# Does Chaos Theory prove a Mathematically Ordered Universe

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Write4U ;
The Physical Properties and the Environment of the object and/or objects , in space . Singularly and in atoms . Some have affinity some don't .
But you cannot start in the middle. Atoms are the smallest "physical" objects (matter), but they are not the smallest "mathematical values".
Matter is made up of sub-atomic values called "quanta" (smallest known immaterial values).

Physical Properties of objects and the Environmental conditions all have mathematical (quantum) values which determine the actual specific interaction between objects. It is these values that determine the interactive behavior between the objects, not their physical description.
Quantum state
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states. A pure quantum state can be represented by a ray in a Hilbert space over the complex numbers,[1][2] while mixed states are represented by density matrices, which are positive semidefinite operators that act on Hilbert spaces.[3][4]
Pure states are also known as state vectors or wave functions, the latter term applying particularly when they are represented as functions of position or momentum.
For example, when dealing with the energy spectrum of the electron in a hydrogen atom, the relevant state vectors are identified by the principal quantum number n, the angular momentum quantum number l, the magnetic quantum numberm, and the spin z-component sz. For another example, if the spin of an electron is measured in any direction, e.g. with a Stern–Gerlach experiment, there are two possible results: up or down. The Hilbert space for the electron's spin is therefore two-dimensional, constituting a qubit.
https://en.wikipedia.org/wiki/Quantum_state#

Chirality
An object or a system is
chiral if it is distinguishable from its mirror image; that is, it cannot be superimposed onto it. Conversely, a mirror image of an achiral object, such as a sphere, cannot be distinguished from the object. A chiral object and its mirror image are called enantiomorphs (Greek, "opposite forms") or, when referring to molecules, enantiomers. A non-chiral object is called achiral (sometimes also amphichiral) and can be superposed on its mirror image.
The term was first used by L
ord Kelvin in 1893 in the second Robert Boyle Lecture at the Oxford University Junior Scientific Club which was published in 1894: "I call any geometrical figure, or group of points, 'chiral', and say that it has chirality if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself."[1]
https://en.wikipedia.org/wiki/Chirality

IMO, what we call Physics is a scientific discipline which uses mathematics to "describe and "formalize" the observed phenomena. The successful practical use of mathematics suggests that mathematics are "sufficient" to describe the "necessary" physical states (densities) and behaviors of physical objects.

But you cannot start in the middle. Atoms are the smallest "physical" objects (matter), but they are not the smallest "mathematical values".
Matter is made up of sub-atomic values called "quanta" (smallest known immaterial values).

Physical Properties of objects and the Environmental conditions all have mathematical (quantum) values which determine the actual specific interaction between objects. It is these values that determine the interactive behavior between the objects, not their physical description.
Quantum state
https://en.wikipedia.org/wiki/Quantum_state#

Chirality
https://en.wikipedia.org/wiki/Chirality

IMO, what we call Physics is a scientific discipline which uses mathematics to "describe and "formalize" the observed phenomena. The successful practical use of mathematics suggests that mathematics are "sufficient" to describe the "necessary" physical states (densities) and behaviors of physical objects.

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but limited to what the mathematics is based on .

Mathematics is always confined upon the knowledge given .

The question is the symptom of to much quantity thought ; not enough quality thinking .
Is that an argument for or against? Read the question and do think this through. You'll will come to the conclusion that it is the extant mathematical values which determine the "pattern formation" of matter.

Physics describes matter, mathematics describes the type, properties, and behavior of matter.

river said:
The question is the symptom of to much quantity thought ; not enough quality thinking .

Is that an argument for or against? Read the question and do think this through. You'll will come to the conclusion that it is the extant mathematical values which determine the "pattern formation" of matter.

Physics describes matter, mathematics describes the type, properties, and behavior of matter.

What does Quality mean to you ?

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but limited to what the mathematics is based on .
I agree.
Mathematics is always confined upon the knowledge given .
I agree.

But that is only in reference to human discovered knowledge and understanding. If we knew all the maths of the universe we could form a TOE.
But the universe does not need to know human symbolic mathematics. The Universe uses it's own universal mathematical "relative values" and "mathematical functions".

The invention of human "symbolic" mathematics to accurately describe (symbolize) Universal values and functions is man's greatest "discovery" of a fundamental Universal Truth that the Universe is a mathematical object and can be described with the use of mathematical language.

Note that all sciences use mathematics to accurately describe "quantity" and "quality" of universal properties and dynamics.

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I agree. I agree.

But that is only in reference to human discovered knowledge and understanding. If we knew all the maths of the universe we could form a TOE.
But the universe does not need to know human symbolic mathematics. The Universe uses it's own universal mathematical "relative values" and "mathematical functions".

The invention of human "symbolic" mathematics to accurately describe (symbolize) Universal values and functions is man's greatest "discovery" of a fundamental Universal Truth that the Universe is a mathematical object and can be described with the use of mathematical language.

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TOE , theory of everything , does it include magnetism ?

The problem is , is that the mathematics is always behind . The Physical Root of the mathematics .

What does Quality mean to you ?
Yeah, that's one of those multi-definitive words.
Quality, noun
1 The standard of something as measured against other things of a similar kind; the degree of excellence of something.
In this context;
Quality (physics)
In response theory, the quality of an excited system is related to the number of excitation frequencies to which it can respond. In the case of a homogeneous, isotropic system, the quality is proportional to the FWHM.
This sense of the phrase is the precursor of the usage of the word in music theory. In music theory, quality is the number of harmonics of a fundamental frequency of an instrument (the higher the quality, the richer the sound).
https://en.wikipedia.org/wiki/Quality_(physics)#

Note: "number of frequencies and harmonics".

Potential is a measure of an object's qualities.

"Potential"
, noun
latent qualities or abilities that may be developed and lead to future success or usefulness.
1. Similar: possibilities, potentiality, prospects, promise, capability, capacity, capacity for hard work, ability,
power, talent, flair, what it takes.
2. 2.
PHYSICS
the quantity determining the energy of mass in a gravitational field or of charge in an electric field.

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TOE , theory of everything , does it include magnetism ?

The problem is , is that the mathematics is always behind . The Physical Root of the mathematics .
I understand what you are saying, but that is from a human perspective. We discover the mathematical values and functions which are being used in the course of universal evolutionary processes.

When our scientist observe and measure they are only discovering pre-existing mathematical behaviors.
The Universe was a mathematical object with mathematical properties and potentials from the very beginning, long before man came on the scene and started asking questions.

p.s. There are no physical roots to mathematics. There are only mathematical roots of physics. The root of mathematics is Logic.

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I understand what you are saying, but that is from a human perspective. We discover the mathematical values and functions which are being used in the course of universal evolutionary processes.

When our scientist observe and measure they are only discovering pre-existing mathematical behaviors.
The Universe was a mathematical object with mathematical properties and potentials from the very beginning, long before man came on the scene and started asking questions.

p.s. There are no physical roots to mathematics. There are only mathematical roots of physics. The root of mathematics is Logic.

Logic does not rule the Universe .

And the Root of logic is based on physical things existing .

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Write4U
When our scientist observe and measure they are only discovering pre-existing mathematical behaviors.

What is the foundation of these " pre-existing mathematical behaviors " ? Why do they exist ?

River said: Logic does not rule the Universe

Of course Logic rules everything. It is the foundation of reality itself. This excellent article describes the "function" of Logic in the Universe.
Is the Universe Logical?
Valid logic cannot – by definition – be invalid. If the system is internally consistent and satisfies all fundamental rules, then it works.
Because such systems require only internal validity, I do not think that there can be a universe in which they are not valid. Therefore, 1+1=2 everywhere, even in a universe with different physical laws (if that is even possible).
But logic an math also do describe the real world. This does not mean, however, that they are dependent upon the physical world. Rather, they can be used to describe the real world because they are tools that can be used by empirical investigation – science.
Science can use math and logic to construct its models of how the universe works. Scientific statements must be logically valid and mathematically correct, so math and logic help scientists arrive at conclusions about nature that are valid.....more.
https://theness.com/neurologicablog/index.php/is-the-universe-logical

Write4U
What is the foundation of these "pre-existing mathematical behaviors" ? Why do they exist ?
It is a required property for consistent "self-organization".

Is the Universe made of Math By Max Tegmark on January 10, 2014
The Mathematical Universe Hypothesis implies that we live in a relational reality, in the sense that the properties of the world around us stem not from properties of its ultimate building blocks, but from the relations between these building blocks.
The external physical reality is therefore more than the sum of its parts, in the sense that it can have many interesting properties while its parts have no intrinsic properties at all.
This crazy-sounding belief of mine that our physical world not only is described by mathematics, but that it is mathematics, makes us self-aware parts of a giant mathematical object.
As I describe in the book, this ultimately demotes familiar notions such as randomness, complexity and even change to the status of illusions; it also implies a new and ultimate collection of parallel universes so vast and exotic that all the above-mentioned bizarreness pales in comparison, forcing us to relinquish many of our most deeply ingrained notions of reality.
We humans have gradually discovered many additional recurring shapes and patterns in nature, involving not only motion and gravity, but also areas as disparate as electricity, magnetism, light, heat, chemistry, radioactivity, and subatomic particles. These patterns are summarized by what we call our laws of physics. Just as the shape of an ellipse, all these laws can be described using mathematical equations.
But if we assume that reality exists independently of humans, then for a description to be complete, it must also be well-defined according to non-human entities – aliens or supercomputers, say – that lack any understanding of human concepts. That brings us to the Mathematical Universe Hypothesis, which states that our external physical reality is a mathematical structure.

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Reasonable
In what way?

Both Religion and Physics describe observable "irreducible complexities", i.e physical patterns.

But as demonstrated there is no such thing as irreducible complexity. Fundamentally we are looking at abstract "relational (relative) values" and mathematical (algebraic) functions, which result in the physical patterns and potentials that may be scientifically analyzed for their intrinsic values and ability to do work and can be "read" and understood by any intelligent or quasi-intelligent observer (the Mathematical Universe).

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In what way?

Both Religion and Physics describe observable "irreducible complexities", i.e physical patterns.

But as demonstrated there is no such thing as irreducible complexity. Fundamentally we are looking at abstract "relational (relative) values" and mathematical (algebraic) functions, which result in the physical patterns and potentials that may be scientifically analyzed for their intrinsic values and ability to do work.

Whether irreducible complexity exists or not . Mathematics has nothing to do with the manifestation of the physical .

Give me the mathematics that can manifest a physical thing , devoid of any reference to any physical thing and the three fundamental dimensions , length , breadth and depth , manifestation of the physical .

Whether irreducible complexity exists or not . Mathematics has nothing to do with the manifestation of the physical .

Give me the mathematics that can manifest a physical thing , devoid of any reference to any physical thing and the three fundamental dimensions , length , breadth and depth , manifestation of the physical .
Pretty sure you do not know what you are talking about river...in fact positive!

Oh, and don't forget the fourth dimension...TIME!!

river said:
Whether irreducible complexity exists or not . Mathematics has nothing to do with the manifestation of the physical .

Give me the mathematics that can manifest a physical thing , devoid of any reference to any physical thing and the three fundamental dimensions , length , breadth and depth , manifestation of the physical .

Pretty sure you do not know what you are talking about river...in fact positive!

Oh, and don't forget the fourth dimension...TIME!!

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It has never been possible .

Both Religion and Physics describe observable "irreducible complexities", i.e physical patterns.
Mathematics is the language of physics and science generally speaking...that as far as I can see is the best simplest description.
River will not accept that because as detailed in
"The Electric.Plasma Universe: A mixture of mysticism, pseudoscience and nonsense:" thread, here.....
that hypothetical debunked nonsense, exists without any language [mathematics] therefor river 'must"deny its definition and requirement.

river said:
Whether irreducible complexity exists or not . Mathematics has nothing to do with the manifestation of the physical .

Give me the mathematics that can manifest a physical thing , devoid of any reference to any physical thing and the three fundamental dimensions , length , breadth and depth , manifestation of the physical .

Well .....

Whether irreducible complexity exists or not . Mathematics has nothing to do with the manifestation of the physical
So you are still opting for Intelligent Design? If not, mathematics is the only self-organizing ( self-ordering) Universal Imperatives, or Natural Guiding Equations.
river said: Give me the mathematics that can manifest a physical thing , devoid of any reference to any physical thing and the three fundamental dimensions , length , breadth and depth , manifestation of the physical .
Well .....
That is an irrational question. What you are asking is if the universe can manifest a physical (not mathematical) object without using mathematical values and functions.

The answer is "No", but Physics can describe these mathematical patterns (objects) with descriptive symbolic nouns; i.e. "Universe, Galaxies, Stars, Earth, Clouds, Oceans, Land, Trees", Ants, Apes, Humans, Scientists, Geometrics, Coordinates, Fields, Quanta, Energy.

Dimensions, length, breadth and depth, (and duration) are the physical manifestations (properties) of chronologically self organizing mathematical patterns into durable objects . This is also agrees with the definition and mechanics of Evolution by Natural Selection, IMO.

3.1 Euclidean Dimension
Any space that can be conceived of also has a characteristic number associated with it called a dimension.
From the time I began the serious study physics and mathematics up until I discovered chaos and fractals, I had what I thought was a complete definition of dimension.
My definition of dimension (which I had assumed to be the definition) was the number of real number parameters needed to uniquely describe all the points in a space. Thus, the real number line is one-dimensional as it only takes one real number (parameter) to describe each real number (point).
Dimension is invariant so that a plane, for example, requires two parameters in rectangular (x, y) or polar (r, θ [theta]) coordinates. Other suitable examples come to mind. The set of lines in a plane is two-dimensional as describing any one of them uniquely requires two parameters: the slope and y-intercept (m, b) or the x and y-intercepts (x0, y0), for example. The set of all circles in a plane is three-dimensional (two for the coordinates of the center and one for the radius) and the set of all conic sections in a plane is five-dimensional (trust me).
This situation is great for physicists, and other scientists too, as it enables them to mine the wealth of mathematical knowledge about curves, surfaces, and all the rest and apply them to the rigorous study of the natural world.
It takes four numbers to adequately describe the thermodynamic state of a region containing a gas: pressure, volume, temperature, and amount of material. If we limit ourselves to a fixed amount of material and assume that the gas is ideal, we can reduce the system down to two dimensions: pressure and volume (a reasonable assumption believe it or not).
Thus, anything that any mathematician has ever done in a two-dimensional space could, at least in principle, be used in the study of ideal gases. The work done by a gas as it expands isothermally turns out to be a problem in finding the area under the curve y = a/x. Luckily, for the physicists of the nineteenth century, a mathematician had already determined the solution.
https://hypertextbook.com/chaos/euclidean/

For some interesting visuals. https://hypertextbook.com/chaos/eyecandy/

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