Dear Sreenath,

I like that you've considered the question of us as observers - it was an enjoyable essay to read! Also your conclusion that Bit may come from It is nicely explained.

Well done & best wishes,

Antony

Jim,

Well written, good use of history and you've certainly told the reader a story. Flowed superbly too. The conclusion that we are not divine yet observers was nice.

You've covered a lot of ground in a very clear and concise way.

Great job!

Best wishes,

Antony

Dear Antony,

You have written a very imaginative article on the application of Fibonacci numbers to black hole information paradox and have come out of it with flying colors. You know that Fibonacci spiral is also called logarithmic (log) spiral and I have identified this spiral with the path described by particles in the QG field which exists inside black holes. In fact, my last two essays in the last two fqxi essay (especially 2012, Questioning the Foundations) contests deal with the problem of QG. If you have time, please, go through it and you may find it relevant as it helps you in your long voyage to find solution to black hole information paradox.

Wish you all the best in the contest.

Sreenath

Antony,

Enjoyed your essay, including your demonstration sequence for mass entering black holes. Does the Chinese study of the ubiquitous presence of the Fibonacci sequence in nature, explaining it in terms of stress engineering, impact your study? It tends to see the sequence as nature's attempt to minimize stress. Thanks for your effort. It's always educational to study views of others, even with my limited knowledge of math.

Jim

Dear Sreenath,

Thank you for your extremely kind comments. It's especially nice to hear that we have common areas of interest and that the sensible answers arise around the same topic. Your previous essays sound very interesting and I shall read them soon!

I'm delighted to have found somebody else who I believe is looking for the answers to foundational questions in the most logical of places.

All the best in the contest,

Antony

James,

Thanks - I found this link which elaborates on the stress engineering concept you mention.

The maths here is relatively simple, which is always a good starting point for a good theory. I think that minimum energy states are important when we're transitioning from 3-dimensional space towards singularity, as they perhaps define certain "boundaries" or borders which are crossed.

Also this ties in nicely with the entropy aspect of the Fibonacci approach.

Thank you for highlighting another part of the ubiquitous nature of the sequence.

I agree with what you say and think you perhaps have hit on a way to perhaps test my theory.

Best wishes,

Antony

Dear Antony,

Thanks and congratulations for your essay. I like to inform you that, apart from the conventional approaches, we may have also a set of new other rules and unknown constants which are remain hiding ourselves in the world of quanta; and that will reveal if we can restart again from the foundations of de Broglie's universal wave-corpuscular relationship as an inverse information sharing process among quanta. Even we can able to condense all the information in digital nature or "It" in merely two sets (you may say it as 0 & 1 as well). Characteristically, even if one likes to voyage after event horizon to a black hole, the information can be remain intact with the help of those constants. Although this process is not not yet applied in non-inertial conditions.

Thank you once again. I also invite you in my essay.

Regards

Dipak

    Hello Dipak,

    Thanks for reading my essay and your comments. Interesting that you envisage information surviving the Black Hole process. I shall read you essay over the weekend.

    Best wishes,

    Antony

    Antony,

    thank you for your kind comments on my essay. I just read your work and found your making Fibonacci sequence going backwards past 0 intriguing. I've never thought of it and only now realized that it continues in the opposite direction with the same values except that every other one is now negative.

    In your application of the sequence to black holes you interpret the numbers as dimensions. Couple of years ago I spent some time learning how to visualize 4D and maybe even higher (not a chance lol) and must say that it's hard for me to imagine a negative dimension, even if it is just -1 or -2. I guess I am too attached to the view that +/- mean direction. Thus in my mind the negative numbers in the Fibonacci sequence going backwards appear as mirror reflections. And so I find it fascinating that perhaps also in our view of the picture of reality the real 'its' are intertwined with 'bits' of mere reflections, like in a kaleidoscope, where only some of the pieces of glass are 'real' and the rest are only reflections, but the beauty of the patterns shines in symmetries.

    I too love fractals and all things cellular automata to which Fibonacci, in my mind, belongs. It is instructive that Nature conforms its infinite variety to such simple rules. And if so, why not black holes too? I wish I knew more about them to be of use to you. My practical take on them is more in line with Peter's above.

    Having read your essay, I am intrigued by possibility that Fibonacci sequence where 'bits' are interchanged with 'its' every other step is how things may be in the world of quantum, and that this may explain some of its mysteries. LOL the idea is so novel to me -- I must sound incoherent.

    Thank you again for commenting on my essay and good luck with the competition :)

    Dear Dr Vasilyeva,

    Thank you for your comments and I'm glad you found the essay intriguing. Ha - yes the negative dimensionality does sound hard to visualise, as are dimensions generally. However, the -3 represents, as you say, a sort of mirror inverted situation.

    The Black hole takes in some matter, represented by 3 (dimensions) in the sequence, then this "decays" backwards to 2 + 1 event horizon and spaghettified structure. Then further "decay" to 0 (singularity) more 1, -1, 2 again and importantly -3.

    The -1 I would suggest is Hawking Radiation. Whereby it is produced as the "decay" of the 0 (singularity) to -1, 1, such that the 1 is emitted and the -1 remains inside to cancel other +1 to conserve overall states.

    -3 is the neatest part, this conserves spatial dimensionality both inside and outside the Black Hole!

    3 in is the same as saying -3 out. Which is similar to what you suggested nature may do. :)

    Perhaps this allows information to survive.

    Thanks for raising these great points and all the best with the contest too!

    Antony

      Antony,

      lol I'm NOT a Dr. but I've seen one on TV.

      Re negative dimensions, I decided after posting in your thread that it is indeed a reflection, exactly like in a mirror. The information is there, but no substance.

      As far as black holes go, I tend to think that the number of dimensions actually increase in them. This is because I consider space to be sort of made of 'space stuff' and when you start squeezing this stuff it responds by increasing the number of dimensions. Sort of like you crumble a sheet of paper -- well, not exactly of course, but you can squeeze a large sheet into a small ball, this sort of thing. I think the opposite process is unfolding a.k.a. expansion of space. Say, in the beginning, the universe fit into a point with infinite number of dimensions. As it cooled off, it unfolded and expanded into 4D. Sort of like a crumbled sheet of paper. Makes sense no? :)

      Dear Ms. Vasilyeva,

      Sorry, I misread you bio. There are lots on TV (and on here) ;)

      This does make sense and would reflect what I found with regard to entropy of Black Holes using the Fibonacci sequence. Also, the -1, 1, 0, 1, 1 part of the sequence means that "decay" from 1 would replenish 1-dimensionality within the Black Hole.

      Where you consider the opposite - pre-Big Bang singularity expanding into 4D space-time, the sequence can explain why there are 3 spatial dimensions from nothingness.

      The 0D singularity conserves dimensionality allowing 3D to exist, by Black Holes continuing to exist in the current Universe, such that -3D exists, curving space-time. Moreover, the 1 and -1D mirror differs, because of the double 1 (-1) parts of the sequence, allowing multiple points in space (particles) to exist.

      3-spatial dimensions perhaps are empirically observed in our current Universe because that is the first dimension (and part of the Fibonacci sequence) where balance is maintained both "sides" of the event horizon.

      Best wishes,

      Antony :)

      Very interesting essay. Perhaps this formula is interesting for your researchs

      s= spin

      Phi = Golden number

      (Phi)^3 = factral dimension of space-time

      mpk = Planck mass

      Gn = Newton constant = 6.67428 x 10^-11

      +-e = electric charge

      Im(Zeta1(s)=0)= imaginary part of the first zero of riemann zeta function

      s= 0.5 +14.134725141734693i; Re(Im) = 14.134725141734693

      [math]Re[Im(\zeta_{1}(s)=0)]-{\displaystyle (\sum_{s}\sqrt{(s+1)s}-\varphi^{3}-2)/2}=\ln(m_{Pk}/\sqrt{(\pm e)^{2}/G_{N}})

      [/math]

      Regards

        Thank you Angel,

        I will keep hold of it. Certainly plenty of terms you'd expect around Black Holes.

        Best wishes for the contest & thanks for writing another interesting essay - so many good ones this year!

        Antony

        Thanks for your response Antony. Yes now I do see your point about the possible connection between quantum superposition and the black hole. It is interesting undoubtedly.

        What I had in mind is also the situation where there is no black hole, say in the laboratory - where too we see breakdown of superposition during measurement. Could you think of a way to relate the sequence and superposition, in this context?

        My best wishes for your success in the contest,

        Tejinder

        Hello Tejinder,

        Great question! I think in this case I'd utilise the simplex representation again, because simplexes are what I utilised in the parent theory to this, where I partly unified gravity, electromagnetism, weak and strong forces. This also gave entangled spin results of a cosine rather than linear nature based on geometry.

        Anyway, the theory would suggest that simplex geometry is at the foundation of particles, such that rather than hidden variables, we have fixed constant geometry, this could explain entanglement too.

        In the context of wave function collapse, the particle would be observed as, for example, a 2D geometric entity in 3D space (4d Space-time) with 1D vacant.

        Overall this gives the particle 3D of spatial information about its overall characteristics. But when measurement is carried out either the 2D or 1D component is observed only. So again dimensionality plays a part in observation/being observed. In this instance the sequence 1, 2, 3. But for Photons and Neutrinos this ought to extend down to 0, 1, 1. Further, there is the expectation that the negative numbers represent antimatter.

        Best wishes for the contest too!

        Antony

        Antony,

        I have to say I generally avoid most arguments which take current cosmology as a given, because I find it completely out to lunch. For one thing I see time as an effect of action, the only problem is we try to build our perception of it as a sequence from past to future into the model, rather than the actual cause of the change which turns future potential into past circumstance. For example, it is not the earth traveling a fourth dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates. Hence caused by the action. This means that spacetime is a correlation of measures of duration and distance, not some physically real "fabric" which can be expanded, bent, bound, etc. It is similar as the giant cosmic gear wheels to explain the efficacy of epicycles.

        Duration is not some dimension external to the point of the present, but is the state of the present between the occurrence of events.

        Rather than residue from the big bang, cosmic background radiation could well be the solution to Olber's paradox, the light over ever more distant sources redshifted completely off the visible spectrum.

        Black holes and gravity are treated as vacuums for everything falling into them, but not only do most gravitational sources about black holes radiate enormous amounts of light and other radiation, but the black holes shoot enormous jets of cosmic rays across the universe and binary stars eventually explode. That seems to me the Hawking radiation.

        Since gravity is considered a collapse of space because mass points contract, I suspect the expansion between galaxies is a function of the expansion of radiation, creating a convection cycle of expanding radiation and collapsing mass. It's just we can only observe the light crossing these intergalactic spaces. Light is Einstein's cosmological constant. Universal, but also balancing gravity.

        I would also point out there is an inherent contradiction in the theory; 1) Space is what we measure with a ruler. 2) Intergalactic space expands. 3) The result is that it will take ever longer for light to cross the space between galaxies. Based on 1, 3 contradicts 2, since our most basic measure of intergalactic isn't being stretched, since it requires more to measure the stretched distance. This makes it an expansion IN space, as measured by C, not an expansion OF space. This would necessarily make us the center of the universe, unless redshift is a form of optical effect, due to distance, then it would create a similar effect for every point in space.

        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.

        I do think as part of this cycle, that gravity is not so much a property of mass, as an effect of energy condensing into mass and mass condensing into ever more dense matter. Remember when mass is converted to energy, it creates pressure, so the opposite of this would be a vacuum.

        Not trying to start an argument, since it seems quite futile to fight city hall on this, but just offering up my own position.

        Regards,

        John

          Hi John,

          Thanks for your comments. Do these relate to my essay. Forgive me if they do, but I can't see in what context. Perhaps I've read too many essays today, so I'll re-read your remarks another day afresh to see if they are relevant.

          Best wishes & many thanks for your time,

          Antony

          Hello John,

          I've just had another look at your essay and think this ties in. I'll take a thorough look again at it with your comments. I think I'll then be able to offer an explanation of my essay that will be mutually beneficial.

          Best wishes,

          Antony

            • [deleted]

            • Post #79

            Antony,

            I have read your essay and commend you on what appear to be original ideas about information and black holes. You have read my essay so you probably realize that I focus on nonlinear gravity at the particle level, (where few other researchers spend much time) and I really have no expertise in black holes. Your linking dimensionality to the Fibonacci numbers is unique, as far as I can tell. You seem to have struck a chord with a number of others! I am agnostic on the black hole information problem.

            One of the comments above questioned the applicability of the binary base to the real universe. My approach to information is based on a transfer of energy from a source to a detector, where the energy either triggers a threshold (changing or 'informing' the local structure, thereby registering information) or not. This provides the two possibilities represented by 0 and 1 and therefore establishes a binary basis fundamental to a physically real (energy-based) universe.

            You have a number of interesting comments on this page. I'm pleased that, per Gupta's essay, you've concluded that, "at the very least, I would not say that information is likely more fundamental than reality itself." I concur.

            I also agree that Eckhard Blumschein's essay is excellent and it is good to be consistently aligned with his points.

            And you say (per Kyle Miller's page): "I too feel that nature ought to have one singularity [...] although the possibility that there are no singularities works well too." I agree with you here. I've been reading papers recently that claim no black hole singularities. They are somewhat convincing. On the other hand, I'm not bothered by a possible singularity at the 'point' of creation of the universe.

            Patrick Tonin, above, says: "I also think that numbers in nature are linked." As I develop in my essay, based on the existence of energy thresholds and local structures, it's easy to create logic circuitry (in silicon or in neurons) that leads to counters and hence, Peano-like, to all integers, and, per Kronecker, to all math. Thus I view numbers as emerging from physical reality, but they are clearly our best language to describe reality and to reveal new features of reality.

            Finally, I think the best measure of the quality of your essay is all the thoughtful comments by the other essayists above.

            Congratulations,

            Edwin Eugene Klingman