# The universe is a mathematical construct

exchemist:

As usual, I agree with you. Clearly Write4U is in the grip of a religious fervour. He believes he has found The Answer.*

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* And it's 42.

Write4U:
All the religions say they do.
I think you missed the part about gods being supernatural. If you're supernatural, who says you need a physical brain?
Metaphor. Remember?
Metaphor for what? Brain or no Brain?
The kind in which people speak in metaphors?
And in this instance the metaphor is....?
Nonsense. I'm not using any mathematics to type this post, for instance.
You have to be kidding!
That's just a faith-based claim you're making. This really is a religion for you, isn't it?
No, it is absolutely contrary to religion and it's mystical metaphors.
Please research what an equation is.
Equation
In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=".[2][3][4] The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any equality is an equation.[5]
Solving an equation containing variables consists of determining which values of the variables make the equality true. Variables are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variable. A conditional equation is only true for particular values of the variables.[6][7]
An equation is written as two expressions, connected by an equals sign ("=").[3] The expressions on the two sides of the equals sign are called the "left-hand side" and "right-hand side" of the equation.
The most common type of equation is an algebraic equation in which the two sides are algebraic expressions. The left hand side of an algebraic equation will contain one or more terms. For example, the equation ;
, has left-hand side
, which has four terms, and right-hand side
, consisting of just one term. The unknowns are x and y, and the parameters are A, B, and C.
An equation is analogous to a scale into which weights are placed. When equal weights of something (e.g., grain) are placed into the two pans, the two weights cause the scale to be in balance and are said to be equal. If a quantity of grain is removed from one pan of the balance, an equal amount of grain must be removed from the other pan to keep the scale in balance. More generally, an equation remains in balance if the same operation is performed on its both sides
I understand this narrative very clearly.
I still don't understand why you're fixated on God, while at the same time saying that your mathematical universe doesn't have one. Have I misunderstood your position? Do you think mathematics is God, or something? Why all this God talk. Does Tegmark go on about God the way you do?
God is the only other metaphysical object which describes the existence of the Universe without the help of an intelligent brain or a quasi-intelligent mathematical essence.
We've been through this before. They use mathematics as a tool. If you want to call it a "language" then you're using a metaphor.
I can say that your "life" is a metaphor. What does that prove?
If you can communicate with a language, then that proves that the language is an acceptable mode of addressing the properties that are described or symbolized by that language.
His wall? What are you talking about?
WOW, you have not seen Tegmark's wall. It's the wall in his office which contains all (but one) of the required numbers and equations necessary to explain the mathematical essence of the entire Universe.

"So here is the crux of my argument. If you believe in an external reality independent of humans, then you must also believe in what I call the mathematical universe hypothesis: that our physical reality is a mathematical structure. In other words, we all live in a gigantic mathematical object – one that is more elaborate than a dodecahedron, and probably also more complex than objects with intimidating names like Calabi-Yau manifolds, tensor bundles and Hilbert spaces, which appear in today’s most advanced theories. Everything in our world is purely mathematical – including you." Max Tegmark.

How would one go about falsifying Tegmark's Level IV universe idea, then?
i'll let Tegmark speak for himself. Tegmark writes:
"Abstract mathematics is so general that any Theory Of Everything (TOE) which is definable in purely formal terms (independent of vague human terminology) is also a mathematical structure. For instance, a TOE involving a set of different types of entities (denoted by words, say) and relations between them (denoted by additional words) is nothing but what mathematicians call a set-theoretical model, and one can generally find a formal system that it is a model of."
He argues that this "implies that any conceivable parallel universe theory can be described at Level IV" and "subsumes all other ensembles, therefore brings closure to the hierarchy of multiverses, and there cannot be, say, a Level V."[20]
https://en.wikipedia.org/wiki/Multiverse#:
Good-oh! Tell me what could falsify his theory, then.
Discarding any of the mainstream scientific equations on his Wall, such as E = Mc^2 It would falsify the entire theory and most of mainstream science at the same time. All of Tegmark's mathematics have been tested and have been falsified. They are, after all, mainstream scientific theories.......Tegmark does not introduce anything new, he compiles and assembles mainstream science and proposes a comprehensive whole, which can in principle explain everything about the nature of the Universe.
Okay then! Back to the drawing board. Toss that theory in the bin!
That is your considered conclusion? Junk all of mainstream science and it's mathematics.
Hey, we may even end up with a theory of God yet......!

continued

continued....
You're right that his idea is not exactly new. For that reason, it suffers from all the same philosophical flaws that ideas like classical Platonism have.
Just like the English language is a flawed language, but sufficiently sophisticated for Shakespeare.
It's a claim that is counter-intuitive and which needs explanation, which Tegmark has not really provided. As I previously suggested to you - and I now see that Massimo Pigliucci (for one) holds essentially the same view I do - maybe Tegmark is just muddled and is making a basic category error.
You have touched on the crux .
IMO, Tegmark's claim is eminently intuitive. To posit that the universe has only some mathematical properties instead of only mathematical properties fractures the entire concept that mathematics is the language of the Universe.
Who told you that a supernatural God needs a physical brain?
You did. You said intentional decision making requires a brain.
Creating physical stuff out of numbers would, in itself, be a miracle, in my opinion. Tegmark hasn't suggested any mechanism for that, as far as I can tell.
He doesn't need to. QM has taken care of that. Tegmark uses mainstream science to make his case!
You've examined and ruled out all other possibilities, have you? Or is this just one more proclamation of the faith?
Me? Nooooo....I am not aware of any other possibilities, are you?
If all you are saying is that theories in physics are most precisely quantified using mathematics, that's uncontroversial.
Well, seems we are making progress.....
It doesn't appear to me to be driven by a motivated intelligence.
Half the worlds'religions are based on that premise.
What kind of brain is required for motivated intelligence? Will any sort of brain do? Can you be more specific?
The same motivated intelligent brain you stipulated to earlier. What other sort's of brains are there?
I can visualize a dynamical quasi-intelligent process based on relational mathematical values and functions.
Tegmark doesn't countenance a "partial mathematical universe". I'm not even sure what you mean by that. Is it some kind of sub-sect of Tegmarkism?
To me that is most persuasive argument Tegmark makes.
To assume that only part of the universe is mathematical but not other parts is patently illogical in my mind.
As I noted before, that is fractured thinking which can never lead to a comprehensive TOE, whereas Tegmark's purely mathematical Universe can in principle lead to a comprehensive understanding of everything in and about the universe.
Of course you do. You're his fanboy. It doesn't occur to you to look for flaws in his ideas or arguments.
What flaws? I see no immediate flaws at all in Tegmark's logic.
If you see flaws why do you not list them so I may consider them.
Correct. As far as I can tell, though, he has his work cut out for him to convince the physics mainstream.
of course, that's how hypotheses are honed on the way to becoming theory.
They are trained in physics, but not necessarily in philosophy, as I pointed out. What they think they are doing is not necessarily what they are doing. Also, don't get the wrong impression: there's no consensus among cosmologists about this stuff.
There seems to be, as far as the mathematical structure of the universe is discovered rather than invented.
I love stage drama, but my dramatic talents are more musical than literary.
You might try literature, you do have a flair.....
Falsified? Is that what you meant to say? (That's at least twice now that you've said that.)
Yes, isn't all of mainstream science falsified? that's all Tegmark uses.
You think that current science is randomly assembled? Interesting.
No, that was David Bohm's observation and prompted him to write "Wholeness and the Implicate Order" . Consider the implied message in that title just for a moment.
Then why your fixation on him? If he is just recycling old ideas that have been shown to have flaws, where's the scientific revolution you're so keen to promote?
That is just another dramatic incorrect interpretation of Tegmark's hypothesis. He seeks to combine all of theoretical science and combine it in a single mathematical equation that is able to describe everything when appropriately applied.
I'm beginning to think you don't really understand what Tegmark is saying, or what his opponents' objections are.
Tegmark doesn't say that because mathematics exists therefore the universe is nothing but mathematics.
Yes, that is exactly what he does.
Similarly, none of his opponents say that mathematics doesn't exist or is absent from the universe. I have no idea what you're saying.
Then why do they reject the notion of a Mathematical Universe? That is what I am saying. is that so hard to understand. I find it remarkable simple as Tegmark posits with his wall of 32 fundamental numbers and a handful of equations. He stipulates the hypothesis is NOT complete . Yet the consternation persists because of every other scientist's pet little nook to which they are wedded is threatened by a single overarching theory.

Tegmark is attempting to fashion a perspective that will allow for a complete understanding of the Universe and how it may be understood in toto.

exchemist:

As usual, I agree with you. Clearly Write4U is in the grip of a religious fervour. He believes he has found The Answer.*

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* And it's 42.
Drama...Big Time Drama......

Cosmological principle
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throughout the universe, and should, therefore, produce no observable irregularities in the large-scale structuring over the course of evolution of the matter field that was initially laid down by the Big Bang.
https://en.wikipedia.org/wiki/Cosmological_principle#

Hence, Mathematics in parts of the Universe, Mathematics throughout all of the Universe.

Wave

In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities, sometimes as described by a wave equation.
In physical waves, at least two field quantities in the wave medium are involved. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction it is said to be a traveling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero.
Wave equation
Not to be confused with Wave function.

A pulse traveling through a string with fixed endpoints as modeled by the wave equation.

Spherical waves coming from a point source.

A solution to the 2D wave equation
The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves (e.g. water waves, sound waves and seismic waves) or light waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics.
Historically, the problem of a vibrating string such as that of a musical instrument was studied by Jean le Rond d'Alembert, Leonhard Euler, Daniel Bernoulli, and Joseph-Louis Lagrange.[1][2][3][4][5] In 1746, d’Alembert discovered the one-dimensional wave equation, and within ten years Euler discovered the three-dimensional wave equation.[6]
https://en.wikipedia.org/wiki/Wave_equation

And Pythagoras?

Wave function

Comparison of classical and quantum harmonic oscillator conceptions for a single spinless particle. The two processes differ greatly. The classical process (A–B) is represented as the motion of a particle along a trajectory. The quantum process (C–H) has no such trajectory. Rather, it is represented as a wave; here, the vertical axis shows the real part (blue) and imaginary part (red) of the wave function. Panels (C–F) show four different standing-wave solutions of the Schrödinger equation. Panels (G–H) further show two different wave functions that are solutions of the Schrödinger equation but not standing waves.
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively).
The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the wave function can be derived from the quantum state.
https://en.wikipedia.org/wiki/Wave_function#

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Geometry
Zero-dimensional[show]
One-dimensional[show]
Two-dimensional[show]
Three-dimensional[show]
Four- / other-dimensional[show]

An illustration of Desargues' theorem, a result in Euclidean and projective geometry

Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that are related with distance, shape, size, and relative position of figures.[1] A mathematician who works in the field of geometry is called a geometer.
Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry,[a] which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.[2]
During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Gauss' Theorema Egregium (remarkable theorem) that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in an Euclidean space. This implies that surfaces can be studied intrinsically, that is as stand alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry.
Later in the 19th century, it appeared that geometries without the parallel postulate (non-Euclidean geometries) can be developed without introducing any contradiction. The geometry that underlies general relativity is a famous application of non-Euclidean geometry.
Since then, the scope of geometry has been greatly expanded, and the field has been split in many subfields that depend on the underlying methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc.—or on the properties of Euclidean spaces that are disregarded—projective geometry that consider only alignment of points but not distance and parallelism, affine geometry that omits the concept of angle and distance, finite geometry that that omits continuity, etc.
Often developed with the aim to model the physical world, geometry has applications to almost all sciences, and also to art, architecture, and other activities that are related to graphics.[3] Geometry has also applications to areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental for Wiles's proof of Fermat's Last Theorem, a problem that was stated in terms of elementary arithmetic, and remainded unsolved for several centuries.
https://en.wikipedia.org/wiki/Geometry

The above is what Tegmark seeks to represent with a single equation that links all separate relational values and equations into a single theory of the Mathematical nature of the Universe.

It seems an exercise in logic.

Everyone feels a need to conform to the scientific-consensus cosmic opinion that the universe is all random happenstance, without any creational input, and without any otherworldly technological maintenance involved. What if the various galaxies and cosmic bodies were not randomly placed, but rather, that the patterns of this are beyond our ken, yet were purposely emplaced, in such ways as to balance unseen, ethereal, cosmic forces, so that parts of the cosmos where entities exist are kept stable? Does the word "UFO" ring a bell?

Everyone feels a need to conform to the scientific-consensus cosmic opinion that the universe is all random happenstance, without any creational input, and without any otherworldly technological maintenance involved. What if the various galaxies and cosmic bodies were not randomly placed, but rather, that the patterns of this are beyond our ken, yet were purposely emplaced, in such ways as to balance unseen, ethereal, cosmic forces, so that parts of the cosmos where entities exist are kept stable? Does the word "UFO" ring a bell?
The Universe is not fine-tuned to life on Earth. Life on Earth is fine-tuned to the Universe.

You better look up the definition of "Necessity and "Sufficiency".
https://en.wikipedia.org/wiki/Necessity_and_sufficiency

The properties of the Universe were "sufficient" to make it "necessary" that Life should evolve.

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* And it's 42.
No, it's just 32 numbers. I don't know why 32 . Apparently there are 31 + 1 unknown

Dimensionless constants, cosmology, and other dark matters
The modern SU3 SU2 U1 standard model of particle physics provides a much more sophisticated reduction. Key properties (spin, electroweak and color charges) of quarks, leptons and gauge bosons appear as labels describing representations of space-time and internal symmetry groups. The remaining complexity is encoded in 26 dimensionless numbers in the Lagrangian (Table I).1 All current cosmological observations can be fit with 5 additional parameters, though it is widely anticipated that up to 6 more may be needed to accommodate more refined observations (Table I).
http://www.nat.vu.nl/~wimu/Varying-Constants-Papers/Tegmark-PRD-DimensionlessConstants.pdf

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"Match the frequency of the reality you want and you cannot help but get that reality."

"This is not philosophy, it's a mathematical equation."

Write4U;

Science is still philosophy augmented with a system of measurement, its validation tool.Mathematics is a language of symbols and rules, with a rigid syntax, formed with the intent of consistent interpretation. Like all languages, it has a base of fundamental terms that are circular in definition or accepted on faith. Every equation can be expressed in words of a local language, which express relationships between entities; matter, force, motion, etc.There are intangible things like love, charity, compassion, hope, etc, which are not quantifiable. Thus the validation tool does not work for all aspects of the world.

The stick figure a child draws, represents a person, but without all the details.Mathematics is also a form of representation. The moon is pictured as a sphere, yet in a magnified view, the perimeter is revealed as a variable surface with mountains, valleys and plains, so where is the circle? The nonsensical dimensionless point is only visible if a blob of material is placed on a surface, with the understanding that the point is somewhere within the blob. The same treatment applies to the 'line' and thus all geometric forms. Mathematics is a good approximation for measurement, but did not come down from a high place on a stone tablet.It is used in science because human thinking is ignorant of the nature of the physical universe and how it functions. A case of 'something is better than nothing'.The universe was present before the appearance of human life, therefore we can conclude that it exists without human opinions or speculations.

For me, the mystery is why theoretical predictions so closely agree with human experience.

For me, the mystery is why theoretical predictions so closely agree with human experience.
Yes, the question affects me exactly the same and we are not the only ones. The question plagued Plato and Socrates and a host of the old great philosophers since the beginning of observation of natural regularities.

Don't forget we are long past drawing stickmen on the walls of caves.

This apparent dichotomy between the question if mathematics are a human invention or a human discovery has existed since the very beginning.

IMO, the answer is "both". Humans discovered the measurable regularities that appear to self-form by natural and evolutionary processes and invented a symbolic language that is able to closely represent these regularities and use them to understand how and why these regularities function and if we can use this knowledge to discover how fundamental these regularities are to the existence of the universe itself.

Some mathematics are clearly recognizably axiomatic. The concept of "one" and "two' are so ubiquitous throughout nature that every living thing recognizes it and uses it for say triangulation in hunting. Interestingly, many animals are able to "count" and tell the difference between more from less. Mathematics are used by many animals in one way or another.

This is why scientists are confident in using the invented symbolic "language" of mathematics to explain natural causal regularities. Things in Nature do not need to know human mathematical symbolism as long as humans know what relational values and functions our mathematical symbolisms represent in nature.

" input --> function --> output" is a natural mathematical functional equation, regardless of the symbolic (algebraic) representation used by humans.

There are intangible things like love, charity, compassion, hope, etc, which are not quantifiable.
And that answers one of those metaphysical questions if mathematics applies to the concept of "life" and "love" and 'pain". When you dig deep enough you always come to some mathematical equation that explains the emergence of metaphysical phenomena, such as consciousness and emotions.

One thing to remember above all other considerations . Everything in the biological world has evolved for one single purpose and that is survival. There is no greater imperative because all other options lead to extinction! (95% of all life is now extinct).

An excellent example is the Fibonacci Sequence, discovered and mathematically formalized by Fibonacci who observed this regularity and symbolized it in the familiar exponential form we know today.

It is one of the most amazing regularities found all throughout nature. This is a mathematical regularity that existed long before humans walked the earth. The sequence appears in botany because it offers an evolutionary advantage in gathering and distribution of energy in plants and trees.

This sequence is a clear proof of a naturally evolved mathematical growth function which existed in nature long before Fibonacci recognized the sequence and symbolized it.

Daisies and Sunflowers (and a host of other plants) don't know that they grow in accordance to the FS, but they do grow in that precise order. Natural Selection over millions of years "found" the inherent efficiency in that growth arrangement and uses it in many places everywhere because it offers a survival advantage to living organisms.

This is why most all scientist recognize that there is at least some naturally occurring mathematical aspects to the physical world, based on the naturally occurring constant relational values and processing functions as symbolized in our numbers and equations.

Tegmark asks the question, that if we can recognize some mathematical aspects to nature, why can we not propose that everything in nature has a mathematical aspect to it?

The aspects we normally identify as falling outside the scope of mathematics is really an unknown world of "metaphysics" which we are just relatively recently are becoming able to explore, due to our ever improving observational technology and ability to apply mathematics to previously mysterious natural phenomena. There are no known miracles.

What intrigues me about Tegmark's Mathematical Universe is the potential that mathematics may be able to explain everything and we might be able to fashion a mathematical TOE of the universe, whereas we have some seemingly unsurmountable obstacles in the current mainstream science which seems otherwise functional but does present some contradictions which are just as, if not more, problematic than Tegmark's hypothesis of "everything is mathematical in essence".

Any other metaphysical interpretation leads inevitably to an unanswerable (unfalsifiable) question and that just seems futile to me.

but did not come down from a high place on a stone tablet.
Nothing came down from a high place on a stone tablet. That metaphor is so much more confusing than the numbers 1 to 10 used to identify the mathematical order of the moral commandments as Moses understood them and inscribed them on the stone tablet. There was no lightning in some language that came down from the heavens and inscribed the commandments. There are no and never have been miracles.

Everything has always been natural.

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Whether or not the universe is a construct is down to whether or not it's a construct that is self-assembling.

Mathematics might exist for humans only because the universe is mathematical, a self-assembling universe must have some kind of algorithm behind it.

After all, humans developed mathematics initially to explain celestial objects, phases of the moon and so on. How this was done independently of lunar and planetary etc, motions, is a bit hard to explain I think.

Or if humans just have brains that can handle the math that's apparently 'at work' up there, then that might be why we developed all that notation.

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Write4U:

Tegmark asks the question, that if we can recognize some mathematical aspects to nature, why can we not propose that everything in nature has a mathematical aspect to it?

The aspects we normally identify as falling outside the scope of mathematics is really an unknown world of "metaphysics" which we are just relatively recently are becoming able to explore, due to our ever improving observational technology and ability to apply mathematics to previously mysterious natural phenomena. There are no known miracles.

What intrigues me about Tegmark's Mathematical Universe is the potential that mathematics may be able to explain everything and we might be able to fashion a mathematical TOE of the universe, whereas we have some seemingly unsurmountable obstacles in the current mainstream science which seems otherwise functional but does present some contradictions which are just as, if not more, problematic than Tegmark's hypothesis of "everything is mathematical in essence".
It is important to realise that Tegmark's "mathematical universe" hypothesis is not a scientific theory, as such, but rather a metaphysical philosophical position. His assumption is that mathematics will be used to find a "theory of everything" in Physics, but as far as I can tell his ideas propose no particular research programme that is likely to advance us towards that goal any faster than everyday physics research is taking us in any case.

This is why Tegmark's ideas, in the end, are just a moderately-interesting philosophical excursion, as opposed to anything that is likely to help the progress of science in any direct sense.

Whether or not the universe is a construct is down to whether or not it's a construct that is self-assembling.
I believe that self-assembly is a proven fact.

Moreover this self-assembling is in accordance to some, metaphysical (mathematical) organizing principle, rather than a physical principle, which is an inherently variable value for each physical object.

Self-assembly

Self-assembly of lipids (a), proteins (b), and (c) SDS-cyclodextrin complexes. SDS is a surfactant with a hydrocarbon tail (yellow) and a SO4 head (blue and red), while cyclodextrin is a saccharide ring (green C and red O atoms).

Transmission electron microscopy image of an iron oxide nanoparticle. Regularly arranged dots within the dashed border are columns of Fe atoms. Left inset is the corresponding electron diffraction pattern. Scale bar: 10 nm.[1]

Iron oxide nanoparticles can be dispersed in an organic solvent (toluene). Upon its evaporation, they may self-assemble (left and right panels) into micron-sized mesocrystals (center) or multilayers (right). Each dot in the left image is a traditional "atomic" crystal shown in the image above. Scale bars: 100 nm (left), 25 μm (center), 50 nm (right).[1]

STM image of self-assembled Br4-pyrene molecules on Au(111) surface (top) and its model (bottom; pink spheres are Br atoms).[2]
Self-assembly is a process in which a disordered system of pre-existing components forms an organized structure or pattern as a consequence of specific, local interactions among the components themselves, without external direction. When the constitutive components are molecules, the process is termed molecular self-assembly.

AFM imaging of self-assembly of 2-aminoterephthalic acid molecules on (104)-oriented calcite.[3]
Self-assembly can be classified as either static or dynamic. In static self-assembly, the ordered state forms as a system approaches equilibrium, reducing its free energy. However, in dynamic self-assembly, patterns of pre-existing components organized by specific local interactions are not commonly described as "self-assembled" by scientists in the associated disciplines. These structures are better described as "self-organized", although these terms are often used interchangeably.

Although self-assembly typically occurs between weakly-interacting species, this organization may be transferred into strongly-bound covalent systems. An example for this may be observed in the self-assembly of polyoxometalates.
Evidence suggests that such molecules assemble via a dense-phase type mechanism whereby small oxometalate ions first assemble non-covalently in solution, followed by a condensation reaction that covalently binds the assembled units.[4] This process can be aided by the introduction of templating agents to control the formed species.[5] In such a way, highly organized covalent molecules may be formed in a specific manner.
Self-assembled nano-structure is an object that appears as a result of ordering and aggregation of individual nano-scale objects guided by some physical principle.
https://en.wikipedia.org/wiki/Self-assembly

Scientific law

Scientific theories explain why something happens, whereas scientific law describes what happens.
Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena.[1] The term law has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, astronomy, geoscience, biology).
Laws are developed from data and can be further developed through mathematics; in all cases they are directly or indirectly based on empirical evidence. It is generally understood that they implicitly reflect, though they do not explicitly assert, causal relationships fundamental to reality, and are discovered rather than invented.
https://en.wikipedia.org/wiki/Scientific_law

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Write4U:

It is important to realise that Tegmark's "mathematical universe" hypothesis is not a scientific theory, as such, but rather a metaphysical philosophical position. His assumption is that mathematics will be used to find a "theory of everything" in Physics, but as far as I can tell his ideas propose no particular research programme that is likely to advance us towards that goal any faster than everyday physics research is taking us in any case.

This is why Tegmark's ideas, in the end, are just a moderately-interesting philosophical excursion, as opposed to anything that is likely to help the progress of science in any direct sense.

I believe that David Bohm had an important perspective. In his "Wholeness and the Implicate Order" he observes that current mainstream science has become so fractured that no comprehensive whole can be "visualized" and that in order to understand the universe we must posit a "wholeness" with an "implicate" (enfolded) order and an "explicate" (unfolded) order.

It seems to me that this implicate enfolded order is of a mathematical nature and the explicate unfolded order is of a physical nature.
And this seems to agree with Tegmark's position that objects in reality are the physical expressions of mathematical patterns with different values.

Wholeness and the Implicate Order
Implicate order and explicate order are ontological concepts for quantum theory coined by theoretical physicist David Bohm during the early 1980s. They are used to describe two different frameworks for understanding the same phenomenon or aspect of reality. In particular, the concepts were developed in order to explain the bizarre behavior of subatomic particles which quantum physics struggles to explain.
In Bohm's Wholeness and the Implicate Order, he used these notions to describe how the appearance of such phenomena might appear differently, or might be characterized by, varying principal factors, depending on contexts such as scales.[1] The implicate (also referred to as the "enfolded") order is seen as a deeper and more fundamental order of reality. In contrast, the explicate or "unfolded" order includes the abstractions that humans normally perceive.
As he wrote:
"In the enfolded [or implicate] order, space and time are no longer the dominant factors determining the relationships of dependence or independence of different elements. Rather, an entirely different sort of basic connection of elements is possible, from which our ordinary notions of space and time, along with those of separately existent material particles, are abstracted as forms derived from the deeper order. These ordinary notions in fact appear in what is called the "explicate" or "unfolded" order, which is a special and distinguished form contained within the general totality of all the implicate orders" (Bohm 1980, p. xv).

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")[1]
In everyday language refers to a sense of harmonious and beautiful proportion and balance.[2]
In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling.[4] Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music.[5]
This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry, which refers to the absence or a violation of symmetry.

.......

I like that, it's beautiful....I don't like that! It leaves me dissatisfied.

If this is of scientific importance I leave to the better minds. As an ex-bookkeeper and musician it satisfies my desire for a balanced symmetry......

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I believe that David Bohm had an important perspective. In his "Wholeness and the Implicate Order" he observes that current mainstream science has become so fractured that no comprehensive whole can be "visualized" and that in order to understand the universe we must posit a "wholeness" with an "implicate" (enfolded) order and an "explicate" (unfolded) order.
I disagree.