MATHEMATICS, PHYSICS, PLANTS …. FIBONACCI SERIES by MIROSLAW KOZLOWSKI

Intuition does indeed point the way for physics. Evolution has bred the ability to sense patterns into us.

You noted the example of the central force in 3-D space. The core math is in several other examples in our universe. There are sources and sinks of heat (the heat equation), sources of diffusion, sources and sinks of heat (the heat equation which is the diffusion equation with a constant diffusion coefficient), this may reduce to the Schrodinger like equation with varying diffusion coefficient, etc. These are all the same math with differing parameter definitions. At what point does ``2'' (2 strands of DNA, mitosis, sex, etc.) and powers of 2 become a cardinal number? That is, what we sense in our size scale is seen in all scales.

Like you I suggest this is not accidental, that life and physics obey the same fundamental principles 2014 contest paper. Further, like you, I suggest in this years entry that math and physics are part of the universe so closely intertwined they are one.

I pointed out the fractal idea. You pointed out the Fibonacci series.

Dear Prof. Kozlowski,

Without a doubt, Schrödinger's young friend was correct. You appear to believe that reason implies "not only a capacity for logical sequence of argument, but also a sensitivity to balance, as detectable by the intuitive faculty of consciousness. In my opinion, you are correct in your analysis that one needs guard against fantasy. You nailed it:

"Structure as disciplined as that of a mathematical argument, is capable of transfiguring the merest nonsense into divine nonsense."

Comments surrounding the '50 year Celebration of Bell's theorem' speak of hagiography.

I suspect some of the divine nonsense of which you speak is the overthrow of the innate and intuitive sense (having passed both Darwinian survival required by innate, and developed the consciousness required by intuition) of local reality, a.k.a. local causality, a.k.a. local determinism, those aspects of reality that almost everyone understands to be true, in favor of the divine nonsense of non-locality, which no one claims to understand, for fear of being asked to explain it to the rest of us non-dummies. I attempt in my current essay to explain how Bell raised mere nonsense to divine nonsense. I invite you to read it and comment.

I very much like the manner in which you transfer 1/distance to the harmonic equation with a constant on the right-hand side of the equation only for quadratic-in-u-forces (u=1/r) You say: "Only for that force! Can you imagine! This is miracle, is not?" I see that you have not lost your sense of wonder.

But, not stopping there, you going to show that, for Newton and Coulomb, "stable elliptical planetary orbits can exist in support the existence of the highly developed organisms, only in three-dimensional space. The second miracle!" This you support with the 3-D non-interfering neural network, impossible for flatlanders.

As for who teaches plants about Fibonacci series, I attempt to show the innateness of the process in 'The Automatic Theory of Physics',

Thank you very much for your very interesting essay. I wish you luck in the contest.

Edwin Eugene Klingman

Miroslaw,

The wonder of discovery ... it is truly a joy is it not? And those coincidences ... more than two dimensions but less than four dimensions. Hamilton would agree completely regarding the uniqueness of a three dimensional universe.

Good Luck and Best Regards,

Gary Simpson

``...which as the hyperbolic equation has the thermal wave solution with wave velocity "

The dispersion equation seems to describe a point source and sink and waves if the velocity is high. To get the double slit experiment, I assumed the plenum (or ether if you prefer) wave velocity to be much greater than the velocity of light. The plenum has a density at each point. The diffusion (heat) equation has a long term 1/r term from a source or sink. This is needed for gravity.

Treating a second time derivative (hyperbolic) equation as heat transport equation (or diffusion of a scalar to get 1/r) seems odd to me. How do you get 1/r dependence?

Hodge

Dear Miroslaw,

Yours is a nice essay, pretty clear. I gave your essay a 9, and down graded it by one point because of a couple of funny aspects, such as referencing equation 1.181 that made things a bit odd. There is I think another aspect to this, which is Bott periodicity and the 8-fold (mod-8) condition with the dimension of spaces. The Cayley numbers 1, 2, 4, 8 play a role in the structure of division algebras, and quaternion bundles on SU(2) or SO(4) have a moduli space of 5 dimensions. The dimension of space is involves with the quaternion Hopf fibration. With quaternion Hopf fibration 3 --- > 7 ---- > 4 there is a connection between dim = 3 and 4, with 7 as the "linking space." I think this has something to do with your observation about 2, 3, 5, 8. I am less clear about whether this continues with the Fibonacci sequence. However, 13 mod 8 is 5, 21 mod 8 is 5, 34 mod 8 is 5, 55 mod 8 is 7, 89 mod 8 is 1, 144 mod 8 is 0, 233 mod 8 is 1, 377 mod 8 is 1 and so forth. A computer program might be written to find what "FIBO mod 8" looks like for a large set of numbers. Then maybe a theorem could be proposed and proven. Maybe this excludes the number 6. It might be that this gives 0 and either Cayley numbers and 2, 3, 5, and 8.

You might be interested in my essay where I discuss aspect of the Bott periodicity and the mod-8 structure. I am largely interested in connection between what are at first apparently unrelated things.

http://fqxi.org/community/forum/topic/2320

Cheers LC

Thanks for your assessment of my essay. I suppose you have not entered it yet, and somebody gave it a 1. I might look this up, but if the Fibonacci sequence in a mod-8 setting does not have the number 6 that might be curious. We would then have the numbers 2, 3, 5, 8 as one set, 1, 2, 4, 8 as one set and 0 has having some sort of relationship with each other that might lead to surprises.

Cheers LC

Dear Miroslaw,

I just read your nice essay. While wishing you speedy recovery from your health challenges, I have two assignments for you to think and work out.

1. You say by conservation of mechanical energy T V = constant in orbits. Can you calculate the Total energy at Perihelion and the Total energy at aphelion, is there not a difference? By Total, is the sum of the Potential and Kinetic at each position. From the formulae, the Total energy (P.E. K.E.) is lower at perihelion than it was at aphelion. Where has the 'lost' energy disappeared to? Then from whence is it regained after perihelion and replenished at aphelion?

2. You talked about centripetal force acting and Newton tells us that a force continues to act in its direction unless opposed by another force. After perihelion, the orbiting body starts moving in a direction opposite the centripetal force. If Newton is correct, we must search for a force acting to oppose the centripetal attraction force, do you agree?

When you have the time you may also wish to read my essay and ask some questions.

Best regards,

Akinbo

Dear Professor Kozlowski,

It would be physically impossible for "interplanetary space" to exist.

Cheers,

Joe Fisher

Dear Professor Kozlowski,

Abstract definitions of abstract "interplanetary space" abound. The real planet earth that we actually know something about is embedded in a real material atmosphere. Real physical conditions must be consistent throughout the real Universe. There is no such a thing as "planetary space". There is no such thing as space.

Glad to help you understand reality,

Joe Fisher

I do apologize.

Dear Professor Kozlowski,

Of course it is not your fault that you do not understand how the real Universe is occurring. You have been taught that light comes from the stars. It does not. Real light stays near its source. Real stars are held in place by real stellar radiation. Real planets are held in place by real atmospheric accumulation. There is no inner or outer space. It is quite a simple system.

Do let us agree on this matter,

Joe Fisher

Dear Sir,

Dimension is the perception of differentiation between the internal structural space and external relational space of objects. Since we perceive through electromagnetic interaction, where the electric and magnetic fields are perpendicular to each other and both move perpendicularly, we have three mutually perpendicular dimensions. These are invariant under mutual transformation and can be resolved into 10 different combinations. Thus, the n-dimensional space is a figment of imagination. After failure to find the extra large or compact dimensions, we should not continue with this and scrap all papers dealing with fantasy.

Regards,

basudeba

Your conscious effort is appreciated!

Best of Luck!!

Regards,

Miss. Sujatha Jagannathan