Tegmark's Mathematical Universe

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

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,

"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).

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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,

Lorraine,

Hi. I'd agree that everything exists within the universe. My view is that for the universe to be here at all, there must have been some indivisible (e.g., not further subdividable) physically existent state. Whether this state is called a particle, mathematical construct, law of physics, etc., it doesn't matter. It's some existent state. This state must have a way of creating additional states that can interact physically to produce the motion, forces, etc. that are in our universe. Then, after the fact, humans came and invented mathematical symbols and rules to describe these existent states and their interactions. So, I'd say that the type of math that represents the most basic underlying reality is actually the number 1. "One" represents the presence of a single existent state. Later, humans than invented addition, substraction, etc. to represent the presence of additional existent states, removal of states, etc. My vote is that equations are way down the road from this. I'm not sure if this is related to your component parts view?

Anyways, that's my vote. Thanks!

Marcel and Roger,

When I wrote "underlying fundamental reality", I didn't mean to imply some sort of ultimate fundamental reality or some original indivisible state. I just meant the fundamental information and relationships that science has detected, and has represented symbolically as mathematical equations (Laws of Nature).

Does Marcel's example of a Law of Nature represent an indivisible reality, or does it represent a whole that is somehow constructed from particular aspects of reality: energy information represented by "E"; mass information represented by "m"; (perhaps) relationship represented by the implied multiplication symbol "ﾃ--"; (perhaps) balance or transformation represented by "=" etc. If "E" and "m" represent fundamental aspects of reality, why wouldn't the necessary symbols "ﾃ--" and "=" also represent fundamental aspects of reality?

Why is science seemingly blind to these symbols? Is science avoiding facing up to essential, but non-measurable, aspects of reality?

Lorraine

Lorraine Ford (feb 21 22:59),

Your question about the relation between primary reality and algebraic equations is really amazing. Indeed, I realize we practise mathematical equations only to compare phenomena and their relations (empiric science). Do we need equations when we describe the primary reality? No, you are right. Describing something "absolute" (an infinite whole) don't involve equations.

Your next question is: "Why is science seemingly blind to these symbols? Is science avoiding facing up to essential, but non-measurable, aspects of reality?"

No, I don't think so. I suppose everyone likes a reality that is "comfortable". A reality that looks like an altering image. You can imagine it, you can discuss it, you can draw it. Personally, I don't think a mathematical universe is a pure algebraic universe. We use algebra to calculate. So an algebraic universe have to represent a geometric universe: just like our daily world. There is only one problem: we cannot observe this reality with our senses/instruments. So the mathematical reality forms general relativity and quantum fields too.

For scientist, the most important question about the mathematical reality is: "How can I explore this reality? Where do I begin?" The answer is obvious: foundational mathematics. That is logic and set theory. So don't make the unrecoverable mistake to start describing a detail/phenomenon somewhere in the universe (like string theory). You have to describe absolute space and absolute time. Anyway, it isn't difficult. You have to choose the right starting point.

Henk

2012-02-24

Lorraine, Roger, Henk,

How do I start? Step back and look at the whole picture. What are we missing? Oh! Yes! Nowhere do we admit that anything exists by itself. Physics is about our relationship with this universe. What do I use then to explore or address the non physical? Mathematics? Hum.... It is numbers... involves quantities and measurement ... then the observer is still there, involved.. No! Something more primitive than mathematics yet eminently connected to it; logic! To look at quantities means measurements and the intention to describe how things work. That is nice, but the universe has no need for measurements. The HOW question is for our intellect. The universe evolves spontaneously so the real question is WHY?

So, we have the question 'why" and a tool that is simple logic. This would call for metaphysics but this field is in a poor state and is still a system of opinion. In order to go somewhere with this you have to work with a truth system, a system based and made of inferences drawn from a fundamental impossibility. Euh... the rule of non-contradiction is definitely the right one, as the starting rule of impossibility! As case in point all other truth systems abide by it, maths the first one.

Beyond and as basis of our perceptions there must be something that really exists we will call a substance. This substance could undergo logical operations but only on itself or variations (still of the same nature) of itself. For these reasons and a few cosmological pointers we will accept that the whole universe is and has to be made of this single substance. We are in business!!

Now, logic is taken here as having its full meaning. First it describes a valid operation on the substance like addition, substitution etc. .... Secondly, logic describes a spontaneous becoming i.e. the logical spontaneous outcome of a given state or situation. This spontaneous logical operation is the CAUSE. We have now recovered both the SUBSTANCE and CAUSE of the foundation of metaphysics. After some work, you should find out that there can only be one single type of logical cause in the universe. And this cause HAS to be built into a property of the substance; it can`t be otherwise. And this substance and this cause are.....

Marcel,

Henk,

You refer to mathematics, algebra, logic and set theory as though you think mathematics can be taken for granted: something that is assumed to exist that requires no further explanation. But surely "the right starting point" is to ask what mathematics is, and where it fits into the scheme of things? I think 4 points about mathematics are relevant:

First there is the question of a Platonic realm. I start from the assumption that there is no Platonic realm - that is, I think everything exists within this universe including mathematics: mathematics is part of the universe - it is not external to the universe. Unfortunately, even physicists who profess to not believe in a Platonic realm seem to treat their mathematical equations (laws of nature) as though they were external to the universe i.e. things unable to be explained, or things not requiring explanation in the context of this universe.

Second, I assume that mathematics arises out of the reality of living things: mathematics started out as, and continues to be, a system of symbolic representation. We are made out of the underlying reality of the universe; we are not separate from this underlying reality: I consider that mathematics could only make sense to us if and only if the basic elements /symbols of mathematics faithfully represented corresponding basic elements and relationships in the underlying reality. So there was no mathematics in the early universe - there was only the underlying reality, much of which we can represent using symbols*. These symbols include "+ - ﾃｷ ﾃ--" and "=", which presumably represent aspects of the underlying reality in this universe, not things that exist in a Platonic realm. These symbols, alone or as part of "law of nature" mathematical equations, seemingly represent aspects of reality that are not measurable, whose existence can only be inferred.

Third, while the basic elements/symbols of maths can be utilized to represent the underlying reality (e.g. as laws of nature), mathematicians or physicists can also creatively assemble mathematical symbols to represent artificial realities: this is similar to the way words in a story, or colour and line in a painting, can be used to represent actual experienced reality or to represent imagined, artificial realities**.

Fourth, the above views might lend support to a view that numbers found 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, then "(d +d + d)/d" represents a number similarly constructed. This 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

* But seemingly not all aspects of the underlying reality are able to be represented with mathematical symbols e.g. the precise "random" outcomes of quantum events are seemingly not representable as one side of a mathematical equation.

**This view would indicate that mathematics is both discovered AND invented: the type of symbols used in mathematical equations, and the form of a mathematical equation, represent discoveries about aspects of the nature of reality; but mathematics is invented in the sense that it is a creative reworking using these types of symbols.

Marcel,

You say "Physics is about our relationship with this universe" and "the universe has no need for measurements", but what do "relationship" and "measurement" mean in the context of these statements? You mention numbers, but what is a number? You say "the rule of non-contradiction is definitely the right one, as the starting rule of impossibility" - but where is the evidence that such a rule really exists - does it exist in a Platonic realm?

Lorraine