Tegmark's Mathematical Universe

What is the final word on this?

If reality is a manifestation of Mathematics, or the patterning found therein, does it not make sense that what is most central to Physics about Math is that which is most essential to Math itself, or is in some way invariant? It comes to mind that there are precisely four normed division algebras, R, C, H, and O. Also, objects like E8 and the Mandelbrot Set seem to validate the External Reality Hypothesis, by existing apart from our discovery of them. But if nature is shaped by these mathematical objects as Lisi and I have suggested (respectively), then there are a host of other mathematical objects and invariant forms in the structure of Math - which also influence nature. The thing is; we first discovered a bunch of these things over the last 100 years, but there remain other invariants of Math yet to be discovered. However; we must assume that nature has already put them to use.

Phil Gibbs has a very nice concept to help filter all of this content, which he calls the theory of theories. Briefly; this idea states that all Mathematics applicable to Physics takes a role in shaping reality, where the entirety of all the theoretical bases for a given tendency contribute to its reality in a kind of path integral which grants physical reality to those notions whose basis is strongest. And of course; this would be meaningless if there was no internal patterning to unify the structure of Math, but the fact that Math is a congruent entity which hangs together on its own engenders a meaningful basis for Physics. In this sense the Mathematical Univese Hypothesis is a no-brainer. It is absolutely true, given that we include all of Math, even the part we have not yet discovered. But indeed; this rests on the ERH being true, in the sense that Plato envisioned - where eternal ideal absolutes shape the ephemeral reality - and on Math being that external reality.

All the Best,

Jonathan

I could point out..

The existence of the Octonions implies E8, which is simply O x O. Similarly the existence of Complex numbers somehow implies the Mandelbrot Set, which in effect illustrates their properties. But it could also be said that E8 is the culmination of the octonions, or that the Mandelbrot Set is the reason for the complex numbers to exist.

It is better, in some ways, not to imagine that such chicken/egg questions yield a final answer, but rather to understand that each is a piece of the puzzle, and that all of the invariant forms are important cornerstones of Mathematics, which serve to create meaningful order which can engender Physics. So I'll leave off there.

All the Best,

Jonathan

Taking things to the next level...

It is often imagined that things proceed from simpler forms to more complex ones, but if what counts is algorithmic complexity in a universe born of Math, this may be backwards. An idea I've played around with, that Fred Diether articulated quite well a while back, is that higher-order numbers are more basic - because they require fewer rules to define. S15 and the Sedenions may offer the closest thing possible to a blank slate, as there is no preferred direction or orientability and all 16 dimensions are on an equal footing. This is sort of like Math without rules.

But if we assert that our number system must be alternative, we get the Octonions; if we assert the algebra must be associative, we get the Quaternions; if we add the rule that it must be commutative, we are left with the Complex numbers; and adding another restriction gets us to the Reals. This makes the Octonions more fundamental, as well as more general, while the Quaternions, Complex, and Reals, are the product of adding more conditions, leaving a more restricted set of possibilities that are successively restricted cases of the higher-order types - which are algorithmically more basic.

All the Best,

Jonathan

MATHEMATICS ARE YOU

You are part of life, the Universe and everything. You and that greater whole have to be grounded in some fundamental bedrock that connects everything into a logical and unified whole. Most would say that's the role of the laws, relationships and principles of physics. But there's a deeper level yet. Mathematics are the ultimate foundation that make physics a logical (if not quite yet unified) whole. So ultimately life, the Universe and everything is based on maths. Maths is ultimately your reality. It's what makes you tick!

The Universe IS just mathematics according to physicist/cosmologist Professor Max Tegmark (Department of Physics, MIT). It's called the "Mathematical Universe Hypothesis (MUH)" or the "Ultimate Ensemble", one of those proposals for a 'Theory of Everything' (TOE), that ultimate theoretical equation so beloved by physicists that describes life, the Universe and everything. It will be so concise that it can be printed on just the front of a tee-shirt. Tegmark's mathematical universe hypothesis is: our external physical reality is a mathematical structure. All structures that exist mathematically exist also physically. That is, the universe IS mathematics in a well-defined sense. Mathematics has an external reality, and since everything is built from the ground (i.e. - mathematics) up, everything ultimately is mathematics and therefore can be expressed in that ultimate theoretical TOE tee-shirt equation.

Mathematics is the universal language. Whether you're a Frenchman or a Chinaman; an Englishman or even ufonauts like those alien LGM (Little Grey Men); a Klingon or a Romulan; you understand the Pythagorean Theorem and the quadratic equation; topology and the calculus.

The most fundamental science is physics. That's the bedrock on which chemistry is formatted. The earth and space sciences are in turn supported and explained by those two building blocks. All of those collectively form the foundations of the biological sciences, which in turn support anthropology, psychology and the other social and behavioural sciences. Even economics and the arts have ultimate foundations in mathematics.

But what supports physics? Mathematics, that's what. Ultimately that's where it all begins. The Universe (including life and everything) is mathematics. You exist inside of geometry. You are receiving information about life, the Universe and everything encoded in mathematics; it takes mathematics to reveal the information. You cannot come to terms with understanding space and time, matter and energy, and the four (or more) fundamental forces that govern the Universe, hence ultimately you and your surroundings, without resorting to maths.

Your day is constantly filled with how much, how many, and how fast - mathematical relationships. 'Where' is maths; 'when' is maths; 'what' is often pure maths. You may not be a physicist, but economics probably rules your roost. There's gambling (even if just on the stock market or getting away with running a red light) involving probability theory. Every day in every way you add and subtract and multiply and divide numbers. You even do fractions! Your calculator may crunch the numbers, but you press the buttons.

Music and sounds in general play a massive role in our lives. Acoustics, harmonics, sound waves, and the like are all expressible in, and based around, mathematics. Ditto for navigation and GPS and related.

Now think of the mathematics supporting the physics (or its applied alter ego, engineering) behind your home, your transport, your entertainment, your comfort conveniences, and what goes into making you able to get through your day. What holds all your bits and pieces together and holds you to the ground yet doesn't allow you to go through it can be expressed in equations? What mathematical physics fuels the sun that ultimately gives you your daily bread? What mathematical physics keeps your home planet a goldilocks planet, not too far away from, or too close to the sun with an atmosphere over your head? 24/7/52 you are governed by time and space; matter and energy, all of which have reality as mathematical constructs. And where would sports teams*, NASA and the military be without the basic mathematics behind the basic physics that guide and govern their activities?

There's another kind of mathematical universe apart from the one promoted by Max Tegmark, though maybe they are actually one and the same. That's my hypothesis. There's another way of looking at this. There's another possible, even probable, Mathematical Universe - the Simulated Universe. Could these two universes be one and the same?

Firstly, why is a Simulated Universe our probable Universe? Well, for the exact same reason that while you suspect there is just one real Universe, the one real Universe the really real you lives in, you would be aware that Planet Earth in that really real Universe has an intelligent human population that has evolved computer technologies and has created thousands upon thousands of virtually real simulations, both for the purposes of instruction (say astronaut flight training) as well as for entertainment (video games). The ratio of virtually real landscapes to really real landscapes is therefore multi-thousands to one.

Further, in most cases there are thousands upon thousands of copies of those simulations, a sort of Multiverse, where say a character in one video game has thousands of 'clones' because there are thousands of copies of that game. That character of course couldn't meet any of his or her or its identical copies, which is probably a good thing. However, if you could ask that character whether they felt they were really real or simulated, they would of course answer really real not knowing or suspecting that a human being was their creator and the creator of their simulated landscape.

Go one level up from Planet Earth and humanity's numerous simulation creations and extrapolate and the odds are high that someone or something out there, a Supreme Programmer, created a simulation that's our Universe. There are numerous copies of this video game simulation called say "The Life and Times of Planet Earth" created by this unknown and probably unknowable Supreme Programmer, and thus there are really numerous copies of you, but fortunately only one copy per game! Your day-to-day reality is just a virtual reality because you don't really exist in the way you think you do.

Another way of thinking about the numerous copies of the video game "The Life and Times of Planet Earth" is that this amounts to the concept of Parallel Universes. In another copy of "The Life and Times of Planet Earth" another copy of you has led a different life and lifestyle to the you that exists in your copy or version of "The Life and Times of Planet Earth".

Now, the interesting bit, IMHO, is what if our Universe or Max Tegmark's Mathematical Universe which is also our Universe was just a Simulated Universe; a virtual reality computer software generated Universe? Well, what is computer software? Computer software is just bits and bytes, ones and zeros, binary code, or in other words mathematics. You can construct life, the Universe and everything via mathematics by constructing or programming appropriate computer software. Ultimately a video game 'Universe' or landscape is just mathematics. An astronaut's training simulator is just a mathematical construction. If you are a computer software generated, simulated being, inside a virtual reality, then you are a mathematical construction.

What's the appeal of a Simulated Universe? It explains a lot that's currently unexplainable.

Why are all electrons (or positrons or up and down quarks, etc.) identical? Because all electrons have the exact same binary code, that's why. Forget vibrating strings as the reason. String theory isn't even in the hunt. Any and every anomaly is explained as easily as "run program" as there is no such thing as the concept of impossibility in a simulation or a video game. Joshua can indeed make the Sun and the Moon stand still in the heavens! You can even have a virtual reality afterlife! In fact, for the physicist, a Simulated Universe scenario should be pleasing since in fact there are two separate sets of incompatible mathematical software running the Simulated Universe - gravity software and quantum physics software. I bring this up because physicists have been trying to marry those two branches of physics for decades now into a Theory of Everything, and haven't scored a run yet.

In conclusion, our Universe is a Mathematical Universe; a Simulated Universe is a Mathematical Universe. Therefore, it's possible or even probable as I noted above, that our Universe is a Simulated Universe and you therefore live in a virtual reality landscape that exists as a mathematical construct!

*There's an entire book, for example, devoted to the physics of baseball, and no doubt many "How To Play..." books focus on the physics behind the scenes and the mathematics behind the physics. Baseball can be reduced to pure mathematics apart from the mathematical physics relating to bat and ball, which will come as little surprise to most baseball fans, players and managers. There's percentages this; statistics that, all of which make baseball about the most mathematical oriented sports on the ground.

I argue that the Universe is fundamentally logic, not maths. What do you think?

As Wittgenstein puts it: ''6.22 The logic of the world, which is shown in tautologies by the propositions of logic, is shown inequations by mathematics.''

http://www.academia.edu/8991727/Phenomenal_World_as_an_Output_of_Cognitive_Quantum_Grid_Theory_of_Everything_using_Leibniz_Kant_and_German_Idealism

In order to perform any mathematics, one must first have a surface upon which one can depict symbols of value. This surface need automatically destroys all mathematical logic. For instance, if one inserts a 1 anywhere on the surface, one is indicating that the surface has no value even though the surface obviously covers a greater area than the symbolic 1 does.. When the mathematician inserts a zero on the seemingly valueless blank surface, he creates a beguiling abstraction that has nothing to do with reality. In effect, the mathematician is trying to organize ordinary human triadic perception. There is 1. There is 0. They can be represented on a surface that has no value. This translates into: There is Heaven. There is Hell. There is Purgatory. There is the Id. There is the Ego. There is the Super-ego. Unfortunately, although there is indubitably real quanta, there is no real nothing, therefore there cannot be a anything else but quanta wherever one looks.

Joe Fisher

Joe,

"...therefore there cannot be a anything else but quanta wherever one looks."

True. But can quanta cease to exist? Or is it eternally existing?

Akinbo

Dear Akinbo,

Quanta has to be eternal.

Joe Fisher

Dear Joe,

As I just told Jim in a post, unless the Universe exists eternally, Quanta can perish. Quanta cannot outlive the universe or exist before the creation of the universe.

Regards,

Akinbo

You are absolutely correct Akimbo. Quantum singularity has to be eternal. The mathematical duality of zero and 1 is utterly illogical. And for physicists to pretend that NOTHING exploded in the Big Bang a finite time ago which obliterated all none of nothingness and produced all all of somethingness is utter codswallop.

Joe Fisher

The only thing I know is that I exist and so do you Thomas.

Joe Fisher

how do you know?

Because it is impossible not to know.

So knowing and existence are identical?

It seems that Max Tegmark is equating mathematics with patterns of information that comprise the external world.

However, an interpretation of such patterns could only exist relative to a conscious mind perceiving them.

I must be misunderstanding something since this theory appears to contradict itself, as a static reality would need to change in order to create any illusions in the first place.

According to Max Tegmarg, quantum suicide experiment can make only the one performing the experiment realize that there are parallel universes(if any),why only the one performing it?

I agree with Tegmark's MUH, and have written a paper defining a class of mathematical structure, and a particular mathematical set, which seems to have emergent properties matching our Universe.

The set has quantised space and time which are themselves emergent, and emergent phenomena such as spacetime warping consistent with gravity and dark energy. It has early behaviour similar to inflation. It dynamically creates universes with three space dimensions and dark matter. The dark matter feature constitutes a fifth level in Tegmark's Level IV Multiverse, which makes this mathematical set more likely to be the one we are in.

I submitted it to Foundations of Physics citing Tegmark's paper, and received a strange response: "The author of this manuscript fails to make clear how his/her work relates to current discussions in the foundations of physics. This is not a judgement about the quality of the contents of the submission, but, regrettably, does place the submission outside the scope of Foundations of Physics. Perhaps a theoretical physics journal would be more suitable?"

I would appreciate some feedback, and have included the paper as an attachment.

Yours sincerely,

Ben Edmundson

Here is a link to the paper. I think it needs to be downloaded to see the video portion.

https://www.dropbox.com/s/3d5yr6otzv9asor/Emergent%20Cosmology%20from%20Quantised%20Spacetime.pdf?dl=0

Hello,

I have made a 26 minute video to explain my version of the MUH on my YouTube channel. It's called 'Universe on a T-Shirt AKA How Nothing = Everything' - Meat on the Bones of the Mathematical Universe Hypothesis. Link below:

Universeonatshirt

The hypothesis predicts that:

a) Dark Energy is a warp caused by Entropy information, just like Gravity is a warp caused by Energy information.

b) One dimension of Space is warped by Energy and Entropy information - in the extreme cases forming Black Holes and Cosmic Rips, which each dynamically add a Space dimension, forming 3D space.

c) This 3D Space further warps to an infinite dimensional space, Matter in these higher dimensions would seem like Dark Matter to us, and the fractal structure means the infinte copies make this type of universe most likely, so we are in a typical universe.