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FQXi FORUM
October 23, 2019

CATEGORY: Ultimate Reality [back]
TOPIC: Limits of mathematics in cosmology [refresh]
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FQXi Administrator Brendan Foster wrote on Jul. 26, 2010 @ 14:36 GMT
By special request, this forum is opened and dedicated to discussion of the limits or not of mathematics when applied to cosmology.

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SLG's Ghost replied on Nov. 15, 2010 @ 06:42 GMT
The ultimate limit of mathematics in cosmology is spelled out quite clearly by Gödel's theorem that even Stephen Hawking acknowledged in 2002.

Alas, it appears that only a small minority of honest physicists and mathematicians appreciate the ramifications of Gödel's theorem, which sets forth that no non-trivial system of arithmetic propositions can have proof of consistency within itself. As Hawking finally recognized (See his Gödel and the End of Physics speech/paper, 2002.), Gödel's theorem definitely applies to physics and the vain quest for an absolutely final TOE based on higher mathematics.

Hawking was, however, slightly in error in his "end of physics" lamentation. A total theory of all is still possible, but it will never contain the proof of it being necessarily true and absolutely final within itself since Gödel's theorem shows this to be impossible. Something else could always come into play to compel a change in a theory that could hold for thousands or even billions of years.

If all physicists/cosmologists would be a bit more honest as Hawking was(at least in 2002), greater insights into the nature of the universe and its creation/contingency would be readily apparent and open to greater discoveries, but even Hawking's latest collaborator Mlodinow simply dismisses Gödel's theorem as "not applicable to a TOE" (of course, he offers no evidence to support his bogus disdain, which is quite telling) in direct contradiction to what the theorem demonstrates, plus he ignores what his more accomplished co-author admitted about the theorem.

Such ignoring is definitely a most pernicious form of "ignor-ance" that does not want to accept the truth if it goes against an ideology of belief that should be absent in legitimate scientific inquiry.

So, to understand any limits of mathematics in cosmology, start with the ultimate (how ironic) limit as demonstrated by Gödel's Theorem.

Onward!

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Lev Goldfarb wrote on Jul. 26, 2010 @ 15:36 GMT
I did ask Brendan to start the forum under a longer name "The Intrinsic Inability of All Conventional Mathematical Structures to Model the Conception of Expanding Space and the Ways Out", but he decided on the shorter name.

I believe the issue is relevant not just to cosmology but to physics too.

So, I would like to discuss the situation in cosmology and physics that has been overlooked. The situation is described in the above longer title, and very briefly the main point is this.

If we are to take seriously the inflationary scenario, we need an appropriate fundamental mathematical structure for modeling it, but the conventional mathematics can offer no such structure (there are really only several basic math structures). Again, I believe--and the history of science supports this belief--that without the help of such basic formal structure we will not be able to gain a satisfactory insight into the nature of such inflationary processes, which might be critical to the development of physics and cosmology.

A possible way out I intend to discuss later (see also my essay).

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Frank Burdge replied on Jul. 27, 2010 @ 06:08 GMT
Lev, I read your linked essay with great interest. The evolving transformations system (ETS) could indeed be a very useful way to describe the evolutionary processes. I see within ETS elements of process flow, such as those incorporated in manufacturing process planning, computer program design, and project planning. Process flow charting is, and has been, a very useful tool. I apologize if my obvious simplification of the ETS is offensive. I do, however, question your inclusion of the parenthetic "irreversible" in Postulate 1, copied here for the convenience of readers:

Postulate 1: the universe is a family of evolving and interactive classes of (irreversible) processes.

If the universe is, as I suspect, cyclic, it will eventually collapse, thereby returning to a hot soup of photons, electrons, quarks, and gluons, or some similar conglomeration. In that event, all of the evolutionary processes that formed the structure of the universe during its expansion phase, will have been reversed. Hence, the processes that constitute the family of evolving and interactive classes of process, may entirely reversible. I also suspect that any gains in understanding cosmology, or physics in general, that result from the application of ETS, will be readily definable in the language of mathematics.

I look forward to reading the comments of those more qualified to comment than I.

Best regards,

Frank Burdge

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Lev Goldfarb replied on Jul. 27, 2010 @ 11:47 GMT
Frank,

Thank you for your comments!

However can we postpone the discussion of ETS till later? My main objective in starting this forum was to address the basic inadequacy of the conventional mathematical structures to deal with the inflationary scenario.

(By the way, if what you mentioned at the end is true "that any gains in understanding cosmology, or physics in general, that result from the application of ETS, will be readily definable in the language of mathematics" the ETS would be a futile exercise, and although I'm very eager to address all these issues, but first things first. ;-) )

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T H Ray replied on Jul. 30, 2010 @ 13:15 GMT
Lev,

I'm glad that you reopened this disccusion, because as you might remember from our Email exchanges, I think a lot was left unsaid in the essay contest forum.

For one thing, although it is clear in your essay and other works, that the role you assign to time is identical to that of physical information, you often seem to downplay that aspect in favor of talking about the limitations of mathematics.

Physical information has a mathematical model, however. Could you explain why you don't think that model can be extended enough to overcome your objection to using mathematics in the ontology of physics? You know I am a fan of your "structs" concept -- and that construction is time dependent, is it not? It seems to me that it already has a constructive property suitable to mathematical modeling and computation.

I want to go further, but I'll leave it at that pending your response.

Thanks.

Tom

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Cristi Stoica wrote on Jul. 27, 2010 @ 12:24 GMT
Dear Lev,

could you please develop the title "The Intrinsic Inability of All Conventional Mathematical Structures to Model the Conception of Expanding Space and the Ways Out"?

mainly, I think it would be useful to have a description of "the Conception of Expanding Space", and a justification of "The Intrinsic Inability of All Conventional Mathematical Structures to Model" it.

Do you mean that current mathematics or that mathematics in general cannot resolve this task?

Best regards,

Cristi

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Lev Goldfarb wrote on Jul. 27, 2010 @ 17:12 GMT
Cristi,

You are pointing us exactly in the right direction.

By "the intrinsic inability" I mean that all known math. structures (topological in particular) don't possess the capabilities to model the conception of expanding space, as it relates, for example, to the 3d (or higher dimensional) space of the universe as it expansion.

Again, I'm suggesting that to come to grips with the physical evolution of the universe we need a clearer formal guide as to the nature of the process that is responsible for the inflation/expansion. All the usual cosmological talk of inflation or expansion rely on the NUMERIC calculations and not on some qualitative formal structure. The mathematical concept of space does not give us a reasonable clue as the nature/structure of those processes. Hence, instead of trying to look for handicraft 'interfaces' just to bring us to the familiar concept of space, we need to look for new formal language that may clarify the situation. In this respect, several known forays of quantum gravity researchers into various discrete models that are responsible for 'generating' space are not accidental.

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Frank Burdge replied on Jul. 27, 2010 @ 19:58 GMT
Lev,

I believe that it is not an "intrinsic inability" of mathematics that limits our ability to describe expanding space. The limitation lies in our lack of understanding of the roll of dark matter (DM) and dark energy (DE) in the evolution of the universe. It is only a matter of time and effort until physicists, theoretical and experimental, will discover the nature and evolution of DM and DE. Once a successful model of DM and DE is established, the topological structure of space will be clearly seen, and the mathematical modeling of that evolving topology will be relatively straightforward.

Regards,

Frank Burdge

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Lev Goldfarb replied on Jul. 27, 2010 @ 20:37 GMT
Frank,

"Dark matter" and "dark energy" are simply first signs of the troubles to come.

However, before we jump to the "evolving topology", we should understand the logic of generalization. Topological spaces are the generalization of metric spaces, which are generalization of the Euclidean spaces, etc. What is a prototype basic concept we will be generalizing when introducing evolving topology?

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Lev Goldfarb wrote on Jul. 27, 2010 @ 19:34 GMT
Let me try again, Cristi.

In physics, if we want to explain to a graduate student relevant concepts of space, we can point to a Riemannian (in GR) or Hilbert (in QM) spaces; but what can we point to if we are asked about the concept of an expanding space? (The concept of expanding Riemannian space doesn't exist and for good reasons.)

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Cristi Stoica wrote on Jul. 27, 2010 @ 21:23 GMT
Lev,

when you say "The concept of expanding Riemannian space", I think at Friedmann-Lemaitre-Robertson-Walker models. This is because expansion is change of distances, hence change of metric. I don't see (yet?) the problem with this model.

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Lev Goldfarb replied on Jul. 28, 2010 @ 01:00 GMT
Cristi,

I was talking of the situation in mathematics, in which there are no concepts of expanding metric or Riemannian spaces. As you pointed out, physicists do operate with related concepts introduced initially via Friedmann equations, but

Perhaps a more complete assessment is that the interpretation of the metric expansion of space continues to provide paradoxes that are still a matter of debate.[2][3][4][5] The prevailing view is that of Chodorowski: "unlike the expansion of the cosmic substratum, the expansion of space is unobservable".[6]

However, my main point is this. The concept of expanding space is so different from the classical concept of space (as the 'founding fathers' of physics envisioned it), and the very process of universe expansion is so unlike any of the classical/dynamical processes, that such process warrants its fuller explication by a radically new, structural model. Structural (as opposed to just equations) in the sense that it should elucidate the nature of the processes that drive the expansion of space, i.e. it appears that the expanding space is the RESULT of such processes. (By the way,the conventional depiction of the expansion by means of the expanding balloon makes a mockery of such a fundamental process.)

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Cristi Stoica replied on Jul. 28, 2010 @ 06:15 GMT
Lev,

The truth is that I (think I) understand how semi-Riemannian geometry can account for expansion of the Universe, and I don't see where the problem is. Maybe you can point out clearly a phenomenon, an 'element of reality' or what else would you consider, which is inherent to the expansion of our universe but not compatible with the expansion as viewed in general relativity. This may help me to see where the problem is.

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Anonymous replied on Jul. 28, 2010 @ 12:03 GMT
Dear Cristi,

If you are happy with "semi-Riemannian geometry" as the model of the inflation/expansion, I don't feel I should be trying to make you unhappy about it. ;-)

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Frank Burdge wrote on Jul. 27, 2010 @ 22:46 GMT
"What is a prototype basic concept we will be generalizing when introducing evolving topology?"

Lev,

I was afraid you might ask a poignant question such as this. Your are, without question, infinitely more qualified than I am to discuss the topics at hand. I'm just a retired guy collaborating with another retired guy on a model of dark matter. I'm reluctant to say too much about our half-baked model because of my lack of formal training and the fact that I don't have answers to many questions. Let me just suggest that dark matter particles establish a continuum that occupies and defines the extent of the universe. In other words, we would redefine space to include only the volume contained within the continuum of dark matter, and, of course, including any interstitial gaps among the closely packed DM particles. Further we would stipulate that any volume outside the DM continuum is not part of our universe and is therefore undefined. In our emerging model, DM is, and has been, evolving throughout the expansion of the universe. An important aspect of the evolution of dark matter is that it occupies more and more space as it evolves. It is this property of DM evolution that is driving the accelerating expansion of the universe.

So, when I used the term "evolving topology", I was thinking in terms of a particular model of dark matter. In the context of these remarks, am I misusing the term "evolving topology"?

Regards,

Frank Burdge

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Lev Goldfarb replied on Jul. 28, 2010 @ 01:16 GMT
"In the context of these remarks, am I misusing the term "evolving topology"?"

I believe so Frank, and although I appreciate your generosity, still you should not assume that I'm "without question, infinitely more qualified than ... [you are] to discuss the topics at hand."

;-)

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Kirk Lancaster wrote on Jul. 29, 2010 @ 03:19 GMT
I just discovered this site; please excuse my naive question. (You can find me using MathSciNet (or Web of Science) or look at the Sept., 2010 issue of the Pacific Journal of Math for a new article.) :-)

It seems to me that Ricci flows, mean curvature flows, etc. include the ideas of "evolving topology" (after pinching off, the topology could change), "expanding metrics" and expanding Riemannian manifolds. Ricci flow is about changing the metric with "time." Geometric measure theory allows stranger objects (e.g. varifolds, currents.)

What am I missing here? (Sorry if this is a dumb question.)

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Lev Goldfarb wrote on Jul. 29, 2010 @ 13:04 GMT
Hi Kirk,

No the question is not really dumb, but I take the word "evolution" more seriously.

First, the short answer, again, is: I don't think there is any basic math. text in which such concepts as, for example, EVOLVING topology is introduced. Probably because we take the term "evolution" seriously.

The longer answer is this. Yes, indeed, in general, one can introduce, a parametric family of metrics (dependent even on several continuous parameters). But--in our context, i.e. evolution of the universe--can one safely assume that such parametric family capture such evolution?

My answer is NO: it appears that the underlying processes driving the evolution are not continuous (QM), and hence, I suggest, the resulting space cannot evolve in a ANY continuous manner. And so the big question I would actually like to discuss is: How does the space evolves?

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Kirk Lancaster replied on Jul. 29, 2010 @ 15:18 GMT
Hi Lev. I don't claim to be an expert in this area but the criticisms you mention don't seem convincing.

1. If you use GMT flows (e.g. level set method), you don't get "continuity" in some sense. I would have to dig around for references or examples if I wanted to be more specific but "Brakke flows" can exhibit this type of behavior. If you work with BV (or SBV) functions, varifolds or various types of (rectifiable) currents, "discontinuous" behavior can occur.

2. I'm not sure that one can model quantum mechanics very well. If your goal is a "theory of everything (in physics)," then I would start with an easy project like proving the Riemann Hypothesis. :D (What are the existing "good models" of QM? What besides probability measures, functional analysis, PDEs, etc. are involved with these models of QM? This is a vague question. One of my colleagues does QM & QC and has been a "fellow" (?) at KITP; I'll eventually try to formulate my question in a better manner.)

3. Varifolds are Radon measures on the manifold crossed (Cartesian product) with the appropriate Grassmannian. Don't people like Robert Bartnik, Tom Ilmanen, etc. (maybe Gerhard Huisken, Klaus Ecker) use GMT to study general relativity? (Maybe I should throw in Fred Almgren's "multi-valued functions" for fun.)

I don't think "basic math texts" would ever cover this stuff at a serious level. I'm not sure what you mean by "EVOLVING topology" as a concept; it sounds completely trivial. Now "evolution" is not trivial but the idea that topology changes as a parameter (e.g. time) changes is trivial.

What is evolution? Imagine the praise if the evolution of the universe turned out to be the solution of some flow problem and you identified this flow problem. Could QM be included in a "measure-theoretic" flow problem? I have no idea if this even makes sense but it reminds me of "string theory - banes - M theory" and multiverse (meta-universe, metaverse) theory.

I understand that physicists want to understand "reality" and not just some mathematical theory. If you would be so kind as to define "reality" this would help. ;D

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Lev Goldfarb replied on Jul. 29, 2010 @ 17:45 GMT
Kirk,

First, I'm not trying to "convince" anyone, simply because at this stage in our understanding of the evolution of the universe this would be a foolish undertaking.

Second, as I mentioned above, my reason for opening the discussion is this: it stand to reason that the reality of the Big Bang, in addition to many other reasons I'm planning to give, including those outlined centuries ago by Leibniz, strongly suggest that "the conventional mathematical and physical concepts of space are due for a radical rethinking and that--in contrast to the previous scientific developments--there is absolutely nothing on the mathematical shelf that can be remolded for this purpose"(with my apologies for the repetition). We need to start practically from the beginning (and hence, quite understandably, the tremendous reluctance).

Your line of thinking appears to me as follows: whatever the nature throws at us we can handle it within the conventional formal (continuous) paradigm.

Now back to the "reality" of the Big Bang:

How, within the conventional/continuous paradigm, do you 'grow' the space when all kinds of new "particles" and other entities are emerging and interacting? I don't believe, continuous models, can offer compelling models for the ongoing emergence and interaction of qualitatively different kinds of entities. (I intend to elaborate on this later.)

By the way, even well known physicists, e.g. Frank Wilczek (slide 5), wish to see "more meat to be put on inflation" (i.e. "structure" and "mechanism").

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Lev Goldfarb replied on Jul. 29, 2010 @ 21:22 GMT
Kirk, I forgot to answer your question about what evolution is. To simplify, I believe it is about the ongoing generation of structurally novel entities.

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Kirk Lancaster wrote on Jul. 29, 2010 @ 23:31 GMT
Lev: It is difficult to argue for or against your statement "the conventional mathematical and physical concepts of space are due for a radical rethinking." Look at the richness Dirac added to mathematics (with the help of L. Schwartz); distribution theory might not exist otherwise. On the other hand, I can't tell if you understand the mathematics that exists now; your claim might be wrong.

Perhaps you could help by explaining your knowledge of mathematics, especially basic (e.g. real analysis) and more advanced (e.g. geometric measure theory, differential geometry) mathematics. For myself, my knowledge of general relativity and QM is limited; I talk to colleagues in physics who do astronomy or QM, study some differential geometry, etc.

To veer wildly off topic, I have become interested in harmonic coordinates; my search for information led me to this site. I believe they were introduced by Einstein and some really nice math papers have appeared starting in 1981 (DeTurck & Kazdan); now Michael Taylor and others use them. Are people here familiar with harmonic coordinates?

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Lev Goldfarb replied on Jul. 30, 2010 @ 13:36 GMT
Kirk,

About my interests and background see the above essay (in my first post) and my web page given in the essay.

I guess we differ a lot in how we evaluate the really great progress in mathematics at present. For example, the line of development of distributions (or 'generalized functions') I would not call 'great', since I rely on the external historical evaluation of mathematics (as opposed to your, internal): as an arsenal of various useful formal languages for science, I believe the true greatness of mathematics is proportional to the power and beauty of the languages it offers. And my point is that today--for the first time in the history of science--we need new formal languages that we have NEVER had before.

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Kirk Lancaster replied on Aug. 1, 2010 @ 00:09 GMT
Lev: I'd love to be "that guy" (who invents a "new formal language that we have NEVER had before" which proves highly useful for physics.) Wish me luck. :D

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Lev Goldfarb replied on Aug. 1, 2010 @ 01:11 GMT
Kirk, somehow I don't believe you wish to be "that guy". ;-)

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Cristi Stoica wrote on Jul. 30, 2010 @ 05:06 GMT
Dear Kirk,

A lot of work in harmonic coordinates was done by Vladimir Fock, presented in his book The Theory of Space, Time and Gravitation.

Best regards,

Cristi

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amrit wrote on Aug. 1, 2010 @ 08:59 GMT
How big is the Universe?

Size and geometrical shape of the universe depends on mathematical models we use for its description. By using Euclid infinite flat space universe is infinitely big. We could travel with a light speed for ever and would never come to the border of the universe. By using Riemann spherical finite space universe becomes finite. By traveling with the light speed after many of years we would come back into the same place.

In Euclid geometry is known that “infinite distance + 100 kilometers” is still “infinite distance”. When we use Euclid geometry for describing universal space and we say “Universe is infinite” this does not mean a concrete measurable distance.

Regardless which geometry we use for describing universal space Universe is too big to be fully comprehended by the rational mind. In order to know universe deeply we have to use consciousness as a scientific research tool. Consciousness reveals us infinite nature of the universe that reaches far beyond rational understanding.

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Jonathan J. Dickau wrote on Aug. 2, 2010 @ 01:50 GMT
So here goes...

If the general topic is whether Mathematics offers sufficient tools to encompass Cosmology, and the specific emphasis is whether the Physics of the expanding universe can be explained thereby, I have some thoughts. I have not read your essay yet Lev, but reading the question (short and long form) and comments I already have quite a lot to say. So I'll offer a few preliminary comments.

While it may be a valid claim that conventional Math can't deal well with some things we observe, perhaps like an expanding Cosmos, there is unconventional Math and unconventional Physics which uses more conventional Math in novel ways. So the real issue seems not to be whether Math is ultimately good enough, but how far into the frontiers do we need to go, to find the right stuff for the job. Since there are plenty in my knowledge who have grappled with these questions in one way or another, I'll cite some examples.

I'll start with Brouwer's intuitionism which became Constructive Math and Geometry. This does incorporate in some ways the idea of procedural evolution whereby geometric features and topology emerge. This idea has also come out in recent work marrying Twistors and Strings, which was inspired by a meeting of Penrose and Witten and has more recently been championed by Arkani-Hamed and others. And of course, there is a notion of evolving spaces in NCG. Alain Connes said in one paper "Noncommutative measure spaces evolve with time" so this gets into some of the same territory you are exploring.

I'll leave off here, and go to some Physics examples next time.

Regards,

Jonathan

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Lev Goldfarb replied on Aug. 2, 2010 @ 19:13 GMT
Since it seems I have not gotten my point across, I will try to describe the situation again.

If we rely on the conventional mathematical concept of space or ANY of its possible modifications (including those described by Jonathan), any expansion of space cannot be accompanied by the generation of structurally novel entities inside, simply because, by any definition of space, the basic structure of space has to be preserved (otherwise it would not be an expansion of that space).

Can we agree on this point?

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T H Ray replied on Aug. 3, 2010 @ 10:54 GMT
Lev,

We agree. However, one is reminded that we only allow "the structure of space" as a time-distance measure among spatial coordinate points, and we only allow knowledge of the expansion of spatial coordinate points by changes in position among _mass_ points.

So it is not the basic structure of space that we are concerned with preserving; it is the basic structure of _spacetime_. You're right -- space has no structure of itself (we construct points and lines to make sense of it.)

The reason that I think your idea of "structs" is brilliant, is that it makes a clear formal distinction between time-dependent events which are irreversible, and spacetime events, which are reversible in the language of classical physics.

A time dependent system implies self organization of random fields in a scale invariant universe. Would not random fields be identical to unstructured space?

Tom

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Lev Goldfarb replied on Aug. 3, 2010 @ 13:13 GMT
Soooooooo, if we agree on that, I suggest that we should not look right now for a new concept of space (since it will not look like anything we know), AND worry about it later, when we understand better how the space is instantiated based on some new structural/temporal representational formalism, e.g. ETS.

NOW this is a much more interesting/productive topic, as far as I'm concerned.

Let me repeat it again. It seems to me (and to some physicists and philosophers) that the concept of space is derivative, and more importantly, we can now--in contrast to Leibniz and Whitehead--intelligently guess how it could be 'grown' based on the information provided by the structure of corresponding events in the struct (which is being instantiated). What would be also nice to discuss is to which extent ETS offers a better/worse scenario for space instantiation as compared to some current attempts in quantum gravity, e.g. Fotini Markopoulou and Renate Loll.

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Jonathan J. Dickau wrote on Aug. 4, 2010 @ 15:27 GMT
Hello again,

I made a brief addendum to the above comment stream which is now in the overflow zone. But this topic looks very interesting. I enjoyed the comments on CDT and related topics. Would like to mention 't Hooft's CA based QG model, and other stuff. So I'll likely take up later down here at the bottom of the page, when there is time.

Regards,

Jonathan

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T H Ray wrote on Aug. 4, 2010 @ 18:20 GMT
Lev,

I think even Brendan might agree that structs are a higher level of programming object than identical triangles. For one thing, instead of being simply connected, structs have the capability of forming systems that evolve at different rates (like natural biological evolution) and thus bring complex system, non-hierarchical, nonlinear dynamics to the fore -- just the way that nature appears to actually evolve. CDT gives us classical spacetime (which may itself be a struct).

Nevertheless, CDT is a solidly impressive experimental result, because it unequivocally shows the importance of orientation in a scale invariant spacetime; i.e., if we take seriously the notion that time structures space, the implications that time drives system change and that time is therefore identical to information, follow.

I see the advantages of a class-based event space of discrete objects in which a dynamical model produces quantum coherence and decoherence on the large scale. I also see the advantages of recovering smooth spacetime from self similar discrete objects. At the end of the day, a self organized complex network depends on the duality of these models.

Tom

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Lev Goldfarb wrote on Aug. 4, 2010 @ 18:59 GMT
Of course, it would nice to hear the involved physicists, but probably this is too much to ask ;-))

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T H Ray replied on Aug. 5, 2010 @ 13:27 GMT
I think we should be patient. Brendan has already joined the conversation, with an important piece of clarification, and he is certainly one of the involved physicists.

This is pioneer territory for all of us, Lev, and while I think you're doing a fine job of marking the trail, you might want to pause and let the rest of the party get within shouting distance. :-)

Tom

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Lev Goldfarb replied on Aug. 5, 2010 @ 14:25 GMT
Tom, that's exactly what I was planning to do.

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Jonathan J. Dickau wrote on Aug. 4, 2010 @ 20:45 GMT
Hello again,

I left another 2 comments above, and I'll return later with more thoughts. There are so many interesting threads to this conversation already. So I'll be back, but I need to get some work done still today.

Regards,

Jonathan

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Lev Goldfarb wrote on Aug. 12, 2010 @ 14:50 GMT
I thought it might be useful to restate once more the topic of the forum. ;-)

My claim is that we need a fundamentally new formalism for modeling the physical reality of expanding universe.

Why? Because there is nothing in the conventional math. which would allows us to come to grips with such process of expansion that is accompanied by the ceaseless CREATION OF QUALITATIVELY DIVERSE NEW 'STUFF'. No existing concept of space can offer any help in this respect (and, frankly, I am somewhat surprised at how this situation has been overlooked).

I also would like to discuss some proposals for dealing with such process (including my own). Thus, we can address the wish, mentioned in one of my posts, by Frank Wilczek that "more meat to be put on inflation", including "structure" and "mechanism".

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T H Ray replied on Aug. 18, 2010 @ 16:14 GMT
Lev,

I am disappointed, as I know you must be, that the topic hasn't generated the kind of interest that (at least I think) it deserves.

Suppose the question were framed:

Does there exist a computable non-numeric representation of evolving novel forms that accurately describes the evolving physical world?

Then suppose that rather than assuming the positive, we try to rule it out.

I'll ask first: what do we mean by "computable?"

Tom

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Lev Goldfarb replied on Aug. 18, 2010 @ 19:04 GMT
Tom,

Let's be patient and wait (after all it's summer), and let's also be optimistic about it. ;-)

Thanks for your continued interest! I hope you will stay with the topic.

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Lev Goldfarb wrote on Aug. 19, 2010 @ 22:42 GMT
Here is yet another summary of our topic. ;-))

As I stated above, in contrast to the line of generalizations of the concept of 'space'--reals, vector space, metric space, topological space--we have absolutely no concept with which to start the corresponding line of generalizations for the concept of 'evolving' space. And there are perfectly sensible (formal and informal) reasons for this situation: the present mathematics has developed in such a way that it is not 'equipped' to deal with evolving structures, except by means of formulas and sequences. But those cannot deal with the underlying mechanisms responsible for the structural 'evolution'. I submit that it is the ubiquitous spatial/ point representation that, on the one hand lies at the foundation of all math. concepts, and on the other hand is standing in the way of the new formalism which can adequately deal with the evolving structures: since the 'point' cannot evolve, it must be replaced by some dynamic/evolving structure, which requires complete rebuilding of mathematics as we know it. Evolution of the universe is about creation of novel structural entities, and such entities cannot be built out of non-structural entities, i.e. 'points'.

Of course, the ease with which it became possible to add adjective "evolving" has partly to do with the light hand of Darwin and the modern biology. But if Darwin, as a non-technical fellow, can be forgiven for this, in mathematics and physics such attitudes are standing in the way of real progress, which, by the way, would also have a transforming influence on biology itself.

The hypothesis, which would be interesting to discuss, is that 'space' (and its 'content') is being incrementally instantiated on the basis of the more basic informational mechanism, which builds the space based on the relational/structural information captured in the structural "event" (see informal introduction in my essay). In particular, such event has sufficient information as to where to attach the space 'patch'.

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T H Ray replied on Aug. 20, 2010 @ 14:54 GMT
Lev,

Ever since being introduced to your work, I have wondered if I could be persuaded that a more fundamental structure than the integers underlies the idea of order. I was taken by your coinage, "struct", and its description, almost immediately. Structs seem to fit naturally with the kind of "black box" relation that characterizes a system of components evolving at different rates (like the Ashby/Bar-Yam multiscale variety)*; the internal evolution of the black box is unavailable, but the time dependency of the network forces a visible relation among hubs of coordinated activity**, such that even though the system state shows little change in the aggregate of elapsed time, at any two particular adjacent time measures, the locations of central hub activity may differ radically. (Cf. Gould-Eldredge punctuated equilibria^ for a connection to evolutionary biology, and self-organized criticality^^ in the extended model of evolution.)

If black boxes are structs and structs are nodes, network vertices are time paths, which leads to the important conclusion that you and I share: time is identical to information. In such a network, information is physical (quantum information)accounting for dynamic activity. In other words, the time we measure is independent of the internal "black box" time; the struct is self contained and independent of the network and only enters via a time-dependent relation of measured quantum information.

I understand the lack of evolutionary potential in your "non-structural point." However, what always hangs me up when I engage with your work, is that points of the complex plane are not "non-structural." Points are analyzed as lines in complex analysis, and the complex plane compactified with one point at infinity (Riemann sphere) _does_ give us space and content; i.e., the algebra is closed and the space has dimension 2. From the chaotic field of non-ordered complex numbers, we do get ordered relations in real time and space, from analysis on the Hilbert space. I still don't grasp what in your concept would obviate such a mathematical approach.

Tom

*Bar-Yam, Y. [2003] “Multiscale Variety in Complex Systems,” NECSI Technical Report 2003-11-01 (Nov.)

**Braha, D. & Bar-Yam, Y.[2006]. “From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks.” Complexity vol 12, no 2, pp 59-63

^Eldredge, N., & Gould, S. J. [1972]. “Punctuated equilibria: an alternative to phyletic gradualism.” In: Models In Paleobiology (Ed. by T. J. M. Schopf). Freeman, Cooper and Co.

^^Bak, P. [1996]. How Nature Works: The Science of Self-Organized Criticality. Copernicus.

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Lev Goldfarb replied on Aug. 20, 2010 @ 18:05 GMT
"I understand the lack of evolutionary potential in your "non-structural point." However, what always hangs me up when I engage with your work, is that points of the complex plane are not 'non-structural.' "

Tom,

Points of the complex plane, or of any vector space, are just these, points. They can be algebraically decomposed via other vectors, that's true, but this decomposition is not unique and hence cannot really be called structural in the temporal sense:

11 = 2 plus 9 = 7 plus 4 = 5 plus 6 etc.

We have no (temporal) information on how number '11' (or any vector in a vector space) was *actually* formed.

Also remember set theory (set = collection of points) as the foundation of mathematics.

For temporal/formative information to be present in the object representation, you need a fundamentally new representational formalism, hence our ETS.

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T H Ray replied on Aug. 20, 2010 @ 20:03 GMT
Lev,

We're on the same page. I dealt with that issue of decomposability in my NECSI ICCS 2006 paper here specifically in section 5.0.

I do not rely on the set theory of classical mathematics. A time dependent complex network method frees us of that constraint.

Tom

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Lev Goldfarb wrote on Aug. 23, 2010 @ 14:48 GMT
Tom,

When I speak of "representation", I'm talking about the form of data representation in science.

Any field theory or, for that matter, *any* current physical theory still relies on numeric measurements, while I'm suggesting non-numeric "measurements".

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T H Ray replied on Aug. 24, 2010 @ 11:19 GMT
Lev,

Isn't an ordered structure what "measurement" implies? Then, isn't temporal order fundamental? And doesn't numerical order follow from temporal order?

I think about Brouwer, who called mathematics "a languageless activity of the mind." That same Brouwer allowed that doing mathematics entails "a move of time ... a twoity."

The twoity you seem to suggest is the independence of semantics and syntax, and I agree with that -- a congruence of semantics and syntax would seem to imply meaning -- yet how does such meaning differ from that we find in the congruence, e.g., of identical geometric angles?

Do understand that I am not asking these questions to be contrary -- there is so much in your concept that I find agreeable. I am just looking for a handhold that would obviate numerical representation of physical phenomena, and I haven't found it yet.

Tom

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Lev Goldfarb replied on Aug. 24, 2010 @ 15:11 GMT
Tom,

I'm quite comfortable with any question. ;-)

I came to ETS formalism very gradually, trying to model inductive (biological) processes, which I and many other consider central to unlocking the nature of biological information processing: How is an object represented in order to be able to 'recognize' later another object that belongs to the same class of objects. This led to the search for the concept of structural representation: conventional numeric representations are not rich enough for the purposes of induction.

I guess the 'easiest' way to approach ETS is the direct way: think now of the generalized measurement process in which numbers are replaced by their structural generalization, structs. A numeric/spatial measurement is based on the repetitive application of the same "stick", while the result of ETS measurement is a struct also obtained during the interaction with the corresponding object/process (all objects are, in fact, processes) . Of course, the conventional measurement is a very special case of ETS measurement.

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T H Ray replied on Aug. 24, 2010 @ 16:00 GMT
Thanks, Lev.

This gets me the closest yet, to understanding your research program. As a student of complex systems, I grasp the terms of a recognition algorithm, and I have always been impressed, as you know, with the power of structs to generalize relations to this extreme degree.

Scale has got to play a role here, though. Consider an infinitely self similar set. One does not measure with the "same stick" across different scales; scale, in fact, determines the stick one chooses -- a jagged coastline may be of infinite or finite length. And surely the Mandelbrot set is also a process as well as an object, which evolves according to a simple algorithm into an exceedingly complex form.

Anyway, may I make a suggestion to narrow this discussion a bit, and also accommodate your emphasis on biological processes? An important unsolved problem in both biology and computation is that of protein folding -- could we possible focus on an ETS strategy toward that singular case?

Tom

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Edwin Eugene Klingman wrote on Aug. 24, 2010 @ 23:06 GMT
Dear Lev and Tom,

This looks like an interesting topic, if I understood it, but several points leave me confused.

When Lev says "representation", this typically implies some sort of graphical picture or map. Yet he states that "...graphs (with nodes and edges)... are not such temporal representations. So are you foregoing all graphical (i.e., visual) representations?

Lev states, "we have no (temporal) information on how number '11'...was formed. What does this mean? Using logical circuitry I can create a counter to generate *ALL* integers (with appropriate carry extensions) and also build adders and subtractors. They are generated in numerical order that can be interpreted as temporal order. What exactly is the problem?

Tom says, "...isn't temporal order fundamental? And doesn't numeric order follow from temporal order?"

Eons ago, in physics lab, we attached a weight to a paper tape, running between two electrodes and the spark 'marks' recorded 'measurements' of acceleration on the paper. if I now add simple counter circuitry to encode the marks (as binary integers) then I have integer marks, existing as spatial order, that we can interpret as temporal order. Where is the problem?

Lev then states, "...I'm suggesting non-numeric "measurements"." What does this mean?

Thanks for any explanation,

Edwin Eugene Klingman

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Lev Goldfarb replied on Aug. 25, 2010 @ 01:59 GMT
Hello Edwin,

1. "When Lev says "representation", this typically implies some sort of graphical picture or map."

Please note that yours is not a formal meaning of the term 'representation': the formal meaning has to do with the formalism chosen to represent data.

2. "Lev then states, '...I'm suggesting non-numeric "measurements".' What does this mean?"

This is the case when you represent your data not by numbers but by some (preferably properly formalized) entities other than numbers. Note that "graphical pictures or maps" are not properly formalized entities that can be reliably manipulated for the purposes of "data processing" (in the same sense as we 'manipulate' numbers). So far, in science, this has not happened yet, but there are important reasons for moving in that direction.

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Edwin Eugene Klingman wrote on Aug. 25, 2010 @ 23:55 GMT
Lev,

Thanks for the answers. Since you stated that you are comfortable with questions, I'll continue.

Are you saying that your 'structs' cannot be represented graphically?

And would you attempt to explain about "(temporal) information on how '11'..was formed."?

Edwin Eugene Klingman

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Lev Goldfarb replied on Aug. 26, 2010 @ 04:38 GMT
1. "Are you saying that your 'structs' cannot be represented graphically?"

Edwin, let's not confuse their *pictorial depictions* with their formal definition (see our main paper, p.29).

2. "And would you attempt to explain about "(temporal) information on how '11'..was formed."?"

I'm simply following the the temporal spirit of Peano definition of natural numbers (and, of course, more generally, the concept of struct).

For example, '11' could have been obtained as '7' "followed" by '4', which is different from '2' "followed" by '9'. But when you look at '11', you can't see which temporal sequence of events produced that struct (in primitive cultures, one new what was going on simply because you had to make knots on the rope, or notches on a stick, or find the right number of stones) . And this is a general problem with all conventional mathematical representations (since they are not temporal).

A temporal representation (such as struct) is not only more accurate but is also much richer, simply because it allows for the existence of qualitatively different events, which of course we have admitted in physics (e.g. qualitatively different particles).

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Edwin Eugene Klingman wrote on Aug. 26, 2010 @ 18:28 GMT
Lev,

I will look at your paper to try and understand your point of view of graphic depiction.

But on the following:

You say: "I'm simply following the the temporal spirit of Peano definition of natural numbers (and, of course, more generally, the concept of struct).

For example, '11' could have been obtained as '7' "followed" by '4', which is different from '2' "followed" by '9'. But when you look at '11', you can't see which temporal sequence of events produced that struct (in primitive cultures, one new what was going on simply because you had to make knots on the rope, or notches on a stick, or find the right number of stones) . And this is a general problem with all conventional mathematical representations (since they are not temporal)."

The basics of quantum electro-dynamics is the counter, the sum of creation and annihilation operators over a particle space. The basic logico-arithmetic circuit is the counter. It is basic because it gives rise to the integers *in order*. It is the physical implementation of Peano's axiom. Probably an infinite number of other logic circuits can be defined to produce any number of logical combinations of binary bits, but the primary ones that are useful are comparators, adders, and subtractors. The use of these to accomplish 2 plus 9 or 4 plus 7 are of no consequence and have nothing to do with the nature of time. I think the point about "(temporal) information on how '11'..was formed" is non-sensical and based on a misunderstanding of the nature of number in a physical universe that supports logic.

Edwin Eugene Klingman

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T H Ray replied on Aug. 26, 2010 @ 19:37 GMT
Edwin,

You seem to find Lev's concept nonsensical on the assumption that time is identical to number. I think you'll have a hard time supporting that assumption, for if it were true, the equations of classical physics would not be time reversible. We know that they are.

My own research does find a well ordering of the time sequence as a sequence of integers from a field (the complex numbers, z) that is non-ordered. But I think I get what Lev is saying about the noncommutativity of number combinations; these orderings are time-dependent, just as in the dynamics of QED that you cite. Thus, "temporal order."

Tom

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Lev Goldfarb replied on Aug. 27, 2010 @ 04:04 GMT
"The use of these to accomplish 2 plus 9 or 4 plus 7 are of no consequence and have nothing to do with the nature of time. I think the point about "(temporal) information on how '11'..was formed" is non-sensical and based on a misunderstanding of the nature of number in a physical universe that supports logic."

Edwin,

I'm afraid you are not reading my posts carefully and missed the main point: numbers do not allow us to record adequately what's going on in nature, since temporal processes have formative/temporal structure that cannot be captured numerically. In general, it looks that with the development of quantum physics we are led to face the reality that the temporal structure of (physical) events is the only structure of interest.

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Edwin Eugene Klingman wrote on Aug. 26, 2010 @ 22:16 GMT
Tom,

You have incorrectly stated my position. I do not believe that time is identical to number. I am still trying (along with many others) to get a handle on time, including your assertion that "time is identical to information."

I generally agree with Marcel LeBel that the most basic property of the physical universe is logic, in the sense that physical contradictions do not exist. He further states that "maths are based on logic. They are the metric extension of simple rules of logic." Based on physical reality and logic, I can construct logical circuits (AND, OR, NOT...) and from these construct arithmetic circuits. One of the simplest is the counter, which, as I noted, is the basis of QED and physically instantiates Peano's axioms. Unlike Kronecker, I do not count on God to supply the natural numbers (as long as a logical physical reality is available.) The numbers derive from physical logic. Before the logic existed, I do not believe numbers existed.

The addition operations that Lev references are further derivative and are simply the most useful of a possibly infinite set of logico-mathematical circuits that can be implemented. Since the natural 'temporal' characteristic of 11 is to be generated after 10 and before 12, I do not see that it makes any sense to ascribe a problem to the fact that 11 can be generated by many different logico-mathematical operations.

I am trying to understand why, when one has a physically real "natural" source of well-ordered integers that can be placed in one-to-one correspondence with time sequence, one would go to a non-ordered field looking for the same property. I'm sure this is related to your view that "...time is an n-dimensional infinitely orientable metric on a self-avoiding random walk", which I am trying to relate to "time is identical to information."

That's the fun of these fqxi conversations. They stimulate thought.

Edwin Eugene Klingman

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T H Ray replied on Aug. 27, 2010 @ 11:02 GMT
Edwin,

That time is identical to information is a result, not an assumption.

Mathematical logic is a branch of mathematics, not the other way around.

Boolean logic doesn't capture the time dependent relations of quantum states, the "something somewhere" -- it only informs us of the "doing what" in a classical computation.

I can't understand why you think I have mischaracterized your position as a claim that time is identical to number, when you say " ... one has a physically real "natural" source of well-ordered integers that can be placed in one-to-one correspondence with time sequence ..." If you don't mean that the time sequence and number sequence are identical, I can't figure out what you do mean.

Neither Lev nor I assume temporal order, however. We get to the identity of time with information by different routes -- Lev (if I understand correctly) from a hypothesis that the time-dependent structure of events is fundamental, and I from a hypothesis that the 2-dimensional structure of the complex plane is fundamental.

Tom

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Edwin Eugene Klingman wrote on Aug. 27, 2010 @ 19:58 GMT
Tom,

You are very well informed and bright, but you believe things that I do not believe.

First, one-to-one correspondence is not 'identical' to me. Identical means essentially, "the same as" and time and numbers are not the same as each other, to me. Nor are time and information.

The fact that Feynman was correct when he said "no one understands quantum mechanics" has not changed with his death. That no one of the five or more current interpretations of QM can explain it 'logically' does convince me that QM violates logic.

As for "Mathematical logic is a branch of mathematics, not the other way around.", it seems to me that perhaps the most significant dividing line among physicists is the one that divides those who believe that mathematics is a useful tool to map the territory of physical reality from those who believe that mathematics is the essence of the universe and can somehow create the real physical territory from the map. The latter is perhaps best represented by Tegmark's "Mathematical Universe". It is basically a Platonic view or reality.

Your statement "Mathematical logic is a branch of mathematics, not the other way around." is true as stated, but does not contradict my position (LeBel's position) that physical logic underlies math. This is based on the fact that physics does not support contradictions and that I can build physical devices that produce all of logic and all mathematics based on natural numbers. (I don't take real seriously any math that cannot be linked to numbers.) Once math arises, it is natural that the mathematician attempts to go back and 'capture' logic in the framework of math. But since I can demonstrate to you that math derives from physical reality, and you cannot demonstrate to me how you can derive physical reality from mathematics, I believe my view is correct. I don't expect this to change your view, because in the wake of Tegmark's paper I have come to believe that this is more a religious question than one of logic. Many on these blogs simply believe that math is primary and physical reality is secondary. This is perhaps attributable to the lack of significant new physics discoveries over the last half century, and the corresponding focus on more and more abstract math, but I suspect it really has more to do with psychological quirks. I no longer hold out much hope that the two sides will ever see the same universe.

I view math as a game, and have no objection to the wildest assumptions being employed as the basis of the game. I view physics as more constrained, and if temporal order and numbers can be linked in a useful manner, as I have described above, I see no need as a physicist to look for 2D alternatives.

Edwin Eugene Klingman

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T H Ray replied on Aug. 28, 2010 @ 13:56 GMT
Edwin,

If numbers map 1 to 1 with time intervals, as you say, there is absolutely no difference between the number sequence and the time sequence. They are identical. Particularly, as you claim that "physical logic underlies math." Things that are not differentiable are identical in physics; e.g., the vacuum and the ether.

In fact, quantum mechanics _does_ violate classical logic. That's no secret.

And while my own research does aim at an organic continuation of mathematical models with the physical world, it requires no metaphysical assumptions. (I've been through this with LeBel, BTW). Metaphysical realism is constructed bottom up, not top down. That's not Platonism. And personal belief has nothing to do with it.

Physics absolutely does support contradictions -- all the time. The most fundamental contradiction is between quantum theory and general relativity. One has to be careful of specifying domain and range. Sure, I agree that mathematics is a game. So is life.

Tom

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Edwin Eugene Klingman replied on Aug. 29, 2010 @ 01:23 GMT
Tom,

I think we are getting to the heart of the problem. You make two statements that I find incredible:

1) "If numbers map 1 to 1 with time intervals, as you say, there is absolutely no difference between the number sequence and the time sequence. They are identical. Particularly, as you claim that "physical logic underlies math." Things that are not differentiable are identical in physics; e.g., the vacuum and the ether."

and

2) "Physics absolutely does support contradictions -- all the time. The most fundamental contradiction is between quantum theory and general relativity."

Perhaps I have been careless and said "physics" when I meant "physical reality". I try to maintain the distinction. I don't care that "physics" is contradictory, since it is clear from the state of today's physics that all of the current models, from the Standard Model to General Relativity are in big trouble. Lev thinks it's because of problems in math, I think it's because of problems with physical concepts.

I've remarked in several comments that the dividing line as I see it is between Unitarists and Dualists, loosely defined as those who believe in one physical substance from which the world self-evolves, and those who believe in some Platonic world of math that replaces God in governing the physical world.

Those who believe in the Platonic world of math can make statements such as yours, that if two entities map into each other, 1-to-1, they are identical. Mathematically perhaps true, physically false.

I have come to believe that those who live in the 'mental' world of math and logic have, to a serious degree, actually lost touch with the physical world. Drastic, I know, but it's the only thing that I can comprehend that explains the general view which I think you are expressing.

So when you say "Physics absolutely does support contradictions -- all the time" you should notice that I said: "the most basic property of the physical universe is logic, in the sense that physical contradictions do not exist." Either you are not paying attention to the words, or else you do not distinguish between "physics" and "physical reality". Contradictions do not exist in *physical reality*. The fact that they may exist in physics should simply be considered as proof that physics is off the mark.

I don't know whether we have a language problem or, as I suspect, a more serious perceptual problem, which I believe is reflected in both these fqxi discussions, and in the wider world of politics, where there appears to be a large percentage of humans who cannot (or do not) distinguish between abstractions and reality. Math is abstraction, physical reality is not.

I do appreciate your comments,

Edwin Eugene Klingman

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T H Ray replied on Aug. 29, 2010 @ 17:12 GMT
Edwin,

How can one do science, while making a distinction between "physics" and "physical reality?" Reality is superfluous -- as Laplace said of a certain supernatural character, "I have no need of that hypothesis."

All scientific explanations are rendered by theory alone. There is thus no operational difference between abstraction and "reality." If there does exist some underlying reality beyond that which we can explain objectively, science won't find it.

Tom

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Lev Goldfarb wrote on Aug. 27, 2010 @ 21:53 GMT
I guess everything comes back again and again to the confusion created in the last century (particularly with the advent of computing) whose source is the blurring of the distinction between *coding* of 'reality' and its *representation*.

There are many different means of coding information, and digital is one of them. But coding does not have to address the nature of information being coded, i.e. the meaning/semantics of this information. The reason confusion appeared in the first place has to do with the situation that so far mathematics has not dealt with the *meaningful* encoding, i.e. with representation. (Actually, I had to face this problem in the 80's.)

I suggested in my paper Representational Formalism in Which Syntax and Semantics Are Congruent: Towards the Resolution of Searle's Chinese Room Challenge that the best way to approach this confusion is to rely on the formalism in which syntax and semantics are basically the same. What it means is that if you use such formalism in physics (or any other science) your 'encoding' is meaningful, i.e. it is a 'faithful' copy of 'reality'. (By the way, I believe that there is, basically, only one such formalism.)

It goes without saying that, first of all, one has to face the central issue: What is an adequate view of 'reality'? The answers to such question will be investigated in this century, but the ETS formalism was developed to address precisely this question. I postulated that 'the reality' is an interconnected net of structured events. Again, natural numbers can be obtained/realized ("physically", to use Edwin's language) in this manner.

Mathematics, for obvious historical reasons, has adopted the numeric view of reality, but as I have discussed in several papers the reduction of *all events in nature* to a single event of the simplest structure (corresponding to the successor operation in the Peano axioms) although allow us to encode reality but in a very 'primitive' manner. For example, an event in QED has a more complex structure.

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T H Ray replied on Aug. 28, 2010 @ 14:23 GMT
Lev,

I don't think you mean to say that syntax and semantics are the same. "Congruence," the term you use elsewhere, does not imply "same." The technical difference is critical, because congruence implies recognition of characteristics between this object (or event) and that -- not sameness.

An "... interconnected net of structured events ..." where congruence of syntax (meaning) and semantics (language) has a temporal ordering effect and faithfully emulates physical reality results in zero difference between the emulation and the reality.

Because we know that not all syntactically correct sentences are meaningful, however, reducing the noise-to-communication ratio does require a richer -- and time-dependent -- representation of the "something somewhere" because classical computation does not capture it. Why, however, would not quantum computation do the job, with its richer structure of Hilbert space and superpositions?

Still trying to rule out mathematical models, on a sounder theoretical basis than I have yet seen.

Tom

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Lev Goldfarb replied on Aug. 28, 2010 @ 15:44 GMT
Tom,

1. I don't think you mean to say that syntax and semantics are the same. "Congruence," the term you use elsewhere, does not imply "same." The technical difference is critical, because congruence implies recognition of characteristics between this object (or event) and that -- not sameness.

Yes, of course.

2. An "... interconnected net of structured events ..." where congruence of syntax (meaning) and semantics (language) has a temporal ordering effect and faithfully emulates physical reality results in zero difference between the emulation and the reality.

Yes. By the way, this is *exactly* what Helmholtz was saying.

3. Why, however, would not quantum computation do the job, with its richer structure of Hilbert space and superpositions?

I guess the shortest answer is this. We need qualitatively different structured events (e.g. QED) and we need irreversibility, i.e. to retain formative history.

For another short answer, may I recommend Milic Capek's "The Philosophical Impact of Contemporary Physics", 1961 (actually it should be called "fundamental inadequacy/incompleteness of contemporary physics"), esp. pp. 135-140, 231-240, 361-374. Here is the most profound paragraph which starts at the very bottom of p.373 (just before that paragraph he was discussing auditory, esp. musical, perception):

------------------------------------------------
---------------------------------------------------

"Two successive "specious presents" are not separated by imaginary durationless instants, but *by their qualitative differences*. The term "separation" is misleading; it suggests separation in a spatial sense. We need to realize that the qualitative differences of successive moments of duration are untranslatable into spatial imagery. To differ qualitatively and to be distinct in space are two different notions." (his emphasis)

---------------------------------------------------
--------------------------------------------------

(The inadequacy of the conventional physical concept of time, chronon, "separation" of temporal segments, etc. is discussed throughout the book.)

To me this paragraph also suggests that since such successive qualitatively different events cannot originate in 'space' they must originate elsewhere!!!

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Lev Goldfarb replied on Aug. 31, 2010 @ 01:33 GMT
"I don't agree, however, that " ... successive moments of duration are untranslatable into spatial imagery ..." when we allow n-dimension calculus. We simply make the space as big as it needs to be."

Tom,

(You replied in the wrong thread, so I am trying to continue the right one.)

The issue is not resolved with the increase in the dimensionality of the space.

The issue has to do with the ability of any space to support structural events. That is the whole crux of the matter!

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Edwin Eugene Klingman wrote on Aug. 27, 2010 @ 22:51 GMT
Lev,

I've looked at (and around) page 29 as you suggested. At first glance it appears not entirely unrelated to my "Automatic Theory of Physics" based on automata theory as the most promising means to understand both "the unreasonable effectiveness of mathematics in the sciences" and as the model of how physics theories are generated from observations. I'm sure there are significant...

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Lev Goldfarb replied on Aug. 28, 2010 @ 02:09 GMT
Dear Edwin,

Please, forgive my sincerity, but with all due respect, I can't help but be amazed at how such formally trivial (i.e. not rich) computational concept as automaton can inspire one to view it as "the most promising means to understand both 'the unreasonable effectiveness of mathematics in the sciences' and as the model of how physics theories are generated from observations.

You see, I am a firm believer in the currently not so popular aesthetical principle that to respect Mother Nature means not to allow formally trivial models as the basis for understanding the universe, i.e. this is absolutely the least we can do as our 'quality control' (after all, each of us has only one life to live). The evolution of the universe has exhibited its awesome *constructive* power.

Best wishes,

--Lev

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Edwin Eugene Klingman wrote on Aug. 28, 2010 @ 03:26 GMT
Lev,

As I indicated in my remarks, there are those who think complex math is the answer and those who think the answer has nothing to do with complex math. I am of the latter persuasion. I realize that the schools have overproduced physicists and assorted types, that must keep busy with esoterica, and math offers the best playground for these games.

It is way beyond me to conceive of how one could believe that a formalism, any formalism, can exhibit 'constructive' power (of the type exhibited by the universe), but that was what I referred to when I spoke of the religious aspects of these pursuits. Since you seem to be enjoying your pursuit, I wish you well. It will clearly carry you to retirement, with no fear of actually solving the problem.

Edwin Eugene Klingman

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Lev Goldfarb replied on Aug. 28, 2010 @ 04:57 GMT
Edwin,

Since you are of the persuasion that "the answer has nothing to do with complex math", and you also don't believe in radically changing the basic math. language (as I'm advocating), what do you think the "answer" is about?

You must, then, believe in miracles. ;-)

Cheers,

--Lev

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Edwin Eugene Klingman wrote on Aug. 28, 2010 @ 08:49 GMT
Lev,

Some fqxi players believe that the problem lies in math (as you seem to); others believe that the problem is in the basic concepts of physics (as I do). Few look to miracles as the answer.

I spent a little more time looking through your paper and it appears that most of the diagrams in your paper could be reformulated as diagrams in my Automatic Theory, and hence have some level of equivalence. Much of my approach was based on pattern recognition and how this can be used to 'automatically' derive theories of physics from (numerical) observational data. Although this was my 1979 dissertation, I decided to publish it when a 3 April 2009 Science paper, Vol 324, "Distilling Free-Form Natural Laws from Experimental Data" presented essentially the same approach as novel.

Having spent over four years on Albert's Molecular Biology of the Cell, 4th and 5th editions, Robert's Embryology, Epigenesis, and Evolution, and about a dozen similar texts, including Immunology texts, I understand why you are frustrated with math and would like to be able to build a 'Bubble Man' of bubble legs, bubble limbs, bubble torso, etc., but I find it difficult to take such an approach seriously. I mention these studies because it appears we have been focussed on solving essentially similar problems: of life, growth, and consciousness. While I have been very interested in biological problems, including protein folding, my real goal has been consciousness. My guess is that you exclude consciousness from the problems you deal with, since a search of your paper did not find the word.

My belief, after four decades of effort, is that consciousness is fundamental and not an artifact. This means that consciousness does not pop into existence when all of the bubbles are in place, but has a more essential existence as a field phenomenon that interacts with the physical world at all levels, from QM entanglement to biological growth and development. The mathematics necessary to describe the interaction of this field with matter are not complicated. The "internal" aspects of the field, awareness and free will, are not susceptible to mathematical analysis. Instead of positing the essential unpredictability of Nature in mysterious quantum fields, I place it in a mysterious consciousness field. You might be surprised how much physics falls out of this approach.

Edwin Eugene Klingman

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Lev Goldfarb replied on Aug. 28, 2010 @ 14:31 GMT
Edwin,

By the way, I am a firm believer that "consciousness" is a convenient cop-out (practically in the category of miracles), since what we need is *one* formalism that explicates both physical reality and biological information processing: the latter could have emerged only if its fundamental principles were embedded in the former.

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T H Ray replied on Aug. 30, 2010 @ 13:42 GMT
Thanks, Lev. I'll order Capek's book. I don't agree, however, that " ... successive moments of duration are untranslatable into spatial imagery ..." when we allow n-dimension calculus. We simply make the space as big as it needs to be.

Tom

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Edwin Eugene Klingman wrote on Aug. 28, 2010 @ 19:51 GMT
Lev,

Your reply is unsurprising. And the fact that you are a "firm believer" is confirmation of the essential religious aspects of our theories. Everyone I've dealt with on fqxi is a firm believer in their own theories. Not surprising when the theories typically represent a decade or more of pursuing a unique approach to understanding a personally pressing problem. To the casual observer a specific theory may seem full of holes, but the believer has long ago filled most of these holes satisfactorily, and the whole makes sense to him. Clearly mental models have been learned. It probably requires inventing a few new categories along the way, but the final result hangs together in the mind of the believer. And who knows, one of us might just be right.

You say "what we need is *one* formalism that explicates both physical reality and biological information processing: the latter could have emerged only if its fundamental principles were embedded in the former."

We are almost in agreement here, except that I believe we need *one* physical substance (real) as opposed to one formalism (abstract). Reality proceeds from something real, not something abstract. But that is the major dividing line I mentioned earlier. Roughly speaking, it separates the Unitarists from the Dualists. The Unitarists seem to recognize the primacy of consciousness and of physical reality, while the Dualists envision some Platonic world of relations that somehow plays the role of God in designing and governing our world. I have my theories of the types of mind that gravitate to each, but it's probably nonsense. Anyway, it's a fun game, and keeps many of us busy. As you mentioned, we (probably) only get one life.

Edwin Eugene Klingman

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Lev Goldfarb replied on Aug. 28, 2010 @ 20:26 GMT
"We are almost in agreement here, except that I believe we need *one* physical substance (real) as opposed to one formalism (abstract). Reality proceeds from something real, not something abstract."

Dear Edwin,

Do you realize that practically every post by you contains *fundamental* contradictions, which you don't seem to notice. So as *the very last thing* I point out the latest one:

On the one hand, you believe "that consciousness is fundamental" (Aug. 28) and on the other hand, you just claimed "that I [you] believe we need *one* physical substance (real)". So how do you 'put' your 'reality' in the mind: you can't put trees, stars, and clouds in the mind, can you? Or, Is you 'reality' is not really real? Moreover, do you really believe that automata, which you like so much, are 'real'?

Thank you for you comments!

My best wishes to you,

--Lev

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Edwin Eugene Klingman wrote on Aug. 28, 2010 @ 20:54 GMT
Lev,

A consciousness field, as I propose it is a *physical field* and physical fields distribute energy over space. According to the field equations I have proposed this field can essentially *condense* under big bang conditions into particles-- neutrinos, electrons and quarks. The theory produces both the fine structure constant, massive neutrinos (with approximately correct mass), neutrons with negative cores, and an explanation for the recent finding that the proton radius for muonic hydrogen is 4% smaller than QED has computed it to be (so much for the vaunted 15 place accuracy of QED). All of these explanations are currently missing from the Standard Model.

You opinions simply reflect your undeveloped understanding of consciousness, and have no relevance to my theory. This is the problem with most religious opinions, incomprehension leading to intolerance.

Your consensus understanding of consciousness as something occurring in the mind is conventional, but I'm surprised that you haven't at least heard of or considered alternative conceptions. I would suggest that you think of the ability of the gravity field to 'pull' on mass, but you probably believe that the gravity field is simply geometry.

Try not to take new ideas personally.

Edwin Eugene Klingman

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Edwin Eugene Klingman wrote on Aug. 29, 2010 @ 00:43 GMT
For any reading the above thread, who are unaware that there is an alternate conception of consciousness, (alternative to the consensus of consciousness as artifact) the following fqxi is a blitzkrieg introduction to the topic:

http://www.fqxi.org/community/forum/topic/561

"Fundamen
tal Physics of Consciousness" -- essay and extensive comments

Other more detailed info available here and at Amazon:

http://www.geneman.com/books/klingman_book_list.htm

Ed
win Eugene Klingman

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Lev Goldfarb wrote on Aug. 29, 2010 @ 20:33 GMT
Let me start a new thread, closer to physics.

I have noticed that one of the FQXi essays written by Don Limuti (his website), discusses motion of a particle as
Now, if this kind of hopping, or pulsation, can be modified to mean that the particle is being instantiated on the basis of the events in the corresponding struct, that might be a way to proceed.

Does anyone knows any other work on a similar view of particle motion? (Don talks of the original (1925?) Heisenberg paper.)

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T H Ray replied on Aug. 30, 2010 @ 10:56 GMT
I don't see what you see in this lambda hopping idea, Lev. It postulates that there is no simultaneous particle position and momentum. If that were true, rest mass would be incalculable, spacetime would not be physically real and general relativity would be falsified.

This looks like another version of Mach's Principle to me, which Einstein has already incorporated into GR.

Tom

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T H Ray replied on Aug. 30, 2010 @ 13:18 GMT
Lev,

A large part of the reason that theorists turned to extra dimensions, I think, is the problem you describe as "instantiation." Fact is, we only know motion by what motion is not; i.e., relative motion as an instantaneous relation between bodies obviates time dependence.

Jumps in action demand time dependence. We can't have a jump in zero time, so whatever interval "instantiates" the action is measure zero. Measure zero is on the boundary of whatever internal structure may (or may not) exist at a more fundamental level. This leads in a quite natural way to brane models and holography, because the boundary of the boundary is where we receive information from our vantage of d + 1 dimensions.

Tom

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Lev Goldfarb replied on Aug. 30, 2010 @ 14:15 GMT
Tom,

The hopping is about the pulsational nature of movement which is predicted by the struct hypothesis: in space, you can observe *only* the instantiated events of the corresponding struct.

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Edwin Eugene Klingman wrote on Aug. 29, 2010 @ 20:44 GMT
Lev,

What is physics?

Some say there is dark matter and energy. Some say there is a God Particle (Higgs boson) to create mass. Some say there are universes without number. Some say nothing changes in Einstein's 'block universe' of General Relativity. Some say the world is made of mathematics. Some say axions exist. Some say E8. Some say gravitons and gravity waves exist. Some say there is SuperSymmetry. Some say inflatons exist. Some say QCD 'color' exists. Some say the world 'splits' with every quantum decision. Some say 9 to 26 dimensions exist. Some say 'strings' and 'branes' exist. Some say lambda hopping. Some say bubble men made of bubble limbs. Some say information and time are identical. Some say syntax and semantics are the same. And on and on. What do *all* of these have in common? The have *never* been seen! They are inferred from various theories (guesses!) about the world.

These are the maps. What actually exists is the reality. And that includes consciousness.

It's been fun. Don't take it too seriously.

Edwin Eugene Klingman

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Lev Goldfarb replied on Aug. 30, 2010 @ 01:14 GMT
Ed,

Thanks for the advice, but since some of us are not "taking things too seriously", some of us have to. ;-))

Cheers,

--Lev

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Edwin Eugene Klingman replied on Aug. 30, 2010 @ 03:13 GMT
OK, Lev,

If you're serious, address all of the above...

I'm prepared to.

Edwin Eugene Klingman

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Lev Goldfarb replied on Aug. 30, 2010 @ 04:11 GMT
Ed,

With all due respect, as I already mentioned, I see the "above" as a soup of contradictions, so, to be honest, I really lost the interest.

Thanks for asking!

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John Merryman wrote on Sep. 2, 2010 @ 20:18 GMT
Lev,

I agree with you that reality is more about streaming events, than particles, but it seems all three are levels of emergence.

Here is a point I make about the nature of time: If two objects, be they particles or automobiles, collide, it creates an event. Now the physical reality of the objects go from past events to future ones, say from the factory to the scrap heap. On the...

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Lev Goldfarb replied on Sep. 4, 2010 @ 17:55 GMT
"On the other hand, the events go from being in the future to being in the past. Tomorrow becomes yesterday."

"Ultimately, even our lives are units of time which start in the future and recede into the past."

John,

I believe that this is an illusory perception of reality. If you take the view of reality as a flow of interconnected events (and you agreed with this), there is only one direction of flow: unless you have a very 'primitive', i.e. cyclic, universe, an unlikely scenario, an event that appears in the flow again, does so in a different 'context'. That is why, except for the basic events and very short processes, there are no two absolutely identical objects/processes, even when they belong to the same class, e.g. a protein of a reasonable size, a bacterium, an ant, a tree, a star, or a screw.

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John Merryman replied on Sep. 5, 2010 @ 10:09 GMT
Lev,

I would say our perception of time is a flow of interconnected events, but there are some inherent caveats in that. I think it reasonable to say there are many events which are not directly connected, ie, exist outside each other's light cones, such that there is no single timeline tying them all together. Even in the context of Big Bang theory, mutiverses and dark energy provide example of one, completely (theoretical) outside events(multiverse), as well as apparent additional input into the given cause and effect timeline, that of dark energy.

It's not that I'm arguing against the one direction of of the flow of events, but I'm posing the question of: What is it flowing against? What is the constant? Is it these series of occurences, or is it the physical reality of the present? As objects we move from one event to the next, but as processes, we only exist in the present. So are we moving along a metadimension of time, whether Newton's absolute flow, or Einstein's fourth dimension, from past to future, or does the changing configuration of what is cause one event to be replaced by its successor and thus recede into the past?

For much of human existence, we viewed the sun as moving across the sky, from east to west and constructed increasingly complex explanations for this, from Apollo's chariot to epicycles. It was only been within the last five hundred years we understood it was the rotation of the earth, moving the other waqy, west to east, which caused this effect. Could it be the view of time as a dimension along which the present moves is equally reversed?

The effect of time is caused by a multitude of motions, which we tend to intellectually coalesce into one cumulative motion. A good example is how the measure of the cycles of the moon were adapted into units of the solar year and no longer reflect an accurate moon cycle.

One of the main functions of relativity is to try and explain why clocks do record their own time and are not reflective of some universal time.

Have to run.....

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John Merryman replied on Sep. 5, 2010 @ 16:02 GMT
Lev,

Sorry for the rushed response this morning. From your essay:

"As we know, objects in nature do not pop up out of nowhere but always take some time to appear,

and in each case, the way an object appears is similar to the way some other, ‘similar’, objects

appear. In other words, as far as we know, there is no object in nature that does not belong to some

class of closely related objects, be it an atom, a cloud, a star, a black hole, a stone, a worm, a protein,

or a stop sign. Since we view objects as processes, we have



Postulate 1: the universe is a family of evolving and interactive classes of (irreversible)

processes."

In making a distinction between objects and processes, I would view the process as that which creates and the object as that which is created. A process usually creates innumerable distinct, but similar entities, whether it's the rotation of the earth relative to the sun creating days, or an automobile factory creating cars. The processes and entities go in opposite directions though, with the process going from past entities to future ones, while the particular entities go from being in the future to being in the past.

This is not a cyclical process, but a relational one.

Of course there are internal processes within entities, much as your brain is an entity that is also a process of distilling information into useful observations, as well as processes which are entities on a larger scale, such as that car factory being a unit within the larger economic process.

In terms of a clock, the process is the hand which moves from one unit of time to the next, while the units of time go from being in the future to being in the past. It should be noted that clocks evolved from sun dials, so the hand of the clock models the motion of the sun through the phases of the day, but to go back to an earlier point, we now know it's the earth which moves, not the sun, so if we were to translate that to the clock, it's the hand, which represents the present, that is constant and it would be the face of the clock, as the dimension of time, moving counterclockwise.

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Edwin Eugene Klingman wrote on Sep. 5, 2010 @ 20:46 GMT
John,

I'd like to ask you about your idea that time is an emergent phenomenon, like temperature, that arises from the ever-malleable 'substance' of the universe which is generally represented by energy-momentum relations.

In other words, 3-space dimensions exist 'NOW'. These dimensions 'contain' the universe. The future may be implied, but does not exist. The past may be remembered, and the present is in a sense the 'record' of the past. But the physical, energetic universe exists only at this moment, which we know as 'now'.

Aside from questions of directionality, is this a fair characterization of your position?

Edwin Eugene Klingman

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John Merryman replied on Sep. 5, 2010 @ 23:11 GMT
Edwin,

Basically, but remember the concept of "now" is part of the temporal construct. As such, it's generally considered as a dimensionless point between past and future, since any attempt to measure it constricts down to nothing and logic likes measurements. So in that sense, I'd tend to use the term "extant." Sort of a fuzzy "now," because motion is a prerequisite for change and if we constrict duration to nothing, there is no motion.

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Anonymous replied on Sep. 6, 2010 @ 08:16 GMT
John and Edwin,

Please allow my entry here.

I posted the following in http://www.fqxi.org/community/forum/topic/59

"If we admit the idea that duration in time and motion (mass-energy) in space do not interact with duration and motion being simply concurrent realities, then the idea of an infinite past and future time would be easy."

If we allow the idea that duration and motion are separate and non-interacting but concurrent occurrences, then the whole physical/material universe would be just a construct of motion (i.e., energy) with the overall motion (energy) transformations occurring 'alongside' the temporal occurrence.

The whole dynamic existence of corporeal motion transformations would then have the irreversible history, with the temporal (duration) 'transformation' simply an abstraction.

The way I see it, there'd be the separately fixed 3-D space dimension and the 1-D time dimension. The motion and duration occurrences would be the only 'changes' that occur - i.e., the energy transformations and the temporal transformation with the space and time dimensions merely the backgrounds.

castel

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John Merryman replied on Sep. 6, 2010 @ 16:43 GMT
castel,

From my reading of what you wrote, we would seem to be in general agreement, in that the changing configuration of what exists is the underlaying reality, while spacetime geometry is a mental model of the narrative process in a spatial context.

The essential reality amounts to a fluctuating vacuum, resulting in an expanding background, interspersed with contracting gravity wells to balance it, resulting in an overall flat space. Time being an emergent effect of this process.

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Edwin Eugene Klingman wrote on Sep. 6, 2010 @ 17:47 GMT
John and Castel,

I will reread Castel's essay, but agree with John that spacetime geometry is a mental model. What I have the most trouble with is the 'fuzzy' now, the "point" when it is all happening. I hope we can make sense of that. I'd like to try to nail down some of the reasons for concluding that now is the ultimate reality.

In GR 'block time' nothing changes. There is no 'now', nor can there be free will if the future already exists (I don't consider splitting universes worth thinking about.) GR 'block time' is surely a mathematical fiction.

However, let's assume that the future does not exist, but that the past really does exist. This would mean that the past physical reality grows larger with each moment. This would imply that new universes materialize every moment, bringing into real physical existence all of the energy and information of the universe, endlessly. This is inconceivable to me.

For these reasons I don't believe that the past or future exist as physical reality, but only as conceptual ordering categories.

What are the problems with 'now'? Some argue that Einstein's special relativity demolished the concept of 'simultaneity' (as in it's simultaneously 'now' over all 3-space.) I disagree. What he did was demolish the picture of a 'God's eye view' of the whole thing in which all reality is seen at once. He replaced this with operational local observations requiring the speed of light be taken into consideration.

If we're in rough agreement on these points, let's move on to the 'fuzzy' now, and try to deal with 'momentary duration' or whatever is implied by the existence of change in space.

Edwin Eugene Klingman

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Edwin Eugene Klingman wrote on Sep. 6, 2010 @ 19:06 GMT
The main problem, if time is not to be considered as an everlasting linear 'dimension' stretching from the eternal past to the far future, seems to be the need for some concept of 'duration' or 'time of change'.

First, does duration exist? That is, is now 'fuzzy' or a perfect 'point'?

If we consider physical reality to be best characterized by energy and momentum, then these seem to imply some finite or infinitesimal time duration that is real in some sense.

But momentum and energy, useful as they are, do not seem to be fundamental. What *does* seem to be fundamental, both in my theory and in the rest of physics, is 'action', in units of Planck's constant, h.

Conceptually, we seem to have a hard time with 'action', and I suspect it's because of this 'built-in' duration. My basic quantum flow condition is presented in my essay,

http://fqxi.org/community/forum/topic/561

as

(dm/dt)(dx)**2 = h

but lets look at Heisenberg's version:

dE dt = h

If a given local event exhibits one Planck unit of action, h, then we see that both the change in energy, dE, and the duration, dt, are somewhat 'fuzzy'.

This is my first cut at understanding the concept of 'duration' as it applies to the reality of 'now' in 3-space. I think that the next effort might be focussed on understanding the meaning of 'local' in the above description.

Edwin Eugene Klingman

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Edwin Eugene Klingman wrote on Sep. 6, 2010 @ 20:01 GMT
My discussion of the 'built-in duration' implied by Planck's constant of action led to the concept of 'local', so I'd like to examine a few relevant concepts here.

Since we are focused on the energy that characterizes the changes in 3-space, then an obvious related concept is that of "energy density" which almost certainly means "local energy density".

There are several things to note here. First, quantum electrodynamics (QED), our most 'successful' theory until recently, was developed with the idea of a "roiling frenzy of quantum foam" (Brian Greene in 'The Elegant Universe'). The major problem here is that circa 1998 we learned from cosmology that the 'vacuum energy' was off by 120 orders of magnitude. That's a big deal. In fact, if you or I were off by that much, we would be expected to recalculate everything that depended on vacuum energy. Wanna bet whether all QED calculations since 1948 were redone? I didn't think so.

Further, Greene makes the following statement:

"...the uncertainly principle tells us that the size of the undulations [in the quantum foam] of the gravitational field gets larger as we focus our attention on smaller regions of space."

This may be what Greene and other QED'ers believe, but this is most definitely *not* what the uncertainty principle tells us. We cannot 'focus' on smaller regions of space! We can 'probe' smaller regions of space via the use of higher energy (shorter wavelength) particles. But in this case *we* are putting the energy into the smaller region of space. Heisenberg's principle did not put the energy there simply because we "focused" our attention on the space.

This is examined in more detail in my book, "Gene Man's World".

Next I'd like to look at the consequences of this misunderstanding of vacuum energy.

Edwin Eugene Klingman

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Anonymous wrote on Sep. 6, 2010 @ 20:52 GMT
The idea of excessive vacuum energy led to further concepts such as a 'sea of quarks' and the general idea of the 'polarization of the vacuum' due to the virtual particle sea. Brian Greene again:

"Even in an empty region of space... energy and momentum are uncertain. They fluctuate between extremes that get larger as the size of the box gets smaller. It's as if the region of space inside the box is a compulsive 'borrower' of energy and momentum, constantly extracting 'loans' from the universe and subsequently 'paying' them back."

[I don't mean to pick on Greene, but his 'Elegant Universe' has apparently met the approval of most QED'ers, since these comments are over a decade old, with no corrections.]

The above misunderstanding is the source of problems in quantum field theory. [For those who haven't heard, the vaunted dozen place accuracy associated with the hydrogen atom has just been reduced to almost one place accuracy WRT the proton radius seen in muonic hydrogen!] In essence "unlimited credit is the root of the ultraviolet catastrophe", where the ultraviolet catastrophe is the name for the fact that infinite values always show up at high energies. In Gene Man's World I explain that:

"In terms of the 'borrowing analogy', it's as if one believed his local bank had all the money in the world, only to find out that it holds only one peso."

Physicists speak of 'borrowing energy' from the field, yet they seem to believe in 'unlimited credit'. To assume that the (local) region can borrow energy, without specifying where the energy is to come from, is just sloppy thinking. I cannot go to my local bank and borrow billions of dollars. My local bank does not have billions of dollars! Similarly, a particle cannot borrow large amounts of energy from a local region of space that does not have a huge amount of energy. The implication is that no particle can be supported in a volume of space that has no dimensions greater than or equal to the particle wave length. If true, so much for the 'sea of virtual particles' that QED is based on. Since the fqxi comments are not equation or diagram friendly, I simply refer to Gene Man's World for the details of this analysis.

Since the above has been conceptual, I should touch base with experiment. In 2007 a HAPPEX collaboration of over 100 physicists reported Jan 2007 Phys Rev Lett that:

"there is little room for observable nucleon strangeness dynamics."

In other words, they don't see any sign of the strange quarks that they expected to find in the 'sea'.

This hasn't resolved our problems of 'fuzziness' of now, but it's been fun.

Next I want to treat some consequences of the above, but I'll back off now and let others have their say.

Edwin Eugene Klingman

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John Merryman wrote on Sep. 6, 2010 @ 23:24 GMT
Edwin,

The idea is that time is an effect. How do we experience it? Our lives exist as series of perceptual impressions and so it's natural to think in terms of the narrative effect. So what would a point in time be? It wouldn't be an event, as they require some duration of activity to exist, be perceived and processed into a conceptual impression. This duration is a unit of time, like a...

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Anonymous wrote on Sep. 7, 2010 @ 04:09 GMT
John,

Apparently, the idea is more like - the space dimension, the time dimension, the ethereal substance of existence, the ephemeral instance of existence, the motion, and the duration are all co-existential essences.

To KISS all these (as per Occam's suggestion), the space dimension would simply be the 3-d volumetric container of the ethereal substance of existence; the time...

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Anonymous wrote on Sep. 7, 2010 @ 04:26 GMT
corrections -

(Duration reversal is never a possible effect on duration, since we only HAVE a single temporal vector in the time dimension.)

and

(It does NOT look proper that one would be emergent because of the other, after all they simply co-exist as the two main aspects of the change that occur in nature.)

Sorry about that...

castel

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castel wrote on Sep. 7, 2010 @ 14:56 GMT
John,

Apparently, the idea is more like - the space dimension, the time dimension, the ethereal substance of existence, the ephemeral instance of existence, the motion, and the duration are all co-existential essences.

To KISS all these (as per Occam's suggestion), the space dimension would simply be the 3-d volumetric container of the ethereal substance of existence; the time...

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John Merryman replied on Sep. 7, 2010 @ 17:36 GMT
castel,

I would take issue with the idea that "dimensions are the unchanging realities."

If we consider the evolution of the concept, dimensions originate as a modeling tool. They are based on geometric coordinates. As they were applied in real world situations, such as geography, it became evident such models were inherently flexible, such as a straight line in space and a...

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castel replied on Sep. 8, 2010 @ 02:04 GMT
John,

I tend to simplify to the most fundamental.

I simply see six fundamentals: space, substance, motion - these have both the phenomenal and noumenal aspects/characteristics; and, time, instance, duration - these have only the noumenal aspects/characteristics.

Space contains the corporeal (the tangibles); the substance fills space; motions move motions and form kinetic constructs that render definitions in the substance; the substance per se is aethereal because it is the kinesis/motion that renders tangibility.

Time contains the abstract (the intangibles); the instance reside in time; the transformation effected by duration renders cumulative definition to the instance; the instance per se is ephemeral (must be what Tegmark refers to as "ephemeris time") because it is constantly transformed by the fundamental essence of duration.

My analysis takes the breakdown of the existence to the most fundamental level of the existentials.

I understand the dimensional analysis methodology that has been evolved and confused as a representation of the dynamic. But I believe the correct approach is to use the vectorial analysis methodology because fundamentally vectors are used to represent the dynamic.

I adhere to the fundamental suggestion of the pure kinematics wherein fundamentally "motions move motions" - that is why I prefer the idea of the transformations of motion instead of the idea of the transformations of space and time.

There used to be time - the dimension, time - the instance, and time - the duration. And there used to be space - the dimension, substance - the aethereal space-filler, and motion - the definitions wrought in the aethereal substance... The ideas regarding time was rather clear in Newton, but later confused by Einstein. The ideas regarding space, the aether, and motion were somewhat clear. But it has never been clarified that mass and energy are kinetic constructs - not by Newton, Maxwell, nor Planck. There was the suggestion in Einstein, but which he also later confused. I like my own clarity now on all these ideas (although I am considered irrelevant by many).

Also, it used to be that 'dimension' refers to 'length' (specifically when we talked about space) and we say that a point is dimensionless because it is without any length. But now the idea of dimensions has conventionally been very much confused - foremost by Einstein... Yet, try to closely consider the conventional 'dimensional' methodology in the analysis and you will find that the 'dimensions' referred to are actually 'vectors'.

castel

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castel replied on Sep. 8, 2010 @ 04:11 GMT
I must add.

Dimensions are dimensions. Vectors are vectors.

Dimensions remain constant and hence unchanged. Vectors effect change - especially motion on the substance of existence and duration on the instance of existence.

When we say "there is more substance here" we normally mean there is more motion in a construct of motion (mass-energy) in a given volume of space. This is because motion renders the definitions on the substance.

When we say "a moment or an instant" we normally mean a measure or span of the duration of the instance of existence, a "narrative" segment of duration of the instance of existence along the time dimension.

There is also the "point in time" as the 'pointed' instance of existence itself. And we make "appointments". But often we mean a span of the duration of the instance of existence along the time dimension.

castel

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Edwin Eugene Klingman wrote on Sep. 7, 2010 @ 23:46 GMT
John,

As to how we experience time, I'm having trouble distinguishing between a feeling of duration versus simply a feeling of continuity as I write this now and then write this now. Your 'narrative effect' captures a lot, but doesn't quite resolve the 'duration' problem.

I don't buy a 'dimensionless point in time' and I do believe particles are real, not wave functions. And...

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John Merryman replied on Sep. 8, 2010 @ 02:33 GMT
Edwin,

(I realize you probably prefer Gene, but Edwin's an old family name, brother, cousin, uncle, grandfather, great...)

Doesn't solve the duration problem, as in?

Consider it from my point of the dimension of time going future to past, rather than traveling the dimension from past to future: The clock ticks. Duration isn't it moving along a fourth dimension to the next...

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Edwin Eugene Klingman wrote on Sep. 8, 2010 @ 05:49 GMT
John,

The main problem with discussing consciousness is that it takes quite an initial period to agree on the terms. You and I overlap in many of our ideas, but we diverge in the details. For example, the particle generation 'mechanism' of the C-field is a self-reinforcing vortex that reaches the limit of curvature of space. This is spelled out in complete detail in Chromodynamics War...

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John Merryman wrote on Sep. 8, 2010 @ 10:08 GMT
Edwin,

Since we both agree the basis of consciousness is easier to explain as primordial, rather than emergent, I guess our real point of difference is whether the universe emerged as a singularity, or is an unbound, eternal field. I have to get to work, so I can't go over my arguments as to why I think the Big Bang theory is flawed and I admit I have the full weight of the establishment against me on this, but In all the arguments I've had on the subject, there are many points I keep raising which don't draw very effective responses. How is it that we can observe a universe that is flat, has mature galaxies and galaxy structures as far as can be seen, have a theory by Einstein describing this balance, of which there is increasing evidence of and still hold with this current model, without any dissent and even only marginal dissent from the fringes, such as myself?

Yes, a singularity provides a source of energy, but leaves open the question of where it came from? how can we have space expanding from this point, but still have a stable speed of light? Ifspace expands, wouldn't the yardstick of C increase as well? But that would blow the whole Doppler effect out of the water, because it isn't based on stretching the units of distance, only moving away within them.

On the other hand, why couldn't we have an unstable vacuum as the primordial source? Big Bang theory even adds one as Dark Energy to explain one of its various discrepancies. What if this Dark Energy/Cosmological Constant is the source and above a certain density, say 3.7k, it starts collapsing into gravitational vortices. That would provide spin on a local scale.

Got to get to work....

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Edwin Eugene Klingman wrote on Sep. 8, 2010 @ 22:55 GMT
John,

We've actually covered a lot of ground in this back and forth, in highly compressed manner. For example, I explained above why 'unstable vacuum' does not cut it. So we're ignoring things already covered. That's a sign it's time to stop and either review our earlier comments or just cogitate some.

I've seen your comments on consciousness on other blogs (after they had died down) and have looked forward to talking with you. I do think we agree on the primordial basis. I do not have the answers to your questions because I have not spent much time thinking about redshift and associated issues. Almost immediately after finding my key equations, the inflationary aspect appeared, and I took this as reason to accept the big bang, which also provides the source of strong enough vortex fields to produce the requisite particle zoo. My twin goals were to understand the nature of consciousness and to match this with *known* physics (not the hodge-podge of current theories based on things that have never been seen, that I mentioned above). I don't give much credence to the establishment. They have to play by their rules if they want to stay in their game. My absolute requirement was that my theory match my conscious experience and that the basics of physics makes sense. Beyond that, the interaction of the consciousness field with body-brains accounts for every map, model, scheme, and idea that the human mind comes up with, and, as I said, none of these will reduce the universe to a non-mysterious answer. As amrit and others say, and as you allude to, one can 'jump off into the void' and *know* the truth, but when one returns from the void, one cannot construct a map and show it to others, just as one cannot explain 'being aware' to someone who is 'unaware'.

If, as we seem to agree, *now* is the reality, and our ideas of past and future are mental maps, and if, as we may agree, consciousness is the field of which the parts are made, then in theory (many swear in practice) one can 'decouple' from the local body-brain mass and experience the universal awareness of the ALL, but the body-brain soon reclaims its hold on locality and we're once more inside looking out.

As for the big bang, my brain is happy with my theory and not happy with the other, but obviously we have as many theories on fqxi as we have body-brains, and I don't believe they will ever converge to the best theory. Too many dollars, too much power, to big egos, and etc. When they don't find the Higgs or any of the other SUSY particles, they'll just claim they need more money.

I plan to spend more time thinking about 'duration' as implied by 'c' and 'h'.

I've very much enjoyed our talk and look forward to the next one. These conversations are stimulating and worthwhile.

Edwin Eugene Klingman

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John Merryman replied on Sep. 9, 2010 @ 01:38 GMT
Edwin,

Sound's like you are dropping the conversation. Sorry to hear that, as the discussions on fqxi have been a bit thin lately and I haven't found any sites quite like it. I suspect things will liven up when they start the next contest though.

I must say we do hold fairly opposing positions on the validity of the Big Bang model though, but it doesn't look like I'm convincing...

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Edwin Eugene Klingman wrote on Sep. 9, 2010 @ 04:37 GMT
John,

I've got to take care of some other time-consuming business and don't think we're close enough on the BBT issue to really get anywhere. I'm glad that we agree on the primordial consciousness as opposed to emergent, but my theory ties everything together into a unified whole. If I have to cut out large pieces of it, it will kill the theory, and I've seen no reason to do so (yet). In...

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John Merryman replied on Sep. 9, 2010 @ 10:11 GMT
Edwin,

Than you for the consideration. We all have to frame our views on the basis of what we understand and you have a far more technical and fine grained view than I. I tend to come at it from a philosophical direction and that doesn't have much credibility these days.

As for predictions, I was arguing redshift is actually evidence for a cosmological constant, rather than a singularity close to ten years before they discovered the need for the dark energy patch in '98 and then qualified it as being comparable to predictions made by what a CC would look like, around '02. As for future predictions, I also suspect the Higgs will continue to be elusive, since I've been arguing for space as having an equilibrium effect, but won't be surprised if they find some activity which they will call a potential Higgs field, since there are likely layers of undiscovered activity. My other prediction will be that the James Webb telescope, for studying the infrared background radiation, will find evidence of it being light from ever more distant galaxies that has been completely shifted off the visible spectrum, rather than afterglow from the singularity. Whether they devise a convenient patch, likely drawn from inflation, or admit it is a real problem for BBT, time will tell.

My email is brodix@earthlink.net, if you want to add it to your list of contacts completely outside the fold.

As for living in enough space not to be constantly in others energy fields, it does give one the space to think. When I was little, I realized all those voices in my head were of older siblings and it took a bit of effort over the years to block my mind from others, when necessary. I think we are all one big organism, for better or worse.

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Don Limuti (digitalwavetheory.com) wrote on Sep. 13, 2010 @ 21:53 GMT
Seems like a good time to curve the thread a little.

1. I wanted to acknowledge Sabine Hossenfelder for the award process she started. It is easy for me to be a physics outlaw because I have little at stake (well maybe my big ego). But there are many physics professionals who risk their futures by going against the party line. From their ranks the future physics will emerge.

2. Thanks Lev for giving my website and wavelength-hopping some visibility. When wavelength-hopping is viewed as particles appearing as events it is a much more palatable concept.

3. T H Ray, your criticism is right to the point. I will comment on it in next post.

4. Edwin Eugene Klingman, yes wave-length hopping is just another theory, but it differs from the theories that you listed in that it is testable in several ways. I think the best test for it could be performed by the Vienna group (University of Vienna) on a Buckyball to show that it wave-length hops. see http://www.zenophysics.com/DWT/13a__Buckyballs.html

Don L.

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Don Limuti (digitalwavetheory.com) wrote on Sep. 13, 2010 @ 22:25 GMT
Hi Tom (T H Ray), It is obvious you have read my theory and know its implications which I do not try to hide. But I can add a few comments:

1. rest mass would be incalculable: This is true. But "rest mass" is a misnomer for a particle because particles are never at rest. Lowest energy mass would be a better term.

2. spacetime would not be physically real: I believe I leave space-time intact, however I consider particles as moving on space-time in an unreal way as experimentally verified by Alain Aspect.

3. general relativity would be falsified: General Relativity was not created to work on the particle level but it works very well on the classical level where the assumption of a static point mass is just fine.

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T H Ray replied on Sep. 14, 2010 @ 16:03 GMT
Hi Don,

1. True, particles are never at absolute rest (absolute zero temperature); however, relativistic rest mass allows us to compare energy content between masses. Special relativity's conclusion, E_0 = mc^2 is based on the rest mass state. The "lowest mass" is zero; energy exchange particles (bosons) are massless. When special relativity is generalized to general relativity, we find...

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Don Limuti (digitalwavetheory.com) wrote on Sep. 15, 2010 @ 02:16 GMT
Hi Tom,

I am in the unenviable position of defending something that is unproven. So, I say something like particles are blue, then everyone who read the book that says particles are red respondes to me that blue is silly particles are red. Never mind the fact that the red color came from a theory also. The only difference is that red was in the book.

I say that a fundamental particle in isolation moves in a peculiar way "wavelength-hopping". There is no thermal motion. IF you want you can say that the particle is at absolute zero. Almost everyone will say wavelength-hopping is not true even thought no one has investigated the phenomena of how or if a particle moves in isolation.

I did not pull wavelength-hopping out of the air, it the result of a logical thought experiment. But as Edwin Eugene Klingman points this is just another far out theory out of many. He is right and more than a theory is required. I think an experiment can be made.

At first it may seem simple to put a particle in isolation. I was thinking of taking a Buckyball and dropping it in a vacuum. But on second thought that is not enough isolation because the Buckyball will accelerate too fast due to gravity to see wavelength-hopping. A very low speed accelerator will need be designed to do this experiment the LHC will not do the job. The experiment may need to be done in space. see http://www.zenophysics.com/DWT/13a__Buckyballs.html

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T H Ray replied on Sep. 15, 2010 @ 12:35 GMT
Hi Don,

If I understand you correctly, you define a system to be one particle and the vacuum.

Then I am compelled to agree with you -- the particle is at absolute zero.

Something has to move, though, or the system is not physical. By definition, a particle at absolute zero does not move. So the vacuum must be moving -- what does that mean?

Actually, your experiment was done long ago, and the phenomenon is called superconductivity. What happens is that at temperatures close to absolute zero, all resistance to electronic motion disappears, and "electron waves" are self sustaining, indefinitely. One could describe the system, then, as a particle at rest relative to the wave motion, because the free electrons conducted by this artificial vacuum are in an almost pure wave state. A similar quantum coherence effect is Bose-Einstein condensation.

"Wave hopping" as you describe it would then be alternating cohering and decohering states, and that's actually what we do observe in natural systems in the form of local positive feedback loops -- such as superconductivity -- and negative feedback like the decohering effects of thermal noise.

It is contradictory to speak of the vacuum as an isolated system upon which one can conduct experiments. The closest we come is conducting experiments near absolute zero where particle motion can be observed at the low velocity range you seek. In fact, the search for high temperature superconductivity (whose discovery would be a great gift to humankind, and a huge technological leap) does include buckyball experiments. One doesn't "drop a buckyball into the vacuum" though. One creates as much vacuum as possible around the substance and witnesses resistance to wave motion (conductivity) decrease to zero, at a critical phase transition, in proportion to the drop in temperature.

Tom

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Don Limuti (digitalwavetheory.com) replied on Sep. 15, 2010 @ 17:36 GMT
Hi Tom,

You say a particle at absolute zero does not move. This is part of a long held conventional theory that has it as a definition. It has never has been observed in nature. I say that a particle in isolation moves all by itself. This is part of a new theory. It also has never been observed in nature. What is true?

The phenomena of superconductivity involves many particles in proximity. It is not the experiment that is optimum for showing wavelength-hopping.

I believe theories are good and we need them, and well designed experiments are better than theories.

Don L.

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T H Ray replied on Sep. 16, 2010 @ 00:23 GMT
Don, how would one go about designing an experiment to record the sound of one hand clapping?

Tom

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Rainsmith wrote on Sep. 15, 2010 @ 11:15 GMT
Hello Forum. I have not had time to read all the posts in this forum but I would like to address the initial question concerning the suitability of mathematics to address issues in cosmology and physics.

I would like to ask forum members how they believe mathematics could be 'engineered' to be more suitable for this task. It os my understanding that mathematics has 'two poles' that of its set theoretic foundationsn and the limits of the logical resolutions that lead to the advanced mathematical fields.

My issue with the inappropiate nature of mathematics begins at its foundational level, the axioms of set theory. In particular, the concepts of continuity and sequence are forced upon the integers.

Ot is atb this level I believe that many of the semingly baffling notions of experimental cosmology and physics are born, our mathematical systems is out of sync with the reality to which we apply it.

I have been wondering for some time whether ny research in this area is being conducted. This area is the philosophy of mathematics where subtlty rather than complexity is what needs to be explored!

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Lev Goldfarb replied on Sep. 15, 2010 @ 13:05 GMT
"My issue with the inappropiate nature of mathematics begins at its foundational level, the axioms of set theory. In particular, the concepts of continuity and sequence are forced upon the integers.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I have been wondering for some time whether [a]ny research in this area is being conducted."

*************************************************
***********

You have come to the right place. ;-)

Check my essay mentioned also in my opening post.

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Don Limuti (digitalwavetheory.com) replied on Sep. 15, 2010 @ 17:50 GMT
Hi Rainsmith, Along with Lev and others I agree that the math/physics is a core issue.

The assumption that 1 +1 = 2 in the world of experience.

1 plus 1 = 2 is something that is taken for granted and is held to be true in both math and physics. I do not believe it is true in physics. I will try to explain, here goes:

a. How do you add things that are physical? The grade school teacher will demonstrate by taking an apple from far away and present it to the class, then she will bring another apple from far away and put it close to the first apple and say "One apple plus another apple is two apples." This is the physical interpretation of addition. It is very useful and essentially correct but it needs a minor correction when considering the apples as real objects with mass. I will explain in a moment.

b. How do you add things that are mathematical? The math instructor will say consider an apple (an ideal object in the imagination) and call it a 1. Now consider another apple and call it a 1. The 1 and the 1 can be added to produce 2 which can be considered to be the sum of the two idealized apples. This 1 plus 1 = 2 is completely correct for idealized apples. The math is perfect when there is no real mass and no space-time.

c. What is wrong with the physical 1 plus 1 =2 ? The answer is the space-time that the apples exist in. When the apples are brought together to demonstrate their sum they have to move thru space and time. (see http://www.zenophysics.com/DWT/19__Math-Physics.html)

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Lev Goldfarb replied on Sep. 15, 2010 @ 19:19 GMT
By the way, "1 plus 1 = 2" is not really a 'physical' statement. It was simply adopted by physicists from the math developed by that time. Moreover, again before physics, the 'spacial' measurement practice was developed in Egypt and Mesopotamia. Ironically, although the space is not a 'physical' concept, once it has been adopted in physics it has become a fundamental concept.

In fact, this is probably true of all basic physical concepts.

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Rainsmith wrote on Sep. 17, 2010 @ 03:08 GMT
It is unfortunately, aa novel idea I would like to put forward, about the solution to the short comings of mathematics and its ability to map onto the 'reality' which we intend it to describe.

My proposition is based upon the following logic.... @ Mathematics can only be meaningful to the extent that the axioms upon which it is based have neaning@

To date, the axioms of mathematics, the axioms of set theory, 'impose' a linear sequential meaning all phenomina upon which it is employed. The major effort in the mathematical sciences has been to extend the axiomatic model, and the point at which we begin to see this model fail is the point at which effort ought to be turned not to extend this model further, but to seek more meaningful fundamental axioms.

This line of inquiery is, by definition, pre mathematical, that is, the search for mathematical axioms canot be guided by existing mathematics,n neither is this axiomatic search necessarily a mathematical task.

The study and search for a more meaningful axiomatic system is a disipline in itself and the expectations of 'meaningful' set of axioms need to be put forward 'first' before the search is engaged in order to obtaain a 'goal set' of axioms. This can possibly be posed by the question ' what do we want'? and thewn set about phrasing a set of axioms based upon our requirements.

This is a bold step, for it implies that experience gained over the centuries using our supposed 'objective axioms' must be replaced by our hopefully informed subjective requirements, obtained during our experience of the shortcomings of the previous 'objective axioms'.

I cannot see any way around this issue. A transformation from objective to subjective axioms, for one issue is clear here and that is the admission that our supposedly objective axioms of set theory have been subjectve all along, in favour or a system of mathematics which favoured our 'linear and subjective experience' of reality.

Any suggestions?

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Rainsmith wrote on Sep. 17, 2010 @ 03:19 GMT
I would just like to add here that 'everything', quite literally all advances we can possibly make do only one thing... They advance or attempt to advance the axioms of set theory. This is all that modern science is about, how could it be about anything else? Mathematics is, by definition, the imposition of a linear sequential view upon reality.... why we should expect it to be able to wrap itself around phenomina which do not suit this view is at best 'complicity', at worst, ignorance of the actual situation.

I know many professional scientists who are wholly unaware of this situation and who would be hard pressed to even give the notion that the spectacular gains of mathematics to date, are spectacularly 'one dimensional'!

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Rainsmith wrote on Sep. 17, 2010 @ 03:30 GMT
I keep being drawn back to this issue.

I once saw some graffiti on a wall when I was a teen. It was a terrible message..

"The courage of your convictions"

was the message. Perhaps the time has come for science to get over the shock that 'it exists at all' and move on to the idea that we have to decide what it is we want from it!

Pretty scary stuff!

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Roy wrote on Oct. 17, 2010 @ 21:51 GMT
I have read some of the initial posts here, but I think that the status of Set Theory has been inappropriately stated. First of all set theory is not a single theory but a collection of Axiom systems of different strengths and types. As an initial example we have ZF set theory versus NBG set theory which introduces objects called Classes. The simple equation that a Set = Point is too simple also.

Perhaps the most relevant formulation of Set theory for the purposes of the process centric ideas discuessed here is the version of Set Theory from Axcel with the "Anti-Foundation Axiom". In this form of set theory we can have:

a member a

a member b member a

and so on. This has been used to model processes. Admittedly none of these forms of set theory are intended directly to model space-time or its components directly, but we need to be more general in our views of what Set theory (and hence Logic) actually is.

Also the attempt to formulate a system of axioms as a subset of Peano axioms is certainly possible. There are many simpler structures than Peano axioms which capture concepts of ordinal relations which can be formed. In doing so we are being "pre-number" in a sense.

In fact certain kinds of computer scientists use these formulations a lot for giving abstract descriptions of computation systems (which are not necessarily number based systems). There may be links here with the original question of the first post, although a I would need to see (or develop) an axiomisation of the "struct" concept or similar to see what the relationship was.

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Lev Goldfarb replied on Oct. 18, 2010 @ 02:34 GMT
Dear Roy,

I'm glad you are trying to see what the relationships are between the conventional concept of set and that of the set of structs. However, it appears that you are simply *assuming* that one of the developed versions of set theory should fit the bill. Unfortunately or fortunately, this cannot be so, for a number of reasons: none of the known approaches deals with such temporally and finely structured entities as structs.

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Roy replied on Oct. 18, 2010 @ 12:30 GMT
Hi Lev,

Yes I am *assuming* that set theory is a place to start - sort of. It is actually the methodology I have developed since encountering several formalisms (mostly in the computation context) which claim to be Foundational - and which then ask for comments. To make sense of such formalisms I have tried to develop a better understanding of the foundational classics: set theory, automata theory, lambda calculus - and then see what the new formalism offers.

Having now read a 96 page paper on ETS theory (only once though) I think that I would now describe the situation a little differently. There is a straw man argument that:

Set Theory is a foundation for Mathematics;

Mathematics is a foundation for Physics;

Physics and Mathematics is a foundation for Biology

implies that

Set Theory is a foundation for Physics and Biology. (ditto with Peano arithmetic)

Having studied Set theory for some time I have no idea whether Set Theory has anything to say about physics or biology, although it does have remarkable logical things to say.

The ETS theory seems to be challenging Set theory for this straw man role of "foundation of physics and biology" - except in ETS theory we might have a genuine candidate for that latter role. However this also assumes that a single framework can fullfill all the tasks ETS seems to have set itself:

1. Foundation for Quantum Processes

2. Foundation for Epigenesis and biology

3. Foundation for Space-Time and cosmic inflation

An earlier post asked to apply ETS theory to protein folding. For me, still trying to understand how much is in the theory, I would ask (for the biology case) "where is the DNA?" That is could ETS theory have predicted the need for DNA if we didnt already know about DNA - and if so where does the strut formalism "hide" the parameter that is DNA?

Also a video presentation of ETS theory would be helpful to make sure that we are grasping it propertly.

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Lev Goldfarb replied on Oct. 18, 2010 @ 17:11 GMT
Roy,

Yes, indeed, Tom (T. H. Ray) also asked about protein folding.

The point is that the corresponding struct is supposed to store this (temporal) information about folding, so that the spatial instantiation of the protein struct relies on that representation.

As to "where is the DNA?" I would reply, that DNA is a part of the *particular hardware* implementation of the spatial instantiation process: on some other planet this hardware most likely would look different.

By the way, here is a simplified visual illustration (Windows Media Player) of the process of spatial instantiation of the struct representation for the Bubble Man example from Part III of main ETS paper.

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Lev Goldfarb wrote on Oct. 20, 2010 @ 15:45 GMT
"Does the struct formalism use syntactic structure (ie grammar) to encode temporal information?"

To elaborate a bit more, I should mention that a struct simply records a stream of (observed) events, but it is postulated that the generation of such a stream is guided by the corresponding generative structure (class representation, a generalization of the grammar concept).

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D. Hilbert V wrote on Nov. 13, 2010 @ 19:45 GMT
Even Stephen Hawking, in a moment of honest revelation ("The End of Physics"), acknowledged that any so-called final theory in cosmology cannot be proven to be ultimately the case, or it could always be eclipsed by new information. Why?

Godel's theorem.

In fact, this theorem places an unassailable boundary on any non-trivial mathematical axiom, etc., like those involving cosmology.

Many insightful and quasi-ultimate theories are still possible, but Godel's theorem puts a limit on mathematics that honest mathematicians and physicists would be wise to acknowledge.

Of course, accepting the reality of Godel's theorem also brings back the idea of contingency involving the universe, and since this is a philosophical concept that brings up the possibility of something outside the universe responsible for its creation, such honesty is not expected to come from those intent on disproving such a creation.

For those who cannot handle the limitation imposed by Godel's theorem, the best thing to do is ignore it as if it, too, doesn't exist. The second best thing to do is to deny the application of the theorem that even Hawking admitted applies to theories of physics. The third best thing to do is to simply claim that the theorem itself is limited to minor applications that Hawking did not realize.

There are indeed many ways to put your heads into the sand when confronted with a reality you just don't like.

But more is to be gained by just a little bit of humility as all good scientists should have, especially when trying to come up with ultimate mathematical theories that will never be and can never be completely ultimate.

DH

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Sridattadev wrote on Jan. 18, 2012 @ 20:42 GMT
Dear All,

Everything in the universe is connected eternally in singularity, separability is an illusionary perception when one is in duality.

Relativity is the theory that best describes duality, where as singualrity is the absolute truth and several quantum mechanic observations are closer to this truth.

who am I? I am dualilty, I is the singualrity.

Please see the mathematical equation representing the absolute truth of

zero = i = infinity

Love,

Sridattadev.

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Sridattadev replied on Jan. 18, 2012 @ 20:46 GMT
If 0 x 0 = 0 is true, then 0 / 0 = 0 is also true

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

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

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

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

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

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

Love,

Sridattadev

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Louis Brassard wrote on Oct. 28, 2012 @ 17:34 GMT
Any (mathematical) cosmology theory that posits the a priori existence of highly complex mathematical structures prior to the creation of the universe is implicitly positing the existence of a mathematical world which is eternal. There are not theory of creation of the whole universe but instead explain how the mathematical eternal part of the universe at some point rules the evolution of our world from it. Nothing explain the existence of this relatively complex mathematical core, and nothing explain the connections between the mathematical world and reality.

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Louis Brassard wrote on Nov. 5, 2012 @ 03:51 GMT
Hi Lev,

In the 1990's I developed a theory of visual perception (Ph.D thesis: Perception of the image world") that developed a concept of image structure hierarchy corresponding to the ontogeny/phylogeny of objects.

"In light of this, the ‘similarity’ of objects should be understood as the ‘similarity’ of their formative

histories, and hence this formative history (or object’s structure) must be captured in the object’s

formal representation."

In my approach, the detection process of an image structure recapitulate in its sequence and structure the morphogenesis process. This is a modern version of the old aristotlean conception of the actualization of the object's form into human mind at it intellectual level. The platonic world in this model in implicitly built-in in the hiearchical structure of the vision system of animals.

Postulate 1: the universe is a family of evolving and interactive classes of (irreversible)

processes.

I would prefer:the universe is an evolving family of evolving and interactive classes of processes.

Notice that with the structural hiearchical representation, it is not necessary to represent time by a parameter, or a dimension of space. By the universal principle that STRUCTURAL HIERARCHY IS HISTORY, you get a Bergsonian duration built-in.

- Louis

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James Dunn wrote on Jun. 5, 2014 @ 14:59 GMT
All of mathematics is limited by Axiom of Choice. I propose that Axiom of Choice can be extended to include Relativity, and therefore define a model by which ALL of observable physics can be modeled.

Axiom of Choice extended to include Relativity

This model potentially describes the foundations under quantum entanglement and related decoherence, time independent photon interactions within fringe patterns, entropy, duality, time, gravity, subatomic particles, deformable space, ...

This is only a foundation for a cosmological model based upon quantum causality that allows for building evolving relativity upon a base of causal states. The system has the potential to model diverse physics environments different then our own; but our own as one set of non-relativistic singularities that moderate relativistic singularities (sub-atomic particles).

The remainder of the thought mapping that has accumulated is found at:

QESdunn

Until corruption can largely be eliminated, I do not want space-time manipulation to be developed. The reason is that then weapons will otherwise be developed to enslave the masses. Manipulating space-time allows for remote manipulation of subatomic particles. Which with advanced application can mean automatically detecting distraction, and causing pain. Not just in self, but in all those whom you care about. Ultimately causing death if acting outside of boundaries.

Eliminate ALL Corruption

retweet: Part of Civil Rights is that Representation is free of Treason http://tinyurl.com/lpqsur5

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James Dunn replied on Jun. 5, 2014 @ 15:03 GMT
Errata:

QESdunn

should be

QESdunn

Eliminate ALL Corruption

should be

Eliminate ALL Corruption

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Darius M wrote on Oct. 31, 2014 @ 16:30 GMT
My theory on the limits of mathematics:

Theory of Everything using Leibniz, Kant and German Idealism

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larens imanyuel wrote on Dec. 1, 2014 @ 02:48 GMT
James,

The Axiom of Choice may be replaced by an Axiom of Exclusion that isolates a Natural Index of 12 numbers that index (by dimension) the mathematical structures encompassing physics. Incorporating this into proof theory leads to a proof of the Riemann Hypothesis. Of course, to get the $1,000,000 from the Clay Mathematics Institute requires that you also convince them that you are allowed to change the rules of proof.

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Darius M wrote on Dec. 5, 2014 @ 09:46 GMT
My theory on the limits of mathematics:

http://www.academia.edu/8991727/Phenomenal_World
_as_an_Output_of_Cognitive_Quantum_Grid_Theory_of_Everything
_using_Leibniz_Kant_and_German_Idealism

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