Tegmark's Mathematical Universe

The human term 'number' and the concepts of a counting system are descriptions of difference between topologically whole areas. 'Two fish' decribes two discreet entities within a set 'fish'. What we call number theory is the detailed analysis of how areas of difference within topologically whole entities organise efficiently within that entity.

The differences described however are not the result of human numbering, human numbering is a classification of already existing areas of difference within a given set. A number of fish existed, in an awful lot of discreetly different ways, before the human number system. If we insist that the different areas only existed as areas of discreet difference after they were perceived to, we are what is commonly termed 'creationist'.

It is accepted that the universe (by definition) is a topologically whole entity. Physics is the analysis of the areas of disceet differences, and how they interact, combine and divide within the topologically whole universe. In physics these areas of difference, and the way they 'organise' are treated as the results of naturally-occurring phenomena. Physics has always used mathematical tools to analyse these 'physical' areas of difference, and many words have been written about the miraculous coincidence that the language of mathematics is so well suited to do such analyses.

but instead of numbers being miraculously suited to describing the universe; what WE call number is how the universe 'describes' its differences.

the relationship between the 'naturally-occurring areas of discreet difference in the topologically whole universe, and their behaviours' and 'human numbering system, number theory and mathematics' is the equivalent of the relationship between 'the naturally-occurring force between masses' and what we call 'the theory of gravity'.

relationship N->n

equivalent to

relationship G->g

where the capital letter represents a natural phenomenon and the lower-case represents the human analysis of the natural phenomenon.

The implications are that the naturally-occurring processes that we call 'number theory' will result in the naturally-occurring processes that we call 'quantum mechanics' and further to all other naturally occurring processes that we eventually call 'physics'.

If the universe IS a topologically whole entity, and everything within that universe is composed of various fractions of the whole: then inflation is in fact division and subdivision. The expansion is in the 'numbers' ie the discreetly different areas within the whole.

it is not a set of sets, which is then a set of set of sets... the set of sets is absolute by definition and any introduction of further sets merely shows subdivision of the original.

[inserted note for Prof Schiller, with added lolz --> the term 'discreet difference' is used to indicate that although there may well be a continuum of difference it's only when such differences are discreet that they interact as differences. i love my analogies, so think of a magnet. there is a continuum between N and S (the physical object is a whole unit), and the differences in polarity gradually converge to the grey areas where we can't tell if it's more N than S or more S than N... but when the interactions of each pole are examined, we see they act in discreetly different directions. The continuum isn't discreetly different, so it isn't analysable through number. As soon as we're analysing using number we're separating it into discreetly different interactions. A curve on a graph is a continuum, but as soon as you wish to examine the value of a point on that line, you are separating it discreetly from the continuum of line before and after./note for prof schiller]

It is eminently testable as it predicts that 'number theory' and 'quantum mechanics' will become increasingly converged (ok, all areas of physics... but I say quantum mechanics because it's at the narrow end of the decreasing complexity).

the prediction is: more and more 'coincidences' such as the riemann-zeta function will be 'discovered' at the LHC and other high-energy early-universe particle experiments. (In fact anywhere all naturally-occurring topological wholes being subdivided over time, when analysed mathematically should show evidence's of 'strange' similarities between each other, whether it's in physics, biology or any other field).

still with me?

:P

[oh... and if space, energy and matter really are just expressions of naturally-occurring mathematical functions governing the discreet fractions of a single existence... then shouldn't there be a new unit of existence? how about: Subatomic-To-Universal-Functions ... :D ]

I will list some observations then some theories which try to explain them, including my Gravity For Patterns theory which explains the Copenhagen Interpretation of quantum physics as an approximation of the most infinite version of Manyworlds.

DEFINITION: Laws-of-physics is the statistical behavior of a subset of the universe, usually the subset closest to Earth.

OBSERVATION: The only known laws-of-physics is very accurately approximated by small math equations.

OBSERVATION: The only known laws-of-physics has arbitrary-appearing (not like pi or e or integers) constants in its equations.

OBSERVATION: The only known laws-of-physics has never been observed changing (same equations), or only a small amount.

OBSERVATION: When in superposition, 1 particle/wave can be in thousands of places at once without being between those places, and when 1 of those thousands of places is touched, 1 gets more dense and the others get less dense.

OBSERVATION: Quantum wavefunctions can be split by a half-mirror and reassembled by the same process in reverse at a different half-mirror. Its branches can cancel each other out or strengthen each other, depending on the angles and number of bounces etc.

OBSERVATION: More often than would happen randomly or through normal communication or observing the environment etc, there are small statistical dependencies between the brains of people and/or quantum physics devices. See the "main results" list at http://noosphere.princeton.edu for the results of those experiments.

OBSERVATION: The E8 math structure very accurately approximates the only known laws-of-physics. It is many rotations of a 57-dimensional shape in 248-dimensional space, where each dimension represents a quantum particle/wave type. There are levels of organization built on top of levels between 248 particle types (including some not observed) and the small number of types at the top of the Standard Model.

THEORY (by Max Tegmark): "All structures that exist mathematically exist also physically."

LOGIC: If Tegmark is right then: For any subset of the universe, there are an infinite number of unique ways to simulate that subset and recursively simulations of simulations to infinite depth, all averaging to nothing because of the symmetry of math.

DEFINITION: Pattern is any subset of math. A wavefunction or any subset of it is a pattern. A statistical similarity between 2 patterns or subsets of them is a pattern.

THEORY "Gravity For Patterns": The universe is the set of all possible wavefunctions of patterns instead of simply wavefunctions of particles/waves, and patterns attract patterns more when they are more similar.

LOGIC: If Gravity For Patterns is right then: Collapsing a wavefunction is the superpositioned parts falling toward each other, pulled by the mostly-collapsed parts (the parts of reality they agree on) being similar patterns. The E8 shape is 1 of many possible shapes, and (possibly, but not necessarily practical) new shapes can be rotated in while E8 is gradually rotated out, to locally change the laws-of-physics to any arbitrary pattern you can amplify through chaos-theory.

THEORY: The "statistical dependencies between the brains of people and/or quantum physics devices" are caused by such a rotation between E8 and whatever pattern fits the combination of brainwaves/devices which become statistically dependent, and that is probable to happen because infinite recursions of "Gravity For Patterns" (patterns about patterns attracting) will pattern-match any 2 patterns in 2 brains and ***exponentially*** increase the chance such patterns will connect through the multiverse. Its exponential because the recursion of patterns always finds an effective path between the 2 patterns. It finds an infinite number of other things, but the gravity part gradually changes that, and a small change goes exponential because of the recursion.

Gravity For Patterns is a theory of everything, including how the laws-of-physics form and how to locally change them using small amounts of energy and large amounts of intelligence.

Hello.

I found this site yesterday and I have to say tha I´m very glad to find people who share my own interest.

I´m deeply interested in Tegmark mathematical multiverse hypothesis. Looking at the notion of existence, this concept does not need to be absolute, but local. I mean, rather than assuming a mathematical nature for existence, and then to consider life as a fortunate epiphenomenon in some of the mathematical universes, we instead may consider as criteria for existence the existence of some observing entities within the universe, that is, the existence of life.

looking at the preconditions for life and evolution I found that the absence of contradictions must be a pre-requisite for life, as well as smooth macroscopic phisical laws, both conditions may demand a mathematicity in the candidate universe. Also , due to the intrinsic nature of life and natural selection, it is necessary, in the universe, a direction of increase of entropy to create an arrow of time:

I explain all of this here:

http://docs.google.com/View?id=dd5rm7qq_198c4xrrx6q

More details abut the arrow of time,entropy and life:

"Arrow of time determined by life´s easier direction for computation":

https://docs.google.com/present/view?id=0AW-x2MmiuA32ZGQ1cm03cXFfMTQyZDhkamh2Yzg&hl=es&pli=1

Dear All,

The absolute mathematical truth of

">zero = i = infinity](https://sridattadev-theoryofeverything.blogspot.com/2010_01_01_archive.html

) can be deduced as follows as well.

If 0 x 0 = 0 is true, then 0 / 0 = 0 is also true

If 0 x 1 = 0 is true, then 0 / 0 = 1 is also true

If 0 x 2 = 0 is true, then 0 / 0 = 2 is also true

If 0 x i = 0 is true, then 0 / 0 = i is also true

If 0 x ~ = 0 is true, then 0 / 0 = ~ is also true

It seems that mathematics, the universal language, is also pointing to the absolute truth that 0 = 1 = 2 = i = ~, where "i" can be any number from zero to infinity. We have been looking at only first half of the if true statements in the relative world. As we can see it is not complete with out the then true statements whic are equally true. As all numbers are equal mathematically, so is all creation equal "absolutely".

This proves that 0 = i = ~ or in words "absolutely" nothing = "relatively" everything or everything is absolutely equal. Singularity is not only relative infinity but also absolute equality. There is only one singularity or infinity in the relativistic universe and there is only singularity or equality in the absolute universe and we are all in it.

A great scientist once thought what would it be like to travel at the speed of light and came up with the theory of relativity, now it is our time to wonder on what would it be like to be the space-time itself or experience the singularity and realize the absolute truth.

Truth is simple, accepting it is not.

Love,

Sridattadev.

Dear All,

Absolute Truth

Love,

Sridattadev.

Max Tegmark, and others that support his contention that the Universe is mathematical in nature, will be interested in a paper published in July/August 2011 IEEE Potentials.

The paper, titled, "A Methodology to Define Physical Constants Using Mathematical Constants" supports Tegmark's contention, but such was not mentioned in the paper; it had to remain as non-controversial as possible. The IEEE link is below.

Methodology to Define Physical Constants

It is on the second page of the Contents. For those without IEEE membership, the postprint can be read/downloaded from my web page.

Methodology Postprint

"Level 4: Other mathematical structures give different fundamental equations of physics" (Tegmark)

To start with our own universe--

Maybe it's close to the point where our fundamental equations of physics are supported by a chosen mathematical structure, but this chosen mathematical structure supports no fundamental equations involving dark matter or dark energy.

It is possible to search for a different mathematical structure that loses nothing gained so far with this chosen mathematical structure, and which may support new fundamental equations involving candidates for dark matter and dark energy.

Something like this has happened before. Abraham Robinson used a tool from logic called enlargements to enlarge the mathematical structure of standard analysis into the mathematical structure of nonstandard analysis. In the process, a new object appeared-- the monad.

To paraphrase p.55 (Non-standard Analysis, Robinson)-- If R is the standard model of Analysis and *R the nonstandard model of Analysis, every mathematical notion which is meaningful for R is meaningful for *R. Every mathematical statement (e.g., every fundamental equation of physics) which is meaningful and true for R is meaningful and true also for *R....

But in the nonstandard mathematical structure, one can say more. It's within the nonstandard statements where one could search for those that involve dark matter and dark energy.

For example, in a monad of spacetime there is a structure I've been calling the Born infomorphism. (The latter term comes from the book Information Flow: The Logic of Distributed Systems by Barwise and Seligman. The distributed system in this case is the monad of spacetime, within which there is as nonstandard past and a nonstandard future. Due to the Born infomorphism, at the time of "now" within the monad there exists a perfect translation from language about nonstandard past into language about nonstandard future.)

Wish I could have made that deadline for the contest about time.

http://www.wexedesign.com/theBornInfomorphism.pdf

link

link

Some notes on the Born infomorphism

Tegmark do not distinguish between "mathematical" and "physical".

Change for example is physical reality

numerical order of change (time) is a mathematical reality.

He thing physical universe is a set of mathematical equations what is not more than a bed joke.

Hi all :)

Please excuse my largely lay knowledge of the subject at hand. I am currently researching Tegmark and Godel as part of a thesis in the literary theory philosophy of mathematics.

I am in agreement with you regarding the unsatisfactory nature of Tegmark's CUH when confronted by the Incompleteness Theorem. However, a 'devil's advocate' question remains to bother me:-

Why is it not possible that we are simply updating mathematics, and that Tegmark's view is now simply more contemporaneous than others preceding it, including Gödel's Theorems? Could there not be a form of mathematics without the restrictions of Gödel's theorem, which would then make all those unattainable proofs available to us?

Of course, the fact that mathematics is itself able to be updated would negate Tegmark's frog perspective and further confirm Godel's Theorems, but I can't help feeling that I'm missing something here.

Hi Anon,

Yes, I agree we've all been missing something, and important. It's why can't we derive maths from logic, and why do all systems of logic, and predicate calculus etc, (representing 'nouns'), ultimately fall to paradox.

I think I may have found why, but you have to dig really deep for the fundamental wrong assumption. Check out my conversation with Georgina on 'Much Ado..." which discusses the most basic pretext; a = a.

I've suggested this cannot be a valid physical proposition without a wavy equals sign, only metaphysical. This is consistent with Godels finding. My essay itself also discusses the 'hierarchical' nature of logic (propositions and compound propositions) and also maths, which we've ignored. ('position' counts, as even in the Mayan system, which was way ahead of the Greeks and Romans).

I've proposed that causal relativity emerges from such 'non-absolute' background relationships.

Best of Luck

Peter

It could be there is no "bird's eye view" of reality and perspective/knowledge is inherently subjective, including math. Which is reductionism and a form of perspective.

When we combine perspectives, it's like all the colors running together as brown, or all light as white. Leaving the camera shutter open gives you more information, but blurs the picture. Information, being transmitted by energy, cancels out.

The presumption is that information can be distinguished from the energy manifesting it. Which is about as illogical as the opposite; energy bereft of information.

Consider that billions of years of evolution provides complex biological fauna with two primary systems; One, the central nervous system, to process information. The other, the digestive, respiratory and circulatory systems, to process energy. Mathematicians are simply way over on the mental side of the spectrum. Ask the rest of society how important energy is.

The Mathematical Universe of Pythagoras and Plato may be nothing more than wave modulation... we do it all the time, modulating radio waves according to mathematical functions that our receiver can recognize (AM, FM, FHSS, wifi...).

We need a basic electromagnetic 'wave' which is a unit of Planck momentum, the velocity of this wave which is of course 'c', Planck time (a wave has '3 dimensions'; momentum, velocity and frequency = time) and God's tel number - the fine structure constant alpha.

Particles become mathematical functions that modulate this Planck momentum wave.

I demonstrate this with a calculator that solves the natural constants to 10 digits with CODATA 2010 precision using;

1. c (exact value)

2. Planck time (derived from vacuum permeability - exact value)

3. Planck momentum (derived from Rydberg constant - 12 digit precision)

4. alpha (user input - 10 digit precision)

constants online calculator

Atomic orbitals become photons trapped as standing waves (albeit of opposite phase), atoms are the sum of these physical orbitals. Gravitational waves are also standing waves of Planck momentum. There is no need for an electric or gravitational force.

gravitational wave online calculator

Cheers,

Malcolm

Quoting Lubos Motl

"However, I am confident that we pretty much know that this "seemingly infinite" process inevitably stops at some point - the Planck scale. There are no distances shorter than the Planck scale that may be physically resolved, that make sense in the usual physical sense"

I think Lubos made "Sacred cow" from Planck length.

It seems to me first and foremost to solve problem of discrepancy of Planck units.

I mean to separate Planck mass from Planck length .

Does all Planck units are sacred or only one?

We don't have guarantee G, c, are real constants during

the evolution of the Universe.

We don't have guarantee they depend of each other or not, or both depend from density energy of vacuum, or they two sides the same coin.

Imagine that G and c simultaneously vary,because energy of vacuum vary following the evolution. Doesn't matter the Universe shrinking or expanding.

No comprehensive proof of the cosmological constant running, there is no proof of the non-running either.

But we believe naive:

1.Schwarshild black hole R radius G/c^2

2.Planck unit L of length G/c^3

3.Planck unit T of time G/c^5

4.Planck unit M of mass c/G

What is correspond to real world?

If all,it would be absurd.

To my opinion only #4 linear link between G and c is real,eternal

and vary together..

And #1,2,3 are fake that only teasing physicists

Possible conclusion:

1.Only Planck unit of mass have sense.

2.Only h is fundamental constant

Hi Anon.

There is absolutely no need to fuss about Godel, mathematical logic and what not. We use the math that we know and trust 100% IN ITS TRUTHFULNESS no matter what. And it has worked miracles for us. Dr. Tegmark is largely correct. It is so obvious that the mathematics we use works to describe nature, there is absolutely no doubt about that. The only question is why, and what is it actually describing.

My theory "Quantum Statistical Automata" shows the origin of the laws of the universe and how QM arises. it basically says that Reality is nothing but a mathematical structure. This structure arises by default when you try to design a universe yourself. Just like if you try to design anything, you need the building blocks. After some process of elimination you end up being forced into a unique design that its natural outcome is our reality.

The system is made up of the most basic math there is (like addition, greater than and so on). So no fancy Godel to ponder. the design is the only one possible that generates dynamic universe that is ours. all other designs lead to a static or quasi-static.

QSA Theory

Anon,

David Joyce confirmed that I made some interesting points in contest 3. While I do not claim having found out all weak points in post Dedekind/Cantor mathematics myself, I managed to make most fundamental questions hopefully immediately obvious in some Figs. of contest 4. Nobody felt challenged and in position to take issue.

I merely noticed elsewhere Yuri D. quoting "The Unreasonable Effectiveness of Mathematics" by Wigner.

Eckard