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

``...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

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

Dear Kozlowski,

Number rules the Universe, it is no doubt.

The problem is where to start.

I point out the views of Ruder Boskovic, who anticipated some scientific achievements two centuries earlier.

Thus, for him there are zeros of force, cohesion and non-cohesion limits. He subdivides them to zeros by zero, first, second... order. The determination of these zeros is of fundamental importance. My view is that it is easier to determine the zeros lower order. In this sense, the Fibonacci series is ideal but not a zero order. I think it is easier to reach conclusions which have the power of prediction in physics using the following mathematical concepts:

bit (it was the subject of the contest FQXi 2013);

exp (x) (You know the unique features of this function);

Euler's identity.

Suitable use of pervious can describe features of the physical World.

If you agree with me, part of the solution can be found in my essay.

Best Regards,

Branko Zivlak

Miroslaw,

My take from your essay finds a novel approach to math, its aesthetics, and its failure to explain all natural phenomena. I thought of the Nova series on Math and Nature: http://www.pbs.org/wgbh/nova/physics/describing-nature-math.html wondering if you'd seen it. Its perspective reminds me of yours.

Considering your different perspective, I would like your thoughts on my essay.

Jim

Dear Professor Kozlowski,

I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

Miroslaw,

I am revisiting essays I've read to assure I've rated them. I find that I did not rate yours, so I will rectify that. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345.

Jim