Dear Antony,

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

Regards and good luck in the contest.

Sreenath BN.

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

    Dear Antony,

    I read your essay and found it interesting and imaginative. Perhaps my main concern, a result I am sure of being grounded in conventional physics for far too long, is your early remark :

    "Perhaps it isn't too much of a leap of faith to include reality's relationship with information, "It

    from Bit", as another of Fibonacci's attributes."

    Personally, I would say it is an enormous leap of faith, however attractive it may be :-) It would be great if one day we could show that the physical laws of quantum theory and quantum gravity reduce to an aspect of number theory intimately related to the Fibonacci sequence. But right now we are very far from being there, isn't it?

    It would also seem interesting if you could relate the Fibonacci sequence to quantum probabilities and the Born rule, as well as with quantum linear superposition - key principles underlying the qubit and quantum information.

    But caveats apart ... it is nice to come across an imaginative idea ...

    Best,

    Tejinder

      Dear Tejinder,

      Thanks for reading my essay and your comment - it is very much appreciated.

      I can see that it appears a leap of faith, as I decided to mention in the essay, because I assumed the reader may think so - which is why I'm glad you raise the point.

      From my other cosmogony work it is more empirical in nature.

      Quantum superposition should be related to the Fibonacci sequence around a Black Hole since spatial dimensions outside allow all theoretically possible states, but according to the sequence (and my extended theory) measurements become limited, reducing to eventually one possible state only at the singularity.

      It is very, very logical, but hard to prove though.

      In the context of the contest though, I thought information and reality had to be at their mutual most fundamental at a Black Hole/singularity.

      I really am grateful for your discussion with me and glad you found it interesting and imaginative too.

      Best wishes,

      Antony

      Antony,

      If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, "It's good to be the king," is serious about our subject.

      Jim

        Hello Jim,

        I have both those attributes - yours is near the top of my list in the coming days.

        Best wishes,

        Antony

        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