Dear Sridattadev,
I have also found that 0 can display infinite characteristics. I agree that zero/singularity such as that we envisage at the start of time, is still mathematically conserved.
Good points and thanks for reading and commenting too.
Best wishes,
Antony
Hi Zoran,
A singularity surely has fewer than 3-dimensions doesn't it? Also, the 2 and 1 dimensionality I spoke of, was with regard to information process and pathways tending away from 3 towards zero. I found that there are definite separate points where information should only exchange at Fibonacci numbers of dimensions.
The negative dimensionality explains (-1) negative energy, hence particles being ejected via Hawking Radiation.
-3 dimensionality explains what happens to the Universe as the Black Hole grows - it loses some curved space-time or shrinks - it gains some space. I.e. it balances perfectly. Dimensionality is conserved.
Best wishes,
Antony
Dear Antony,
I was playing with Fibonacci series this evening while sitting in my backyard and came across two other series of numbers. I will put down how I arrived at them.
I wrote the Fibonacci series on a paper up to 12th degree on either side of 0 as follows
-144 89 -55 34 -21 13 -8 5 -3 2 -1 1 0 1 1 2 3 5 8 13 21 34 55 89 144
I virtually folded the paper in my mind at 0 so that the numbers on either side overlapped and added them to each other where they aligned.
I got a new series
0 2 0 4 0 10 0 26 0 68 0 178 0 466 0 1220 0 3194
ignoring the 0's it read as 0 2 4 10 26 68 178 466 ....
Soon I realized that this can be defined by an equation
Sn = 2 * Sn-1 sigma (I=2 to n) Sn-i
with the seeds of
S0 = 0
S1 = 2
S2 = 2 * S1 S0 = 2 * 2 0 = 4
S3 = 2 * S2 S1 S0 = 2* 4 2 0 = 10
S4 = 2 * S3 S2 S1 S0 = 2 * 10 4 2 0 = 26
I also found that division of the two successive numbers soon converges on 2.618 which happens to be the square of golden ratio 1.618.
Now I went back to the original Fibonacci series and virtually folded it at 0 in my mind again and this time I subtracted the numbers where they aligned and I got another series as
0 2 0 6 0 16 0 42 0 110 0 288
Ignoring the 0's this read as 0 2 6 16 42 110 288 and I realized that this can be defined as an equation as well
Sn = 3 * Sn-1 - Sn-2
with S0 = 0 and S1 = 2 as the seeds
S2 = 3 * S1 - S0 = 3 * 2 - 0 = 6
S3 = 3 * S2 - S1 = 3 * 6 - 2 = 16
S4 = 3 * S3 - S2 = 3 * 16 - 6 = 42
S5 = 3 * S4 - S3 = 3 * 42 - 16 = 110
I also found that division of the two successive numbers in this series also soon converges on 2.618 which happens to be the square of golden ratio 1.618.
Finally I did another interesting thing, merged these two series and got another one which read as
First series --->0 2 0 4 0 10 0 26 0 68 0 178 0 466
Second Series ---> 0 2 0 6 0 16 0 42 0 110 0 288 0
Merged series -->0 2 2 4 6 10 16 26 42 68 110 178 288 466
I realized that the merged series is a new Fibonacci type series with a different second seed of 2 instead of 1. Even this series successive number division yields the golden ratio of 1.618 eventually.
Now I asked my self if we can have 2 as a second seed and produce another series which yields the same golden ratio why not 3 and soon found that
0 3 3 6 9 15 24 39 63 102 .... is also a series that also converges on the golden ratio 1.618.
0 4 4 8 12 20 32 52 84 136...... is also a series that also converges on the golden ratio 1.618
So any Fibonacci type series with 0 as the first seed and I ( from 1 to infinity) as the second seed will have the successive numbers ratio in them converging on the golden ratio of 1.618. This again proves the point that I, the singularity, is equally the same everywhere. Mathematics is pointing to the absoluteness of I in Fibonacci too.
Love,
Sridattadev.
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.
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.
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
Thanks Sridattev - Antony
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
