# Chaos, the wellspring of living systems

Being that the original state of the universe was chaotic, it would be useful to examine that condition and discover how order self-organizes within such a dynamic environment.

This should be possible due to the fact that chaos is a mathematical object and
individual events may occur probabilistically, but are in themselves deterministic and if the individual values are mathematically compatible, it results in a deterministically defined pattern or value.

## 1. Defining Chaos: Determinism, Nonlinearity and Sensitive Dependence

The mathematical phenomenon of chaos is studied in sciences as diverse as astronomy, meteorology, population biology, economics and social psychology.

While there are few (if any) causal mechanisms such diverse disciplines have in common, the phenomenological behavior of chaosâ€”e.g., sensitivity to the tiniest changes in initial conditions or seemingly random and unpredictable behavior that nevertheless follows precise rulesâ€”appears in many of the models in these disciplines.

moreâ€¦

1.2.1 Dynamical Systems and Determinism

To begin, chaos is typically understood as a mathematical property of a dynamical system. A dynamical system is a deterministic mathematical model, where time can be either a continuous or a discrete variable.

Such models may be studied as mathematical objects or may be used to describe a target system (some kind of physical, biological or economic system, say). I will return to the question of using mathematical models to represent actual-world systems throughout this article.

For our purposes, we will consider a mathematical model to be deterministic if it exhibits unique evolution:

(Unique Evolution)
A given state of a model is always followed by the same history of state transitions.

A very good and easy to follow video by Roger Antonsen will introduce the viewer to some very interesting mathematical phenomena.

We donâ€™t know the original state of the universe. Did the Big Bang begin from a singularity?

Generally, chaos is not solved mathematics. While quoting a philosophical encyclopedia from Stanford can help someone understand some fundamental ideas, the maths are very limited in most real problems.

Solving the Three Body Problem

And while I enjoy Antonsenâ€™s delivery, he is illustrating cleverness more than maths. I.e, he is showing how powerful basic maths can be. He is not exploring advanced maths. I donâ€™t understand how this relates to a wellspring of life.

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[quote=â€ścoffee, post:2, topic:10961, full:trueâ€ť]

We donâ€™t know the original state of the universe. Did the Big Bang begin from a singularity?

It is pretty well established that this universe started as a singularity. We know this because this universe had to start as a smaller object than it is today, else we could experience the continual expansion since.
The background

That does not negate the possibility that this singularity was the result of a prior collapsing universe, but THIS universe began @ t = 0 and was a small but very energetic object, expanding at FTL for a moment, resulting in an explanding plasma of superheated energy, a state of pure chaos.

As the fledgling universe cooled energy began to convert into matter and the first (mathematically) self-organizing elementary particles emerged from the dynamic quantum fields.

Generally, chaos is not solved mathematics. While quoting a philosophical encyclopedia from Stanford can help someone understand some fundamental ideas, the maths are very limited in most real problems.
Solving the Three Body Problem

Behavior among multiple bodies may be chaotic , but but always mathematical in origin.
This is what results in probabilistic, but ultimately deterministic action among all relational objects in a dynamic environment.

And while I enjoy Antonsenâ€™s delivery, he is illustrating cleverness more than maths. I.e, he is showing how powerful basic maths can be. He is not exploring advanced maths. I donâ€™t understand how this relates to a wellspring of life.

I see that more as a demonstration of the general mathematics inherent in all recurring patterns.
The Table of elements is a perfect example of mathematical patterns, where the organization of the pattern determines the character and potential of each atom, which all consist of the same constituent parts arranged in unique patterns that determine the same unique value of same atoms (patterns).

IMO, the first example that the whole is greater than the sum of its parts.
Note that the earliest atoms were the simplest patterns emerging from the cooling plasma.

This is what I gleaned from the folks at Cern:

## The Big Bang

In 1929 the American astronomer Edwin Hubble discovered that the distances to far-away galaxies were proportional to their redshifts. Redshift occurs when a light source moves away from its observer: the lightâ€™s apparent wavelength is stretched via the Doppler effect towards the red part of the spectrum.

Hubbleâ€™s observation implied that distant galaxies were moving away from us, as the furthest galaxies had the fastest apparent velocities. If galaxies are moving away from us, reasoned Hubble, then at some time in the past, they must have been clustered close together.

Hubbleâ€™s discovery was the first observational support for Georges LemaĂ®treâ€™s Big Bang theory of the universe, proposed in 1927. LemaĂ®tre proposed that the universe expanded explosively from an extremely dense and hot state, and continues to expand today. Subsequent calculations have dated this Big Bang to approximately 13.7 billion years ago. In 1998 two teams of astronomers working independently at Berkeley, California observed that supernovae â€“ exploding stars â€“ were moving away from Earth at an accelerating rate. This earned them the Nobel prize in physics in 2011.

Physicists had assumed that matter in the universe would slow its rate of expansion; gravity would eventually cause the universe to fall back on its centre. Though the Big Bang theory cannot describe what the conditions were at the very beginning of the universe, it can help physicists describe the earliest moments after the start of the expansion.

## Origins

In the first moments after the Big Bang, the universe was extremely hot and dense. As the universe cooled, conditions became just right to give rise to the building blocks of matter â€“ the quarks and electrons of which we are all made.

A few millionths of a second later, quarks aggregated to produce protons and neutrons. Within minutes, these protons and neutrons combined into nuclei. As the universe continued to expand and cool, things began to happen more slowly. It took 380,000 years for electrons to be trapped in orbits around nuclei, forming the first atoms.

These were mainly helium and hydrogen, which are still by far the most abundant elements in the universe. Present observations suggest that the first stars formed from clouds of gas around 150â€“200 million years after the Big Bang.

Heavier atoms such as carbon, oxygen and iron, have since been continuously produced in the hearts of stars and catapulted throughout the universe in spectacular stellar explosions called supernovae.

IOW, there is clear evidence that since the beginning, the universe has been engaged in a probabilistic but individually deterministic self-organization into ever greater complex patterns, eventually self-organizing into bio-chemical patterns that allowed for dynamical growth of â€śliving patternsâ€ť.

Note that extremely complex biological growth patterns like humans did not emerge until some 14 billion years of dynamical interactions and pattern forming.

But also note that the single celleld bacteria (prokaryotes) and paramecium
and slime mold (Eukaryots) exhibit mathematical behavior, not from knowledge but from inherent mathematical properties of non-chaotic self-organized patterns .

Living system emerged very gradually. On Earth it took 4 billion years after 10 billion years of elementary pattern-forming.

Following that chronology, I am personally convinced that the universe is a dynamical toroid.

This pattern answers all the necessary qualifications for a universe as I described above.

A perfectly cyclical universe, which itself may be part of a multiverse of variously shaped and organized universes.

Note the abundance of black holes that may well be centers of smaller or bigger toroids.

In a 3 dimensional space a black hole must be the center of a toroid, no?

If by that you mean we donâ€™t know how the universe started, then we agree. Since the definition is

Mathematical singularity, a point at which a given mathematical object is not defined or not â€śwell-behavedâ€ť, for example infinite or not differentiable

It is well established that the starting point of the universe is undefined, and the math for that beginning point is not well behaved.

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I am not positing that the BB itself was the result of a mathematically deterministic causality, but the resulting dynamic energetic values enfolded in the quantum fields (Bohmâ€™s Implicate order) allowed for mathematical pattern forming and unfolding in reality (Bohmâ€™s Explicate order).
The Higgs boson is proof of that.

Okay, first I feel like a BB occurred between the OP and the response. The amount of omitted content required to follow the OP is quite large. Iâ€™m generally of the opinion that if someone really understands something then they can present it in bite-sized bits without (much) external reference. At any rate,

Well, now youâ€™re saying that the universe might bounce rather than bang. This reminds me of a perpetual motion machine. And that really piques my skepticism.

And as mentioned, physics breaks down at infinitesimal scale. So I think the reality of a singularity is not established so much as kicked down the road.

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Really? Never heard that. How so?

And that infinitely small scale is during the hot plasma state of pure energy, which is chaotic because of the overwhelming chaotic energy present.

that incredibly small moment of inflation happened at FTL and was the original creation of spacetime (t=0+1). It is only after that infinitely small epoch that the plasma began to cool and the first emenets began to form via probabilistic but deterministic processes (functions). Determinism is the result of mathematical processes. The maths are the guiding principles that define the deterministic functions.

Note that it took the cooling before any matter began to emerge from the quantum fields. My chronology is perfectly consistent with mainstream science.

The difference in my model is the inclusion of mathematics that the universe employs in the formation of regular patterns, such as fractals, which are self-similar down to Planck scale.

Self- similarity is by definition mathematical in essence. It is when mathematical order becomes observable is when we recognize it and include it in our models.

Note that ALL models of the universe rest on mathematical order.
Even religion speaks of a watchmaker and intelligent design.

There is no alternative to the concept of mathematical order.
I have never heard of a self-ordering universe that does not employ native mathematics which humans have been able to symbolize and codify.

Bosons cannot exist in our spacetime. They are part of a quantum field.
But under the right conditions they can be made to manifest for an instant before they decay again and disappear.

This is what they do at Cern and it took the maths of Peter Higgs to create the right energetic conditions for a probabilistic quantum collision at near SOL, to make the boson manifest for an instant.

The Higgs boson is peculiar in many respects. Like most other elementary particles, it is unstable and lives only for an extremely short time,
1.6 x 10^-22 seconds , according to the established theory of particle physics (the standard model). Life of the Higgs boson | CMS Experiment

So,
When after inflation the original plasma state began to cool and massive particles began to form inside the plasma, is it possible that a central gravitational â€śwellâ€ť began to form at the center of the plasma and a universal toroid began to form, creating a naturally recycling process in time?

Does a continuous parabola eventually form a toroid?
If so, that would suggest a toroid with a white hole spewing energy and a black hole swallowing energy in endless recycling of the universe.

It also solves what came before the BB (a misnomer), and explains what came before THIS universe. Itâ€™s just a recycling of the old one that has completed its parabolic trajectory around the center of the universal wellspring.

## Ellipses, Orbits and Galleria Vittorio Emanuele

Letâ€™s start with ellipses. It took millenia to figure it out, but the motions of the cosmos arenâ€™t made of perfect circles as it was long thought. Rather, as asserted by Johannes Keplerâ€™s laws, the trajectories of objects of the universe are ruled by the geometry of ellipses!

But why is that?
This was a troubling mysteries for a century! Until came the brilliant Isaac Newton.

What did Newton do?
Newton proved that a few basic laws of mechanics could explain the elliptical motions of planets! And since these laws also matched Galileoâ€™s laws of motions (including the parabolic curve of free falling objects weâ€™ll get to later),

Newton postulated that they were universal laws of Nature! 18 months later, he published the most important book of the History of physics, the Principia Mathematica. This book was to transform our whole understanding of the Universe, since, for the first time in History, there was a claim of a universal law! Something that was true at all levels, everywhere and always. This is illustrated in this extract from another of NOVAâ€™s awesome science documentaries.

Could this be a a crude representation of a multiverse with many recycling toroid universes.

Watch the white holes spewing water, which is ciculated via black holes at the edge of the greater pool.

## Embracing Biophilic Design Principles:

Beyond functionality, the future of fountain design is deeply intertwined with biophilic principles â€“ the innate human tendency to seek connections with nature.

Fountains are being reimagined as vibrant ecosystems that support biodiversity and ecological balance. Incorporating native plants, aquatic habitats, and natural filtration mechanisms, these â€śbiophilic fountainsâ€ť not only enhance urban green spaces but also contribute to water recycling and conservation efforts.

I have no idea. And donâ€™t know where Iâ€™d start to figure that out

A gravitational well at the center of this universe? Everywhere we look we see spiral galaxies with black holes at their center.

Why not a central blackâ€“>white hole at the center of this universe?

IMO, this model solves all kinds of hidden forces such as dark matter, dark energy, the universal wavefunction, variations in the CMB.

All these mysteries become explainable in a model of a toroid uiverse.

I really try to track down these thoughts of yours. I wish you would tell us where you get them and where the evidence is. I found this,

astrophysicist Thomas Buchert, of the University of Lyon, Astrophysical Research Center in France, told Live Science in an email.

I feel like I am reading Deepak Chopra.

That sounds contradictory. They canâ€™t exist here but they do â€śmanifest for an instant.â€ť If they canâ€™t exist here then how did we discover their mass?

I find your posts to be very strange. You often proffer a complex conclusion and then support that conclusion with some basic maths; conic sections, for example.

No. Why must it?

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[quote=â€ścoffee, post:14, topic:10961, full:trueâ€ť]

I feel like I am reading Deepak Chopra.

No, this is not metaphysical. Quantum fields do exist.
I got that from here

That sounds contradictory. They canâ€™t exist here but they do â€śmanifest for an instant.â€ť If they canâ€™t exist here then how did we discover their mass?

This info comes from here:

The Higgs boson canâ€™t be â€śdiscoveredâ€ť by finding it somewhere but has to be created in a particle collision . Once created, it transforms â€“ or â€śdecaysâ€ť â€“ into other particles that can be detected in particle detectors. Physicists look for traces of these particles in data collected by the detectors.

The Higgs boson | CERN

I find your posts to be very strange. You often proffer a complex conclusion and then support that conclusion with some basic maths; conic sections, for example.

Yes, ultimately all complexity stems from simple mathematics.

No. Why must it?

A black hole is a black hole viewed from every angle because in a 3 D space, a black hole is surrounded by space .

Ultimately. Okay. The request was for some math to back up your theory. I donâ€™t need to understand every detail of it, just see that someone did the work and had it checked. A comment on experiments that need to be done to â€śproveâ€ť the math wouldnâ€™t hurt.

All of mainstream science rests on the mathematical proofs applicable to that specific phenomenon.

There are only 4 fundamental mathematical functions ( +, -, x, : )
All other compound functions consist of multiples of these 4 functions.

Okay, in technical writing, you cannot say, â€śBosons cannot exist in our spacetime.â€ť

And then say, â€śI got that from here.â€ť Where that here says they certainly can exist in our spacetime, but you have to do some work.

Your posts do nothing but frustrate this reader. But I wish you well. Peace.

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[quote=â€ścoffee, post:18, topic:10961, full:trueâ€ť]
Okay, in technical writing, you cannot say, â€śBosons cannot exist in our spacetime.â€ť

You are right. I meant to say that the Higgs boson cannot be directly observed.

AFAIK, the Higgs boson exists as a mathematical object and can only be â€śobservedâ€ť by its effects. We know they exist because they produce what we mathematically predicted they would produce, i.e. mass

Particles get their mass by interacting with the Higgs field; they do not have a mass of their own . The stronger a particle interacts with the Higgs field, the heavier the particle ends up being. Photons, for example, do not interact with this field and therefore have no mass.
The Higgs boson | CERN

And then say, â€śI got that from here.â€ť Where that here says they certainly can exist in our spacetime, but you have to do some work.

I welcome the correction. My post was sloppy.

Because the Higgs boson decays very quickly, particle detectors cannot detect it directly .
Higgs boson - Wikipedia

Your posts do nothing but frustrate this reader. But I wish you well. Peace.

Iâ€™m sorry to have disturbed your tranquility. I hope this correction is more accurate.

Toroid universe is not mainstream