What If The Universe Is Math?

In his essay “The Unreasonable Effectiveness of Mathematics”, the physicist Eugine Wigner said that “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious”. This statement was inspired by the observation that so many aspects of the physical world seem to be describable and predictable by mathematical equations to incredible precision especially as quantum phenomena.
But quantum phenomena have no subjective qualities and have questionable physicality. They seem to be completely describable by only numbers, and their behavior precisely defined by equations. In a sense, the quantum world is made of math. So does that mean the universe is made of math too?

Host Matt O’Dowd
Written by Euan McLean & Matt O’Dowd

Fun little presentation, gives both sides some credit.

I figure it might offer a diversion. :slight_smile:

This “describable,” seems to me the key to why I can’t take Tegmark’s, Math as everything, notion seriously.

Math is an exercise in the human imagination, its various invented forms provide an excellent tool for describing nature to ourselves. Still, it remains a construct of our brain & mind - since it returns to nothing outside of the context of humans’ operating brain & mind.
So I wonder what’s there to argument about, when considered within the grand scale of deep time?

Tegmark’s genius coupled with a sadly all too natural, human longing for ultimate answers, has wound up turning mathematics from a tool of science, into a something belonging to the family of philosophical and religious ideas.

I rest my argument. :v: :wink:

The universe is not full of numbers, it is full of generic values and the logical interaction between these natural generic values.

The issue is the difference between generic and human assigned values.
This is why algebra is a more accurate description of universal generic values

However the fundamental logical relational functions are made of what we call mathematical processes. Addition, subtraction, multiplication, division, and all variations of these 4 fundamental processes are universal and timeless in concept.
Numbers and equations are human interpretive symbols and codification of these natural generic inherent “values” and “logical relational functions”.

There is no argument that everything has a “value” and that these values can be codified symbolically. That’s why it works!

I believe that the statement “the universe is mathematical” is not addressing the concept of relational values correctly even as we address the Universe as a “geometrical” object, a mathematical term.

I believe that a better description is "Universal relational processes are guided by logical relational functions which can be described with mathematical equations.

This is why David Bohm spoke of a universal “guiding equation”, which would be a generic logical (mathematical) function that guides the interrelational processes of physical values.

i.e. (value) input → (mathematical) function → (value) output.

I find this exerpt a profound observation :thinking:

Therefore, the wave function cannot be the complete description of the state of the composite system. There have to be additional variables that contain the actual result of the formal measurement.

Such variables often are called “hidden variables” because they’re not part (or functionals) of the wave function. But, this name turns out to be a misnomer if you remember that these variables contain the visible result, the only thing visible, in fact.

Now, the question is, what are these additional variables? Let’s see what the formalism suggests: the wave function is a function of the configuration, that is, of the particle positions. So, what’s simpler than assuming that “particles” means particles and that a configuration actually exists? Indeed, what would be the meaning of the wave function being a function of the particle positions if there were no particle positions?

If we assume that quantum particles have trajectories too, then the motion of these particles should be guided by the wave function. The precise formula of Eq. (1) can be obtained as the simplest one defining a Galilean invariant theory.2

Well, sure but this is philosophy and not science.

mathematical logic not withstanding.

[quote=“citizenschallengev4, post:3, topic:10139”]
Well, sure but this is philosophy and not science.

Not really.
By all accounts, Bohm was a brilliant physicist , but when dealing with the nature of the universal spacetime itself, these hypotheses can only be theoretical.
Note that Bohm’s “Pilot Wave” theory provides a theoretical proof of a dynamic spacetime geometry .

This is very similar to Roger Penrose’s hypothesis that instead of “observation causing wave collapse”, “wave function collapse is causal to observation”, i.e. (Objective Reduction)

mathematical logic not withstanding.

It cannot be anything else. If the function is a constant it is mathematical by definition.

The function is universal (universally constant), the symbolic representations are human.

The imperfections (variations) of actual expression in reality is due to the dynamic nature of the universal spacetime fabric.

Come on Write, that doesn’t mean Bohm didn’t do philosophy.

And now you brought me back to the need for an explicit appreciation of the Human Mindscape ~ Physical Reality divide. I think that’s what happens to many of these old geniuses, and young ones. They fall into thinking they’re striving to actually touch “reality”, or worse think that they have touched “reality.”

A sober thoughtful appreciation for that simple divide, a divide that really is at the foundation of our human biological/intellectual experience, or human condition if you like.

It can provide a benchmark to help balance our intellectual longing with the limitations of our being.

It’s theater as much a philosophy. Penrose has gotten to be very good at theater since his retirement.

But my opinion about him means nothing, so allow me to pass let others fight my fight for me.

This realm of physics becomes religious, reaching for the stars. Finding the ultimate answers and such conceits. Lots and lots of notions besides not being testable, they have nothing to relate to our squishy biological reality. Sure you can come up elegant couplets of how the tiniest of atoms creates rocks that are more nothing than matter. But that’s not real, take that rock and tap it against your head. That is no hallucination, the rock is very solid, even if the poetry of the tiniest tells us there’s more to the story.

Remember I’m dedicated our living macroscopic realm.

I believe in the bottom up approach. Sure quantum reality creates atoms, and atoms create molecules and molecules can create life, but all that sinks into the depths of cosmic oceanic currents. Here on Earth, molecules became something spectacularly more and rare, they become biology. Then biology evolved into life and then life into creatures.

I say we ignore too much about ourselves, that our obsession with the stars and and math, and running technology at lunatic speeds, and oh that longing for the ultimate answers - it’s all a way of hiding from the essence of “ourselves.”

For me, the deep questions worth wrestling with belong in this realm. If you haven’t read this book, you really own it to yourself.

The Deep History of Ourselves|Home
Deep History argues that the key to understanding important aspects of human behavior lies in viewing evolution through the prism of the first living organisms. By tracking the chain of the evolutionary timeline he shows how even the earliest single-cell organisms had to solve problems similar to those we and our cells do each day.
Along the way, LeDoux explores our place in nature, how the evolution of nervous systems enhanced the ability of organisms to survive and thrive, and how the emergence of what we humans understand as consciousness made both our greatest and most horrendous achievements as a species possible.

Oh, he did a lot of philosophy, but he was also a brilliant physicist. You accused him of philosophizing and I am defending him on his physics qualification.

Theoretical physics is by necessity speculative, being that it cannot be “proven”, but must rely on what is “known” about physics.

It is known that the current Copenhagen Interpretation has an unresolved paradox in the particle/wave duality. Bohm resolved that conundrum and stayed within all the known physics

David Bohm, (born Dec. 20, 1917, Wilkes-Barre, Penn., U.S.—died Oct. 27, 1992, London, Eng.), American-born British theoretical physicist who developed a causal, nonlocal interpretation of quantum mechanics. Read more
David Bohm | American physicist | Britannicawww.britannica.com › biography › David-Bohm

Nature of the wave function[edit]

A wave function is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the wave function together with the rules for the system’s evolution in time exhausts all that can be predicted about the system’s behavior. Generally, Copenhagen-type interpretations deny that the wave function provides a directly apprehensible image of an ordinary material body or a discernible component of some such,[[42]](Copenhagen interpretation - Wikipedia)[43] or anything more than a theoretical concept.

Probabilities via the Born rule[edit]

Main article: Born rule

The Born rule is essential to the Copenhagen interpretation.[44] Formulated by Max Born in 1926, it gives the probability that a measurement of a quantum system will yield a given result. In its simplest form, it states that the probability density of finding a particle at a given point, when measured, is proportional to the square of the magnitude of the particle’s wave function at that point.[note 5]
Copenhagen interpretation - Wikipedia

From your link

One of quantum physics’ greatest paradoxes may have lost its leading explanation

It’s one of the oddest tenets of quantum theory: a particle can be in two places at once—yet we only ever see it here or there. Textbooks state that the act of observing the particle “collapses” it, such that it appears at random in only one of its two locations. But physicists quarrel over why that would happen, if indeed it does. Now, one of the most plausible mechanisms for quantum collapse—gravity—has suffered a setback.
Science | AAAS

Bohm’s Pilot Wave theory resolves all this and on second thought, has been making a comeback in physics.

I know about the snippets about Penrose, but I believe that instead of the current view that "observation causes a quantum collapse of “superpositions”, his theory of quantum collapse causing an instant of an observable threshold “event”, actually confirms Bohm’s Pilot Wave model and does away with the duality problem.

The matter is far from settled.

p.s. thanks for that excellent link

At first glance, I like the comprehensive illustrations that clarify the written descriptions. Looking forward to reading it.

Well said.

Then the infinite human ego takes over.

“Is by necessity speculative,” which is exactly why I believe we should take our own certitude with a grain of salt, and spend a tad more time trying to appreciate our limitations. That is our Physical Reality ~ Mind divide that is ultimately unbridgeable.

Then I come across tidbits where genuine experts point out that my misgivings are grounded , (perhaps teasers is more accurate, since this article accelerates beyond my comprehension in a hurry). For instance:

On Formally Undecidable Propositions of Principia Mathematica And Related Systems


Translated by B. MELTZER Introduction by R. B. BRAITHWAITE

“Kurt Gödel’s astonishing discovery and proof, published in 1931, that even in elementary parts of arithmetic there exist propositions which cannot be proved or disproved within the system, is one of the most important contributions to logic since Aristotle. Any formal logical system which disposes of sufficient means to compass the addition and multiplication of positive integers and zero is subject to this limitation, so that one must consider this kind of incompleteness an inherent characteristic of formal mathematics as a whole, which was before this customarily considered the unequivocal intellectual discipline par excellence.”

"Every system of arithmetic contains arithmetical propositions, by which is meant propositions concerned solely with relations between whole numbers, which can neither be proved nor be disproved within the system. This epoch-making discovery by Kurt Gödel a young Austrian mathematician, was announced by him to the Vienna Academy of Sciences in 1930 and was published, with a detailed proof, in a paper in the Monatshefte für Mathematik und Physik Volume 38 pp. 173-198 (Leipzig: 1931). This paper, entitled “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I” (“On formally undecidable propositions of Principia Mathematica and related systems I”), is translated in this book. Gödel intended to write a second part to the paper but this has never been published.

Gödel’s Theorem, as a simple corollary of Proposition VI (p. 57) is frequently called, proves that there are arithmetical propositions which are undecidable (i.e. neither provable nor disprovable) within their arithmetical system, and the proof proceeds by actually specifying such a proposition, namely the proposition g expressed by the formula to which “17 Gen r” refers (p. 58). g is an arithmetical proposition; but the proposition that g is undecidable within the system is not an arithmetical proposition, since it is concerned with provability within an arithmetical system, and this is a meta-arithmetical and not an arithmetical notion. Gödel’s Theorem is thus a result which belongs not to mathematics but to metamathematics, the name given by Hilbert to the study of rigorous proof in mathematics and symbolic logic.

Or to put it in simpler terms,

May 22, 2021 - Veritasium
Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant.

I powered through that video again. It’s got a bizarre attraction for me, and I’ve listened to it a few times, though I’ve definitely started it more often, than actually finishing. But when I’m in the mood, it’s got that magnetism of, I don’t know, perhaps driving by flashing lights around a car wreck, or perhaps a touch of intellectual porn, or something off in the mists of my mind.

In any event, listening to Gödel’s, what is it, 762 page long proof, that one plus one equals two, being described and then Gödel’s card game, and it overwhelms.

I simply listen and try to absorb the words and let my thoughts follow best they can, while other areas of my mind try bursting in. Such as Gödel’s numbers and card game of representing mathematical symbols/formulas as numbers and then manipulating the numbers to prove something about the symbols themselves, and . . .

Suddenly in a burst cinematic glory, the image of Gödel pops up as the master Gordian knot weaver. Best dang knots you ever did see. Then I wonder should I really be impressed with all this. It’s simply a Gordian knot. We know how secure those are. But then comes, the knowledge that all this underlies todays function computers, so I’m told, or at least these sorts of thoughts helped the human mind focus on building actual truly magical computers. Meaning that somewhere in all that mess, there is a there. But why does it matter. At least to me. I don’t want to be a Master of the Universe, I’m too preoccupied with being an element in the flow of Earth’s evolution.

What I believe is that much as we can do, it’s idiotic to obsess over mastering it,
and our self absorption in striving to find all the answers, in search of that ultimate answer to everything, it’s Faustian bargain, as demonstrated ad nausea.

The folly as witnessed by how we treat each other, this Earth and its creatures & varied biospheres, along with how we disregard simple honest facts in favor of hubristic doomed monument building.

Incompleteness only means lack of knowledge, not lack of mathematical logic.
Lack of axiomatic proofs doesn’t mean non-existence of proof, but lack of evidence, not proof of illogical function.

IMO, all mathematical algorithms in a physically dynamic environment become variable and local.

btw. the double slit experiment can be traced back and identify which slit a particular photon has traversed.
This has solved one “incompleteness” and proved that all particles on the left side of the receptor plate entered through the left slit and all particles on the right side of the plate entered through the right slit.

This holds true in the Bohmian Interpretation as well, but for different reasons.

I can well imagine my connection with the Earth as a site and origin of life and our modern way of communication.

Just think,
We have not invented anything that nature has not already put into practice or that may become manifest as an application of already existing potential.

Human inventions are all based on some natural law that has been observed, described, and put into practice. And what we think must be original, often turns out to be something that already exist in some form or another.

Who’d have thought that relatively simple organisms in nature could invent flight, water propulsion, anti-freeze, sonar, speech, communication, and self-organizing patterns.

We copy stuff from borrowed natural phenomena. After all Natural selection has had 3 billion years to test what works and what does not at a rate of 2 billion, quadrillion, quadrillion, quadrillion electrochemical experiments, starting with simple chemical interactions and preserving that which evolves and can stand the test of time.

That in itself is contained in a mathematical “probabilistic equation”;
that and the functional dynamics in nature are physical expressions (patterns) of “differential equations”.

Hell, Earth’s nature even built a nuclear reactor.

Sure, that’s the way we frame it for our human minds to grasps.

And although I know that I’m the center of my world, I, we are certainly not the center of Earth’s reality.

[quote=“citizenschallengev4, post:11, topic:10139”]
Sure, that’s the way we frame it for our human minds to grasp.

Yes and that frame is universally applicable. The human mind is capable of recognizing axiomatic truths. We call them universal constants, not because they are constant to humans, but they are universally constant.

We have made up a symbolic language to identify certain regularly repeating patterns that don’t change, regardless of the symbolic language.

And although I know that I’m the center of my world, I, we are certainly not the center of Earth’s reality.

You are only the center of your own reality. But that does not preclude your ability to observe reality as it generally presents to our range of perception.

[quote=“write4u, post:12, topic:10139”]
But that does not preclude your ability to observe reality as it generally presents to our range of perception.

There’s the rub.