Suchness and mathematical structures

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Suchness and mathematical structures

Postby hyksos on December 16th, 2019, 8:29 pm 

This article will be about the topic of whether the universe is a mathematical structure or not. This topic has ramifications in metaphysics and philosophy, even religion.


Max Tegmark and modal realism.

Tegmark is the loudest advocate for all of reality being a mathematical structure. He has said that if you hold a rose in your hand, that it is nothing more than a "ball of quarks and electrons". Electrons don't have any existence beyond a "list of quantum numbers" that characterize them. By substitution, a rose in your hand is a very large list of numbers, with no content beyond those numbers. In some interviews, Tegmark has toyed with the idea that the universe we are in is a structure called a pseudo-Riemannian manifold.

Sean Carroll

Carroll has asserted that the Big Bang was some kind of saddlepoint in spacetime. Questions about "What happened before the big bang?" are deemed incoherent, as there was no time "prior" to the Big Bang. Instead, Carroll claims that time was, in some sense moving backwards prior to that saddlepoint we call the Big Bang. In lectures, he has invoked a metaphysical principle called `The Causal Closure of the Physical`. This works in tandem with his claims in interviews that is something does not interact with the earth, that is equivalent to it not existing. A central pivot in Carroll's lectures is that the entire universe can be described by a single quantum Hamiltonian equation, denoted H.


So is our universe, indeed all of reality, a mathematical structure, as asserted by Tegmark and Carroll? If it were a mathematical structure, then questions about "Where did it come from?" are made null and void, since mathematics in some sense is not "created" but pre-exists existence itself.

I will be rephrasing the question instead as , given what we know about the universe and its structure, how likely is it that it is a mathematical structure?

I adopt a strong stance on this issue : it is very unlikely that our universe is a mathematical structure. Our universe exhibits a property I call "SUCHNESS". What this SUCHNESS means exactly cannot be described in a neat paragraph. Instead the reader must join me in an adventure of comparing universes that could exist, to the one we actually inhabit. After these examples are thoroughly covered, can I begin to state with any coherence what SUCHNESS means. This will be done afterwards.


Not Our Universe.

1.
By the late 1970s, physicists working in quantum field theory were uniting the various forces of nature in a framework now referred to as the Standard Model. In the early 1980s, a theorem was postulated that certain invariant symmetries require that fundamental particles are also divisible into more structures at all smaller scales. That indeed, all particles must exhibit fractal structure at all scales. This property was later dubbed "Quantum Fractality". Experiments at SLAC and Fermilab confirmed some early predictions of Quantum Fractality. John Voga, Srivinda Narayan, and Natasha Milne were awarded the Nobel Prize in 1996 for their discovery of the initial equations predicting Quantum Fractality.

2.
Data from the Planck orbiting telescope was producing ever better maps of the CMBR, and Hubble telescope data was giving better data for both active galactic nuclei and pulsars. This data showed that out universe exhibits positive curvature. Positive curvature indicates that the universe eventually folds back onto itself, forming a kind of large-scale "bubble". An idea was proposed from eternal inflation, that each bubble gives rise to other exponentially expanding bubbles in small subregions, and that these bubbles will form even more bubbles. The universe at the largest scales is expected to exhibit fractal structure, as each bubble gives rise to ever more bubbles. Russian quantum cosmologist Leonid Tkachev had already suggested that our local universe is a patch on a much larger "bubble" of spacetime, and that the CMBR would give telltale signs of this positive bubble curvature. The data matched Tkachev's predictions, and he was awarded the Nobel Prize in 2008.

3.
Danish physicist Stefan Hawkins was working in the unification of quantum mechanics with general relativity, and was finding equations to describe the entropy of black holes. Hawkins discovered a principle he dubbed "Singularity Imprinting". It predicts that if an observer falls past the event horizon, that as they approach the singularity, they will see the entire history of formation of the black hole as they approach. Indeed, it is expected that the inside of a black hole is a very complex place, containing a kind of hologram of the entire history of the object that eventually formed it (usually a star). So out of all forms of matter in the universe, a black hole has the most complex internal structure.

4.
At IAS at Princeton, American physicist Bearo Berenstein had come to a similar conclusion as Hawkins, but instead of the singularity, he found that spacetime will repeat at all scales approaching the outside of the event horizon, forming a kind of "Fractal firewall". Berenstein's equations matched those of Tkachev's. As if a black hole is a kind of "local mini universe" inside the larger universe outside it. This was strong evidence that our universe is actually just a large fractal structure, repeating infinitely at all scales.


Our actual Universe.

The last four paragraphs, (1) (2) (3) (4) are fabricated lies. None of those theories exist and none of those people are real. I concocted them up in my imagination. None of the claims made in those paragraphs match what is observed. In contrast to the faux universe described in those paragraphs, I will now enumerate the actual properties of the universe we actually live in.

Planck Scale

THere is a particular size at which matter cannot probe, called the Planck Scale. If a particle of some kind or another, tried to probe distances smaller than Planck, it would need a wavelength smaller than that distance. But the energy of a particle scales with its wavelength. The samller the wavelength, the higher the energy. A particle with a wavelength smaller than 1.5 x10^-35 meters would have so much energy that it would immediately form into a black hole. So you say "Oh well that's okay because black holes have complex internal strucutre!" except no -- they don't.

No-Hair Theorem

The only properties a black hole can have are charge, rotation, and mass. No black hole can have any other parameters. This is a clean prediction of something called the "No-Hair Theorem" , which is universally excepted by all working physicists today. For the purposes of this article, black holes do not have any internal structure.

Flatness

The universe we live in is not positively curved, nor does it exhibit negative curvature ("hyperbolic" curvature). Instead, all data collected by human civilization shows that our universe is geometrically flat. Spacetime does not flare out at greater distances, nor does it "fold back onto itself" in some kind of bubble-like geometry. This is not mere theory. This is textbook cosmology with a universal consensus among cosmologists.

Structure ends.

The largest known structures in the universe are collections of galaxy clusters. The Sloan Great Wall is a contender, and something called Laniakea is another such structure. Whether one is the largest depends on one's definition of "structure" regarding clusters. However, all working cosmologists today beleive that this is where structure "tops out" -- as it were. Beyond those scales, 10^26 meters and larger, it is expected that no further structure will be found in the universe. At scales of 10^27, the universe is a featureless fog.
Image

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https://i.imgur.com/HaUgPA7.png


SUCHNESS

Us humans on earth live on a physical scale around 1 meter. For us, the existence of structure is a foregone conclusion. Everything science has told us about our universe shows us clearly that structure is not given a-priori. Instead all this interesting structure (if it exists at all) must occur in a peculiar interval, between 10^26 m at the large, and 10^-36 m at the small. Outside this peculiar, special interval of sizes, there is no structure and there can be no structure of any kind. Dare I say that this interval of sizes is inexplicable?

Our universe is not a fractal. Instead it is a bizarre situation of interesting structure squeezed in an interval , flanked on both sides with solipsistic faceless featureless existence. At large scales : a fog of galaxy clusters with no rhyme or reason. At the tiniest material structures it is a featureless flat piece of a quantum wave. Attempts to game the system at small scales, causes the universe to opt out, forming a black hole, which lacks all features of the particles that were used to form it in the first place. (c.r. The No Hair Theorem). It is not merely the case that spacetime at such scales cannot be "understood by the human mind". Rather physical law appears to proactively prohibit such probing.

If the universe were fractal, then structure would be given a priori, de novo. There would be structure at human scales because, as it would be said, there is structure at all scales. Structure is inherent; given, because the universe is a fractal. We humans would be a particular structure at our scale, arbitrarily chosen from a continuous spectrum of scales. Arguments about whether the universe is a mathematical structure or not would be definitively and concretely lain to rest. If the structure appeared at all scales, the universe would be a fractal , and by definition, a mathematical structure. As stated earlier, a mathematical structure requires no explanation for its origins or its properties. Math exists and always existed.

Unfortunately, this is not observed. The laws of physics maliciously select a particular interval of scales to form structure, and then go about systemically disallowing any structure outside the magical inexplicable interval. Our universe is not a fractal, and it has parameters that have been tweaked to peculiar settings -- this is Suchness.

A universe with suchness is mysterious and begs the question as to the peculiar selection of its parameters. The "come from?" questions come snapping back to the center of rational discourse.


Information Content

The Holographic Principle was discovered when the thermodynamics of black holes was subjected to the conservation of Information. The fundamental claim of the Holographic Priniciple is that the information content of a region of spacetime is bounded above by its area. The shock-and-awe of this discovery is that the information content does not scale with volume, but instead scales with the area of an enclosing surface outside the region.

In regards to the topic of Suchness, we see again that the universe defies mathematical continuums. In real functions, there is no limit to the amount of "information" that can be packed into an interval on the real number line, and hence no limit to its repeated structure. Our universe does not do this. Our universe places a tight upper bound on the amount of information that can be squeezed into a location in spacetime. You might still be thinking that the bound scales with the volume, as common-sensical geometrical thinking would demand. But it does not. For all we know about the world, the information content in a region of spacetime scales with the area.

The metaphors given to us about mathematics are metaphors of continuous real number lines, fractals, and infinite indivisibility of calculus and its epsilons and deltas. These metaphors are useless. Instead the universe appears as a discrete structure that 'stores' some finite amount of information, denoted S, (sometimes written dS). In mathematical structures, information content can increase in a system as chaotic orbits are followed. The classical example is the formation of turbulence in gasses and liquids. At the fundamental scales, our universe prohibits the continual formation of information, and instead ops to ruthlessly conserve S. While turbulence is seen to form in liquids and gasses, it is ultimately an approximation. The approximation is "useful" for engineers since the systems-under-study are comprised of trillions-of-trillions of molecules.



Origins of Structure

Look around you. The objects around you , the light the surfaces and the air. These are all composed of baryonic matter. Given quantum field theory, the question about where this matter "came from" is fairly straightforward. Energy and mass are equivalent and interchangeable. Physics can explain where a featureless gas of baryonic matter "came from" quite easily. QFT allows energy to be stored in fields, and when those fields undergo phase transitions, nothing stops them from forming particles with mass. The hitherto energy stored in the field is converted into the mass of the particles created by pair production. This question is done and done.

The situation here is ironic. Science is very good at explaining where matter "came from" but has a terrible problem describing why it has structures like galaxies and stars. Bald QFT could explain a universe which is a big cloud of gas and nothing more. That's the easy part. The hard part is explaining why there are galaxies and stars. You might be under the impression that this is totally understood but it totally is not. Modern science in 2019 supposes that there are galaxies that formed in the early universe due to the initial clumping of Dark Matter. That sounds straightforward because you have heard it many times. Nothing about it is straightforward. Nothing about Dark Matter is understood by science. Dark Matter does not fit into the standard model. Some professors will claim it is some weakly-interacting massive particle unknown to the pantheon of the S-M, while his colleague across the hall swears it must be tiny primordial black holes.

This revelation has to come to you like ice water down the back of your shirt. Science does not know why there is structure in the universe, at all. In 2019 we have a hodgepodge of educated guesses.

Suchness is a collection of metaphysical puzzles. Suchness is not a rehashing of medieval questions of "come froms". It is a form of scientific honesty.

Why information conservation?

Why structure?

From whence structure?

Why structure at particular scales and not others?

None of these deep enigmas are answered by waving of the arms by Tegmarks and Carrols who wipe them away with "mathematical structure!". Our universe is not a bubble plucked out of a set of pre-given Hamiltonians. Our universe is still inexplicable in the 21st century.
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Re: Suchness and mathematical structures

Postby hyksos on December 16th, 2019, 8:39 pm 

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Re: Suchness and mathematical structures

Postby hyksos on December 16th, 2019, 10:29 pm 

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Re: Suchness and mathematical structures

Postby hyksos on December 16th, 2019, 10:32 pm 

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