Does Chaos Theory prove a Mathematically Ordered Universe

[Michael 345]

Pretty scathing, huh?

Well I don't know Tegmark and from the small sample of the sample of the scathing review I am unlikely to look any further in depth

 

[Write4U]

Noooooo I showed you a example of my magical thinking. The type of magical thinking I assess Tegmark engages in
Please stop with the constant reference to authority

Then stop referring to authority to debunk Tegmark.

Believe or not NOT EVERYTHING NEEDS A SCIENTIFIC REFERENCE

Nothing you have shown me debunks Tegmark's mathematical universe. Talk about LEVELS does not have any bearing on the concept of a mathematical universe.

 

[Write4U]

Logical conjunction


Definition

Truth table

Logic gate

Normal forms
Disjunctive

Conjunctive

Zhegalkin polynomial

Post's lattices
0-preserving yes
1-preserving yes
Monotone no
Affine no



Venn diagram of

In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true. The logical connective that represents this operator is typically written as ∧ or ⋅ .[1][2][3]

is true if and only if

is true and

is true.

An operand of a conjunction is a conjunct.

Beyond logic, the term "conjunction" also refers to similar concepts in other fields:

• In natural language, the coordinating conjunction "and".
• In programming languages, the short-circuit and control structure.
• In set theory, intersection.
• In lattice theory, logical conjunction (greatest lower bound).
• In predicate logic, universal quantification.

• Definition

  Logical conjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both of its operands are true.[2][3]

  The conjunctive identity is true, which is to say that AND-ing an expression with true will never change the value of the expression. In keeping with the concept of vacuous truth, when conjunction is defined as an operator or function of arbitrary arity, the empty conjunction (AND-ing over an empty set of operands) is often defined as having the result true.

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

 

[Michael 345]

Logical conjunction


Definition

Truth table

Logic gate

Normal forms
Disjunctive

Conjunctive

Zhegalkin polynomial

Post's lattices
0-preserving yes
1-preserving yes
Monotone no
Affine no



Venn diagram of

is true if and only if

is true and

is true.

An operand of a conjunction is a conjunct.

• Definition https://en.wikipedia.org/wiki/Logical_conjunction

Blah blah blah

 

[Write4U]

Blah blah blah

Ok then, if that's all it is to you......

 

[Write4U]

The beauty and elegance of mathematics is evident in the transformation of a triangle, a pointy object with only straight lines, into a flower, a landscape, a galaxy, ART.

A Sierpinski gasket can be generated by a fractal tree.

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

How a set of straight lines results in a curve.

How a set of Ellipses form a Square

Amazing how these patterns self-assemble as a result of regular motion. This is how it happens in nature, regardless if there is an observer.

 

[Michael 345]

Blah blah with pictures

 

[Write4U]

This is a natural truth, regardless of observation.

Nature never heard of Fibonacci, yet it uses the "golden ratio" all throughout the universe since the beginning as it is an evolutionary deterministic beneficial design.

 

[Write4U]

Blah blah with pictures

I know, the abstract mathematical world is truly amazing. But then Mathematics is not a Conscious Intelligence or an Artificial Intelligence, but a Quasi-intelligent functional property of spacetime geometry.
Spacetime

Artist concept of Gravity Probe B orbiting the Earth to measure space-time, a four-dimensional description of the universe including height, width, length, and time.

In physics, spacetime is any mathematical model which fuses the three dimensions of space and the one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive where and when events occur differently.

Until the 20th century, it was assumed that the 3-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. However, in 1905, Albert Einstein based a work on special relativity on two postulates:
The laws of physics are invariant (i.e., identical) in all inertial systems (i.e., non-accelerating frames of reference)
The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

The logical consequence of taking these postulates together is the inseparable joining together of the four dimensions—hitherto assumed as independent—of space and time.

Many counterintuitive consequences emerge: in addition to being independent of the motion of the light source, the speed of light is of constant magnitude regardless of the frame of reference in which it is measured; the distances and even temporal ordering of pairs of events change when measured in different inertial frames of reference (this is the relativity of simultaneity); and the linear additivity of velocities no longer holds true

.......

In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zürich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the formal definition of the spacetime interval. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded.[1]

Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed how mass and energy curve flat spacetime into a pseudo-Riemannian manifold.

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

 

[Michael 345]

No no no no no no no..........

The Universe is stuff

Now we can LABEL stuff. Nice to LABEL stuff so we understand what stuff we are talking about
LABELLING stuff is NOT anthropomorphising stuff

Where you get into the anthropomorphising is when you give the Universe CHARACTERISTICS like QUASI-INTELLIGENT

***** The Universe*****

It's non living stuff,
it is bereft of life,
life has never graced its firmament
I wandered lonely as a cloud
That floats on high o'er vales and hills,
When all at once I saw a crowd,
A host, of golden daffodils;
Beside the lake, beneath the trees,
Fluttering and dancing in the breeze.
The Universe does not know of
WILLIAM WORDSWORTH the poet
IT KNOWS NOTHING
O death, where is thy sting?
O grave, where is thy victory? or
John Donne
IT KNOWS NOT OF LIFE AND ALSO
NOT OF DEATH

And it's not just sleepy

 

[Write4U]

Nice poems.

But;
No one claims that the universe is a living thing!

Repeat;
No one claims that the universe is a Living thing!

Repeat;
No one claims that the universe is a Living thing!

Remember;
No one claims that the universe is a Living thing!

"Quasi Intelligent" does NOT mean a "Living Thing!

Remember;
No one claims that the universe is a Living thing!

If you think someone is claiming that the Universe is a Living thing, you are wrong.......

Love the poems.....

 

[Write4U]

p.s. The universe IS a Dynamical system!

Dynamical System

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.

In physics, a dynamical system is described as a "particle or ensemble of particles whose state varies over time and thus obeys differential equations involving time derivatives."[3] In order to make a prediction about the system's future behavior, an analytical solution of such equations or their integration over time through computer simulation is realized.

The study of dynamical systems is the focus of dynamical systems theory, which has applications to a wide variety of fields such as mathematics, physics,[4][5] biology,[6] chemistry, engineering,[7] economics,[8] history, and medicine.

Dynamical systems are a fundamental part of chaos theory, logistic map dynamics, bifurcation theory, the self-assembly and self-organization processes, and the edge of chaos concept.

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

"Dynamical system" does not mean "Living system", no, no, no, no, no, no.....

 

[Write4U]

p.p.s. Dynamical systems

Bifurcation theory



Phase portrait showing saddle-node bifurcation

Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.

Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior.[1]

Bifurcations occur in both continuous systems (described by ODEs, DDEs or PDEs) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior.[2] Henri Poincaré also later named various types of stationary points and classified them.

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

and the curious contradiction of ;

Dimensionless physical constant

In physics, a dimensionless physical constant is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used.[1]:525 For example, if one considers one particular airfoil, the Reynolds number value of the laminar–turbulent transition is one relevant dimensionless physical constant of the problem. However, it is strictly related to the particular problem: for example, it is related to the airfoil being considered and also to the type of fluid in which it moves.

On the other hand, the term fundamental physical constant is used to refer to some universal dimensionless constants. Perhaps the best-known example is the fine-structure constant, α, which has an approximate value of 1⁄137.036.[2]:367

The correct use of the term fundamental physical constant should be restricted to the dimensionless universal physical constants that currently cannot be derived from any other source.[3][4][5][6][7][8] This precise definition is the one that will be followed here.

However, the term fundamental physical constant has been sometimes used to refer to certain universal dimensioned physical constants, such as the speed of light c, vacuum permittivity ε0, Planck constant h, and the gravitational constant G, that appear in the most basic theories of physics.[9][10][11][12] NIST[9] and CODATA[13] sometimes used the term in this way in the past.

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

Note that BOTH interpretations and applications can be expressed as abstract measurable mathematically relational values! But how does it do that?
Because Human Mathematics are the human symbolic interpretation and representation of Dimensionless Universal Constants. That is why human mathematics are effective and suggest an accurate interpretation of at least some measurable fundamental dimensionless properties associated with the Spacetime.

E = Mc^2
t = 0 ->

T = 0

The common notation t = 0 simply means "time equals zero." It expresses the radical and fundamental conclusion of standard Big Bang cosmology. It recognizes the connection between space and time by implying that the Big Bang did not occur in time but that time began with the Big Bang singularity.

For many theological thinkers, the scientific articulation of t = 0 has significant implications for understanding creation, particularly the idea of a creation out of nothing (creatio ex nihilo ).

For many mathematical thinkers the scientific articulation of t = 0 has significant implications for understanding evolution in a permittive condition, particularly the idea of a self-organizing evolutionary process in a chaotic dynamical system from the very subtle to gross expression in Reality.

 

[Michael 345]

No one claims that the universe is a Living thing!

Your claim it is quasi intelliegent

QUASI

seemingly; apparently but not really.

supposedly -seemingly - apparently
allegedlyr- reportedly (and a few others)

being: partly or almost

partly - partially - in part

Which quasi?

Dare I say us Minions are intelliegent, but when talking about the Universe as the Universe we normally mean "a whole lot of stuff other than us"

That whole lot of stuff other than us is not within a Planck distance of being intelliegent

While in the area - it is not a arbitrary made up system (maths) Universe either

pisssst - post 313 to long - skipped

Currently I have other distractions

 

[Write4U]

Write4U said: ↑
No one claims that the universe is a Living thing!

Your claim it is quasi intelligent

Yes, but needs not be alive to act (behave) in a quasi-intelligent manner.

QUASI
seemingly; apparently but not really... ✓
supposedly -seemingly - apparently..... ✓
allegedly- reportedly (and a few others)... That would be religious interpretation...
being: partly or almost....................... ✓
partly - partially - in part..................... ✓

Which quasi?

See above.

Dare I say us Minions are intelligent, but when talking about the Universe as the Universe we normally mean "a whole lot of stuff other than us"

Yes, stuff behaving in a regular (measurable) order, "AS IF" it were intelligent. (The original basis for Theism)

That whole lot of stuff other than us is not within a Planck distance of being intelligent

But now we are talking about degrees of intelligent behaviors. i.e. (to name a few);
a) unconscious quasi (proto) intelligence: as found in bacteria (quorum sensing), slime-mold (maze solving)
b) subconscious homeostatic (control) intelligence: as found in flora (heliotropism), insects (hive mind), reptiles (heat sensing).
c) self-conscious intelligence (agency): higher order mammals, octopus, cuttlefish. (complex problem solving)

While in the area - it is not a arbitrary made up system (maths) Universe either.

I agree, universal mathematics are not arbitrary, they are strictly relational. i.e. Constants (differential equations).
Mathematical constant

A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems.[1][2] Constants arise in many areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory, and calculus.

I might add: Chemistry, Minarology,

Basic mathematical constants

Archimedes' constant...................................... π
The imaginary unit.......................................... i
Euler's number............................................... e.
Pythagoras' constant.......................................√2.
The Feigenbaum constants............................. α and δ
Apéry's constant............................................. ζ(3)
The golden ratio.............................................. φ
The Euler–Mascheroni constant......................γ
More items...

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

The symbols used to identify Constants are arbitrary human inventions.
The Constants themselves are universal quasi-intelligent mathematical Functions.

IMO, a mathematical function is an autonomous quasi-intelligent function. It acts in a logical manner, but is not aware of this other than as a passive causal relationship (differential equations)

Schematic depiction of a function described metaphorically as a "machine" or "black box" that for each input yields a corresponding output

A function is a process or a relation that associates each element x of a set X, the domain of the function, to a single element y of another set Y (possibly the same set), the codomain of the function. It is customarily denoted by letters such as

,

and

.[1]

in human symbolic terms.

If the function is called f, this relation is denoted by y = f(x) (which reads "f of x"), where the element x is the argument or input of the function, and y is the value of the function, the output, or the image of x by f.[2]
The symbol that is used for representing the input is the variable of the function (e.g., f is a function of the variable x).[3]

https://en.wikipedia.org/wiki/Function_(mathematics)#

 

[river]

Write4U said: ↑
No one claims that the universe is a Living thing!

But it has life with in it .

And life manipulates the fundamental elements of this Universe in order for Life to manifest .

Minerals , how many minerals are in the your body in order for it to function normally ?

Iron , potassium , boron

16 minerals are needed for the Human Body to function normally .

There are 16 essential minerals: calcium, phosphorus, potassium, sulfur, sodium, chloride, magnesium, iron, zinc, copper, manganese, iodine, and selenium, molybdenum, chromium, and fluoride. Minerals play important roles in maintaining blood pressure, fluid & electrolyte balance, and bone health; making new cells; delivering oxygen to cells; and contributing to normal muscle and nerve functioning. Minerals are widely distributed in foods, with specific minerals being found in certain foods. By eating a variety of nutrient-dense foods from the 5 food groups, you will have a mineral-rich diet.

 

[Write4U]

But it has life with in it .

So does an aquarium...

 

[river]

river said: ↑
But it has life with in it .

Write4U reply ;

An atom is the smallest unit of matter that retains all of the chemical properties of an element. Atoms combine to form molecules, which then interact to form solids, gases, or liquids. For example, water is composed of hydrogen and oxygen atoms that have combined to form water molecules. Many biological processes are devoted to breaking down molecules into their component atoms so they can be reassembled into a more useful molecule.

Highlighted

My point made .

 

[river]

Nice poems.

But;
No one claims that the universe is a living thing!

Repeat;
No one claims that the universe is a Living thing!

Repeat;
No one claims that the universe is a Living thing!

Remember;
No one claims that the universe is a Living thing!

"Quasi Intelligent" does NOT mean a "Living Thing!

Remember;
No one claims that the universe is a Living thing!

If you think someone is claiming that the Universe is a Living thing, you are wrong.......

Love the poems.....

True

But the Universe has life within it . That is the point .

 

[river]

And how do you keep stuff apart? It's not all the same stuff, is it? There is even stuff within stuff. How does it do that?

Is it magical beyond our cognition and understanding ? Or are we able to analyze the mathematical data by which different stuffs may be relationally connected. There is nothing magical about the concept of a mathematically describable relational interaction of fundamental stuffs (values), by means of a symbolic translation of a dynamical but orderly reality and how these interactive properties can be applied to human survival mechanisms.

We do not describe Global warming as "stuff happening". Knowledge of the mathematics in a probabilistic but deterministic world may come in handy some day!

We may not necessarily know "when", but knowing (calculating) "what" may happen in the future is a survival strategy in an "grander" evolutionary context......

The Universe is not an unknowable mystery! It is a physical object and can be abstractly analyzed as to inherent mathematically calculable potentials and probable behaviors.

Else we might as well believe in God, the anthropomorphized imaginary, unexplainable but benevolent spiritual equivalent (=) of mathematically expressed Potential ("That which may become reality"), a potential future probability based on patterns with measurable relational values and mathematical (algebraic) functions.

Agreed Write4U , but at the sametime Micheal345 is right .

Physics ; physical things , real physical things have 3D Inherent properties , such as a fundamental 3D shape , hence by its very Nature will have mathematical implications , its a given .

Mathematics in and of its self can not prove that ; 1+1=2 , the Physical can prove it easily ; .....think about this . For a bit . Write4U .