Hi Sridattadev,

It is incredible how the sequence yields the golden ratio - yes. You show it well.

Added that no matter how we run with the series it always comes out is important. The fact that we start with 0 and 1 is fine, as it's the purest form, but this ties in nicely with Wheeler's Bit and It information being yes/no or nothing and something, where 1 is just a single option of many - up to infinity as an alternative to 0 (including -ve numbers).

This surely does tell us that Fibonacci and the Golden Ratio are built into nature, and that "I" in your case sits well too.

Cheers,

Antony

    Dear Antony and All,

    I have generalized the findings and calling it iSeries and is the universal series, Fibonacci series is a subset of this universal series.

    I give you all a cosmological iSeries which spans the entire numerical spectrum from -infinity through 0 to +infinity and the simple principle underlying it is sum of any two consecutive numbers (any real numbers) is the next number in the series. 0 is the base seed and i can be any seed between 0 and infinity.

    iSeries always yields two sub semi series, each of which has 0 as a base seed and 2i as the first seed.

    One of the sub series is always defined by the equation

    Sn = 2 * Sn-1 + Sigma (i=2 to n) Sn-i

    where S0 = 0 and S1 = 2 * i

    the second sub series is always defined by the equation

    Sn = 3 * Sn-1 -Sn-2

    where S0 = 0 and S1 = 2 * i

    Division of consecutive numbers in each of these subseries always eventually converges on 2.618 which is the Square of 1.618.

    Union of these series always yields another series which is just a new iSeries of a 2i first seed and can be defined by the universal equation

    Sn = Sn-1 + Sn-2

    where S0 = 0 and S1 = 2*i

    Division of consecutive numbers in the merged series always eventually converges on 1.618 which happens to be the golden ratio "Phi".

    Fibonacci series is just a subset of the iSeries where the first seed or S1 =1.

    Examples

    starting iSeries governed by Sn = Sn-1 + Sn-2

    where i = 0.5, S0 = 0 and S1 = 0.5

    -27.5 17 -10.5 6.5 -4 2.5 -1.5 1 -.5 .5 0 .5 .5 1 1.5 2.5 4 6.5 10.5 17 27.5

    Sub series governed by Sn = 2 * Sn-1 + Sigma (i=2 to n) Sn-i

    where S0 = 0 and S1 = 2i = 1

    0 1 2 5 13 34 ...

    Sub series governed by Sn = 3 * Sn-1 - Sn-2

    where S0 = 0 and S1 = 2i = 1

    0 1 3 8 21 55 ...

    Merged series governed by Sn = Sn-1 + Sn-2 where S0 = 0 and S1 = 2i = 1

    0 1 1 2 3 5 8 13 21 34 55 ...... (Fibonacci series is a subset of iSeries)

    The above equations hold true for any value of i, again confirming the singularity of i.

    Love,

    Sridattadev.

    "This surely does tell us that Fibonacci and the Golden Ratio are built into nature, and that "I" in your case sits well too."

    Dear Antony: surely 2000%

    solely two examples:

    The Monster Group:

    Oder Monster Group

    [math]2^{46}\cdot3^{20}\cdot5^{9}\cdot7^{6}\cdot11^{2}\cdot13^{3}\cdot17\cdot19\cdot23\cdot29\cdot31\cdot41\cdot47\cdot59\cdot71=O(Monster\: G)

    [/math]

    sum of squares all primes divisors of O(M_G) ,with power > 1

    2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 = 377 = 14Th Fibonacci number = Kissing number (8d)= (240 ) + 137 ( 137 = int(Alpha^-1) )

    Sum of all primes divisors of O(M_G) :

    2+3+5+7+11+13+17+19+23+29+31+41+47+59+71= 14Th Fibonacci number + 1

    http://mathworld.wolfram.com/MonsterGroup.html

    2) example:

    Relative planetary distances average to Phi

    The average of the mean orbital distances of each successive planet in relation to the one before it approximates phi:

    Planet: Mean distance Relative

    in million Mean Distance with Mercury = 1

    kilometers for

    NASA 1.00000

    Mercury 57.91

    Venus 108.21 1.86859

    Earth 149.60 1.38250

    Mars 227.92 1.52353

    Ceres 413.79 1.81552

    Jupiter 778.57 1.88154

    Saturn 1,433.53 1.84123

    Uranus 2,872.46 2.00377

    Neptune 4,495.06 1.56488

    Pluto 5,869.66 1.30580

    Total= 16.18736

    Average = 1.61874

    Phi= 1.61803398...

    Degree of variance = (0.00043)

    "The shape of the Universe itself is a dodecahedron based on Phi

    New findings in 2003 based on the study of data from NASA's Wilkinson Microwave Anisotropy Probe (WMAP) on cosmic background radiation reveal that the universe is finite and shaped like a dodecahedron, a geometric shape based on pentagons, which are based on phi. The the Universe page for more."

    http://www.goldennumber.net/solar-system/

    Regards

    Dear All,

    As per Antony's suggestion, I searched google to see how Fibonacci type series can be used to explain Quantum Mechanics and General Relativity and found an interesting article.

    d-super.pdf">The-Fibonacci-code-behind-superstringtheory](https://msel-naschie.com/pdf/The-Fibonacci-code-behin

    d-super.pdf)

    Now that I split the Fibonacci series in to two semi series, seems like each of the sub semi series corresponds to QM and GR in some way yet to be fully explained and together they could explain the Quantum Gravity. Seems like this duality is a commonality in nature once relativity takes effect or a series is kicked off. I can draw and analogy and say that this dual series with in the "iSeries" is like the double helix of our DNA. The only commonality between the two semi series of any iSeries is at the base seed 0 and first seed 1, which are the like bits in our binary system.

    I have put forth the absolute truth in the Theory of everything that universe is an "iSphere" and we humans are capable of perceiving the 4 dimensional 3Sphere aspect of the universe and described it with an equation of S=BM^2.

    I have also conveyed the absolute mathematical truth of zero = I = infinity and proved the same using the newly found "iSeries" which is a super set of Fibonacci series.

    All this started with a simple question, who am I?

    I am drawn out of my self or singularity or i in to existence.

    I super positioned my self or I to be me.

    I am human and I is GOD.

    Love,

    Sridattadev.

    • [deleted]

    • Post #136

    Hello Antony

    Well written, and very readable. I think it would be nice to be able to show how the universe might have an action that produces this sequence as a model of a physical reality. In some ways, a universe that adds aspects of its history to evolve is what we find in our own universe. How this occurs is considered in my Armchair Universe.

    Best wishes

    Stephen Anastasi

      Hello Sridattadev,

      I've replied over on your thread. Great way to show the relationship applies at all scales. Very Quantum Gravity like, so especially nice that it fits, as I am working it around a Black Hole at the Foundation of the series.

      Cheers,

      Antony

      Hello Angel,

      More ways to exemplify the series in Nature. Thanks for these! I'll read through thoroughly later - I look forward to it!

      Best wishes,

      Antony

      Hello Stephen,

      Thanks for the kind comments. I'll take another look at your essay in this context. Thanks for answering my question over on your thread.

      I do indeed have a way to show how the Universe produces this sequence!

      Essentially it is 0 decaying to -1+1 (in the sequence) then asymmetry occurs forming particles of mass.

      The action is a quantum fluctuation of nothingness which increases entropy.

      The beauty is that we conserve symmetry overall, but create asymmetry too!

      My theory away from the essay explains more, but this essay entry hints at many more answers that can arise from this approach.

      I'd suggest that instead of thinking of it as an action, it is the Universe doing what comes naturally - increase in entropy- even when we consider nothingness or a zero entropy pre-Big Bang singularity.

      Best wishes,

      Antony

      I'm glad you raised this, as it highlights the cosmogony aspect to my work. I'd suggest nothingness fluctuates in precisely this way towards the negative part of the Fibonacci sequence producing the asymmetries that can be explained by simplex geometries.

      We can partly unify the four forces of nature and relate the masses of the proton, neutron and electron to 99.999988% against prediction. Furthermore, over the past 4 years as new data has emerged on these masses, the figure has improved more!

      Also the theory is potentially testable if a suitable computer simulation can be ran.

      Regards,

      Antony

      Dear Antony,

      you have visited my FQXI-site. Here is my comment to your paper: I agree with you that the Fibonacci number is of fundamental physical importance. My approach to it may help you to understand your approach more deeply.

      The foundation of my approach or view is the Fibonacci Spiral: It is built up - as you know - by a series of squares that are including a corresponding series of circular arcs. I could identify the first geometrical element of this series (i.e. the biggest one) as a physical blueprint of space, time and the velocity of light (c = 1).

      In my paper "The Hidden Face of c, or The True Meaning of the Kennedy Thorndike Experiment" I've sketched this idea. You can google it easily...

      I wish you good luck for your very interesting paper.

      Regards

      Helmut

      P.S. I've rated your paper - of course - high.

        Dear Antony All,

        I am attaching the iSeries that I have envisioned and how it shows the DNA structure in its sequence.

        Its interesting to see the singularity is in the base seed of zero and how it is all pervasive all through out the structure. I have been telling that I is that nothing which dwells in everything and this DNA structure seems to prove that notion. Singularity is right with in the duality. Absolute is right with in the relativity. This proves that both of these states are interconnected and are the source of life.

        Love,

        Sridattadev.Attachment #1: 1_iDNASeries.bmp

          Dear Helmut,

          Thank you very much for the kind comments and rating. Glad to see so many people share the view of Fibonacci's fundamental nature in reality. It is fitting that c, as you have found is connected too. This is also very interesting like your paper overall.

          Well done and best wishes too,

          Antony

          Dear Sridattadev,

          Thanks for the attachment. Good to see you applying your work to nature in every corner of science. This is what the contest wants to encourage. The more areas something so simple, yet elegant applies, the less it can be ignored as simply abstract. Interesting.

          Nice work,

          Antony

          Hello Antony

          Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html)

          said: "It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don't know why that is - it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn't look at all like the way you said it before. I don't know what the reason for this is. I think it is somehow a representation of the simplicity of nature."

          I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.

          The belief that "Nature is simple" is however being expressed differently in my essay "Analogical Engine" linked to http://fqxi.org/community/forum/topic/1865 .

          Specifically though, I said "Planck constant is the Mother of All Dualities" and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism ... and so on.

          Taken two at a time, it can be read as "what quantum is to classical" is similar to (~) "what wave is to particle." You can choose any two from among the multitudes that can be found in our discourses.

          I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!

          Since "Nature is Analogical", we are free to probe nature in so many different ways. And you have touched some corners of it.

          Good luck,

          Than Tin

            Dear Than Tin,

            Thanks for you comments and exemplifying that the nature of the Universe is often seen, even at the highest professional levels, as simple natural occurrences.

            I'll take a look at your paper very soon! Sounds intriguing!

            Best wishes,

            Antony

            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