vector equations and I have written them symbolically to emphasize the dependence on mass m and charge q. Unfortunately, my discussion of the symbolism was deleted due to the ten-page limit. I actually considered this problem but then decided that it would be evident...

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Florin,

I turn my back on my computer and it takes my name away...

Edwin Eugene Klingman

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Dear Edwin,

Continuity equation for electromagnetism is: partial rho/partial t + div J = 0

From your equation curl C = dm/dt + dG/dt take the div and get div dm/dt + d div G/dt = 0 Combined with divG = -m and calling dm/dt = J you get

div J - dm/dt =0 with a wrong minus sign. To fix continuity you need:

curl C = dm/dt – dG/dt if div G = -m. The other option is to keep the curl C equation, but change div G equation into: divG = +m. Now the second case corresponds to repulsive gravity, and the right way to fix the equation is curl C = dm/dt – dG/dt while keeping div G = -m. (last time I gave you the wrong advice on which equation to change)

About the instantaneous change, yes, C evolves and it is affected by G, but your equations are decoupled and G depends only on m, just like in Newtonian gravity. The criticism was about G, not C.

About mathematics, you state: “You believe that mathematicians discover math. I believe they create/invent it.” Then here is a simple question: was Pythagoras theorem valid before Pythagoras? Or was 1+1 not equal with 2 before humans discovered it? Mathematics is an abstraction, which by its very meaning means that it does not depend on its representation, be it for example marks on paper in Chinese, German, or English. As such it exists outside space and time, it is timeless. Compute e = 1+1/1! + 1/2! + 1/3! +… on a PC or on a Mac, here or on Mars, in this universe or in another universe. The answer is the same regardless of its representation. Nobody invented e or pi, the mathematicians only became aware of their properties.

Now consider the unreasonable effectiveness of math in physics and the “why those equations” questions.

Can we find an answer rooted only in mathematics? No, because mathematics is abstract and one cannot write the equations of our universe on paper, say fly and a new universe will form. We have to distinguish between the map and the territory.

Can we find an answer rooted only in nature? No again, because this is only a circular explanation: it is this because it is this and we see it in experiments.

Do we have another option? Yes. Compare mathematical properties of nature which are universally valid in nature, but not universally valid in the world of abstract mathematics. I have found 3: truth, composability, infinite complexity. Now select from the infinite world of abstract mathematics those and only those structures which satisfy those 3 principles. The answer is (so far): quantum mechanics, space time in 3+1 dimensions, electroweak symmetry. So here is an answer to “why those equations?”. I hope more will follow. Is this math based? Yes, the consequences are pure mathematical theorems. Is this reality based? Yes, the 3 principles have to pass all past, present, and future experiments. What we have is in fact a recipe for axiomatizing physics.

Regards,

Florin

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Dear Florin,

Your electromagnetism continuity equation is of course correct. My last post indicated that the appropriate 'mass current' is j = p = mv = mdr/dt and so

div p = m div v = m div dr/dt = m d(div r)/dt = m d(3)/dt = 0

which is correct for a 'perfect fluid', hence dm/dt = 0 is the correct continuity equation.

My essay assumes that the Master equation applies...

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Ray,

The fractal structure is not due to how spheres pack into unit cells, but how the cells tessellate the space or spacetime. A hyperbolic space may be tessellated by dodecahedra, and in four dimensions by dodecahechoria (120/600 cells). The fractal structure comes from the geodesics in this space. They have a self-similar branching pattern given by a modular function. The self-similar or repeated pattern of branching paths is a fractal, and the Laplace-Beltrami operator in the two dimensional version, the Poincare disk, has a chaotic dynamical interpretation.

Cheers LC

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wawww ,in fact maths or physics ,I am deseperated ,I think never The mathematicians shall change their points of vue .

In all case ,your discussions on this thread are very relevants about this foundamental problem in fact .

We see just differently afetr all ,but hihihi the physicians are right hahaha

the war against mathematicians ,hihihi afetr star wars ,maths wars ,

A nice war ,it is the most important .Let's go the physicisians ,the hour is serious hihihi

Laugh is good for health after all .

Take care dear friends ,mathematicians or physicians

Steve

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Dear Edwin,

One can imagine a recursive ontology structure: our reality contains a PC with a simulated reality and inside there is another PC with yet another simulated reality ad infinitum. This is possible because a universal Turing machine can simulate another universal Turing machine. Moreover, the “laws of reality” at each level could be different. Math is valid in each of those ontology, and according to your argument, (an) ontology is required to be able to speak meaningful about mathematical theorems. But which ontology? Any higher level ontology will do the job, and therefore there is no 1-to-1 correspondence required between math and reality. Applying Occam’s razor, no ontology is really needed to have valid math theorems. Ontology is required only for the existence of mathematicians, but not for the existence of the Platonic world of math. (This is like sqrt(2): a limit which requires an approximation series, but ultimately independent on it.)

The second point I want to make is that reality is made out of relational structures. If one forbids the supernatural and metaphysical, then reality is fully comprehensible and this means there is a dualism between reality and math, each one completely describing the other.

So how is reality made out of relational structures? One may think the universe is a giant mathematical theorem (Tegmark’s approach), but this runs into contradiction with Gödel’s theorem. He circumvents the problem by requiring reality to be computable, but this goes against the observed infinite complexity of reality and against free will. I say that our universe is made out of many mathematical relationships, some playing a backbone role (like quantum mechanics and relativity), others only a limited role. Please see my essay: “Heuristic rule for constructing physics axiomatization.”

Regards,

Florin

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Dear Florin,

I agree that one can imagine a recursive ontology. And if one has no sense of the real, then one might as well do so.

As I state in my essay, I sense gravity and I sense consciousness. I do not sense dozens of quantum fields nor do I sense a recursive computer.

Many people report states of consciously being "one with the universe". Last year a book, "My Stroke...

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Dear Florin,

your approach to describe/explain reality is interesting and worth (in my opinion) to be examined further. I am sure your approach will gain some of the higher prices here in the contest (in my opinion), but nonetheless, i have some critics about your lines of thought.

Firstly, the assumption of a recursive simulation of reality, where each instant of the recursive whole...

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Dear Florin,

your approach to describe/explain reality is interesting and worth (in my opinion) to be examined further. I am sure your approach will gain some of the higher prices here in the contest (in my opinion), but nonetheless, i have some critics about your lines of thought.

Firstly, the assumption of a recursive simulation of reality, where each instant of the recursive whole is equipped maybe with different physical laws, but with the same maths/logical relations, presupposes maths as the ultimate reality of it all. This is not only a recursive "simulation"-argument, but literally a recursive argument in the sense of a circular argument. Because it presupposes to know exactly, what ultimate reality is - namely the platonic realm of maths - and then puts a part of this maths into a PC. This argument is then repeated at every instant of this recursive "simulation" and i doubt that it is more than a thought-simulation, a Gedankenexperiment.

Secondly, the implicite assumption of the whole Gedankenexperiment is, that an exclusively mathematical procedure can prove the exclusiveness of mathematics.

Not only this line of reasoning is suspect to me once more, not only because of its obviously recursive, circular argumentation, but also because it presupposes each and every world that is thinkable to be a universal turing machine (here the circle closes by identifying maths + infinity = universal turing machine).

Thirdly, i assume that the whole argument breaks down, if one would eliminate "infinite complexity", means the component that makes your simulation linearly infinite (ad infinitum, you would say). Surely, in none of the simulated worlds must exist some sort of conscious beings. As you stated above, it needs a free space for "free will" (whatever it embraces) and hence for consciousness. I think your assumption of the "observed infinite complexity of reality" that you stated above is once more a circular argumentation, because no one has yet proved this infinite complexity in nature. Once more, in this context the concept of infinity seems to only be a free space, a spaceholder for unknown things (our search for ultimate reality) - and a circular argument to reinforce the infinite simulation of realities - in the sense of mathematical infinite complexity in a platonic realm. Maths may be infinite complex, but i doubt that nature is so, too. At least not in a mechanical, mathematical sense. But if not in this mathematical sense, then there is no reason to assume that reality and maths can completely describe each other.

The "result" of sqrt(2) may be infinite, or at least the procedure to calculate it may be infinite. If all physical constants would be infinite, the whole argument would break down because a simulation of reality on a PC with infinite physical values is only traceable in imagination - not in time. Therefore a world with time in it cannot be produced out of such a procedure. Your claim is that our world is the only world, the exclusive result of infinitely many mathematical relations which only allow one ontology to come into existence - ours. So the question which of the infinitely many "simulated" realities can serve as an ontology, is answered circularly by the person who constructed these lines of reasoning. Yes, i know, the latter can't be otherwise - but those lines of reasoning are nonetheless circular because they exclude all other possibilities (possibilities that ALSO can be imagined) for the aim of the exclusiveness of maths.

Fourthly, assuming that your considerations are the truth and reality is a "recursive ontology structure" (i think it is so and i will make my remarks to that later), then the next circular argument that is tacitly interwoven into your structure of thoughts is following: To overcome the problem that in any exclusively mathematical system there is no room for a proof of non-mathematical ingredients, you try to prove exactly this by inventing the "recursive ontology structure", based on mere mathematical observations of the non-denumerable infinity that can serve as argument that there is no 1-to-1 correspondence required between math and reality.

What you have done is to justify the - obviously true - observation of consciousness, free will, the existence of mathematicians etc. by substituing these "non-mathematical" ingredients by "non-denumerable" ingredients/ontology. That is indeed a "recursive ontology structure". The question is, does this structure only exist in your imagination or is it indeed the truth? My assumption is that you are somewhat right with your claim that there could exist such a recursive ontology strucure.

I assume that the "ontology"-part of this structure is consciousness, the recursivity is self-consciousness and reflection (not only in a logical sense, but also in an emotional sense) and the fact that it is structured in such a recursive way is that it is able to quasi-differentiate itself continuosly on the basis of the ability to pass "duality" on to every instant of this differenciation-process (because the "mechanism" for this division is simple and universal: 1:2 = 1+1 = conserving the form, not the content, because on the right hand side of the equation every "1" is again 1:2; you can read it from right to left, there's not time-direction in it). Duality in this sense means nothing more than each side of this duality describes the other side. "Desribing" also in the meaning of defining. Without this process, there aren't definitions possible. What would remain seems to us as an undefined "thing", not able to percept itself or something else. But that could only be a consequence of duality, our left side of the brain. Because when we percept something, we almost always differentiate something logically. In my opinion logics/maths comes from a timeless/spaceless consciousness, not comparable to human consciousness, but nonetheless vital.

The reason for the overwhelming consistence in nature and logics has its roots in the exact self-similarity of the described differentiation-process. Connectivity is only possible if the parts aren't really separated from each other and i assume that the reason for all this is that the above described formal procedure with which the quasi-differentiation works is conserved under every instant of the whole process. We cannot think rationally without opposites, and therefore all opposites/logics/maths has to form out of the same source.

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You can sense the other gauge fields. The visual experience of light is the EM field. The weak and nuclear forces are not as directly experienced, though some people did live to tell about in Hiroshima and Nagasaki --- one man who died recently experienced both! Other ways to experience the EM field, or its source is to put a (v battery to your tongue. If that is not enough I always thought urinating on a wall socket would be adventurous.

Cheers LC

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Years ago, we had a Dalmation that urinated on the electric fence. That was one stupid dog. My two rescue-shelter mutts are much more intelligent.

Dear Ed,

I know that Florin brought up some mathematical questions regarding your essay. I did not double-check your math. If Florin thinks he sees something wrong, then you should double-check it. What I liked about your ideas was that you tried to model these fields of Consciousness and Gravity. I used your paper as an example of what the physics community expects of Frank (who has no math or concrete modeling in his writings). If your fundamental idea is robust enough, then you should be able to 'tweak' the math to make everything work correctly.

Regarding 'Big Numbers', I don't make such a big deal about "Billions and Billions of stars" (I met Sagan back in the early 90's), but I do think that Dirac's Large Number - the relationship between 10^40 vs. electromagnetic to gravitational couplings vs. size of Universe to size of atom - is relevant mathematical physics that is not yet fully understood.

Have Fun!

Ray

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Dear Lawrence,

I mention in my essay that we sense at least a small portion of the electromagnetic spectrum. Those of us with sight experience colors and shades. Almost everyone experiences infrared on their skin. For this reason the electromagnetic equations are included in my theory, and the mechanism whereby charge and these fields come into being is explained.

While certainly the atomic radiation 'happened to' some humans (as it does when one has an x-ray or MRI scan), nevertheless one does not 'experience' it in the sense that I refer to.

The C-field appears to accomplish everything that the 'weak' and 'strong' forces are believed to do, so they may be a false map. The failure of the Higgs to appear will further call these into question.

I recall someone in high school being talked into urinating on the spark plug of a running jeep, and yes, he did 'experience' electromagnetic phenomena directly.

In my theory the electro-magnetic fields are 'derived' and hence secondary in some sense. They do not exist 'at the creation' but come into existence only after the perfect radial symmetry is broken.

So although we do experience various EM phenomena, gravity and consciousness are sensed in a wholly unique manner that I believe must be somehow represented in any 'theory of everything' worth the name.

Edwin Eugene Klingman

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Ray,

I told Florin that if he still had a problem, after my last explanation, that I would reconfirm the sign of dG/dt in the cosmology work I've done. He did not say that he still had a problem, so I assumed it was now considered ok. The equations are derivable from linearized General Relativity. It is only the curl G = 0 and the kappa constant that I add to the equations. The kappa value was worked out by me and measured by Tajmar, and seems to be real. The curl G condition also seems to be supported somewhat by Tajmar's results (although that's not quite as certain as the kappa is.)

As for 'large numbers', there are almost infinite numbers to play with, so that, in my view, there simply *must* be coincidences similar to Dirac's observation. I don't think it's very significant, but of course I could be wrong. I see no reason that the sizes of atoms and universes should have the same ratio as forces. In 'Chromo War' I explain the particle size, and the size of the universe seems to change over time.

Ed

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Dear Ed,

I too enjoy this back and forth, and I wish I had more time than once a day to reply. About consciousness, I am not an expert in this area, and I cannot offer any meaningful comments.

You state: “I reject all ideas based on multiple universes, multiple layers of recursion, multiple dimensions, etc.”

About multiple universes, you need to answer the following...

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Dear Stefan,

Thank you for your kind words, we’ll see the outcome on Tuesday.

You state:

“Firstly, the assumption of a recursive simulation of reality, where each instant of the recursive whole is equipped maybe with different physical laws, but with the same maths/logical relations, presupposes maths as the ultimate reality of it all. This is not only a recursive...

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Florin,

Thanks for the reply. I'd like to address the sign issue, and reply to your other questions later.

The derivation of the curl C = dG/dt on page 3 of my essay assumes right handed C-field. The actual C-field circulation is left-handed, so that introduces the negative sign that you desire. In most applications I take this into account, but you are correct that it makes a difference in the equation. When I derived these equations in 2006, I did not know the handedness of the C-field, and since the continuity equation for the 'perfect fluid' yields zero correctly, I missed that formal hint. It was only later when I realized that the C-field vortex is the Z boson that I was sure of the handedness, but the dG/dt term is not used in the particle physics applications, so I ignored it. Thank you for holding my feet to the fire. I do remember a sign problem in a cosmology calculation. I hope this fixes it. (Ray, thanks for keeping the issue alive.)

As for Newton's equation and instantaneous change, why would not the same logic apply to Coulomb's equation, since they are formally equivalent. Just as moving charge induces a magnetic circulation, the moving mass induces a C-field circulation, from dG/dt = p - curl C. In fact the change in gravity alone induces C-field circulation. And the change in gravity implies a change in gravitational energy with equivalent change in gravitational field mass. The non-linearity of the fields interacting with the mass and with each other seems to argue against instantaneous propagation. of the G-field. It's not clear to me why this implies infinite velocity any more than Coulomb's law (plus the other EM equations) does.

Stefan - it's nice to see you jump in. I always appreciate your comments.

Edwin Eugene Klingman

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Dear Florin,

thanks for replying.

My gut feeling is, that your approach is thought-out very well and i haven't any doubts that it is also the case with your mentioned and used mathematical tools, like orthogonal groups SO(p,q), elliptic, parabolic, and hyperbolic classes etc. It seems to fit all well together and if one can indeed succeed by singling out certain exclusively unique mathematics for our universe, this would be a great result and of deep philosophical importance. I cannot comment on any of the mathematical tools because i am not an expert in this area, but i don't doubt in any way that you have the deep understanding of these tools to draw the right conclusions out of them.

My only doubt was, that for eliminating an ontology of ultimate reality one had to presuppose that physical reality is indeed "only" a universal turing machine. If the latter would be true, i am not sure if this would mean that an exclusively mathematical procedure can indeed prove the exclusiveness of mathematics. I understand your approach in this way, that if one could obtain indeed physics axiomatization, then this result could serve as a strong indicator that an exclusively mathematical procedure can prove it's own exclusiveness by comparing it to the timless content of the platonic realm and at the same time prove the exclusiveness of this platonic realm of mathematics - by comparing it with the maths of our physical world.

I understood your example with the different PCs, emulating different worlds/ontologies, as an example of the impossibility to fix a certain ontology onto our *physical* universe,if it would be indeed "only" a universal turing machine. The precondition for the physical world to be a universal turing machine is, that the physical universe and the laws within are consistent, coherent and universally true (that's a necessity, but not sufficient). But does your Gedankenexperiment also apply to the *Gödel-restricted* realms of mathematical, infinite landscapes/systems/frameworks? Means, to deduce out of the concept of a universal turing machine that the platonic realm of maths doesn't need an ontology? Or have i to understand it in that way, that every platonic consistent system/framework/part can be understood as a turing machine within its own area?

Eugen - nice to met you again here. Very interesting discussion here, as always on fqxi! Wish you all the best for the contest results!

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Dear Florin,

You state, "I do not know about consciousness, but I do know about free will" "Free will is equivalent to the ability to decide what to measure in QM... there is a 'free will theorem' in QM"

I would not say 'equivalent', but the sense of your statement is correct. Without getting too far into semantics, I question whether one can 'not know' awareness and 'know' free...

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Dear Florin,

You state, "I do not know about consciousness, but I do know about free will" "Free will is equivalent to the ability to decide what to measure in QM... there is a 'free will theorem' in QM"

I would not say 'equivalent', but the sense of your statement is correct. Without getting too far into semantics, I question whether one can 'not know' awareness and 'know' free will. They are, I believe, inseparably intertwined. If as you state elsewhere, you believe that "consciousness is an emergent property" then it is Darwinian, and two things follow: Awareness would have no survival advantage without free will (the ability to act on this awareness) and free will is meaningless without awareness. By this I mean that 'having a math model or theorem for 'free will' is not what I mean by 'know'. Know is for me personal experience; it is the territory of reality. Math and theorems are maps.

In reply to Stefan, you state that "consciousness is an emergent property". This is your belief, and it is the consensus belief, but Climate-gate has recently focused attention on the fact that science is not consensus. It was the consensus belief in the middle ages that "flies emerged from rotten meat". I believe that 'emergent consciousness' is similarly mistaken.

The fact is that no one, anywhere, has developed a model or explanation for how conscious awareness and volition can arise from 'stupid' material. I have written a number of chapters on this -- far too much to go into here. But recall that I define intelligence as 'consciousness plus logic', i.e., the evolution (emergence) of logical hardware is required for intelligence to develop. Intelligence is required to create calculus, even to develop ideas of past and future (based on recall and projection of information stored in the logical machinery).

I am not trying to convert you from your beliefs -- only about twenty percent of the FQXi authors appear to take consciousness seriously as something that physics must deal with. But your statement "consciousness is an emergent property" is so strong and unqualified, I felt the need to throw in a little qualification.

You do state that your gut feeling is that it is not relevant to physics. Depends. At the particle physics level you are absolutely correct. Although I show (Chromodynamics War) how the C-field can explain particle families, provide an intuitive understanding of the mechanism of the weak force, and also provide the quark confinement associated with the strong force, I do not believe that awareness or free will have any significant part to play here.

I do suspect that awareness comes into play in entanglement, and I believe consciousness provides the biophysics explanation for the first living cell, which otherwise is infinitely unlikely to ever occur.

But it is cosmology where consciousness may come into its own. As I show in my essay, the C-field provides an inflation mechanism that is more 'real' than any of the imagined fields currently proposed. Not only is this a 'dark energy' source but the energy of the C-field also offers a dark matter explanation. And the C-field, as I explain in 'Gene Man's World' provides an explanation for Zwicky's 'flat rotation curves' so that a messy MOND is not needed.

Klingman post continued:

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Continuation of Klingman post:

But I'd like to address your question, "why is our universe happening only once? ... Earth is not the center of the solar system, our sun is not the center of our galaxy, etc. etc." You may be unaware that the WMAP measurements, circa 2003?, in analyzing various polar distributions, quadrupole, octupole, etc, expected to find uncorrelated directions for each...

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I wrote more on nonassociativity in physics on the site involving warp drives. This is in keeping with trying to illustrate something about how nonassociative principles might operate in physics. If you (Ray, Florin etc) are interested you could reply here. I am not entirely pleased with the intellectual level of discussion on the warp drive site, or frankly most of the blog sites.

LC

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Dear All,

I checked out the warp drive thread enough to find Ray Munroe's statement:

"Could we control tachyons inside a gravitational bottle? It would be the gravitational equivalent of using a magnetic bottle (such as a tokamak) to confine plasma. If we could contain tachyons thus, we may be able to release them such that we can steer our spaceship. Could we envelope our spaceship with a tachyonic field and trick Gravity into thinking that the entire spaceship is a tachyon? And could we steer such a spaceship?"

I've noted on his thread that this 'gravitaional bottle' forms an explanation for the confinement of quarks, currently attributed to 'the strong force'. It also provides a mechanism for sustaining the 'cigar shape' of deuterium, whereas QCD would predict a six quark 'collapse' to some spherical combination. And it also can explain the negative 'core' of the neutron, whereas all QCD predictions call for a positive core. All of this follows from viewing the C-field as the rotational aspect of the G-field.

Hopping around the threads and essays certainly proves that there is no end of 'wild' speculation. For this reason it seems more important than ever to PREDICT things. To my knowledge there is no place where one may go to find various predictions for the LHC.

I would invite those who make predictions to place them here. It would be nice to see just what is predicted for LHC (or WMAP-follow-ons, etc.) before the results are known and explained 'post-dictively'.

If one can't predict anything, what exactly is the point of intellectual analysis. Is it to see who can describe the universe best by looking in a rear-view mirror?

If predictions still mean anything in physics, let's hear some.

Sincerely,

Edwin Eugene Klingman

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Dear Ed,

I will reply in turn to each message. Let’s start with:

“As for Newton's equation and instantaneous change, why would not the same logic apply to Coulomb's equation, since they are formally equivalent.”

Indeed, but the E and B fields are linked by Maxwell’s equations, and a change in one induces a change in the other and vice-versa. In your equations C depends on G, but G does not depend on C and this is the problem. G depends only on the mass distribution and when that changes G changes everywhere with it instantaneously.

Regards,

Florin

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Florin,

Thanks... But changes in the G-field are linked to the C-field, thereby extracting energy from G. Why is this insignificant?

Ed

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Dear Stefan,

You state: ”My only doubt was, that for eliminating an ontology of ultimate reality one had to presuppose that physical reality is indeed "only" a universal turing machine.”

This is not what I was saying. A universal Turing machine (UTM) violates the third reality principle: “infinite complexity” because the algorithmic information content is limited by the program running on the UTM.

“Or have i to understand it in that way, that every platonic consistent system/framework/part can be understood as a turing machine within its own area?”

Something along those lines, but a bit more general. The platonic world of math is a collection of axiomatic systems. Each axiomatic system exists on its own. In math there are many types of logics which go beyond an UTM ability.

The UTM usage in my argument should be understood in two ways. First, we fully understand the UTM theory and we have a rigorous framework of discussion free of conflicting interpretations. That is, the usage of the UTM adds clarity. Second, different ontologies do not have to be like our own universe’s ontology. In other words, there is an ontological democracy. And indeed, some ontologies are much more interesting and richer in content than other ontologies, but there is no objective value that can be attached to one ontology vs. another. To be able to make judgments about various ontologies, is to have a meta framework in place, and this simply does not exists. The only thing we can use is infinite complexity vs. finite complexity.

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Dear Ed,

Please understand that my ideas are still evolving. My models definitely have a five-fold 'pentality' symmetry that is relevant to the golden ratio (file attached). The fifth vertex corresponds to 'scalar fermions'. These scalar fermions can be chromo-tachyons that obey the strong force, or lepto-tachyons that obey the Electro-Weak forces. They might even be related to the Higgs (research in progress). I don't have a gravitational bottle - it sounds like a worm hole or black hole. I haven't studied the interactions of gravity and consciousness closely. My model also has a triality symmetry. Like Lisi, I think the triality symmetry has to do with three generations. However, there is a possible color triality as well. In my models, the apparent three-fold color triality becomes a four-fold color quartality of (red, green, blue, white). H4 has a four-fold quartality symmetry, and E8 has an eight-fold octality (4x2?) symmetry. Lawrence Crowell also has a triality symmetry.

I agree that it is relevant to state our predictions prior to the LHC's results, however a robust enough idea can be adjusted to fit the data. I am still trying to understand these weird scalar fermions.

Have Fun!

Ray

attachments: 1_goldenratio.pdf

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Dear Ed,

>“free will is meaningless without awareness”

I disagree. Even a frog has free will, but it does not have awareness.

>“'emergent consciousness' is similarly mistaken”.

Not that I am an expert, but can we explain consciousness in reductionism fashion? When a piece of the brain dies, the other parts can take over and consciousness looks to me to have a...

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Dear Lawrence,

I read your post, but I am still having difficulty to make the connection with the S matrix. On the other hand, I have an idea of how to obtain supersymmetry from quantions, it will take me quite some time to finalize it (I hope my intuition is right and it will work out until the very end).

I finished the 12 GR lectures and now I am seeing all the other Susskind’s classes. The mystery of his approach is solved: he lectures continuous education classes with no final exam. Those classes would have been good as preparation for a qualifier: you can just listen to them without taking notes and getting insight into things which escaped notice the first time when you are busy absorbing the new material.

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Ray,

“Like Lisi, I think the triality symmetry has to do with three generations.”

Is this right? Is not triality related to the interaction vertex in Feynman diagrams: one fermion line emits a boson line, and continues as a fermion line? Equivalently, this has to do with the gauge symmetry (for example the A_mu in electromagnetism acts as a connection). But the gauge symmetry of the standard model is independent of the generations and therefore triality should have nothing to do with it.

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Dear Edwin,

sorry for having confused your first/second name in my last post, i was just too deep absorbed in my lines of reasoning... By the way - interesting issue, the wmap measurement and the correlation of the axis to our solar system. I have to read more about it.

Dear Florin,

thanks for your clarifications. Yes, i wondered, if our physical universe would be indeed only a UTM, how could one then ever reach out of this area to the platonic realms of maths? To reach out to new information, one has to consider that at least our ontology/universe isn't a "closed system" in the sense of finite information content. In that way i understand infinite complexity in your approach as ingredient for creativity, free will and consciousness.

As you can imagine, my own approach differs from yours when it comes to the nature of the essence beyond time and space. For me the essence isn't maths, but awareness/consciousness. But not in a human sense of self-awareness. From outside of this awareness, for observers like us, it looks like consciousness could serve as the ultimate ontology, but the question that follows out of this intendation is automatically "What is the cause/root of that awareness?".

From inside of it this question doesn't make sense, because this awareness/source of ultimate reality is simultaneously the source of all opposites - and therefore the source of all questions and answers. By the very first differentiation of that awareness - by exploring the idea of conscious/unconscious for the purpose of some interior intentions, it created the question about identity/difference and the following self-similar differentiation process generates the answer to this idea/question.

This process may be infinite. It may generate infinitely many sub-conscious entities that have to transcend the initial idea of self/not-self to come back to the inital awareness with a richer knowledge of its ontology - in the meaning of quality of experience. This experiences heighten the complete initial awareness. Though this initial awareness doesn't need an explanation of its own ontology, because it's essential awareness is self-evident in each instant of it, it needs to explore its own quantitative meaning and its possible borders to enrich its quality of experience. In this sense, experience is the only "ontology" and it is subjective/interior.

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Max Tegmark has mapped the octopole CMB on a sphere and it looks quite beautifull here.

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There I am happy dear Mr Tegmark ,yes the universe is a sphere in evolution .

But I don't see my name, it is not serious ,I have the habit .

You are going to have the nobel price dear Mr Tegmark and his team .

Congratulations for this splendid disovery ,the universe is a sphere .

PS Mr Tegmark ,you have forgoten the universal center where all turns around .An other poit is the variability of the volume of this universal sphere .A specific dynamic exists since the begining .Expension and contraction .

Regards

Steve

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Serious error ,the center ......

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Dear Florin,

I suspect that in Lawrence's full blown 26-D model, that one octonion is the initial fermion, one octonion (and the global G2 triality operator) is the interaction boson, and the third octonion is the final fermion. This may be related to Mohammed Sanduk's 'Three Gear Model' essay.

But at some level of decomposition, I expect the generational structure to 'make sense'. I am convinced that if there are 3, 4, 5, or etc. generations, then there must be a symmetry that enforces that reality. There seem to be two triality symmetries in Lawrence's 26-D model: one buried within E8 (240 roots = 8x(2x3x5)), and one connected to the global G2 (12 roots = 2x(2x3)). Thus, we could have a generational triality and an interaction vertex triality.

Dear Steve,

Tegmark's map is impressive, but he has non-spherical results mapped on a spherical map. Is that really spherical in evolution? My truncated icosahedon (soccer ball) is more spherical.

Have Fun!

Ray

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The space of the universe is probably R^3, or Euclidean space which extends indefinately. THe CMB represents a radial distance out, and as observed with photons also a time in the past, when the universe ceased to be radiation dominated and became matter dominated. The CMB is then a region of a past spatial surface, with geometry or topology R^3, which intersects our past light cone.

Cheers LC

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The space don't expand indefinately.The radial disdtance must be with the universal center and furthermore this radial distance is variable in time.

The rotations too must be inserted .

The light cone is not sure .

The evolution and the increase of mass by complexification too must be inserted ,ps the complexification here is the mass and its evolution ,not the complexs in maths ,it is totaly different .

The thermodynamic must be too inserted .The pression and the volume are foundamentals and if the rotating spheres ,quantics or cosmologics are correlated ,thus the mass becomes relevant .

The centers must be too inserted with their variabilities of volumes.

The number too of the entaglement ,quantic or cosmologic is the same ,the serie is specific .

An other point ,all these centers (quantic or cosmologic)turns around the universal center .

The fractal is a specific finite serie .

Regards

Steve

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A flat spatial surface (flat on average) is one where the holographic principle works with the Bekenstein bound. There is a bit of background here that I don't want to get into for brevity's sake. The universe still is expanding, as points on a spatial 3-surface keep sliding apart, where any frame at any given point will see distant points slide away at velocities which "approach infinity." Already we observe galaxies with z > 1, which means these are frame dragged galaxies on a comoving frame which has velocity > c. However, there is a cosmological horizon present which precludes any idea of FTL transport on a closed path --- to somewhere and back for instance. Similarly, any particle which passes the event horizon of a black hole is moving faster than light relative to a distant observer.

Cheers LC

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Hi all ,

I am not a supporter of the flat universe.I prefer an spherical finite space wher k takes its real sense about the referential.The bottle of Klein ,Moebie,the torus etc etc all is a question of topology.

Dear Lawrence the problem is not about the infinity or about the quantity of matter.In fact the holographic principe is the opposite of the Luminet principle if I understand well.

My opinion is what, in this two systems, the center ,the topology finite, the constants are not considered, furthermore the rotation of all around this center too must be inserted.

If not all is perceived differently by extrapolations.

A flat universe is not logic on the line time and too about the evolution and complexification of the mass.

Thus you understand I am not a supporter of an accelerated expansion and a flat Universe.I can undertand we can perceive some different steps since the primordial universe.The rotations thus are foundamentals like spheres and thus the past perceptions are more like that.

The system is variable since the begining and thus the FDC(CMD) must have many adaptations correlated with the real toplogy, evolutive furthermore.

PV ..nRT ...RT....density ....the temperature takes all its sense.....

Regards

Steve

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The human term ‘number’ and the concepts of a counting system are descriptions of difference between topologically whole areas. ‘Two fish’ decribes two discreet entities within a set ‘fish’. What we call number theory is the detailed analysis of how areas of difference within topologically whole entities organise efficiently within that entity.

The differences described however are not the...

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I will list some observations then some theories which try to explain them, including my Gravity For Patterns theory which explains the Copenhagen Interpretation of quantum physics as an approximation of the most infinite version of Manyworlds.

DEFINITION: Laws-of-physics is the statistical behavior of a subset of the universe, usually the subset closest to Earth.

OBSERVATION: The...

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Hello.

I found this site yesterday and I have to say tha I´m very glad to find people who share my own interest.

I´m deeply interested in Tegmark mathematical multiverse hypothesis. Looking at the notion of existence, this concept does not need to be absolute, but local. I mean, rather than assuming a mathematical nature for existence, and then to consider life as a fortunate epiphenomenon in some of the mathematical universes, we instead may consider as criteria for existence the existence of some observing entities within the universe, that is, the existence of life.

looking at the preconditions for life and evolution I found that the absence of contradictions must be a pre-requisite for life, as well as smooth macroscopic phisical laws, both conditions may demand a mathematicity in the candidate universe. Also , due to the intrinsic nature of life and natural selection, it is necessary, in the universe, a direction of increase of entropy to create an arrow of time:

I explain all of this here:

http://docs.google.com/View?id=dd5rm7qq_198c4xrrx6q

More
details abut the arrow of time,entropy and life:

"Arrow of time determined by life´s easier direction for computation":

https://docs.google.com/present/view?id=0AW-x2M
miuA32ZGQ1cm03cXFfMTQyZDhkamh2Yzg&hl=es&pli=1

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Dear All,

The absolute mathematical truth of zero = i = infinity can be deduced as follows as well.

If 0 x 0 = 0 is true, then 0 / 0 = 0 is also true

If 0 x 1 = 0 is true, then 0 / 0 = 1 is also true

If 0 x 2 = 0 is true, then 0 / 0 = 2 is also true

If 0 x i = 0 is true, then 0 / 0 = i is also true

If 0 x ~ = 0 is true, then 0 / 0 = ~ is also true

It seems that mathematics, the universal language, is also pointing to the absolute truth that 0 = 1 = 2 = i = ~, where "i" can be any number from zero to infinity. We have been looking at only first half of the if true statements in the relative world. As we can see it is not complete with out the then true statements whic are equally true. As all numbers are equal mathematically, so is all creation equal "absolutely".

This proves that 0 = i = ~ or in words "absolutely" nothing = "relatively" everything or everything is absolutely equal. Singularity is not only relative infinity but also absolute equality. There is only one singularity or infinity in the relativistic universe and there is only singularity or equality in the absolute universe and we are all in it.

A great scientist once thought what would it be like to travel at the speed of light and came up with the theory of relativity, now it is our time to wonder on what would it be like to be the space-time itself or experience the singularity and realize the absolute truth.

Truth is simple, accepting it is not.

Love,

Sridattadev.

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sridattadev replied on Jul. 25, 2011 @ 14:54 GMT

Dear All,

Absolute Truth

Love,

Sridattadev.

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Max Tegmark, and others that support his contention that the Universe is mathematical in nature, will be interested in a paper published in July/August 2011 IEEE Potentials.

The paper, titled, "A Methodology to Define Physical Constants Using Mathematical Constants" supports Tegmark's contention, but such was not mentioned in the paper; it had to remain as non-controversial as possible. The IEEE link is below.

Methodology to Define Physical Constants

It is on the second page of the Contents. For those without IEEE membership, the postprint can be read/downloaded from my web page.

Methodology Postprint

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