Hi John,

No problem - it is good to look at these questions from different perspectives. I'll try to think about where our ideas cross over.

Regards,

Antony

Hello Edwin,

Thank you for your very kind and encouraging comments. Good point that numbers emerging from reality, yet they are our best language to describe it. Again a chicken/egg or even fundamentally equivalent conclusion that is extremely logical.

Great term - black hole information problem agnostic, we all are I guess! I'm glad that we both approach binary with the view of detected/observed or not as a way the Universe works.

Again - thank you very much for the great comments and I wish you all the very best in the contest,

Antony

Hello Steve,

Thanks for reading my essay. I will read yours as soon as possible too and comment over on your page. I'm glad you found it of interest and thought provoking the way number theory might be applied to physical reality.

In answer to your question, I have seen the sequence connected elsewhere - actually before I applied it to Black Holes for this essay. I developed a theory of everything that also solves the paradoxes of cosmogony and the Fibonacci sequence emerged naturally, so a friend/colleague suggested I enter this contest.

Basically the simplex geometries can represent electric charge and mass of the proton, neutron and electron, as well as explain beta decay and strong force. Also a nascent black hole mechanism emerges, which explains why Neutron stars collapse - without disobeying Pauli exclusion.

I'm so glad you mention entropy, as I feel it does indeed suggest an arrow of time, but further, the way it seems to limit dimensionality to 3 spatial dimensions is pleasing - I wasn't expecting so much "information" from the exercise.

Thanks again and speak to you over on your page,

Antony

Dear Antony,

As I promised in my Essay page, I have read your Essay. I find it is intriguing and complementary to my one. In fact, the conclusion is the same for both the Essays: black holes are information preserving. I have been always fascinated by Fibonacci sequence and Golden ratio. Thus, I do not think that the link between Fibonacci and Wheeler is to much speculative. Instead, it has been a stroke of genius constructing a beautiful Essay on such a link. On the other hand, conjectures have been always fundamental in developing science. I enjoyed a lot in reading your work, thus, I am going to give you a high score.

Good luck in the Contest!

Cheers,

Ch.

Dear Christian,

Thank you very, very much - these comments have made my day! Including the score, but also the good point about conjectures being fundamental in developing science. Hopefully we will be able to prove a few from this contest, as there is some fine work on here.

I really enjoyed your essay and pleased that we reached the same conclusion. Black Holes surely ought to conserve information. Fibonacci seems to crop up everywhere, so glad you appreciated it in this context. I too will give you a high score.

Best of luck in the contest and pleased to "meet" you :)

Cheers,

Antony

Dear Antony,

I am also pleased to "meet" you in this beautiful Essay Contest. I am happy that my comments have made your day.

Yes, I think that the Universe requests that Black Holes must conserve information. Concerning the issue that conjectures are fundamental in developing science, a great aphorism by Einstein claims that "Imagination is more important than knowledge".

Cheers,

Ch.

    One of my favourite Einstein quotes! :)

    Cheers again,

    Antony

    Dear Antony,

    I think it is time to rate our essays and I have decided to rate your essay and I want to know whether you have rated mine. Please, contact me at, bnsreenath@yahoo.co.in

    Best wishes,

    Sreenath

    Dear Sreenath,

    I've rated yours now. I'm probably going to wait until I've read them all before I rate every essay.

    All the best with the contest - I really enjoyed your essay.

    Antony

    Dear Antony,

    I just read your essay. You write well, and the idea that fibonacci numbers might play an even more fundamental role in nature than we thought does not seem so implausible. Also, the notion that instead of going from 3 dimensions to 0 dimensions we must go sequentially to lower dimensions by increments of one dimension is at the core of the framework that I work on.

    Unfortunately, I was not able to understand your black hole argument. I failed to see how the Fibonacci sequence is related to the dimensionality of a region inside the black hole, and, as a result, I can unfortunately not comment on that aspect of your paper. Perhaps there is more that could be said about the relation between the two. Assuming the Schwarzschild metric correctly also describes the interior of an event horizon (a big assumption, btw) the transition from the horizon to the singularity is smooth. There are no regions where the dimensionality is reduced. Perhaps you meant to refer to some infinitesimal region outside the singularity that is "too small" to be captured in the metric?

    Also, the connection between entropy and the n-simplexes seems unmotivated to me. Can you think of a real world example of entropy closer to our immediate experience where your model might help understand entropy more deeply? In fact, I would advise you to focus on such situations over the situations pertaining to black holes because if you arrive at an as yet untested physical prediction that differs from standard physics, there is a fighting chance to do an experiment.

    You deserve kudos for some original ideas, hopefully you can develop these further and particularly in empirically testable regimes.

    All the best,

    Armin

      Great points Gupta - I've commented over on your page - Antony

      Dear Armin,

      Thanks for reading my essay and your comments. Glad you find it original and liked the writing style.

      It's interesting that you too find that dimensionality reduces in increments from 3 to 0. The dimensionality of 2 and then 1 inside a Black Hole refers to observation. At the event horizon, say a particle, can no longer release information outwards away from the Black Hole. It cannot receive information from below it - deeper into the Black Hole. In other words ONLY at the event horizon 2D boundary can it BOTH receive and reveal information.

      Also spaghettification tends pathways towards 1 dimension, so this is an extrapolated idea, but essentially there are two unique "altitudes" one where information can ONLY be released, then deeper where information can only be received.

      Then there is 0-dimensionality at the singularity. The negative 1 represents Hawking Radiation, the -3 conserves space, by giving it to the outside - hence the Black Hole grows.

      Entropy wise this is related to simplexes, I've mentioned this earlier in this thread, but essentially similar to Causal Dynamical Triangulation I've formed of Theory of Everything that reconciles the three paradoxes of cosmogony based of asymmetrical geometry arising from nothingness. So I would need a computer powerful enough to run a simulation to test that model. I agree that this is a far more empirically observable way to test the general theory.

      I hope this makes these aspects a little clearer.

      Again thanks so much for your kind remarks.

      Best wishes,

      Antony

      For everybody, and especially for Steven P Sax and the autor of this great essay respect to the fundamental role of fibonacci numbers and number theory

      The neutrality of vacuum due to electric chargue implies the true of Riemann hiphotesis

      In other words the meutrality of vacuum for virtual chargued particles is equal to:

      Sum(n =1,infinity [mpk/sqr({ + e}^2/Gn)]

      x n^-s = 0)

      s is one zero of Riemann function; s= 0.5 ti

      Real part of de imaginary part of the first zero of Riemann function

      14.134725141734693... = Zero1

      [Zero1/(Pi x e x Phi)]^-2 239 =~ exp( 5 (In2)^2)

      e = base of natural logarithms

      Phi = (1 sqr(5) )/2

      Regards

      Hello Angel,

      Thanks for the very kind comments! I'm glad that you, Steve and I (as well as others) are finding common ground in the most fundamental of areas of theory.

      Best wishes,

      Antony

        Hello again John,

        I've had another look at your essay, I see your point about how historically physics has honed in on a certain perception and I like your description of time.

        I approached observation from a very simple position, which happens to then match up to what we have learned from physics. That's what is nice about the Fibonacci sequence, it isn't individual perception, we know that addition works and we see it all across nature. This is biological and chemical as well as physical.

        Best wishes,

        Antony

        The entropy of a black hole has a direct connection to the Fibonacci sequence, given by the following equation:

        [math]S_{BH}=\pi R^{2}=\frac{A}{4}\Longrightarrow\pi=S_{BH}/R^{2}=4{\displaystyle \sum_{k=1}^{\infty}\arctan(\frac{1}{F_{2k+1}})}[/math]

        The entropy of a black hole has a direct connection to the Fibonacci sequence, given by the following equation.Looking at this equation, it follows immediately that: 1) Increasing the spacetime curvature, given by 1 / R ², then entropy increases. That is the curvature of a surface, involves the strong holographic principle: the information is stored and computed on surfaces. It's no wonder that the Fibonacci sequence, to generate spirals aureas, can describe the behavior of a black hole.A black hole can not contain any singularity, entering the quantization of the gravitational field.The spiral aurea (Fibonnaci) represents exactly one black hole.

        The quantization of space-time, ie: there is a length limit, a mass limit, etc., implies that there is no singularity must occur after a certain length, gravitational repulsion, corresponding to the gravitino of spin 3 / 2

        So the mass of gravitinos have to be very high, but less than the Planck mass

        The imbalance between repulsive gravitational force, within the horizon, and the attractive force, is what generates the Hawking radiation

        RegardsAttachment #1: images.jpeg

        Antony,

        Awesome; compelling, original, insightful, and wonderfully written.

        I'll have a lot more to say on your essay when I get additional bandwidth, but wanted to let you know that I greatly enjoyed it. In my view, certainly one of the most interesting essays I've encountered in this contest so far (and I'll be sure to elaborate on why that is in a future post).

        Chris

          Hon Jia Koh wrote the following in their essay thread:

          Your essay is a refreshing great read. The use of dimension as pathway for information travel at event horizon is inspiring. A missing part of my essay which I wish to discuss more is about how information, matter and energy translate (travel) and develop (change) over spacetime.

          The ability to extend the use of a well-studied area like Fibonacci Sequence to a new horizon is impressive. Mathematics phenomenons have a sublime beauty in manifesting and explaining observable nature that capture the imagination of many great people. Challenging their hidden mysteries and limits could be rewarding and illuminating. From Pythagoras up until before Bernhard Riemann and Einstein, Pythagorean theorem was taken to imply that space was flat as opposed to curved.

          Hello Angel,

          Thanks for this. Some great ideas here! I've also found that the sequence wants to skip past singularity state, and the way you explain Hawing Radiation sounds reasonable too.

          Best wishes,

          Antony

          Hello Chris,

          Thanks for the extremely kind praise. Very much appreciated. I too really enjoyed your essay, which I think deserves to do extremely well in the contest!

          Look forward to further discussion when bandwidth permits ;)

          Best wishes,

          Antony