What is Beyond Reckoning? by Jonathan J. Dickau

Jonathan,

As usual, well written essay. Personally I still do not have a intuitive feel for the connection to physics, too busy with Octonions to drill down on what others see.

On that note, recently added canvas to my symbolic algebra suite, of course Mandelbrot set presentation is an excellent choice to try it out. As such revisited the Mandelbrot symbolic algebra code I did for you last essay. I should have been more thoughtful by making it more computationally efficient by simplifying the z^2 calculation for complex-Quaternion-Octonion math. Did so for the canvas exercise to put out 4096x3072 pixels without too much of a wait. Color palette from counts quite critical as I am sure you know. Big fun.

The optimizations did bring into focus the fact that doing the iterations in Quaternion algebra and Octonion algebra really does not bring out the non-commutation and non-associative properties of theses Algebras since the iteration is trivially commutative and associative for both.

The 2d pixel location to 4 and 8 dimension mapping for c is interesting, losing the scalar c term yields circles, rotating complex into other dims tears the complex towards the fully circular. Meaningful? Who knows?

On my symbolic algebra software I put the limited functionality source code up on my essay blog last year, i was severely disappointed nobody but you made a peep about it. I had hoped for collaboration and others banging on it for debugging, no such luck. Do you know of anyone that has tried it? It is a wonderful pedagogical tool as someone interested in Octonion algebra would find, can't really do anything meaningful with paper and pencil.

Rick

Hi Jonathan,

I hope you're well, and well upstate! Good essay again, right on the money and far more readable than many. This is certainly a case for Mandelbrot set recursions, which as you may recall I agree reflects all of nature. I found your take interesting for symmetry breaking and also phase transitions. We also agree on the import of reconciling CSL and QM with gravitation, a matter on which my own essay identifies a coherent hypothesis I hope you'll look at. A few points and questions;

1. I like your comment; "This makes cosmology a bit like a process of fractional distillation, where the entirety of the condensed matter universe is only the denser portion of reality with fixed attributes, the lowest fraction." In my observational cosmologist role I've found something very similar, and likely cyclic for consistency with the peculiar CMB anisotropies, and with no halting issue.

2. Do you think the reductions of the general quintic equation, by Euler or the simplest form; x5 -x + p = 0 can lead to any insights? (I've struggled to see the geometry so far).

3. One thing I have found is that momentum exchange vector addition in a sequence (so complex) of interactions with rotating spheres with random polar axes does produce the increasing uncertainty found, and of Chaos theory. That's due to uncertainty of +/-'curl' at the equator and linear motion at the poles. Can you rationalise that concept?

4. You rightly define limits, but not quite Dirac's idea of a 'sharp cut off' to maths validity. I've suggested that limit is physically at the lowest (and strongest!) particle 'coupling' scale for EM energy, the electron, or condensed e+/- 'pair'. (My essay identifies useful implications).

5. You rightly identify confirmation bias which I find far more common than most realise, but do you think that removing it and embedding of doctrine might lead to understanding without ever larger accelerators?

6. On the same line; Might that also help resolve what you rightly identify as; "the most vexing problem of all, that we know there is something out there - or in there - waiting to be discovered, but to get the answer would require more waiting time than we have".

7. But when a good candidate for a coherent set of solutions DOES come along, likely NOT from doctrinal thinking, do you think academics be able to recognise it, or even bother to study it!? From my on experience I suggest not. Do you have a view?

Nice essay Jonathan, certainly down for a top score from me. Well done.

Very Best. Stay safe.

Peter

So sorry to hear this. Condolences Jonathan.

Hello dear Jonathan,

Ulla tells you Hello too , I live in Finland now I have immigrated and we live together.

I thank you a lot to tell my name, I am honored. I work a lot and study a lot of maths to formalise correctly this Theory of Spherisation, an optimisation evolution of the Universal sphere or future Sphere with quantum and cosmological spheres.

I have found this universal link maybe 13 years ago in ranking a Little bit of all, animals, vegetals, evolution, minerals, maths, Chemistry, physics, biology and you know how I have had this humble Eureka ? in a book of biology I have seen a simple page where we see the Brains of hominids evolving since the lemurians, we see all the Brains on one page and it was for me incredible, I told oh my god, the spherisation is universal, the particles are spheres and the universe too generally and relativelly,

I was excited I must say, like I am not a professional, I have improved a lot this theory in studying many works here on FQXi or on arxiv and in the good books.

I knew that I found in all humility something of relevant, and I was surprised that nobody had thought about this universal link. Even our friend Dr Ray Munroe, I miss him here on FQXi, told me , I don t understand steve the spheric man how I have not thought about this Before lol and he told me the Words of Feynman, one day we shall see all the truth and we shall say oh my god how is it possible that we have not seen a thing so simple Before.

I beleive that maybe the thinkers have too much focus on detaiuls instead to see th generality, the generality is simple. There I work about the publications and I learn a lot of maths like I told you. I beleive that I have reached this quantum gravitation in changing the distances but I must be sure of course.

I am happy that several relevant thinkers work about the spheres, that permits to evolve in physics and maths, I beleive strongly that the foundamental mathematical and physical objects are 3D spheres and that we can superimpose 3 main E8 in replacing the points or strings by finite primordial series of spheres playing between the zero absolute and the planck temperature, the main origin is particles coded instead of fields or Waves.

I like the strings but I consider the spheres at this planck scale and particles coded, I don t consider so that all is made of Waves, fields, branes and from a 1D main Cosmic field, I prefer a kind of gravitational aether made of particles. I didn t know this thinker that you honorate, thanks a lot for sharing, I am going to learn more for the properties of these spheres and the rankings.

It seems very relevant, it could be very well to have John Baez here also on FQXi and Witten and also Connes, we could make an incredible revolutionary work in complementarity, they are good in maths, I study but alone it is not easy all Days lol I must say, it ios a lot of works and unknowns. In all case we can explain our main unknowns I beleive like this quantum gravitation, the dark matter, the dark energy, the consciousness,...

I thank you still to have spoken about me, it is very nice dear friend, take care, I find also very well that you have honored this thinker, best regards

Hi Jonathan,

Thank you very much, it is very nice.

Yes lol indeed , a lot of scientists now have created prisons of thoughts forgetting the simplicity of this universe generally speaking, for me these spheres are the choice of this universe and this geometry is totally different than the others and is the perfect equilibrium of forces and can create all geometries and topologies when we consider these geonetrical algebras and 3D finite series of spheres where space disappears , one coded for the vacuum space and two main fuels, photons and cold DM. Maybe the scientists must understand this general universal simplicity and work on complex details differently.

Regards

Jonathan,

Math! - Its so long ago, that it now resides only in my 'imaginary' brain cells.

'Your paper is to be an exciting exploration of bouncing between what is 'possible to know' and 'what is beyond reckoning'. '.

Perhaps the (interesting) Mandelbrot Set and Planck scale are guides specifically for mathematicians. You are seeking converges or condenses, but shouldn't 'expands' be a third alternative. You say 'one area of Physics for which the Mandelbrot Set provides useful insights is the study of gravity'. However, if you see things as a cosmologist might, the options go beyond the 2 or 3 possibilities, even beyond reckoning'

I suggest that all things can be contemplated as nothing is absolute. Everything under investigation has parts. There is a field between known and 'beyond reckoning' with varying probabilities throughout. 'We reside in a middle ground between fixed realities and variable conditions, over which we have no control.'

Gravity, my interest, seems to reveal that what we know can be just the opposite of how it is. 'When crafting a unifying theory of Physics, a problem is that Relativity time is flexible, while in QM it is absolute'. Supposedly the need to reconcile these theories is the main incentive for quantum gravity theorists and the reason so many worthy approaches to the problem have been spawned. None work well since simple options are ignored. 'There is a growing knowledge gap because, as things become more complex; more things cannot be known, more facts cannot be proven, and more proofs can never be tested.' Seems all are upside down.

The sheer volume of collected data distorted knowledge, as it must be stored and then searched through later hoping to find the bits of information (buried deep within) that contain what we want to know.' 'So time spent is the ultimate barrier to knowledge, since it is the one limitation we can never hope to overcome.'

Best wishes Jonathan.

Paul Schroeder

Hi Jonathan,

I thought about this generally.

It becomes relevant to consider indeed the Clifford algebras for my 3 main series of codes 3D spheres , one for this space , and the 2 fuels, one for the photons and one for this cold dark matter and we can play with the commutativity and non commutativity, we correlate so with these finite primordial series of Spheres, the numbers, reals and complex and the different dimsensionalities maybe but we can consider mainly this 3D in playing with the different volumes, motions, rotations, oscillations for the synchronisations, superimposings, sortings of informations.

he main relevant is that the geonetries, topologies and properties of matters emege when these 3 series fuse if I can say , the spinors and others properties so can be ranked with the scalar Products . The differential structures so can be ranked in converging with the Spheres S1 towards S18-16 , John Baez have worked about thisand it seems very relevant indeed and that can be relevant to know more when we consider these 3 main primordial series and their finite numbers, the same than our finite cosmological serie of spheres, this number is very relevant and the space disappears implying a kind of super universal fluidity for a kind of main gravitational aether.

The morphisms appear and can be ranked and we can better understand the encodings furthermore and so this evolution.It is important in my theory of spherisation, the optimisation evolution of this universal sphere or future sphere. The aim is really to find a kind of universal partition where the space, the informations of these 2 fuels, and the numbers dance in a kind of harmonical periodic distribution. The homotopy of Spheres so can be relevant and the manifold correlations .

Regards

we can also converge with the resonances, fields , strings , Branes,....but in considering mainly particles coded instead of an external main Cosmic field to explain our geonetries, topologies, properties of matters. The philosophy is totally different. But that can converge because they oscillate also and can be in resonance for the sortings, synchronisations, superimposings, that becomes very relevant considering all the properties of these finite primoridal coded series and their number finite.

An other Thing at my humble opinion relevant to superimpose is the Lie algebras, derivatives and groups and the works of Dirac and the Ricci flow also and Hamilton Ricci flow in considering intrinsic codes inside the coded particles , the poincare conjecture of course also and the topological and euclidian spaces, in superimposing all these Tools cited above and here, that can become the secret of this universal partition. And furthermore we can consider finally an assymetric Ricci flow for the deformations and to explain the unique things maybe in the smaller spherical volumes of these finite primordial series.

I try to find the good general way for the formalisation of my general theory and these 3D spheres, I search the good mathematical Tools to superimpose ,it could be very relevant to work in complementarity, alone it is not easy, John Baez, Susskind , Witten, Hooft and Connes more Penrose could come on this platform, together with their skillings in maths, we can create a real revolutionary work at my humble opinion, I know the maths but they are better than me. The complementarity is essential it seems.

wordy essay (your usually are). But I gave you a 9 for content. Had it been more succinct you would have gotten a 10

Your points are well taken.

Andrew

Hi Jonathan,

Your paper was quite interesting. I had no idea about the connections between the Mandelbrot set and Physics. There is a lot I don't understand about it, but it just makes me want to read a lot more about it.

There was one thing you said I could use a little clarification on: 'that which converges or condenses into congruent forms.' What do you mean by congruent forms and what is converging to them?

Do you think the lack of focus on non-linear dynamics is because of difficulty, or possibly something else?

You mentioned the Heisenberg Uncertainty principle, and it made me wonder if we could ever stumble across a mathematical structure to describe the behavior of waves without the limitations of the uncertainty principle. (A little tangential).

One thing you said in your concluding remark struck a chord in me, even if I don't fully understand the full implications. That " the reality in both Math and Physics is that what is relevant or real arose from a larger spectrum of what is possible". It makes me wonder on the limitations of what is possible.

Best regards,

Ernesto