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Lawrence Crowell: on 8/10/13 at 13:08pm UTC, wrote This essay did finish a bit better than the one I wrote last year. I guess...

Lawrence Crowell: on 8/10/13 at 13:06pm UTC, wrote Deterministic models of a logical form, such as states defined in some...

Christian Corda: on 8/9/13 at 19:16pm UTC, wrote Hi LC, Welcome back within the finalists and congrats for the excellent...

Jonathan Dickau: on 8/9/13 at 18:19pm UTC, wrote I replied to your comment above. All the Best, Jonathan

Jonathan Dickau: on 8/9/13 at 18:18pm UTC, wrote Thanks Lawrence, I appreciate the reference to the work of David Foster...

Lawrence Crowell: on 8/9/13 at 13:15pm UTC, wrote My essay was basically a two week effort. I happened to be rereading David...

Jonathan Dickau: on 8/8/13 at 23:57pm UTC, wrote My congratulations Lawrence! Your high placement with this essay is...

Lawrence Crowell: on 8/8/13 at 4:24am UTC, wrote This seems like a fair to decent argument for why there is a role for...


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FQXi FORUM
October 24, 2019

CATEGORY: It From Bit or Bit From It? Essay Contest (2013) [back]
TOPIC: It From Bit is Undecidable by Lawrence B Crowell [refresh]
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Author Lawrence B Crowell wrote on May. 14, 2013 @ 14:24 GMT
Essay Abstract

The digital model of the universe or \It From Bit" is not decidable. A model of the physical universe encoded by algorithmic means will not compute reality. One unknown domain argued to be outside any computerized model based on current quantum eld theory is quantum gravity. A change in axiomatic basis is proposed to address eld nonlocality in quantum gravity.

Author Bio

Doctoral work at Purdue. Worked on orbital navigation and currently work on IT and programming. I think it is likely there is some subtle, and in some ways simple, physical principle that is not understood, or some current principle that is an obstruction. It is likely our inability to work quantum physics and gravity into a coherent whole is likely to be solved through new postulates or physical axioms, or the removal of current ones.

Download Essay PDF File

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Christian Corda wrote on May. 14, 2013 @ 19:40 GMT
Hi LC,

Nice to see you here.

I am going to read your essay and to comment it. I will sent my entry in June.

Cheers,

Ch.

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Author Lawrence B Crowell replied on May. 15, 2013 @ 00:32 GMT
Of course this means I have an added information management issue. I almost didn't submit anything this time. However, this idea came to me last month and after some calculations decided to give it another try. This was a bit fun to work through and write up.

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Christian Corda replied on May. 15, 2013 @ 09:01 GMT
It looks that my previous post was a lucky rabbit's foot for you. In fact, after such a post your Essay became the leading one.

Cheers,

Ch.

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Philip Gibbs replied on May. 15, 2013 @ 12:49 GMT
Glad to see you decided to join in. The essay covers a lot of great material and I will have to read it a few times.

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Robert Bennett wrote on May. 15, 2013 @ 15:58 GMT
" in a nonlocal manner a quantum particle 'knows' how to evolve by sampling all possible paths.......it can still be argued there is either an underlying or a dual perspective on nature which is continuous and not digital."

IOW: an aether

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Author Lawrence B Crowell replied on May. 16, 2013 @ 00:32 GMT
The quantum vacuum is not an aether exactly. It is not an aether in the old fashioned sense with a continuum of degrees of freedom. The vacuum does however admit configuration variables, and these can be continuous.

LC

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Author Lawrence B Crowell wrote on May. 16, 2013 @ 14:51 GMT
All physical theories are effective theories, or ultimately models. One should never take any theory as being somehow absolute. Even if we end up with a cosmology theory that is at the limits of our observing capabilities we should never assume we have it all. "It From Bit" is really a way in which we could run quantum cosmology on a quantum computer. However, the algorithm that is run is...

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John Merryman replied on May. 16, 2013 @ 17:53 GMT
Lawrence,

" the universe is itself incomplete."

And hopefully will remain so. When it is finished, it is finished.

Remaining within the dynamic processes, it seems there are some revealing patterns. One of these seems to be that complexity is part of the overall pattern and is not just a linear progression into ever more complexity, but is a process that leads to...

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Author Lawrence B Crowell wrote on May. 17, 2013 @ 00:46 GMT
I an not sure what you mean by "linear." This is not covered at all in my essay, but I think there is an elementary quantum statistics of a 2 + 1 spacetime that underlies a lot of the complex physics of strings and supersymmetry. I am not going into that in detail, for it would be too much. However, I think there is a degeneracy of states or superselection from which heterotic string theory emerges. Since this involves the octonion group E_8 this touches on the matter of nonassociativity.

LC

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John Merryman replied on May. 17, 2013 @ 03:43 GMT
Lawrence,

I'm no match for you in terms of the leading edges of complex theory. I'm simply making a general point about the nature of complexity. For example, there are literally billions of microbes in a person's gut. What level of computational complexity would it take to describe every relationship? Necessarily it would be far beyond any computational ability we currently have, yet one could make the general statement that it is a digestive process. So do we have to construct a precise, bottom up model of the entire system in order to effectively understand it? We can't. We would drown in detail and lose sight of what we are trying to do. A map can't show every detail, or it is useless for any particular purpose.

So the point is whether physics is drowning in detail, literally off in other universes, to the point of losing sight of what it is trying to understand. There is no ultimate algorithm which will explain the universe to humanity and when even the field is starting to throw up their collective hands over the fact the most developed concepts, such as string theory, have nothing to offer beyond a big question mark, then it might be time to consider if the path taken is anything more than a sticky trap. I know what I say has little weight, but I think you will find there will be more and more people like me. Eventually string theory is not going to be putting food on anyone's table.

You and I have argued over my ideas enough, not to go there, but you do have the ability to clarify your arguments, as you did to Phil in the above comment, so keep it up and keep breaking down all those beautiful ideas and see what further patterns emerge and what are just empty bubbles. If it requires other universes, that should be a hint some factor has been overlooked.

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Anonymous wrote on May. 17, 2013 @ 13:59 GMT
The level of complexity or the amount of information we observe is determined by the number of states, say the dimension of a Hilbert space or the size of a coarse grained phase space, call that dim H and entropy is S = ln(dim H). The amount of complexity we observe around us is huge. However, I think that much of the huge complexity around us is due to a redundant set of copies of fundamental states on different configuration variables. This means potentially there is only one electron in the universe, but where the huge number we observe are copies of that one state in different configuration variables. This huge redundancy has a relationship to the occurrence of event horizons and holography. I will have to leave this conjecture at this stage, for it gets a bit subtle.

LC

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John Merryman replied on May. 17, 2013 @ 17:31 GMT
Lawrence,

Let me go back and clarify my distinction of linear vs. non-linear. Obviously linear is sequential, yet this is a very broad category, from simple steps to complex changes. Non-linear is randomness. For example, think molecules of water. Yet there is a great deal of order in this as well. For one thing, it can be measured as a scalar, be it temperature, pressure, weight. There...

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Author Lawrence B Crowell replied on May. 18, 2013 @ 01:06 GMT
The big bang has a lot of empirical support for it. I don't particularly want to get into trying to argue the points for inflationary multiverse theory. It is though likely that just as solar systems operate not by some geometric order of planetary orbits, but rather by a more fundamental set of principles, so too are the gauge field constructions in a vacuum nucleation or pocket universe. In medieval to the renaissance cosmology it was thought the solar system was arranged by a set of geometrically ordered "orbs." Kepler worked on something like this. It appears likely that the universe is far grander, and what we observe as the spacetime universe is just one bubble out of a vast number of such on an inflationary spacetime that is often called the multiverse.

Cheers LC

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John Merryman replied on May. 18, 2013 @ 02:42 GMT
Lawrence,

I'm not really trying to start the cosmological argument, so much at trying to describe how various dichotomies, order/randomness, linear/non-linear, vector/scalar, node/network, organism/ecosystem, are aspects of an fundamental underlaying process.

It really isn't so much to argue about cosmology, but to make the deeper point that our logical concepts are generally based on one side of this relationship, that of the linear, ordered, singular organism, since it is the basis of our narrative, cause and effect descriptions of reality and the resulting atomized view affects many aspects of our understanding and relationship to nature, from monotheism to the Big Bang.

It's not the math is wrong, since it is distilled pattern, but how we apply it. For example;

" This means potentially there is only one electron in the universe, but where the huge number we observe are copies of that one state in different configuration variables."

"what we observe as the spacetime universe is just one bubble out of a vast number of such on an inflationary spacetime that is often called the multiverse.'

I can see how the math for this might be quite logical, but that in editing the variables, some important details might have been left on the cutting room floor. If the universe is one electron , might it be equally mathematically provable that every electron is a universe? If A=B, then does B=A? I tend to see multiverses as a version of C. S. Escher sketches of waterfalls and stairways going in circles. Quite interesting on paper, but problematic in reality.

So my point is, again, that we are not taking that scalar randomness into account as the background and balance to the logical vector.

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Joe Fisher wrote on May. 17, 2013 @ 15:48 GMT
What on earth does any of this incomprehensible abstract senseless physics babble have to do with reality? As I have thoughtfully pointed out in my understandable essay BITTERS, the Universe is unique, once and every seeming piece of the real Universe is unique once. Each real snowflake is unique. Each man-made particle is unique. Whereas scientists seek out repeatable abstract theories of abstract structures and abstract histories and abstract continuations, real unique has none of these abstract qualities.

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Author Lawrence B Crowell replied on May. 18, 2013 @ 01:41 GMT
The physical world and universe is rather contrary to our common sense. For instance you say that every particle is unique, but it is well known by the Pauli exclusion principle that this is not the case. Two electrons are not distinquishable in quantum entanglement. The advancement of our understanding of the physical world is not going to conform closer to our common sense, it will challenge it.

LC

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Joe Fisher replied on May. 18, 2013 @ 16:04 GMT
Do try to make a better effort to be accurate. The real physical world and real Universe are unique and have to conform to our common sense assessment. There are no quantum entanglements in reality. You can waste your time as much as you like pretending to know how abstract invisible electrons operate, if each particle is not unique, why is CERN trying so hard to isolate the Higgs boson?

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Author Lawrence B Crowell replied on May. 19, 2013 @ 03:10 GMT
The physical world just does not conform to that way of thinking. The trend since the time of Galileo has generally been in this direction. I think it is apparent that you are not have an extensive education in physics. As our knowledge of the universe has increased it has become increasingly removed from our everyday expectations of things and what might be called common sense.

LC

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Jochen Szangolies wrote on May. 18, 2013 @ 10:55 GMT
Hi Lawrence,

this is a very intriguing essay that touches on a lot of things that I have dimly glimpsed in my own thinking. In particular, the issue of how undecidability relates to physics is something that is intermittently on my mind. There's been a recurring trend to look for undecidability as somehow related to the measurement problem, or other quantum mechanical weirdness, starting...

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Author Lawrence B Crowell replied on May. 18, 2013 @ 13:57 GMT
This essay I kept on the level of modal logic so the presentation could be kept on a somewhat informal level. I think on a deeper level this connects with the Langlands program. The proof of the Tanyama-Shimura conjecture is a two dimensional form of a more general theorem, or set of theorems, of elliptic curve cohomology. In four or eight dimensions there are similar results for conformal systems, such as in four dimensions with the Cardy theorem. When extended to eight dimensions this climbs up the Cayley numbers into the exceptional group E8 and potentially octonions. This may connect to some axiomatic basis for a putative proof of the Riemann zeta function conjecture. I think the zeros of the zeta function and prime distribution may be mapped into the set of eigenstates for quantum gravity.

I have been reading the paper by Mathur, where he introduces early on the nature of wave functions on spatial splittings of the Schwarzschild spacetime. Wave functions of different wavelengths near the horizon, here the horizon considered classically, will scatter into the exterior and inferior of the BH in different ways. Those wave functions though are defined by the action of field operators on a Fock space or vacuum occupation space. If the horizon is “quantum uncertain” I think there is then an underlying associative property for these field amplitudes.

I have read a couple of papers by Mittelstaedt. Most of his work was done in the 1970-80 time period. I have not followed anything he may have done later.

I have not yet scored any essays on FQXi. I have only read a handful at this time. I see that you have an essay here as well. I will try to get to it in the next few days. I generally score essays after I have some idea of what a number of them look like. I usually keep a copy of the essay page where I put in a tentative score on the file before I actually score them on the FQXi page.

Cheers LC

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Philip Gibbs replied on May. 18, 2013 @ 15:46 GMT
The undecidable reminds me of Wangs Tiles and how Egan used them in Diaspora. It may be possible to build such tiles out of amino acids and just mix them together to see what happens.

Your idea is different and based on taking out associativity as an axiom, is that right? It's an interesting way of looking at.

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Author Lawrence B Crowell replied on May. 18, 2013 @ 23:56 GMT
That is one way to think of it. Another is if you think of the physics as having two representations. One representation involves quaternions where associativity holds. The other involves the octonions.

A cloth item or garment will when hung over a chair or a hanger or thrown on a surface assume a shape that minimizes the stress per area on it. This is a function of the topology of the garment and the geometry which involves these stresses per unit area. The elementary case is that of a skirt, where the boundary at the top is equal to the boundary at the bottom. These two boundaries define a simple cobordism. A more complicated case is that of a pair of pants. Here the boundary at the top is one circle and the boundary at the bottom consists of two circles. Think of the top circle on both the pants and the skirt as a group G which has some decomposition into SL(2R)^n. The skirt provides a simple deformation retract of G to the bottom. The pair of pants has two circles we think of as a group G' that each decompose into SL(2,R)^{n2/}.

The skirt represents the elementary view, say the 8-bit SLOCC. The pants are more complicated where this decomposes into two copies of a 4-bit SLOCC. These two copies have a duality relationship, such as with Yangians. The pants are then the perspective we have of physics, or fields that are quaternion valued. They are associative = "nice," or nice according to how we normally think of physics, and there are conformal dualities. The skirt represents the world more fundamentally. In moving between the two perspectives we turn on and off the axiom of associativity.

Cheers LC

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Cristinel Stoica wrote on May. 18, 2013 @ 12:23 GMT
Dear Lawrence,

Very nice and rich essay! I must confess that am still trying to connect all the dots, but for what I understand so far, especially after the clarrifications in your comments, I very much agree with you.

I may return with some questions.

Best regards,

Cristi Stoica

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Author Lawrence B Crowell replied on May. 18, 2013 @ 13:53 GMT
Thanks for the positive response. I have been intending to write more fully on your essay, since I have now read it a couple of times. I will try to do that later today or tomorrow.

LC

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Jacek Safuta wrote on May. 19, 2013 @ 14:19 GMT
Hi Lawrence,

I have found your essay interesting and difficult so it took me a lot of time to study and maybe you will find my comment not clear? But I have to try.

I would like to refer to your statements: ‘The quantum computer perspective of the world describes the universe as some master quantum Turing machine that deterministically computes information states. This is really a...

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Author Lawrence B Crowell wrote on May. 19, 2013 @ 16:30 GMT
Hi Jacek,

I have been curious about the role of LQG. I will confess that I am primarily oriented towards the string theory perspective. I do think LQG has some relevancy to physics, but it is uncertain what that is. LQG comes from the ADM approach to general relativity, which give constraint equations NH = 0 and N^iH_i = 0 with no explicit time dependency. The lack of time dependency...

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Jacek Safuta replied on May. 20, 2013 @ 20:18 GMT
Hi Lawrence,

I do not believe that LQG /CLQG is a serious candidate for quantum gravity and it is not my favorite. In LQG the space is granular (a network of finite loops) and this is contradictory to my view of continuous spacetime. However I like its evolutionary aspect in the sense of SOC and the scale-invariance that is crucial to fill the gap between GR and QM. I have mentioned LQG / CLQG only for reference to your determinism in a "clockwork" and evolution. After all the evolution notion is used very often by physicists but usually in the common meaning as a process of a change e.g. stellar evolution. But this has nothing to do with self-organized criticality. I would like to apply Darwinism beyond its original sphere of organic evolution on Earth using SOC.

I like the extremal principle in a sense of non-equilibrium thermodynamics to look for the likely steady states. This is also a kind of evolution of a far-from-equilibrium system to a steady state.

String theories do not generate predictions so they are non-falsifiable.

And finally I am sorry but the language of modal logic is not my ‘mother tongue’… just like English. Maybe I should start to learn...

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Author Lawrence B Crowell replied on May. 21, 2013 @ 00:30 GMT
I think spacetime is continuous or granular depending upon which sort of measurement you make. The Planck scale is just the minimal length scale which can contain a qubit of information. Space or spacetime on a smaller scale can not contain a qubit with any certainty. An experiment that involves the transmission of information over a vast time distance has no uncertainty with respect to the...

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Jacek Safuta replied on May. 21, 2013 @ 16:14 GMT
Dear Lawrence,

I agree we are hitting the technological limits within contemporary experimental physics. However there is a hope - a new idea falsifiable with a simple experiment. I have proposed one that could be even an exercise for students. But to carry out the experiment we need someone who is ready to risk his authority like J.A.Wheeler.

Best regards

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qsa wrote on May. 19, 2013 @ 22:16 GMT
Dear Lawrence,

I have followed your past postings(your personal theories) and they were interesting. But this time you have gone a bit philosophical, so I want to understand what you are saying. Lets say what you are saying is true, so in what sense that affects physics in any meaningful practical way. I mean are you saying no ultimate laws can be formulated, or the constants of nature will never be found, or no ontology exists or can be known, or particles inherently have no trajectories, EXACTLY what?

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Author Lawrence B Crowell replied on May. 20, 2013 @ 02:42 GMT
The metaphysics, or analytical mathematircal philosophy, baseically is that any scheme for causality is going to be incomplete. It will not be able to encode all possible physical states. As a result it means there exists a deeper foundation to the universe. In the second half of this paper I argue this involves the associative property of the vacuum with respect to quantized event horizons.

Cheers LC

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qsa wrote on May. 20, 2013 @ 15:30 GMT
Thanks for the reply.

"baseically is that any scheme for causality is going to be incomplete. It will not be able to encode all possible physical states"

In which physics problem this problem appears. Is it in scattering s-matrix or in describing proton wavefunction. I mean EXACTLY which physical problem you are having trouble solving because of this issue. Sorry for repeating my question, I hope I am more clearer this time.

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Author Lawrence B Crowell wrote on May. 21, 2013 @ 00:14 GMT
The situation pertains when there is an uncertainty fluctuation of event horizons. This is a possible window into quantum gravity. The physical states in the S-matrix channel are entangled states, with entanglements across the horizon. If the event horizon is classical then everything is nicely associative. A fluctuation in the horizon results in this uncertainty in associating states interior and exterior to the black hole/

The graviton has quantum numbers equivalent to an entangled pair of QCD gluons, or a bi-gluon system, that is neutral with respect to color charge. In that sense this form of S-matrix does connect in formalism with the old S-matrix theory or the so called "bootstrap." In fact string theory is really that unitary bootstrap theory in another guise.

I hope this answers your question.

Cheers LC

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William Amos Carine wrote on May. 28, 2013 @ 00:12 GMT
Hello Lawrence Crowell,

First off, I’d like to say I like your style, and the way that you seem to put issues in their proper perspective! It brings a calming sense of reason to an area of question that retains so much hype that it no doubt triggers numerous thoughts every time one hears Q.M. and locality are mentioned. Secondly, I don’t think determinism should dictate the development of a new theory. It, as your historical view has made clearer to me, is an idea used to adapt old world views into current problems.

About the idea that the computer, either a real one or the universe as one idea, being faulty because it doesn't model the entire set of events, could it be that this is not against saying that there is a separateness between real entities in space which unaccounted for doesn't describe all events in the universe? Or, does a clock here have to do with one spatially separated over there? Not being mathematically trained enough to see clearly the math in or around the black holes, I will leave this comment with one question only. As an aside, I’m glad to hear someone say “bottom-up” once in a while.

Best,

W. Amos Carine

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Author Lawrence B Crowell replied on May. 28, 2013 @ 01:47 GMT
The relationship between events in the universe and causality was noted by David Hume to not have a strict logical relationship. As I indicate in a footnote Godel's second theorem according to modal operations is a form of Hume's argument about causality =/= logic.

I sort of have to make this a bit brief due to other things I have to attend to now. I will say that the issue of clocks with a spatial separation and synchronization is a subject of considerable interest. This involves Cauchy data on spatial surfaces and how to integrate the Einstein field equations.

Cheers LC

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William Amos Carine replied on May. 28, 2013 @ 17:13 GMT
Thank you Lawrence C. for giving me something else to look into!

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Helmut Hansen wrote on May. 31, 2013 @ 13:16 GMT
I agree with you that the universe computes itself and thus discovers itself. I've presented an argument that supports this view. According to this argument Plancks constant h is nothing else than the physical expression of something which is commonly known as "natural digit".

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Author Lawrence B Crowell replied on May. 31, 2013 @ 13:38 GMT
The self computation of the universe probably leads to this Turing-Godel limit with Lambda calculus. There is clearly a computational aspect to the universe, which is a causal structure.

I will take a look at your essay soon. The Planck constant is in naturalized units just "one," and does probably reflect a unit of of natural numbers that sum up to give the total action. I notice yours seems to be in the latest introduction of new essays.

Cheers LC

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Peter Jackson wrote on Jun. 4, 2013 @ 16:07 GMT
Lawrence,

When reading; "A model of the physical universe encoded by algorithmic means will not compute reality" I suspected I may enjoy reading your essay. I was right.

You present a very level and balanced view, and more readable by the target audience than previous years. I do suggest something rather radical regarding that above sentence myself!

I also found other resonances with mine; "It is entirely possible this could be used to argue for a 'top-down' physics with the emergence of higher level properties." which I identify in terms of higher 'sample spaces' and subsets and test against the EPR paradox.

I also agree your analysis; "GR is a geometric theory of spacetime, which means that quantum gravity is quantization of spacetime itself. It is not entirely clear what this means. A number of questions have to be answered, and currently there are obstacles in our current theories which do not permit us to address these issues well."

But are the apparent 'obstacles' it not only 'assumptions'? so testing other assumptions may be fruitful (without the feared ether), i.e. that quantized atomic scattering to c maintains the SR postulates locally, (the LT then emerges naturally as a know optical effect).?? (You may recall from my last years effort how modal logic applies to that case).

I hope you can read mine and look forward to your and comments. I'm sure you'll stay in a more elevated position this year.

best of luck.

Peter

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Author Lawrence B Crowell replied on Jun. 4, 2013 @ 22:52 GMT
Hi Peter,

I am true to my usual trend falling behind in reading papers on this list. I just did a scan of your paper. You do reference Godel’s paper on prepositional logic. The main point of my work is that any Lambda-calculus or Turing machine approach to the structure of a causal system is bound to be incomplete. I do get a sense in reading the first couple of pages of your essay that you are leading into something similar.

I probably will not get to reading papers much until this weekend. I’ll post my observations when I do. As I said I am falling behind, and I notice another lot of papers showed up on the list today.

Cheers LC

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Antony Ryan wrote on Jun. 5, 2013 @ 00:01 GMT
Hi Lawrence,

I've just had a complete read and I really enjoyed your essay. The quantum nature of information does seem to point towards us concluding that neither it nor bit are more fundamental. I reached a similar conclusion in my essay. I particularly like the idea that this may have applications in consciousness.

Regards

Antony

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Author Lawrence B Crowell replied on Jun. 6, 2013 @ 00:45 GMT
The icosian or 120-cell has two quaternions with length (1/2)(1 +/- sqrt{5}) where the plus one has length 1.618..., which is the golden mean. In fact these quaternions define something called the golden field in a Galois ring. This is related to the Fibonacci sequence.

Cheers LC

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Antony Ryan replied on Jun. 25, 2013 @ 02:10 GMT
Lawrence,

Thanks for your comments over on my page. From your example above, I find it absolutely fascinating how nature seems to tie things in together. It reminds me of Marcus du Sautoy's show "The Code".

All the best for the contest,

Cheers,

Antony

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Author Lawrence B Crowell replied on Jun. 25, 2013 @ 15:58 GMT
This is a sort of code. The J^3(O) Freudenthal matrix of 3 octonions or E8s embeds the Leech lattice which is a Steiner system S(5, 8, 24) for error correction.

LC

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Torsten Asselmeyer-Maluga wrote on Jun. 5, 2013 @ 08:18 GMT
Hi Lawrence,

a very interesting essay, I enjoyed to read it. It seems (again) that our approaches are related (see my essay). I also claimed about that the information contained in spacetime is undecidable (by the word problem in group theory).

More later after rereading your essay

Torsten

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Author Lawrence B Crowell replied on Jun. 5, 2013 @ 15:33 GMT
Hi Torsten,

I remember reading an article back in the 1990s about how the classification of exotic R^4s was not enumerable, which had connections to Godel’s theorem.

The exotic R4 structure has its origin in the Casson handles as pointed out by Freeman. A thickened disk D^2 --- > D^2xR^2 can produce various structures, which by the self duality of four dimensions leads to these...

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Michel Planat wrote on Jun. 14, 2013 @ 09:02 GMT
Dear Lawrence,

Your essay is very stimulating and certainly enrich the 'it from bit' discussion. It contains several deep relationships between quite sophisticated branches of maths and foundational questions in physics.

First I like that you put the information paradigm in a historical perspective as was the 'clockwise universe'. Then I learned about modal logic from you. I wonder if it cannot be related to the current Abramski's work relating logic and contextuality as in http://xxx.lanl.gov/abs/1203.1352

An important statement of yours is 'this nonlocality is an undecidable proposition of the above modal theory of causality'. For me, it means that the modal approach is not the right one for approaching the subject, as is the von Neumann interpretation of quantum mechanics. My view (to my understanding, Bohr would agree) is that the quantum universe is unknowable, this is even worse that undecidable, because we can only know what is compatible with the questions we ask (through observables), i.e. quantum reality is contextual.

I agree with you that non-associativity, in addition to non-commutativity, may be very relevant for discussing these issues, as is the 'octonionic' Fano plane or further generalizations, see http://arxiv.org/abs/0712.1647.

With my colleagues we just found that the number of automorphisms of the G2(2) geometry (it is related to the octonions as explained in John Baez http://xxx.lanl.gov/abs/math/0105155) is the number of three-qubit pentagrams as well. Thus several of your ideas fit mines.

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Author Lawrence B Crowell replied on Jun. 14, 2013 @ 13:30 GMT
You state that the quantum universe is unknowable. I would say there is some limit to how much we can know about it. This limit is due to the cut-off in measurable physics at the Planck or string scale. As one considers scales beneath the string length and then beyond the Planck scale spacetime folds up onto itself in such ways that quantum fluctuations result in closed timelike curves and...

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Hoang cao Hai wrote on Jun. 17, 2013 @ 09:58 GMT
Dear Lawrence

Your conclusion is too abstract, so what decided for it?

http://fqxi.org/community/forum/topic/1802

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Author Lawrence B Crowell replied on Jun. 17, 2013 @ 15:17 GMT
As a rule when somebody tells me that something is too abstract or is overly difficult I tend to translate that into, "This is to difficult for me, therefore it must be false." That is not exactly the most appropriate form of reasoning.

Cheers LC

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Author Lawrence B Crowell wrote on Jun. 18, 2013 @ 22:48 GMT
Michel,

I reread your paper again this last Sunday. The desin d'enfant leads at the end to Mermin's pentagons. These are of course an aspect of the Kochen-Specker theorem. This is of course the main theorem on contextuality in QM. In my paper I discuss the quantum homotopies of associators at various dimensions, which are pentagonal systems. I copy this post on my essay blog page, so you...

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Michel Planat replied on Jun. 19, 2013 @ 10:15 GMT
Dear Lawrence,

Thank you for these scholarly remarks.

About the 18-9 proof and the 24-cell, there is the interesting work of Waegell and Aravind http://xxx.lanl.gov/abs/1103.6058. I like to see the 9 bases and 18 rays as the vertices and edges of the Mermin square, as explained in equation (6) of http://xxx.lanl.gov/abs/1204.4275. Now there is the dessin d'enfant of Fig. 3 of my essay that adds the algebraic curve/Riemmann surface view to this building block of two-qubit contextuality.

As you emphasize well, the next step is about the building blocks of three-qubit contextuality, they are related to G2 and E8. I already met the Weyl group of E8 for three qubits and see it as just one step of a higher order hierachy leadind to the Leech lattice, as in http://xxx.lanl.gov/abs/1002.4287.

For sure you would also have something to say about this.

All the best,

Michel

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Author Lawrence B Crowell replied on Jun. 19, 2013 @ 15:35 GMT
Michel,

I don’t have as much time this morning to expand on this, so I will just make this rather brief for now. I will try to expand on this later today or tomorrow.

The three-qubit entanglement corresponds to a BPS black hole. The four qubit entanglement is the case of an extremal black hole. I think there is an underlying relationship between functions of the form (ψ|ψ) = F(ψψψ), an elliptic curve with the cubic form corresponding to the 3-qubit, and the “bounding” Jacobian curve that defines a quartic for G(ψψψψ). This I think is some sort of cohomology.

The G2 I think defines a frame bundle on the E8 which defines the F4 condition for 18 rays in the spacetime version of Kochen-Specker.

As I said I should have more time later to discuss this in greater depth.

Cheers LC

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Author Lawrence B Crowell wrote on Jun. 27, 2013 @ 00:38 GMT
Torsten,

I finally got a little bit of time to write more on what I had mused about a couple of weeks ago. This all seems to center in a way around a type of cobordism with respect to these replacements of handles or Casson handles. The replacement of a circle with a knot suggests a type of theory that involves Hopf links. The trefoil for instance is by the Jones polynomial such that a...

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Torsten Asselmeyer-Maluga replied on Jun. 27, 2013 @ 20:11 GMT
Lawrence,

thanks for the reply. Yes, I know TQFT like the Chern-Simons theory with Wilson lines leading to the knot polynomial.

The Seiberg-Witten invariant for this exotic 4-manifold is the Alexcander polynomial, i.e. a knot polynomial but with a complicated TQFT. The Alexander polynomial is rather a classical then a quantum invariant.

I will think about your ideas more carefully.

Torsten

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Author Lawrence B Crowell replied on Jun. 28, 2013 @ 00:58 GMT
Torsten,

I have more of this sketched out. I wanted to write further today, but I got busy reviewing a paper. As for a classical invariant, check out Agung Budiyono's paper. It is the sort of idea of quantum mechanics that sends most quantum physicists screaming in horror. This is a stochastic approach to QM which along with the Bohm QM is weak, but these ideas I think can have their place.

Cheers LC

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Torsten Asselmeyer-Maluga replied on Jun. 29, 2013 @ 22:07 GMT
Dear Lawrence,

I will be absent for the next three weeks with sporadic email check.

You can also write me to my email accout:

torsten.asselmeyer-maluga@dlr.de

I will answer you as soon as possible when I'm back.

All th best for you

Torsten

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Hoang cao Hai wrote on Jun. 27, 2013 @ 03:59 GMT
Send to all of you

THE ADDITIONAL ARTICLES AND A SMALL TEST FOR MUTUAL BENEFIT

To change the atmosphere "abstract" of the competition and to demonstrate for the real preeminent possibility of the Absolute theory as well as to clarify the issues I mentioned in the essay and to avoid duplicate questions after receiving the opinion of you , I will add a reply to you :

1 . THE...

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James Lee Hoover wrote on Jun. 27, 2013 @ 21:56 GMT
Lawrence,

"There is a prospect this may play a role in the emergence of biology and even conciousness."

Would you advocate for consciousness being triggered by the Big Bang and present in space time as some neuroscientists posit? They claim a non-locality quantum-entanglement factor.

Jim

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Author Lawrence B Crowell replied on Jun. 28, 2013 @ 03:47 GMT
My mention of consciousness at the end, in connection with top-down physical or causal theories, was a bit conjectural. In a way I put that in there because I know a lot of people want to hear about consciousness and physics. Call it a bit of self-promotion.

To be honest I don't know what role consciousness has with physcs or the universe. A lot of people think it is a quantum process. I don't know about that honestly. I think it could be argued that consciousness is the ultimate classical or macroscopic non-quantum system. Consciousness at least generates an epiphenonenon of wave function collapse.

Cheers LC

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James Lee Hoover replied on Jun. 28, 2013 @ 17:28 GMT
Thanks for your honest answer. It seems to be an important point, considering whether consciousness emerged after our universe matured.

Jim

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Satyavarapu Naga Parameswara Gupta wrote on Jun. 28, 2013 @ 02:29 GMT
Dear

Thank you for presenting your nice essay. I saw the abstract and will post my comments soon.

So you can produce material from your thinking. . . .

I am requesting you to go through my essay also. And I take this opportunity to say, to come to reality and base your arguments on experimental results.

I failed mainly because I worked against the main stream. The...

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Anonymous replied on Jun. 28, 2013 @ 03:55 GMT
Dear S.Gupta,

I will take a look at your paper soon. I have fallen behind in reading these papers because I have had to review or referee a paper for a journal. Thanks for the interest in my paper.

Cheers LC

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Sreenath B N wrote on Jun. 30, 2013 @ 04:47 GMT
Dear Lawrence,

I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

Regards and good luck in the contest.

Sreenath BN.

http://fqxi.org/community/forum/topic/1827

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Vladimir F. Tamari wrote on Jul. 1, 2013 @ 08:42 GMT
Dear Lawrence,

Congratulations on a well written essay dense with impressive references to many relevant issues raised by the fqxi contest question. The technical aspects of your discussion went over my head (and probably for many others here), particularly in the section about logic and in the applicability of the Incompleteness Theorem to the issues at hand.

That said I could confidently say that I agree with several of your points: 1- The need for a 'philosophy' to approach questions of Reality in physics. 2- The undecidability of It/Bit 3- That a density matrix allows the expression of quantum states as qubits (which was my conclusion). In my Theory (see below) GR is reduced to a density gradient. 4- That "in theoretical physics there may exist assumptions that act as excess baggage that prevent workers from addressing fundamental problems" which was a major argument in my paper, although your saying it sounded much less presumptuous than when I did. Not only in this contest, but in my last year's "Fix Physics!" essay - since most of my ideas are qualitative. 5- The relevance of causality sets which in my Beautiful Universe Theory also found here are simply the Hamiltonians of qubit-like (spherical degree of freedom at every point) transfer of angular momentum locally, causally and linearly in a Universal lattice.

On a personal note I visited Purdue around 1965 to visit my brother-in-law who did his PhD in physics there. One is wont to believe in a Flat Universe in that locale!

With best wishes for your success

Vladimir

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Author Lawrence B Crowell replied on Jul. 1, 2013 @ 16:36 GMT
Hi Vladimir,

Indiana is not just a case of a flat universe, but a flat Earth. It is in many ways socially backwards, and there were Ku Klux Klan rallies in the 1980s when I was there. That is rather embarrassing.

The elimination of excess baggage is important. In my elementary demonstration with modal logic it means that certain physical axioms or postulates can be "turned off" in certain domains. It is similar to Godel's theorem, where certain propositions about a mathematical system are not provable and they can be toggled on or off to create different systems. Euclid's fifth axiom is of that nature and its on and off state define euclidean flat geometry and Riemannian geometry respectively. Your FQXi essay reads a bit like a narrative on this sort of thing.

Cheers LC

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Darrell R. Poeppelmeyer wrote on Jul. 1, 2013 @ 15:58 GMT
As a public non-specialist ... This article was on topic, well written, and an interesting read. Its technical and narrative aspects were well interwoven and a strong assist to non-specialists, such as myself. The struggles I underwent in writing my own essay are resolved in this essay. Thank you Lawrence.

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Author Lawrence B Crowell replied on Jul. 1, 2013 @ 17:35 GMT
Darrell,

Your essay does read as some narrative on a similar idea. You take the perspective of an alien. It will be extremely interesting if we should ever get radio contact from ETI to see how different they perceive the universe. The question is whether their mathematics and physics are in some ways mapped into ours, or if there is some isomorphism betewen their math and physics and ours.

Cheers LC

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Anton Biermans wrote on Jul. 2, 2013 @ 08:53 GMT
Hi Lawrence,

I agree that ""It From Bit" is not decidable", or rather, that it is a question which belongs to what to me is an outdated paradigm.

I have yet to read an essay which treats the question where all information comes from, how information becomes information. What I mean is this: If there would be only a single charged particle among uncharged particles in the universe,...

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Lawrence B. Crowell replied on Jul. 2, 2013 @ 16:32 GMT
Anton,

I am sorry I can’t respond in the length you write. The day is getting a bit on already and I need to attend to other things. There are a couple of points I can make.

If the universe had one charged particle something funny would happen. If we consider the spatial surface of the universe, say on the Hubble frame, as a 3-sphere the lines of electric force from this particle would wind around this sphere endlessly. Indeed these lines of force would densely fill the space. They would also interact with themselves or in effect the charged particle. The charged particle would be “driven” into a divergent condition to rapidly increasing energy. The system would in effect “explode.” It is comparable to an undamped oscillator that is driven by a resonant frequency.

The recent developments with inflationary cosmology now involve bubble nucleations or O-regions that result from a vacuum transition to a small value. This is an aspect of the multiverse. There is some prospect that our O-region, bubble or sometimes called pocket universe interacted with another one in its early phase. This may have left an imprint on the CMB. The de Sitter spacetime where this inflationary expansion occurs may in turn be a vacuum-field configuration on a D-brane, where in this higher dimensional space of 10 or 11 dimensions there is a foliation of such branes. This then leaves the bulk 10/11 dimensional spacetme, which might in turn exist in a 26 dimensional spacetime and so forth. This sort of gets into the proverbial idea, “its turtles all the way down.”

Cheers LC

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Member Giacomo Mauro D'Ariano wrote on Jul. 2, 2013 @ 08:56 GMT
Dear Darrell

how can you assess the "undecidability" of any theory, if we cannot doit for just arithmetics?

Cheers

Mauro

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Member Giacomo Mauro D'Ariano replied on Jul. 2, 2013 @ 08:59 GMT
Sorry, my post was supposed to be addressed to Lawrence.

Apologies

Mauro

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Author Lawrence B Crowell replied on Jul. 2, 2013 @ 14:19 GMT
Undecidability is a universal property, such as it is known that not all propositions in Peano arithmetic are decidable. The Church-Turing thesis states that any computable function is run on a Turing machine that halts. Of course it is known that a universal Turing machine is not capable of determining whether all TMs are halting. Hence the λ calculus is incapable of verifying Hilbert's Entscheidungsproblem.

My paper works with certain correspondences between modal logic, Lob's theorem and the Godel theorem. I did not break this out in great detail to avoid turning the paper into a complicated discussion of symbolic logic. To address your question again; I think what you are asking is how can we determine what is undecidable. This is an area of research for people who delve into this subject. There are mathematics on proof theory and hierarchies of undecidability. I will confess that I am not an expert in this area of work, for this deviates seriously from physics.

My argument is then more physical than formal, where I consider a certain algebraic postulate about observables, that being associativity. The physical argument involves observables or quantum amplitudes in a region that contains a black hole.

Cheers LC

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Chidi Idika wrote on Jul. 4, 2013 @ 11:28 GMT
Dear Crowell,

Now let us call the most natural automaton simply "heredity" (or indeed any cycle, Carnot or whatever). Then the idea of entropy or 2nd law of thermodynamics is that each stage of evolution within an automaton path does in fact depreciate possibility of return to the initial state; so there must be a halt or "fatalism"

My question is: doesn't your undecidableness amount to what we already know as uncertainty? Such that above a cut-off (Heisenberg Cut?) there is higher probability of return to initial state (what we know as determinism) but below the cut (being what we know as the quantum scale) there is no probability of return to initial state i.e. the system is not well-behaved.

Now I put it to you that once you assume that a well-behavedness (or conversely "uncertainty") is simply put an automaton then it qualifies as the ALGORITHM or computer proper. This computer/algorithm is what I call simply THE OBSERVER (perhaps Wheeler's anticipation).

It is a response to your position that: “...a quantum field is propagating on spacetime,but where spacetime is the quantum field. This heuristically appears self-referential, and the physical ansatz is this nonlocality is an undecidable proposition of the above modal theory of causality.”

By quantum theory, this state is rather at once a Godel "incompleteness" (the uncertainty) and yet a Peano (or Planck) "constant" (i.e. the conservation law).

My "observer" is in other words then the SUPERPOSITION proper.See What a Wavefunction is

So Wheeler's proposition does work! Pls see my essay and prove me wrong on this particular approach.

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Author Lawrence B Crowell replied on Jul. 6, 2013 @ 05:10 GMT
I hesitate to call the Heisenberg uncertainty principle some derivative of Godel’s theorem. However, my ansatz that this incompleteness rests with the associativity of fields is really just another form of the quantum uncertainty. There are limited ways of knowing what propositions about a mathematical system are undecidable, so my assumption here is not a form derivation of any sort. So my idea here is more of a physical assumption than a formal proof or derivation.

The role of an observer is in some ways similar to a self-reference in mathematics. Godel’s trick is to let a mathematical system contain predicates that act on their own Godel numbers as the subject. An observer is ultimately made of quantum particles and the act of a measurement has the appearance of being a sort of physical form of self-reference. Of course my paper is not about the measurement problem or the role of observers, but ultimately the universe is as it is so that observers can exist. This is a sort of strong form of the anthropic principle.

As for fatalism, it is of course the case that the universe will end up as a pure de Sitter vacuum in a sort of heat death. This will be reached in around 10^{110} years. It will probably quantum decay from there over a far longer period of time into a Minkowki vacuum. That might sound like fatalism, just as saying that we are all going to die sounds fatalist. However, in the mean time a lot of different things can happen. In the sense of Plato’s final cause the outcome might be in a sense fated, but what happens before then is not.

Cheers LC

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Anton Biermans wrote on Jul. 7, 2013 @ 03:40 GMT
Lawrence,

There are two kinds of scientists, the kind which can perfectly build further on the theories one learned at school, and the kind which tries to find alternative interpretation of observations. However invaluable an education is, its disadvantage is that, since you've learned many theories describing phenomena, it is very hard to dream up a different approach which perhaps might solve some of the many fundamental contradictions and enigmas of present physics. Though it is very understandable that man came up with the big bang idea, I'm afraid that it actually is even a worse 'theory' than creationism which at least honestly, boldly states that the universe has been created by some outside intervention. As far as I am aware of, the universe either has been created by some outside interference (which is the position of both creationism and big bang cosmology), a possibility I reject or it creates itself. If so, then fundamental particles must be as much the cause, the source of forces as their effect, the product of their interactions, meaning that a force cannot be either attractive or repulsive, always, which is the mistaken belief string theory is based upon. String theory, like big bang cosmology don't solve anything but are part of the problem.

Cheers AB

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Yuri Danoyan wrote on Jul. 12, 2013 @ 17:38 GMT
Dear Lawrence

Your quote from comment to Platan essay:

"What do you think of algebraic curves over [0, 1, ∞] and the Langlands program?"

By coincidence i used long time ago similar trick with pseudoscalar mesons.See my essay. I signify as 1 mass of proton and then observed what position would take place other pseudoscalar mesons.That i got phenomenon 18 degrees.

Do you see some explanation?

Yuri

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Author Lawrence B Crowell replied on Jul. 12, 2013 @ 20:37 GMT
The number 18 is important in Jewish mysticism. I am not sure that has any bearing on what you are saying though.

Is your number something similar to a Cabibbo angle or Weinberg angle?

I'll take a look at your paper later today.

Cheers LC

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Yuri Danoyan replied on Jul. 12, 2013 @ 23:18 GMT
It is not common with a Cabibbo angle or Weinberg angle

Just put the values of mass on y=tanx plot, then exploring angles.

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Michel Planat wrote on Jul. 15, 2013 @ 18:47 GMT
Dear Laurence,

(I copy the reply to your post on my page)

Your post is very stimulating. I need time to look at this possibility of relating black-hole physics and entanglement, and non-associativity. On the other hand, I don't consider that entanglement is a primary category in non-local/contextual questions. It may be that conformal arguments adapted to Grothendieck's approach may approach the subject you are talking about. I should say that I am not familiar enough with black-hole physics to have a motivated opinion I intend to read and understand this Maldacena-Susskind paper before discussing more with you on this topic. Meanwhile, may be you can have a look at recent papers by Frédéric Holweck and co-authors (we are now working together) about entanglement and algebraic geometry.

Thanks and best wishes,

Michel

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Lawrence B. Crowell replied on Jul. 16, 2013 @ 04:12 GMT
The program of finding physics with [0, 1, ∞] can be found with the SL(2,C) group and the linear fractional transformation (LFT)

f(z) = (az + b)/(cz + d),

which has a correspondence with matrices of SL(2,C). The Mobius transformation or LFT is an automorphism group on the Argand plane, and this is equivalent to PSL(2,C). This projective linear group is then the automorphism group of C. If we let the constants a, b, c, d be points in C then the LFT

f(z) = [(z - z_1)/(z - z_2)][z_3 - z_2)/(z_3 - z_1)]

is for the identity f(z) = z a case where z_1 = 0, z_3 = 1, and z_2 = ∞. A matrix representation may be found by dividing through by z_i and taking the limit z_i --- > ∞.

From this comparatively simple example we may move up to SL(2,H) and SL(2,O). In the case of SL(2,O) ~ SO(9,1), there is an embedding of SO(9) ~ B_4. This in turn is defined with the short exact sequence

F_4: 1 --- > B_4 ---> F_{52/36} ---> OP^2 --- > 1

where the strange symbol in the middle means that the 52 dimensions of F_4 - the 36 dimensions of B_4 ~ SO(9) defines the OP^2 projective Fano plane or OP^2 ~ F_4/B_4.

The B_4 group is the SUSY group that Susskind employs with the holographic principle.

The group F_4 is a centralizer in the E_8, which means it commutes with the automorphism of E_8, which is G_2. We then have a somewhat Rococo form of the same construction. A projective form of SL(2,O), PSL(2,O), defines matrices ~ aut(O) ~ G_2 which map three points to [0, 1, ∞] with the action of the 7 elements in the Moufang plane. I think I can find this matrix in the near future.

Unfortunately I am moving shortly, so that is complicating plans to do much analysis. If I do this in the immediate future it will have to be in the next week.

Cheers LC

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Vladimir F. Tamari wrote on Jul. 16, 2013 @ 01:31 GMT
Dear Lawrence, apologies if this does not apply to you. I have read and

rated your essay and about 50 others. If you have not read, or did not

rate "link:fqxi.org/community/forum/topic/1756] my essay The

Cloud of Unknowing please consider doing so. With best wishes.

Vladimir

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Vladimir F. Tamari wrote on Jul. 16, 2013 @ 01:38 GMT
Sorry - here is the link: my essay The Cloud of Unknowing

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Author Lawrence B Crowell replied on Jul. 16, 2013 @ 04:30 GMT
I read your essay sometime bzck. I have a list of these papers and which I have scored. I would probably have to reread or at least refresh myself about your paper. As I recall it is a bit of a metatheory.

Cheers LC

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Yuri Danoyan wrote on Jul. 17, 2013 @ 03:10 GMT
Lawrence

Could you please explain where is your theory connected with Golden ratio?

See part Symmetries... PSL(2,Z)etc

http://en.wikipedia.org/wiki/Golden_ratio

Yuri

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Author Lawrence B Crowell replied on Jul. 17, 2013 @ 15:41 GMT
Yuri,

The polytope for the E8 grop, the Grosette polytope with 240 roots can be decomposed into the icosian of 120. The icosian or 120-cell has two quaternions with length (1/2)(1 +/- sqrt{5}) where the plus one has length 1.618..., which is the golden mean. In fact these quaternions define something called the golden field in a Galois ring. This is related to the Fibonacci sequence.

Cheers LC

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Richard N. Shand wrote on Jul. 17, 2013 @ 07:50 GMT
Lawrence,

I loved your explanation of modal logic in causality. Very succinct! You brought back pleasant memories of doing symbolic logic in university.

The notion that "causality is necessary incomplete" can also be appreciated from a quantum information point of view using a complex valued system. When an EPR state is prepared, all entropies are conditional on the observer, who is a subsystem in an "EPR-triplet". However, in making a measurement, the observer throws away her entanglement information so that the subsystem of the EPR pair is no longer conditional. (See my essay "A Complex Conjugate Bit and It".)

A quantum correlated system thus becomes a classically correlated system. Using Venn diagrams, it becomes apparent that this process can be interpreted as a change in associativity.

Best wishes,

Richard

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Author Lawrence B Crowell replied on Jul. 17, 2013 @ 17:18 GMT
Richard,

Thanks for the kinds words. I agree that quantum measurements and even quantum teleportation involve the destruction of entanglement. Maybe better put the entanglement is transferred to a reservoir of states in an unpredictable manner. The entropy of the system is then indeed conditional, and a measurement loses this.

I propose that the incompleteness has to do with associativity in QFT. My argument then involves the situation of fields near an event horizon. There is a profound difference between the classical case and the quantum case. I am not clear how this plays with standard quantum measurements. Zeh, as I recall, talks of a quantum horizon. Maybe there is some parallel situation there which makes associators play a role.

I will try to read your essay soon. I am rather slowly getting around to as many as I can.

Cheers LC

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Yuri Danoyan wrote on Jul. 18, 2013 @ 20:42 GMT
Dear Lawrence

Could you please find out explanation of symmetric angles picture between mass of proton and pseudoscalar mesons? This is simple parametrization proceeding.

My essay

http://fqxi.org/community/forum/topic/1818

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Author Lawrence B Crowell replied on Jul. 20, 2013 @ 04:15 GMT
It could be due to some aspect of the eigenvalues for gluons in a supergroup. The icosian has quaternions (roots) that have magnitude given by φ. The icosian is in a sense half of the roots space of the E8 group. The masses of hadrons is determined by the quark masses, which is induced by the Higgs field, and by the confinement properties of the QCD gauge field, called gluons. The differences in these fields in the Y-B plane is given by certain roots, and those roots in some cases have the magnitude of the φ = (1 + sqrt{5})/2

That is about the best I can conjecture at this point. There might in some way be some semblance of reason for this.

LC

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Douglas Alexander Singleton wrote on Jul. 20, 2013 @ 04:36 GMT
Hi Lawrence,

I read your essay some time ago but only now got around to rating it -- was delayed in moving from ITB/Bandung to Thailand. In any case I very much liked the use of associators/non-associativity in your essay. Two FSU colleagues of mine (Merab Gogberashvili and Vladimir Dzhunshaliev) have worked on trying to include non-associativity into QFT. Merab in particular had some mantra about the connection of different algebras to physical quantities to the effect--> real numbers are connected with mass; complex numbers with charges; non-commutative numbers with spin; non-associative numbers with the quantum wave-function (actually I do not recall exactly what the last connection was but it was something to do with the quantum nature of matter). In any case you might find Merab's work of interest. Sorry it took so long to finally read your essay.

Also I noticed your address (or one of them) is in Hungary. In this regard you might be interested in a conference Elias is arranging in Prague, Sept. 1 --5. It is a fairly large and broad conference but some of the workshops would seem related to your line of work. In any case the conference site is http://www.icmsquare.net/

I hope this is not considered "advertising". Anyway if this post is not accepted we'll know :-).

Best,

Doug

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Author Lawrence B Crowell replied on Jul. 20, 2013 @ 13:13 GMT
Doug,

I have read several papers by Vladimir Dzhunshaliev on octonion field theory, and Merab Gogberashvili is a familiar name as well. Trying to understand how nonassociative mathematics of operators fits into physics is really the hard part. I think that quantum mechanics is purely complex, or C. Of course classical mechanics is R. Gauge theory can be written according to quaternions...

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Wilhelmus de Wilde de Wilde wrote on Jul. 22, 2013 @ 15:19 GMT
Dear Lawrence,

The title of your essay intrigued me because I think that Wheeler wanted us to recognise the same thing.

I read your essay with much interest (I didn't need to understand the math, because the text was clear) and the conclusion that biology and EVEN consciousness will have to play a role is one that I took as essential inmy own contribution.

After reading the essay it is always informative to read your reactions on the posts, which are very informative. Especially one reaction ( of may 20 02.42 GMT was in full correspondence with my own perception :

"Any scheme for causality is going to be incomplete, it will not be able to encode ALL physical states. As a result it means that there exists a DEEPER FOUNDATION to the Universe" This incompleteness I am trying to describe in the infinite number of tones of grey between the digital entities zero and one.

I really hope that can spare some time to read/comment and rate my essay : "THE QUEST FOR THE PRIMAL SEQUENCE" , I am sure you will find some thoughts we share together for a future approach of reality.

respectfully

Wilhelmus

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Author Lawrence B Crowell wrote on Jul. 22, 2013 @ 17:09 GMT
Wilhalmus,

I suffered recently a big computer virus crash. This machine had my voting code on it. I have not been able to get the code back in spite of my petition to FQXi.

I think that consciousness has some epiphenomenology with generating the appearance of measurement outcomes. In the MWI context the mind may be what generates the appearance of being on one of the split off worlds. In the Bohr Copenhagen interpretation I think consciousness may play a similar role in the so called collapse. In your idea of created reality (creatality) it might be that this is in some ways a mentally generated illusion.

I will score essays again once I get my voting code back.

Cheers LC

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Paul Borrill wrote on Jul. 23, 2013 @ 01:04 GMT
Outstanding Paper. Very Logically based. Extremely competent writing.

Similar conclusion as Torsten Asselmeyer-Maluga (incomputable).

I loved the modal logic foundation of this paper, and the expression of Godel’s second theorem in Modal logic, which I had not seen before.

Your proposal to remove associativity as a physical axiom is a profoundly interesting idea. I see how this introduces a different interpretation for quantum nonlocality (similar in some sense to the paper by Ken Wharton?)

But where you come out clearly ahead in here (my favorite quote from the paper):

“This argument employs sufficient and necessary conditions in a tensed fashion, forwards and backwards in time, to give a causal chain.”

Brilliant.

Your figure (on page ? 3) however, seems to assume an irreversible monotonicity in the order of t1, t2 and t3. Is this what you intended to compare to causal set theory? Was this diagram intended to imply a forwards and backwards in time causal chain?

Nice description of the history of S-Matrix, and a very thought-provoking conclusion regarding black holes.

There is also a wealth of tid-bits of mathematical hints in the paper: very insightful. A very worthy read.

Your conclusion that this (causality and undecideability) is a prospect that may play a role in the emergence of biology and even consciousness is very brave. I hope the orthodoxy does not try to dismiss you for this ;-)

I look forward to seeing more of your work in this area.

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Author Lawrence B Crowell replied on Jul. 23, 2013 @ 04:13 GMT
Paul,

Thanks for the very good word on my paper. I see tht you squeeked in a paper right at the deadline. I have entered several essays and I have generally found that submitting a paper around the middle of the time period for entries is about the best. I will read your paper soon. I had a couple of weeks ago a major virus attack on the machine which held my password. I can't vote for essays until FQXi honors my request to have it retransmitted to me.

My essay was inspird in large part by reading David Foster Wallace. He was a philosopher who managed to actually say something. He was also a good writer with his novels "The Broom of the System" and "Infinite Jest." I was reading his essay on the refutation of Taylor's argument for fatalism, and that sort of inspired my FQXi essay. I was originally planning to sit out this essay cycle. I also use the past tense with Wallace for he committed suicide in 2008 since he suffered major depression. I got a deeper appreciation for this problem because my brother suffered from this as well, and the past tense indicates his death by suicide a little over a year ago. He was a molecular biologist of some standing in that community.

I have been in some exchanges with Asselmeyer-Maluga on these issues. There is a theorem that the number of exotic R^4s is uncountable via the Cantor diagonalization and Godel-Turing undecidability. I worked up some calculations on Hopf links and knots with respect to the exotic smoothness of R^4 spaces. He has been on vacation of late, but should have returned this week or so. Generally I tend to leave people at peace during vacations.

As for your question about the mother-daughter relationship between events, which is in Foster's paper, the modal logic employed has no particular sense of reversibility or irreversibility. One could imagine some register or physical memory which permits one to reverse the direction of this diagram.

Cheers LC

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Paul Borrill replied on Aug. 1, 2013 @ 05:41 GMT
Lawrence - Thank you for your reply and pointers to David Foster Wallace and Asselmeyer-Maluga on these issues.

I would be honored by your review of my paper. Please make sure your download the latest version (V1.1a) from the comments section.

Thank you.

Kind regards, Paul

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Author Lawrence B Crowell replied on Aug. 1, 2013 @ 15:33 GMT
Paul,

I am rather intrigued by your paper. I will confess that I think this perspective on time may apply to quantum gravity. I will have to read your paper again to firm up my understanding. The two competing ideas are string theory and loop quantum gravity. In LQG gravitation is background independent. However, this is based ultimately on a classical formalism of general relativity where time does not exist. String theory on the other hand has time, but it is not background independent. It also works best in a holographic perspective where one dimension is reduced near an event horizon. The string/M-theory approach is also best looked at in a dual gauge approach with Yangians, which has some overlap with braid constructions in LQG. So there may be some duality here that has some bearing on your idea about time and entanglement.

Cheers LC

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Jayakar Johnson Joseph wrote on Jul. 23, 2013 @ 06:45 GMT
Dear Lawrence,

In particle scenario as undecidability is the negation of probability, the difference in density of the undecidables with the probability density, is proportional to the nonlocal Lagrangian for the actions at distances with the observer, in that the nature of gravity is unexplainable. Thus a string-matter continuum scenario is considered as an alternative in that gravitation emerges as a tensor product of the eigen-rotational string-matter segment.

With best wishes

Jayakar

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Author Lawrence B Crowell replied on Jul. 23, 2013 @ 15:36 GMT
The undecidablity is a generic result for any causal model. A causal model of any sort can be represented as some modal logical system of necessity and possibility. The exact structure of this model is not given, but only that causality involves necessity and possibility. The next step is to make some possible hypothesis on what is undecidable about explicit causal structures in quantum field theory. This is not a derivation of what is undecidable, which in mathematics is not itself decidable and only found on a case by case basis, but only to offer up possible physical axioms that can be “toggled” to an on or off state.

LC

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Ralph Waldo Walker III wrote on Jul. 23, 2013 @ 18:30 GMT
Dear Lawrence,

I think you hit the nail on the head in your two concluding paragraphs. “The incompleteness of metaphysical models illustrates the general nature of incompleteness that translate to standard physics.” “. . . but the existence of physical states implied by this set means that certain physical states can exist for reasons not computed by the “rule book.” The heuristic invoked here is that this concerns the nonlocality of quantum gravity and the existence of a new structure. The physical axiom that is proposed to be removed is associativity.”

And, “The incompleteness of modal causal models is argued to justify nonassociativity as a means towards nonlocality of the quantum gravity field. This is a “bottom-up" type of argument, where an incompleteness of a higher level physics requires a more fundamental physics “further down.” It is entirely possible this could be used to argue for a “top-down” physics with the emergence of higher level properties. There is a prospect this may play a role in the emergence of biology and even consciousness.”

Yes! I think you’re onto something regarding a “top-down” approach towards physics with an eye on the possible emergence of higher level properties. I believe that you have pointed the way towards discovering the emergence of biology and even consciousness from the foundation of physics.

As a non-specialist (I’m an attorney with a deep interest in the subject) I am encouraged by your conclusions and the direction of your thinking, so although there were sections that were beyond my understanding, I thought it was an outstanding essay. Thank you.

Best,

Ralph

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Author Lawrence B Crowell replied on Jul. 24, 2013 @ 16:18 GMT
Ralph,

Thanks for the positive word. The incompleteness extends potentially to various levels, including the dichotomy between the quantum and classical world. Complex structures like organisms impose constraints on the micro-causal systems that compose it. How this occurs is not well known. It is the possible that in addition there is a top-down element to this. The physics of...

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Chris Fields wrote on Jul. 24, 2013 @ 14:01 GMT
Hi Lawrence,

I do not think that we have a real understanding of "possibility" in physics. We treat possibility as a metaphysical condition (e.g. in arguments against fatalism), but when we then try to describe what is "possible" we fall back on epistemology - what is possible given these data, etc. "These data" always refer to local observations of circumscribed systems recorded in...

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Author Lawrence B Crowell wrote on Jul. 24, 2013 @ 16:38 GMT
The term possibility is not quantified very well for physics. I read a paper quite some years ago which stated possibility and plausibility were "unknown unknows" in a Bayesian sense. It is a probability that is not computable because there is no Bayesian prior estimate. The first part of my essay is metaphysics meant to motivate the need to "toggle" some physical axiom between the "on and off" condition.

Nonlocality of field theory is related to topological quantum field theory (TQFT) A TQFT is a quantum field theory up to homotopy. Physically this means that geometric data is removed and real degrees of freedom are determined by topology. This clearly means the TQFT within some homotopy (or topology) is a class of fields up to the diffeomorphism of space (or spactime). This means that local data concerning geometry is removed by taking a quotient with the space of solutions. In doing this we still want to have some concept of locality, which is usually associated with geometric information. Locality is contained in how the manifold is partitioned into pieces, where locality is defined by how those pieces are joined together. In spacetime this can include a space plus time perspective, where spacetime is defined by thin sections with a local time increment. These pieces have then cobordism defined by spatial surfaces.

A topological quantum field theory may be considered to be any data to every geometric entity from a zero-dimensional point up to an n-dimensional cobordism. The n-functor

Z:bord^m(n) --- > A_n

Where A_n is an algebra of dimension n and the bord^m(n) holds for 0

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Than Tin wrote on Jul. 24, 2013 @ 17:56 GMT
Hello Lawrence

Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/19
65/feynman-lecture.html)

said: “It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the...

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Lawrence B. Crowell replied on Jul. 25, 2013 @ 04:45 GMT
Than,

Nature has an analogical quality to it, or what I see as recherché --- as with Bach’s “Musical Offering.” Certainly one example is how isospin symmetry is applied to the nuclear physics of protons and neutrons in the MeV range and the same symmetry appears in the theory of weak interactions. I base my argument for the need to toggle on or off physical axioms by appealing to a formal incompleteness of any causal model. Godel’s theorem is a recursive aspect of mathematics where a predicate acts upon its own Godel number as the object.

It is taking me a bit of time to get to many of the essays here. Other pressing concerns mount as well. I will try to get to your essay in the near future. I got an email that the contest deadline has been extended a week. That may allow for a bit more time to get to more of the essays.

Cheers LC

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Michel Planat wrote on Jul. 26, 2013 @ 08:11 GMT
Dear Lawrence,

I am almost sure that I rated your essay at an earlier time. For any reason my vote was not recorded or lost when the system was interrupted. So I reproduced the vote with a bonus due to the high level of your replies.

Good luck,

Michel

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Author Lawrence B Crowell replied on Jul. 26, 2013 @ 16:49 GMT
Michel,

Thanks. I have been in the process of moving, so my ability to engage FQXi has dropped seriously. I also lost my voting code for a while after the machine I had it on was virus attacked. I got the code back the other day.

I think there are underlying relationships between F4 as the group for the KS theorem in 4-d and G2 as the automorphism of E8. F4 is a centralizer in E8, which means it is a “constant of the motion” with respect to G2. I have long thought that general relativity and quantum mechanics share some common basis along these lines.

Cheers LC

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eAmazigh M. HANNOU wrote on Jul. 29, 2013 @ 02:38 GMT
Dear Lawrence,

One single principle leads the Universe.

Every thing, every object, every phenomenon

is under the influence of this principle.

Nothing can exist if it is not born in the form of opposites.

I simply invite you to discover this in a few words,

but the main part is coming soon.

Thank you, and good luck!

I rated your essay accordingly to my appreciation.

Please visit My essay.

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Author Lawrence B Crowell replied on Jul. 29, 2013 @ 14:08 GMT
Amazigh,

One interesting duality principle is with Yangians. This is a duality with fields in a braid description that has connections to twistors.

I will try to get to your paper in the near future. My time is pretty limited right now. I have not had much time to engage this contest very much.

Cheers LC

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Hugh Matlock wrote on Jul. 29, 2013 @ 02:52 GMT
Hi Lawrence,

Congratulations on a fine essay! But I wonder whether the arguments you advance are against a straw man... pertinent to an abstract and continuous theory of reality, rather than what may actually be a discrete and non-continuous material cosmos. You wrote:

> Physical systems in some funny sense have a premonition about how to evolve.... There is no information...

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Author Lawrence B Crowell replied on Jul. 29, 2013 @ 13:56 GMT
Hugh,

Your comments are interesting and thought provoking. I don’t think that nature is strictly continuous or discrete. I think there is some sort of dualism between the two descriptions of reality. I don’t think either description is complete.

I agree that Godel’s theorem involves infinite systems. The use of the Cantor diagonalization implies an infinite set. The use of...

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Akinbo Ojo wrote on Jul. 31, 2013 @ 12:33 GMT
Dear Lawrence,

I guess if you have a list of more than 300 essays to choose from it is inevitable you miss out on some of the best. Yours was indeed very well written and argued even though my position is opposite to yours but I was able to follow your thinking especially areas where not too much math is involved. Very nice.

One of the unprovable/ undecidable proposition in mathematics and theoretical physics is whether the fundamental unit of geometry is a zero dimensional or extended object. When I say unprovable I mean using mathematical theorems. However from logic and reductio ad absurdum type arguments a sort of philosophical proof can be found. This is what I have attempted to do.

Following additional insights gained from interacting with FQXi community members, I improved my essay and wrote a judgement in the case of Atomistic Enterprises Inc. vs. Plato & Ors delivered on Jul. 28, 2013 @ 11:39 GMT. You may enjoy it.

All the best,

Akinbo

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Author Lawrence B Crowell replied on Jul. 31, 2013 @ 16:34 GMT
Dear Akinbo,

I will try to read your essay this evening. I am in the process of moving right now, which is taxing me in a number of way --- in particular the growing ache in my back.

Cheers LC

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Wilhelmus de Wilde de Wilde wrote on Aug. 2, 2013 @ 15:29 GMT
Hi Lawrence,

I saw you were very busy, did you already have the chance to read my essay : "THE QUEST FOR THE PRIMAL SEQUENCE" ?

and if so did you already receive a new code for voting ?

thank you

Wilhelmus.

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Author Lawrence B Crowell replied on Aug. 4, 2013 @ 15:29 GMT
Wilhelmus,

I got my voting code back a week ago. I pulled up your essay this morning and started to read it. I will though have to score it later today. I am about to close down and get back to work.

Cheers LC

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Than Tin wrote on Aug. 3, 2013 @ 19:17 GMT
Dear All

Let me go one more round with Richard Feynman.

In the Character of Physical Law, he talked about the two-slit experiment like this “I will summarize, then, by saying that electrons arrive in lumps, like particles, but the probability of arrival of these lumps is determined as the intensity of waves would be. It is this sense that the electron behaves sometimes like a particle and sometimes like a wave. It behaves in two different ways at the same time.

Further on, he advises the readers “Do not keep saying to yourself, if you can possibly avoid it. ‘But how can it be like that?’ because you will get ‘down the drain’, into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.”

Did he says anything about Wheeler’s “It from Bit” other than what he said above?

Than Tin

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Author Lawrence B Crowell replied on Aug. 4, 2013 @ 15:33 GMT
Hi Than,

I guess I am not sure why you posted this. Feynman was right in what he said and was a critic of the hidden variable people who were trying to build up quantum physics from classical like structures. That is not something I am trying to advance.

LC

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Don Limuti wrote on Aug. 5, 2013 @ 14:21 GMT
Hi LC,

We have been in a few contests together. Most the time your entries give me a headache. Of course this is my fault. Your current essay also gives me a headache, But I like it. The conclusion is rational and to my liking. Also your comment to the effect that the informational standpoint may not be correct, but it could be very useful, I find very insightful.

No need to visit my entry. It will just drive you crazy :)

Your score needs a boost!

Don L.

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Author Lawrence B Crowell replied on Aug. 6, 2013 @ 12:48 GMT
Information is sort of a model system. There is nothing logically determined about causality from an information standpoint.

I am traveling now and can only catch some brief wifi time and the like. I hope to be able to give this contest more consideration before it ends after tomorrow.

Cheers LC

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Kyle Miller wrote on Aug. 5, 2013 @ 17:36 GMT
I think the title of your essay pretty much sums up your much more rigorous argument. I'm certainly not a logic master but I think I get the gist of your arguments. The maths are a little esoteric and not totally accessible; however, I think your essay is important because is it one of the more original ones (that I have read). I agree with the conclusion and I think that the possibilities that it opens up are well worth looking into.

Please see my essay: All Your Base Are Belong To Math.

- Kyle Miller

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eAmazigh M. HANNOU wrote on Aug. 5, 2013 @ 22:21 GMT
Dear Lawrence,

We are at the end of this essay contest.

In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

Good luck to the winners,

And see you soon, with good news on this topic, and the Theory of Everything.

Amazigh H.

I rated your essay.

Please visit My essay.

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Charles Raldo Card wrote on Aug. 6, 2013 @ 03:47 GMT
Late-in-the-Day Thoughts about the Essays I’ve Read

I am sending to you the following thoughts because I found your essay particularly well stated, insightful, and helpful, even though in certain respects we may significantly diverge in our viewpoints. Thank you! Lumping and sorting is a dangerous adventure; let me apologize in advance if I have significantly misread or misrepresented...

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Author Lawrence B Crowell replied on Aug. 6, 2013 @ 12:44 GMT
Thanks for the long post here in a summary of things. I am on the road right now and can only catch some brief wifi time. I think "If from Bit" and the converse is similar to issues of causality. there is nothing that id determined about either. They are in a sense model systems imposed by us.

Cheers LC

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David M Reid wrote on Aug. 7, 2013 @ 08:46 GMT
Hi, Lawrence,

Excellent essay, and were your answers to the comments. In one of them, you suggested that the link discovered by Dyson and Montgomery (which has become popularized as the tongue-in-cheek spectrum of the hypothetical "Riemannium") might indeed prove useful in quantum gravity. This is a tantalizing possibility.

What I am a little queasy about is the possibility of inferences by your readers that may be made from your use of the undecidability of an axiom system for Physics. As you pointed out, Gödel's theorem stops the ability of any given system (which fulfills certain conditions, a clause that you left implicit) to prove its own consistency. However, Gödel's second Incompleteness theorem does not stop this system from having its consistency proven by an extension of that system. Whereas it appears from Bell versus EPR that physics is perforce incomplete, this is not the same incompleteness of Gödel's first theorem. That is, one cannot mix ontological and epistemological uncertainties, even though both exist. (It is a mixture that is tempting, of course: see, for example, the Penrose-Lucas fallacy.)

Epistemologically one cannot prove a given non-trivial description of the universe consistent except by appealing to a higher description, yet paradoxically there is a sort of "existence proof" of the possible existence of such a description, since a model for one exists, namely the universe itself. (This does not mean that this hypothetical description would eliminate the ontological uncertainties.)

Best regards,

David

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Author Lawrence B Crowell replied on Aug. 8, 2013 @ 04:19 GMT
The second theorem tells us that an undecidable theorem is self-referentially true. It may be added to the axiomatic system as an extended system. This new system is consistent or ω-consistent. In a sense that is what I argue, where I argue we should extend the system to one where associativity in general does not hold. We might think of P = not-associativity as the proposition which has a Godel number n(p) = gn(P) such that not[prove(n(p))] is true. Hence P must be true, for if it were false this would be a contradiction.

Of course I do not demonstrate this, but rather argue for the case. There must be some level of undecidability, and a reasonable target I suggest is with associativity. The argument is more based on physical arguments than strict logic. There is no procedure for finding undecidably true propositions in formal systems.

Cheers LC

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Jonathan J. Dickau wrote on Aug. 8, 2013 @ 01:08 GMT
Hi Lawrence,

I wanted you to know that I read and enjoyed your essay. It took me a little while to work through, mind you, but it was interesting and educational. I especially appreciate the comments about non-associativity and a new form of non-locality. It makes sense that the boundary zone at the event horizon would be highly indeterminate due to spacetime fluctuations and this would make uncertain to define what is inside the BH or just outside it.

There is a definite correspondence as what is within which parentheses in non-associative algebras much like the interiority and exteriority is at the event horizon boundary - one can't just change places.

All the Best,

Jonathan

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Author Lawrence B Crowell replied on Aug. 8, 2013 @ 04:24 GMT
This seems like a fair to decent argument for why there is a role for nonassociatity in physics. A fair amount of octonion work has been done where people just assume nonassociative operators. This seems to connect a physical argument for such with some structure for axiomatic structure; where that structure being a causal (modal) system.

Cheers LC

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Jonathan J. Dickau replied on Aug. 8, 2013 @ 23:57 GMT
My congratulations Lawrence!

Your high placement with this essay is well-deserved. I think the expert panel will find a lot to like about it, as did I. Good luck in the finals.

Regards,

Jonathan

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Author Lawrence B Crowell replied on Aug. 9, 2013 @ 13:15 GMT
My essay was basically a two week effort. I happened to be rereading David Wallace’s article that refutes the fatalism of Taylor when this idea leapt out at me. I was not planning on submitting an essay this cycle. So with a week of analysis and another week of writing I put this together.

There is a mathematical theory of unbounded but finite mathematics by Jan Mycielski, that I was recently made aware of. This is maybe useful for this work, for physics usually involves finite systems or involves finite numbers that are measured. I have been pondering whether some Godel numbering scheme that maps quantum numbers to integral solutions of Diophantine equations in this setting might lead to a finite and unbounded version of the Godel theorem. This might provide a more firm understanding of what my essay proposes.

Cheers LC

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Jonathan J. Dickau wrote on Aug. 9, 2013 @ 18:19 GMT
I replied to your comment above.

All the Best,

Jonathan

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Christian Corda wrote on Aug. 9, 2013 @ 19:16 GMT
Hi LC,

Welcome back within the finalists and congrats for the excellent result. Now let us cross the fingers for the final judgement by the FQXi experts panel.

Cheers,

Ch.

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Author Lawrence B Crowell replied on Aug. 10, 2013 @ 13:08 GMT
This essay did finish a bit better than the one I wrote last year. I guess we have a fairly long wait to see how the final judging occurs. That will be around the end of October.

LC

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