Tegmark's Mathematical Universe

Hi Marcel,

I'm not imagining an actual collapse either. In my own explanatory framework the equivalent of the hypothetical wave function collapse is just a switching from thinking about an independently existing "reservoir" of potential sensory data and all of the possibilities encoded within it to thinking about the one observed output from processing of a selection of the potential data.

Hello Marcel, Georgina, qsa, Rick and Henk.

Re "Relationship with the universe... Everything we know we learned from our interaction with the universe in the capacity of an observer...You exists, that's all. And existence is the most basic property to consider" (Marcel, 2 March, 20:20):

I argue (e.g. in my essay and posts in the 2012 FQXi essay competition) that apprehended information is subjective experience*. I also contend that information is physical and "the physical" is information. So I agree with you, Georgina and Marcel, about the primary importance of subjective experience/ information in every aspect of the universe.

But here I am interested in examining a different issue related to the topic of Tegmark's Mathematical Universe: the issue of how to interpret the components of "law of nature" mathematical equations. I assume that the 100 years of work by thousands of scientists has not been in vain: the type of equations that they have come up with DO represent fundamental reality and not just a human viewpoint, although the precise details of "random" quantum events cannot be represented symbolically by mathematical equations.

Re "Your example: E = mc2. This equation means: the invariant mass of a system is the total energy divided by the speed of light squared" (Henk, 2 March, 17:01):

Henk, I think you seem to have closed your mind to the possibility that the symbols in law of nature equations could be interpreted in any other way. I'm suggesting that such equations do not live inside a black box, immune from further investigation. I'm suggesting that what we have are:

1. Distinct symbols representing acknowledged aspects of the underlying reality (e.g. E and m, representing energy and mass information respectively)

2. Strings of symbols representing some sort of relationship or structuring of these acknowledged aspects of the underlying reality (e.g. E = mc2 or E2 = (pc)2 + (mc2)2 )

3. Distinct symbols representing this structuring or relationship, where it is clear that "=" represents a different type of thing to the symbols "+", "-", "ﾃｷ" and "ﾃ--".

Take these "structuring" symbols away from law of nature equations and you are left with nothing: no interconnection or relationship, no "balance" between one category of information and other categories of information. I contend that that the symbols "+ - ﾃｷ ﾃ--" and "=" represent vitally important aspects of the underlying reality that really exist, and should not be ignored or denied.

Rick and qsa, my contention is that no matter what type of mathematics, algebra or geometry you want to use to represent fundamental reality, and no matter what particular mathematical equations you use, the above issue is essentially the same.

Lorraine

* I mean information in appropriately integrated physical systems like particles, plant cells and people; but I don't include computers because:

1. Computers don't have the internal physical interconnections to allow subjective experience (subjective experience of a physical object being summary information about the surrounding reality and the internal reality of the physical object)

2. Computers only deal with REPRESENTED information not information per se.

Hi Lorraine,

yes you make some interesting points. IMHO There aren't just static relations as is the case with a block time universe but a changing universe that is continually recycling itself, which makes the mathematical operators seem very important and relevant, as well as the equals which separates inputs and operators from the output.

When applied to physics the equals sign is (at least sometimes) misleading, as the apparent output may not be the result of inputs and operators alone but also local environment,including historical influences and the behaviour of an observer. So it is more of a leads to something but it is not equivalent to the inputs and the obvious operation upon them alone. That's not saying that there is something more than mathematics happening but the mathematics that applies in nature is completely joined up, as is the material universe.Taking a look at an isolated system is not the same as what is going on entirely.

In mathematics it doesn't matter how the number of things are organised 5 separate carbon atoms are equal to 5 carbon atoms in a ring. As 5=5, but in chemistry the organisation of the atoms makes a big difference to how the chemical behaves and they certainly are not equal or the same. The role of organisation as information is very important in nature, It is very obvious in biology, especially morphogenesis. It has been rather neglected by physics.

Sorry, that previous post by Anonymous is mine.

Lorraine,

Twice now, you have explained in detail your question. None of my reply (or others') seems to help you in your research. Yet, we keep trying.

Your question I believe is; Since these mathematical symbols are part of highly successful equations describing the behavior of the universe, why would they not also be part of the way the universe operates? The question then becomes; Does the universe effect an operation similar to (an example) the addition?

To this question about the addition, I have offered a reply in the following. A planet will gain mass by acquiring matter, not by computing the available mass in the vicinity. The physical addition for the universe consists in bringing matter together and therefore it has a dimensional aspect to it. The added matter also add in collocation its properties to that of the whole planet; the total mass and gravitational force of the planet are changed. Of course, it does not tell you why the planet acquires material from the vicinity, i.e. the root cause of gravitation.

In conclusion, the universe may effect some of these mathematical operations, but, they remain just on a need to know basis for an intellect. The main question is a "why" calling for a logical operation (spontaneous as the universe is) on elements of a same dynamical nature. This you may do by stepping into the black box by understanding and acknowledging its unavoidable rules and content.

p.s. The appeal of a question often reside in the prospect of a specific answer. Instead of letting us all pull ourselves slowly to this prospected answer .... why don't you let us know what YOU think?

Cheers,

Marcel,

Hi Marcel and Georgina,

Re "Does the universe effect an operation similar to (an example) the addition? ":

When it comes to the calculation seemingly implied by a "" in law of nature mathematical equations, it seems clear that the underlying reality does not need any space, time or energy to perform the calculation - the underlying reality is seemingly not even performing calculations at all!

Calculations involve REPRESENTATIONS of reality at all stages of the process, so when physicists perform calculations involving law of nature mathematical equations, the result is a symbolic representation of a physical outcome. This is in contrast to actual reality, where physical outcomes are the genuine article, and seemingly no calculations take place.

Seemingly, the underlying reality only requires the "structure" represented by law of nature equations to be in place (together with preliminary conditions) in order to produce a physical outcome. So while a "" looks like a mathematical operator to us humans, I would suggest that it actually represents a structuring relationship in the underlying reality.

Lorraine

Nice thread,

I have been researching and writing along these lines for the last four years. The fruit of that labour is that I have effectively turned the MUH into a full fledged scientific theory, called the Theory of the Structural Multiverse. The conceptual coherence and empirical tractability both gain significantly as a result. To my knowledge, I give the most complete discussion of the evidence yet available. I am looking for peer reviews at this point. If anyone is interested in reading the proposal or a few chapters and give comments please let me know.

Thanks,

Colin

All,

Could the question be framed as follows?

"Are there 'physical laws' which are not and cannot be 'mathematical identities'?"

If so, why should Nature follow our mathematical calculations and derivations? I have argued in The Thermodynamics in Planck's Law and in my fqxi essay The Metaphysics of Physics. that all 'physical laws' can and should be derived as 'mathematical identities'. I have shown, for example, Planck's Law for blackbody radiation is a 'mathematical truism' and not a 'physical law' per se depending on the physical assumption of 'energy quanta'. This explains why the experimental spectrum is so identical to the theoretical curve.

Constantinos

Marcel,

You said

"Although a unique substance makes for an incredibly efficient use of numbers they must support an actual substance that exists by itself"

Isn't this has been the main point of 20th century physics, that there is no such a thing as a "substance". The word is a classical concept that it utterly fails in the micro realm when we try to explain as to what this "substance" is. With QM, which I hope you accept, the substance is a surreal entity with wave-particle duality characteristic, nothing that we can get our minds around it. We can only describe it mathematically, even worse, they exert force by "virtual particles" (what the hell is that).

Then, if you try to say the underlying entity is some "substance", you will then commit a double jeopardy. The only "substance" that we know, we don't know actually what it is and the new "substance" will again be in need of an explanation OR we have to make up something which will be impossible to conjecture since we don't know any other "substance". ONLY mathematical entities will save you from this conundrum. It seems that you have not looked at my website.

The problem of time has already been beaten to death. Fundamentally there is no need for it. Julian Barbour (and others) has already shown how time itself is nothing but a consequence of movement. And movement is nothing but a change of state. A simple example would be a unit circle radius multiplied consecutively by the natural numbers order, so you will get bigger and bigger circles. You can look at it as a movement or just a mundane mathematics.

Sorry, I am not able to understand your example of the circle.

Somehow you did make a good argument as to "substance" and the logic that carries with it. But you did not supply a viable solution, so I did.

Would it hurt if you explain in a couple of paragraphs with a link.

Lorraine,

You write

"Rick and qsa, my contention is that no matter what type of mathematics, algebra or geometry you want to use to represent fundamental reality, and no matter what particular mathematical equations you use, the above issue is essentially the same."

Maybe I am misunderstanding what you are saying but it seems you are missing the basic idea of math and mathematical universe. What Tegmark asserts is that the unit circle exists without us having to represent it by some symbols in an equation. So does the 180 degrees for the triangles. All mathematical structures exist independently of us or how we represent them. So I don't see your argument about representation adding any insight for or against.

2013-03-11

Dear QSA,

Maths must be applied to something other than our REPRESENTATIONS, because these REPRESENTATIONS are from us and for our benefit, not for the universe. The universe works on something else that is much simpler. Bottom line; the universe has existed and evolved without us for the past few billions years; it requires a substance and an internal

Automata work by rule we invent. Causal sets work by rules we invent. I use the simplest and most powerful rule that must be, the rule of non-contradiction. As for the substance, I just gave it the name of the form under which we recognize it. What is it? The original contradiction existence vs non-existence in a continual process of resolution which pursuit creates time and everything else in it as time variations.

QM describes where existence is more probable within a system of particles under constraint. The word "existence" is foreign to physics so we replaced it with the "probability of finding it" there, essentially making sure that we remain in the physical picture.

As for the perception of the circle, the explanation is very simple and constitutes the approach by which one can remove himself from the status of observer. Could be difficult for some.

Anyone else could understood this?

Marcel,

Yesterday I wrote in another discussion on this site about this topic. I can't link to my posting, only to the entire thread, so let me copy that posting here:

Given what we do know from physics, it is reasonable to assume that the World is inherently mathematical of nature. So, what take to be a physical World, may fundamentally just be an abstract mathematical structure and nothing more than that. Then there is nothing needed to "blow life into the equations", as the equations themselves are all that really exist.

My argument for this goes as follows. As I'm sitting in front of my computer and typing this message, everything I feel and experience is due processes in my brain. These processes end up implementing some algorithm that processes information; the details of what is going on in my brain only matter in so far as this algorithm is executed.

If my brain were replaced by a computer that would simulate that would go on in my brain, that would give rise to my consciousness. What matters for me is if the computation is actually being performed, not how it is being performed.

This then implies that running "my program" to let me experience some virtual environment would lead me to experience that virtual world as if it were the real world. I could e.g. experience real pain, even though there is no real body that is being hurt. The fact that the precise way the computation is carried out doesn't matter, means that the computer could run the code in some scrambled way.

Now, an example of such a scrambling, is the time evolution of the World. So, even if one rejects the notion of block time, it will re-enter via the back door, because the past exists in this present moment, albeit in a scrambled way via the time evolution operator (in quantum mechanics, you need to assume the validity of the MWI to make this work).

This means that any computation of me that has ever or will ever be carried out generates my consciousness. So, even if the universe were to effectively end due to heat death, or a Big Rip or whatever, I would still find myself alive, probably discussing physics on a forum like this one, because the World that I'm right now effectively experiencing would still exist in a scrambled way in that future state.

This then calls into question the very relevance of "physical". A more natural interpretation is that the algorithm that desctibes me simply exists as a member of a mathematical multiverse that contains all algorithms. Then on this set of algorithms a natural measure should exist that makes certain algorithms more probable than others. This is, of course, someting that should be derived from first principles, not assumed. But assuming that one can do this, it should be the case that an algorihm describing me experiencing World where things don't add up is vastly more unlikely than me experiencing a World that is describable by the known laws of physics.

qsa,

If by "substance" we mean "what is" then any description of it will be 'metaphysical'. And all metaphysics ultimately fails. But if instead we consider our measurements and observations of "what is" and apply mathematical identities to analyze our data, we would then avoid falling into such metaphysical pits.

I argue in my essay, The Metaphysics of Physics, that all 'physical laws' can and should be derived as 'mathematical identities'. And have shown in The Thermodynamics in Planck's Law this can be done for Newton's Laws of Motion, Planck's Law of blackbody radiation, and others.

This approach to doing Physics will avoid the endless and contentious search for 'substance' and all philosophical debates of why Nature should follow our mathematical calculations and derivations.

Constantinos

Saibal Mitra,

I have no doubt we can believe and live in any Universe of our own making. And endow such Universe with all the mathematical reasoning possible to have. Many many years ago I recall a lecture at Princeton by a well respected philosopher on the topic why he does not exist. This for me is both sad and testament of the power of human intelligence.

Modern Physics is no less the same! And while physicists argue for the rest of us to follow in their 'metaphysical journey' of time-travel and multiverses, my "man in the street" understands such folly is nonsense. Not that it cannot exist as explanation of our World. But rather it shouldn't exist! As this 'metaphysics of physics' puts us at odds with our own senses.

Constantinos

I came across this interesting article...

Incredible design based on the work of mathematician Henry Dudeney

"In 1903 Dudeney invented a way to cut an equilateral triangle into four pieces that could be rearranged into a square, a conundrum he dubbed the 'Haberdasher's Puzzle'. The D*Dynamic house realises this mathematical curiousity as a solution to living in extreme climates. Sections would fold out on rails so interior partitions could become exterior walls in warm weather." Damien Gayle, Daily Mail, 7 Dec 2012

..a mathematical universe should have at least one of these : )

Because of the discussions above I wish to highlight 2 points.

First, in physics there is a general agreement (arisen by experience during centuries). The final description/foundations of reality will be simple. A small set of properties and a few axioms are needed to describe and explain (the alteration of) nature.

Second, the mathematical universe hypothesis - by Max Tegmark - shows why this description will have a mathematical structure. In other words: physical laws and physical properties turn out to be mathematical laws and mathematical properties.

And in spite of these 2 points, there is some confusion about "the nature of mathematics". And some doubt about the correctness of the MUH because some readers reminds themselves Gödel's incompleteness theorem(s) of mathematical logic.

Mathematics is not only applied mathematics (like we use in physics). Therefore, when we describe the foundations of nature (physics) and this description will be completely math, we describe the foundations of mathematics too! Both descriptions have to be identical en both descriptions have to be simple. So in the end there will be no difference between the foundations of physics and the foundations of mathematics.

When someone argued Gödel have proofed that a complete description is impossible, he/she misunderstood the scope of the incompleteness theorem. Gödel's theorem indicates that mathematics lacks a unified theory (like the proposed TOE in physics). He (only) proofed the incompleteness of the formal system that encloses modern mathematics. He didn't proof nature is incomplete...

Because the final description of nature is both physics and math there is no need to shift the attention from physics to (applied) math. In fact, both modern physics and math must hide some very serious flaws. So the problem is not physics or math, but some misunderstanding within our perception of existence.

"If my brain were replaced by a computer that would simulate that would go on in my brain, that would give rise to my consciousness."

Pretty big assumption, and just that, an assumption.

Constantinos,

I really enjoy all the ideas by all the people in FQXI, some more than others. It is very clear that we are not trying to do mainstream here, we leave that for the pro. Here we try to see if we can figure out more fundamental issues that should lead to as a clear idea as possible to actually what is going on, hence the name foundation. So yes, I want to know the origin of reality, nothing less is satisfying. I imagine myself as a rock, I can't measure anything but still I want to know why I am here.

Otherwise, what is the point of the exercise ?