Tegmark's Mathematical Universe

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

Max Tegmark will get Nobel Prize 2013 from native Stockholm.

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

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

Surely we must mentally distinguish the underlying reality from our symbolic representations of it? Mathematical symbols, statements and graphs can REPRESENT the underlying reality, EXCEPT for the precise "random" details of quantum processes, which seemingly cannot be mathematically represented. The underlying reality seemingly does not conform to scientist's expectations of a completely mathematical universe.

But what underlying reality do physicist's mathematical statements (and more complex derivatives and graphs) represent? Should we say that e.g. "a bc = d" is the type of thing that represents the fundamental underlying reality, OR should we say that the above represents 3 aspects:

1) a b c d

2) - * /

3) =

of the fundamental underlying reality?

Lorraine,

Hi. I totally agree with you. IMHO, it's very important to distinguish the mind's conception of something from the thing itself. As you said, mathematical symbols, which our in our heads, describe an underlying physical reality but are not themselves that underlying reality. And, just claiming that mathematical constructs exist in some Platonic realm doesn't explain anything. Please show me this realm now. Point it out. Until then, this argument that mathematical constructs exist outside our heads and are themselves physical reality is nothing more than the God argument. It may be correct but can never be tested.

In regard to a +bc = d, I'd say that your three choices are correct. To me, one has to start with an existent state. That is "one" existent state. Add another existent state, and a mind could say: one existent state plus another existent state gives two existent states. That is, math is just a mind describing, after the fact, physically existent states.

Peter Jackson, above, suggests that we can't even accept "a = a". I agree with that, too, in that I think there can be different and opposing ways of perceiving the same existent state, a. Looked at the same way, a would equal a. But, looked at in a second way, a might not look like a as perceived in a first way. I use this type of thinking in my argument in an earlier fqxi essay contest that "something" and "nothing" are really two different ways of describing the same underlying physical reality, the absolute lack-of-all. If anyone's interested, more of this is at my website at

sites. google.com/site/ralphthewebsite

Thanks!

Lorraine,

"Surely we must mentally distinguish the underlying reality from our symbolic representations of it" Lorraine, you've hit the nail on the head. I just posted something on topic 1229 -Killing Time- before realizing the thread had been dead for 7 months. I re-post it here because it discusses this underlying reality you speak of.

..." The problem is always the same. Not knowing the difference between physics and metaphysics, and the limits of each.

There is EXPERIENCE, what we make up of the world through our senses and mind. EXPERIENCE requires our presence to happen and to exist. So, forget about physics without observer; we are always part and cause of the observation and its interpretation.

And there is SUBSTANCE, that which does not require our presence or observation to exist.

The real universe is made of substance. Our reality is made of our experience of this real universe. We create our own reality which, without our senses and mind, is just a dark place filled with matter and radiations. (Even " matter and radiations" are evolved concepts of ours).

-------------------------------------------------------------------------------

The thing is that we can only know about time indirectly by deducing it from experience like motion, change, etc. The reason that time is so elusive is that it is not physical but rather metaphysical ; it cannot be an experience. It is here and there without requiring our presence. We may only deduce or infer the passage of time from the experience of change.

----- The passage of time is metaphysical and it has to be treated as a substance.(opposite of experience)

When we confront the existence of a substance with the requirements of operational logic, we find that there can only be one substance making the whole universe. Science has effected great stride in the required reductionnism; mass and energy, time and space, electricity and magnetism... But we are facing a wall because time is involved and appears necessary in all of them. If they exist, they are just various forms of the passage of time.

The important things to remember are 1) The passage of time is metaphysical (a substance) 2) It is a process that is dynamical in nature 3) it is a spontaneous process driving all other spontaneous processes. In this, it is the simplest and most basic process making the universe.

For more details, see my previous two FQXI essays."

---- You see in the text above that the basic workings of the universe are in very simple operations of logic (which are at the root of mathematics). Logic, in its prime, is essentially the rules that govern our expectations we have about outcomes that we have acquired from experience in our reality. Logic is scale independant (works for atoms or galaxies) and is system independant (the basis of all systems is logical consistency).

---- As for maths, I have discussed earlier, "natural addition", or adding in a geometrical way as in "moving objects closer together to really add there intrinsic properties i.e. mass etc." . In school we used to learn addition by grouping and piling together objects. So does a planets gaining weight, by aggregation, not by calculations.. It is easy to recognize the difference between this natural addition, which the universe performs all the time, and adding money in my pocket with money in my bank account.

Marcel,

Hi Roger and Marcel,

Thanks for responding to my post.

I guess what I was trying to say (very badly) is that seemingly much of the underlying reality can be represented and its behaviour predicted via the various mathematical formulations of Laws of Science/Physical Law/Laws of Nature.

You can argue about which mathematical statements are the ones that correctly represent reality, but the point is that our representations of the underlying reality seem to take the form of mathematical equations. Something about mathematical equations represents the nature of reality!

If there is no Platonic Realm, and I think there can be no such thing, then everything exists within this universe. So I was trying to ask: is a whole mathematical equation the type of thing that represents the underlying fundamental reality? Or do the common component parts of mathematical equations, like + - / * and the equal sign, represent underlying more fundamental realities? Obviously these necessary symbols would represent non-measurable realities whose existence can only be inferred.

An advantage of the component parts view seems to be that numbers founds in nature, instead of being seen as mysterious Platonic objects, might be seen as being constructed out of the same component parts as Laws of Nature. E.g. if we say that "a + bc = d" represents a Law of Nature constructed out of component part fundamental realities, then "(d +d + d)/d" represents a number similarly constructed. The component part view implies that that numbers found in nature have a hidden structure, but a structure that may be impossible to determine: there are many possible ways to construct the number 3 using mathematical symbols.

Lorraine

Lorraine,

"Something about mathematical equations represents the nature of reality!"

Marcel: It represents the behavior of nature as seen from our reality.

": is a whole mathematical equation the type of thing that represents the underlying fundamental reality?"

Marcel: Yes, in a way. It describes accurately how we perceive the behavior of the universe. But the equation does not run the universe nor does it hint at what does.

"Or do the common component parts of mathematical equations, like - / * and the equal sign, represent underlying more fundamental realities?

Marcel:

I think I may partly address your question in the following....

... Consider E=MC2 . At first glance it is not logical because we multiply or equate elements that are or of different nature; mass, speed , energy.. We get away with it because it works for its purpose in our reality which means that these different elements DO have logical equivalence in the underlying reality. But operational logic cannot accommodate more than one (type) of substance of one nature. (The proverbial apples and oranges). In my theory (see essays) this unique substance is the passage of time (a process). This means that all the elements of the equation represent each a concept, form or variation of time. This way the "equation" could become logical. The problem is figuring out which concept, form or variation of time they represent and how or whether the - / * are or represent valid logical operations.

The equal (=) sign is for accounting a static equivalence. In the underlying reality, operations are spontaneous and logically driven and are transformations as in "before" and "after". So, an equation (=), even "logical" would remain a sentient accounting, not a natural process that runs the universe.

Marcel,