Hi Antony,

Intriguing essay. (And thanks for kindly commenting on my site.)

There are a couple of things I don't understand. Bekenstein and Mayo demonstrated that the black hole is a 1-dimensional information channel, not 2.* The surface -- the event horizon -- is 2-dimensional, because to the observer at a sufficient distance from the horizon, all information on the horizon appears flat. That is, by the rules of relativity, a hypothetical "spaceman" falling into a black hole would to the outside observer appear as a flat picture growing dimmer and dimmer over a long period of time.

You seem to be saying that the black hole exchanges information with the observer; however, the physical interaction is 1-way, i.e., gravity at the event horizon returns information as a continuous wave to the outside observer, while the hapless spaceman is broken into discontinuous bits. Whether he can be reassembled into his healthy coherent self is the black hole information paradox. If a black hole is 1-dimensional, and no information is lost, then all those bits are ordered in a specific way when they radiate away from the horizon; they come out in the reverse direction they entered in. This accounts both for classical time reversibility and quantum-mechanical least action -- and it's why I like Christian Corda's model so much. Professor Corda accounts for pure states of quantum evolution, such that the wave image of the observer at a distance matches the quantum state of the object on the other side of the horizon, all spacetime-symmetric.

Another thing beyond my understanding is how to have a negatively-valued vertex. I grasp that you are avoiding the disappearance of information by avoiding the naked singularity; however, negative spacetime would seem to result in a white hole, not a back-reaction. What I mean, is that if the positive dimensionality is continuous, and if one must deal with a naked singlularity at all, what's on the other side of it must either be continuous as well, or one had better supply a precise limit, and a good physical reason for it.

Don't take this as negative criticism -- you get a good score from me for an innovative and stimulating approach.

All best in the competition!

Tom

*[1] Bekenstein, J. & Mayo, A. "Black Holes are One-Dimensional." General Relativity and Gravitation 33;12, December (2001). (Second-prize winning essay, Gravity Research Foundation, 2001.)

    Hi Thomas,

    Thanks for your comments. Not at all - I don't take them as negative and thanks for kind comments.

    In fact I can easily answer all these points - which is what is nice about these discussion threads. Albeit I don't have time right now - in work after a 72 hour week, so I'll post another comprehensive reply early next week.

    Glad you raised them, as it gives me a chance to clarify.

    Best wishes and thanks again for reading!

    Antony

      Thomas,

      Also as in Christian's essay, both conclude spacetime-symmetry. See Christian's comments above, that the two essays compliment each other with similar conclusions too.

      I look forward to elaborating the very relevant points. Also thanks for your terrific essay.

      Thanks again - very much appreciated - have a ncie weekend!

      Antony

      Dear Antony,

      I liked your essay and agree with you that the information is the basis of the reality that we observe.

      But in detail, I think the bits are the same that things : they are similar, abstract and physical.

      Also, the bits are around us and in us ?

      What do you think about ?

      I will rate your essay after.

      Please visit My essay.

        Hello Amazigh,

        Thanks for your comments. However, I did not really say that information is the basis for reality that we observe. More that information and reality are equally fundamental with the Fibonacci sequence being shown as the way in which information can be exchanged when reality converges with a Black Hole.

        However, it does conclude that we get It from Bit AND Bit zzz from It in this sense. Certainly I'd agree that Bits are around and in us or I couldn't type this to you.

        I will read your essay early in the week. I've only a few left to read now.

        Best wishes,

        Antony

        Hello Jayakar,

        Interesting point. I actually considered the mathematical possibility that the recurrent -1, 1, 0, 1, 1 part of the sequence would result in string type properties within the Black Hole, or in a smaller Black Hole result in Hawking Radiation.

        Sounds like we may have some comment ground!

        I will certainly read your essay early in the week. Only a few more to finish reading.

        Best wishes & thanks for reading my essay,

        Antony

        Hi Anthony,

        I just skimmed your essay and will have a more detailed look, but this is a very interesting idea if I understand correctly -- that as one goes toward the central singularity the number of dimensions *reduces*. An earlier poster in your thread had mentioned the idea that as one goes to higher energy scales/shorter distance scales (i.e. as on falls toward the central singularity) the number if dimensions should increase rather than decrease. This is an idea from Kaluza-Klein theory or string theory that at our current energy scale the higher dimensions have curled up but if one went to larger energy scales these extra dimensions would "uncurl" or somehow manifest themselves. If the large extra dimension scenario in its simplest form had been correct we would have seen evidence of the extra dimensions already. Their non-appearance in this run of the LHC pushes the speculation a bit further "down the road".

        But in your essay you go the other route -- dimensional reduction (from 3 to 2 to 1 to 0 at the singularity if I understand correctly). There is in fact some recent interesting work exactly in this direction called dimensional reduction. A nice paper on a possible observable/testable outcome of this dimensional reduction in cosmological space-times is the paper "Detecting Vanishing Dimensions Via Primordial Gravitational Wave Astronomy", Jonas R. Mureika and Dejan Stojkovic, Phys.Rev.Lett. 106 (2011) 101101, e-Print: arXiv:1102.3434 [gr-qc]. They use the dimensional reduction scenario which comes from "lattice gravity" (the first few references of the above paper give the original article where dimensional reduction was proposed). Anyway have a look since this appears closed related to the idea in your essay.

        Anyway thanks for an intriguing read.

        Best,

        Doug

          Hello Anthony,

          I have read your essay and I see that you suggest some applications of the Fibonacci sequence for fundamental physics. I have some questions, though.

          1) On page 2, you derive the array 3,2,1,1,0 representing how dimensionality of information exchange evolves as one descends towards a black hole. You then say that this matches the Fibonacci sequence. In itself, that is true. But now I define a second sequence; it probably already has a name in literature but I will very unethically call it the Cabbolet sequence:

          a0 = 0

          a1 = 1

          an+2 = an+1*an + 1

          This also yields the beginning 0,1,1,2,3. So the array of dimensionalities that you have derived also matches the Cabbolet sequence. Thus: aren't you using a too small part of the Fibonacci sequence to conclude that it is fundamental, as you do on page 6?

          2) In figure 2, the right margin has the numbers -1 and -3. What do these numbers denote? Dimensionality of information exchange? If so, how can that be negative?

          3) You have defined a simplex as a set, and as I see it, the corresponding Fibonacci number is then the dimensionality of the object that is represented by the set. Correct me if I'm wrong. However, on page 4 you start to talk about the Fibonacci number -1, so we would be talking about a set with dimensionality -1. No such object exists to my knowledge. Could you explain to me what an object with dimensionality -1 is? Or have I misunderstood something?

          I am interested in your comments.

          Best regards,

          Marcoen

          Dear Antony and All,

          Here is more empirical proof of my findings.

          Seems like I found something interesting in the DNA structure related to Fibonacci series as I was seeking it

          Please see this video DNA-RNA

          2 prime

          3 prime

          5 prime

          2,3,5 are the numbers of Fibonacci series.

          DNA is not just limited to life on this planet, its all over the universe and other planets can hold larger primes of the sequence in them, why not?

          One more important correlation that I found in the iDNASeries image is in the template strand (Fibonacci strand in the image) and the non template strand (zero or base strand in the image) as depicted in this video. You will find this around 3 minutes into the below video.

          Fibonacci sequence in DNA

          I am learning how this iSeries really applies to DNA, besides my intuition or inner knowledge. Its all with in us, we just have to know how to access it.

          Human life is like a hide and seek game that I play with the self.

          As I said we will find what we seek, all we got to do is keep an open mind and seek with sincerity. I would like to publish this findings in a peer reviewed scientific journal for the greater good of humanity with the help of FQXI.

          Love,

          Sridattadev.

          Hi Douglas,

          Thanks for reading and your comments. Interesting point about collider results - good news for what I'm saying.

          I'll save those links - thanks for those!

          You sum it up well. The reduction along the Fibonacci sequence results from how limited information is in its exchange.

          If we imagine two particles outside a BH, then they can both receive & reveal information 3-dimensionally.

          At the event horizon, they both can only receive information in something like a half sphere direction because they can't receive anything from past the event horizon.

          Likewise, they can only release information in the opposite direction.

          This means there is a 2-dimensional unique point where information is both released and received.

          Then pathways reduce to 1-dimension. The Fib. Sequence has two 1s before 0. This ought to mean there is a point where information can only be released, then further towards the singularity another point where information can only be received.

          Then there is the 0-dimensional singularity.

          The negative parts I will answer in another in below as another comment asks this.

          But as you point of, dimensionality increasing towards a singularity may be getting less experimental backup these days, so my idea may make sense. Also that a singularity by definition is 0-dimensional, then at least we follow downwards from 3 to 0 in this system

          Best wishes & thanks for the great comments,

          Antony

          Hello Marcoen,

          These are very good points. Thanks for your comments.

          Points 1 and 2 can be answered together.

          The fundamental part comes from two places. Te first is that we begin at a singularity or 0 in the sequence. Also that we balance out the sequence conserving numbers, by using the negative part of the sequence.

          Indeed the part of the sequence used isn't as small as just 0, 1, 1, 2, 3, but also includes -3, 2, -1, 1, before the 0.

          We can extend in both positive and negative directions to fit the conservation, so indeed in some respects we can use the whole sequence. But we are using 9 points of the sequence for a valid reason.

          Te negative numbers do denote information exchange, but moving away from the singularity. In other words the potential to move away isn't real, but virtual. But this is using to explain why nothing escapes - usually. Obviously I explained that Hawking Radiation can occur, and that the smaller the Black Hole, the greater the rate of radiation.

          The empirical aspect that the Universe is spatially 3-dimensional also is matched, not only by the conservation at -3 to balance the inside and outside of the Black Hole, but also for the reasons in point 3 that you make.

          The negative simplex is indeed strange. As soon as we consider the "decay" products of 0 or beyond, we have to consider these negative sets. I'm glad you raised this point, as I too found these strange.

          If we imagine them as inverted real geometries, we give them a negative number. We also take the positive and take the mean of the two numbers. So this is zero. Then we increase by plus 1 for entropy going right down the sequence, but have to stop at 2 in the negative part of the sequence because the decay product breaks the +1 rule for the entropy. Shown in red in table 1.

          As you say, a negative simple sounds crazy. But then this is what makes the whole idea MORE fundamental. We are dealing with black holes where the quantum world is expected to meet general relativity.

          Also pre-Big Bang singularity for instance, we had to create a Universe from nothing. The -1, 1, 0 part of the sequence alone allows for this, but more comprehensively, I have a broader theory where we get geometries from simplexes that partly unify the four forces of nature and resolved the three paradoxes of Cosmogony.

          So what I am saying is that these negative dimensionalities and simplex representations are part of the way space-time curves to conserve nothingness overall.

          Perhaps they exist as real structures with a Black Hole, but I'd suggest that all particles with mass actually consist of these as well as positive geometry. Further we don't see them for the same reason I suggested an Arrow of Time, because a natural asymmetry arises, which the entropy table hints at.

          Sorry if I've not been too clear - rambling is easy around these points, because they are so important.

          Please let me know and I can be be more thorough and/or more concise about these excellent questions.

          I'll try to also read over your paper again once I've finished the few I haven't looked at yet.

          Best wishes,

          Antony

            Another quick point around -1 and -3 dimensionality with regard to information exchange. As we decent into the Black Hole, we lose pathways for exchange, reducing the said dimensionality, such that we need to actually account for these. So the Black Hole remains balanced with the rest of the Universe.

            The singularity being 0-dimensional suggests information can't be exchanged at all. However information can pass over this thanks to the 1s surrounding the 0. Negative information exchange hence means that balance or conservation comes from the Black Hole not releasing information as is, but in a time reversed manner. Thus essentially not releasing most information, and when it does as Hawking Radiation, it is in a jumbled form.

            Hi Tom,

            Thanks for your excellent essay and sorry for the delay in my reply!

            I'm definitely not talking about naked singularities at all. So I can't comment on those unfortunately.

            Also I'm not considering Black Hole not their event horizons relative to an outside observer. Indeed you make the same point of me that physical interaction is one way!

            Open space away from the Black Hole is easy. I envisage 3-dimensional exchange of information, such that information can be received and revealed fully across 3-dimensions.

            At the event horizon (or point when no more information escapes out after the fading stops), from the poor astronauts point of view, information can be released inwards towards the black hole and along the event horizon itself. When no space time pathways point outwards.

            The astronaut can not receive information from inside the black hole. This is a point when information can only be BOTH received and revealed across 2-dimensions.

            Then pathways tend towards 1-dimension deeper into the black hole.

            There ought to be a point, from a thought experiment point of view, where information can only be released, and deeper where it can only be received 1-dimensionally. Then at the singularity there are 0-dimensions.

            As mentioned the sequence allows 0 to be skipped over via -1, 1, 0, 1, 1 part via equivalence amongst other reasons.

            The negative valued vertex is a quantum effect of the Black Hole that conserves space time between the black hole and the outside Universe. I've elaborated on this in a comment below.

            Rather than a white hole emerge from this system, it makes a black hole MORE stable because an arrow of time emerges from the entropy increase, that both conserves numbers and shows a natural asymmetry of space time.

            I'll gladly elaborate further if necessary as your questions are excellent and these points, once understood/explained better by me are very compelling and important.

            Very best wishes & pleased to "meet" you,

            Antony

            Hi John,

            You wrote - "Given all the major patches to keep it working, from inflation to dark energy, not to mention everything from time traveling wormholes to multiverses springing out of it, it is all bizarre beyond belief".

            It being current cosmology. I agree there are too many patches, and I don't think inflation, dark energy multiverse nor wormholes make any sense.

            In fact my model only partly explained with regard to information around black holes,bodes explain things more simply. It partly unifies the four forces of nature and resolves the three paradoxes of cosmogony.

            My essay doesn't hint at agreeing with any of these classical phenomenon, but does agree with current empirical data.

            Best wishes,

            Antony

            All,

            I'll be reading the last few essays which I haven't yet commented on over the next two days. If I happened to have missed yours or missed a reply, please let me know and I'll be glad to discuss further.

            Best wishes,

            Antony

            Hello Sridattadev,

            Thanks for sharing. I'll take a look at the video.

            All the best for your writing,

            Antony

            Hi Antony,

            Just playing the devil's advocate: you say that a set with negative dimensionality indeed sounds crazy, but that this is what makes your idea more fundamental. But a mathematician would answer: no, this is what makes your idea wrong, as no such negative dimensionality exists in mathematics.

            That is to say: can you give a definition of the dimensionality of a set, such that this can be negative?

            Best regards,

            Marcoen

            Hi Antony,

            Yours was certainly an original approach, and I like the possibility that the Fibonacci sequence is more fundamental than we suppose, but I am not sure I understand everything you describe. You wrote:

            > However, any information that passes beyond an event horizon becomes empirically lost.

            Essayist Christian Corda claims that it may not be lost. You may want to look at his argument.

            > The only direction where information can be both received and revealed is 2-dimensionally across this 2-dimensional horizon.

            It is not clear to me whether this is possible either. I thought time appears "frozen" at the event horizon to observers falling in.

            > The final part -3-dimensions, again conserves dimensionality by giving the Universe outside the Black Hole information, confirming that a bit of 3-dimensional space has fallen in, so the Universe gets -3 back out.

            You stated in your abstract that information falling in becomes "empirically lost". What do you mean here by "giving the Universe outside the Black Hole information"? Is the information the fact that a bit has fallen in rather than the value of the bit?

            Your concept of "dimensional conservation" is interesting. Do you mean that the dimensions that a particle can send or receive information (summed over all particles) is conserved?

            In my Software Cosmos essay I do not refer to the Fibonacci sequence. But I can see how it could be involved in an architectural layer below the outer physical layer. This layer would be responsible for Life, music, and aesthetics generally. Contrary to the usual assumptions, I think the material could emerge from it rather than the other way around.

            Hugh