Tegmark's Mathematical Universe

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 ?

qsa,

I am all for intellectual curiosity and venture! Trust me on that! But some questions by necessity cannot have true answers. Example, can you truly know your father? All you can know is your experiences and observations and understanding of him. But you cannot truly know him!

I argue analogously we cannot truly know "what is" ('substance') of the Universe. But can only know our measurements, observations and understanding of "what is".

All religions and metaphysical systems seek to know "what is". And all fail! But in their seeking, these create much destruction and injustice and dogma. We can avoid all this by realizing the limits of knowledge.

Constantinos

Constantinos,

I am 58 and my father is 83 and NOW I do understand his ontology. He always had my best interest at heart but I was too stupid to realize it. Of course, following one's own desires does sound good at the time.

Seriously, this blog about MUH has been going on for six years, do you really think people will stop thinking about ontology. When I came up with my own theory at the time I did not know about Dr Tegmark , Wolfram or Conway. As a matter of fact, I was fooling around just like I have always done ever since I was young. Never ever I thought I would hit the big one, my theory cuts strait to the heart of the issue and directly confirms MUH.

http://www.qsa.netne.net

more detailed explanation are in posts 20,25,43 in this thread.

http://cosmoquest.org/forum/showthread.php?140913-%93

Reality-is-nothing-but-a-mathematical-structure-literally%94

sorry if these links are repetitious for some.

Qsa,

You did not answer my rhetorical question! Happy you now understand your father! But do you truly know him! Perhaps you can be more forthcoming and explain your theory is simple sensible terms. I am interested!

Constantinos

Re "And there is SUBSTANCE, that which does not require our presence or observation to exist. The real universe is made of substance" Marcel, 19 Feb 2013, 04:22 GMT;

"Although a unique substance makes for an incredibly efficient use of numbers they must support an actual substance that exists by itself" Marcel, 2 Mar 2013, 20:20 GMT;

"Isn't this has been the main point of 20th century physics, that there is no such a thing as a substance" qsa, 10 Mar 2013, 01:19 GMT :

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Surely the "substance" is information. It is clear that information (e.g. about mass or charge) is apprehended in the underlying reality. But this information is not an objective reality - it is a subjective reality: information has a point of view; it can only be apprehended subjectively. Information is subjective experience*.

Marcel, one can never "remove himself from the status of observer" (Marcel, 11 Mar 2013, 18:17 GMT) - the subjective nature of information is the nature of reality.

So there is no objective information. The closest thing to objective information seems to be represented information. The phenomenon of represented information is probably due to the subjective nature of information: from the point of view of a subject, the rest of reality in effect represents (many interconnected aspects of) information. So words on the page of a newspaper, or a law of nature mathematical equation displayed on a computer screen, represent information to a subject. These words and symbols must be decoded (by a subject) before the intended information can be apprehended as subjective experience.

Lorraine

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* I mean information is subjective experience ONLY in appropriately integrated physical systems like particles, plant cells and people. 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 perhaps being describable as 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.

Re "Given what we do know from physics, it is reasonable to assume that the World is inherently mathematical of nature" Saibal, 12 Mar 2013, 23:22 GMT;

"I argue in my essay, 'The Metaphysics of Physics', that all 'physical laws' can and should be derived as 'mathematical identities' " Constantinos, 13 Mar 2013, 02:39 GMT;

"The final description/foundations of reality will be simple... this description will have a mathematical structure." Henk, 13 Mar 2013, 18:00 GMT :

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The underlying reality is not 100% representable by mathematical equations e.g. the precise details of the outcomes of quantum events are not predictable because the situation is not representable as a mathematical equation. THEREFORE, one cannot say without qualification that reality has a mathematical structure. The quantum exception to the rule shows that the word "mathematical" is not an adequate description of the nature of reality.

Lorraine

Your analogy between knowing a person and the fundamentals of the building block of the universe is not that strong. Even if they were "similar" it is still an analogy and nothing more, and I will not dwell on it.

As to my theory, all the links I have given explains my theory in a very simple language since the theory itself is simple. Moreover, the write up and the explanation are fairly short. Although, to fully appreciate my theory you might have to run the simulations which I know can be tedious for most.

Reality exists hence we say it is true. But what is really true besides that more than anything else which we can really trust, it is mathematical facts. So, to my mind I connect both since both seem to be a statement of truth. So I took a guess that reality is something akin to a circle (truth). The relations between the points give you a mathematical structure whereby you get PI which defines the structure of the circle.

The structure that leads to our reality is random numbers and certain unavoidable relations (and only possible ones) between them. That is all. It is the most generalized structure possible.

The system (I will not use the word model although you could with some caution) seems to mimic reality by exposing some of the very important essential features of Schrodinger equation, Dirac equation, QFT and Gravity! But only certain essential features of these theories, probably some heavy work and more elaborate simulations needed to map to the standard physics.

On the other hand the system exposes features of reality that standard physics is simply in no position to do so. Particularly, the Lagrangian of the system falls out from the simulation and you get the values of charge, mass, c, h_bar and other values, even the Fine Structure Constant. Not to mention the beautiful unified picture of space (its points are the crossing of the lines-dynamic-), time(change of state-does not actually exist-), mass, charge, and energy.

The other really big result which I obtain is the essence of Dirac equation included the notorious non-locality. When I try to simulate the 2D situation, I am forced to restrict my line throwing activity to only lines that can go between particles directly so as to keep the invariance of quantities calculated in case the frame is rotated. And Wala, I get two particles to interact through their width in the second axis and it does not matter if each is on the other side of the universe, they are both linked!!!! When I calculate spin (what I believe to be) one is up the other down.

There are many other things in the system which I have not tried to do too much yet mainly due to lack of time including gravity which I have done in limited way and I do get the small attractive force but probably much more work is needed.

I should mention that the theory is at heart a generalization of Buffon's needle which ties to many other concepts which are used in high end physics like twisters, categories, network theory, Ising and many others.

The system is very similar to Strand Theory by DR. Christoph Schiller. and this FQXI essay

http://www.fqxi.org/community/forum/topic/950

Constantinos,

Sorry, that last post was meant as a reply to your post.

Re "Something more primitive than mathematics yet eminently connected to it; logic!" Marcel, 24 Feb 2013, 14:49 GMT;

"physical laws and physical properties turn out to be mathematical laws and mathematical properties" Henk, 13 Mar 2013, 18:00 GMT :

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Surely logic and mathematics don't have any independent or primary existence: they are like a PROPERTY or a consequence of representing some of the aspects of the underlying reality? Surely logic, and applied and theoretical mathematics, are predicated on the primary existence of 3 types of things in the underlying reality: information categories; information relationship (represented e.g. by "+ - ﾃｷ ﾃ--"); and the type of thing that is represented by the symbol "="?

Our logical and mathematical representations derive from the existing structure of reality. But while reality moves and changes, these representations just sit there dead on the paper they were written on: they have no ability to effect change in their own right. In other words these representations are limited: they do not adequately represent the full nature of reality.

Lorraine

To QSA Mar 13 22:43

O You may have to read again the part I wrote on truth systems..

O As for satisfaction... Yes! I answer my own questions to my satisfaction. I am my first client.

O If you can`t figure out the "circle" thing, you don't understand space-time, really!

`

Henk Grimm Mar 13 18:00

O ... the final DESCRIPTION of nature in physics and maths ... Agree totally. BUT, if you want the final UNDERSTANDING of nature, it will be about the logic of the universe i.e. how it works by itself. Physicality requires your hand, maths requires your brain; the universe requires neither to function.

Lorraine mar 15 22:44

....One can never remove himself from the status of observer .... Well, it requires more effort than displayed around here 

.....There is no objective information.... Agree! It demands that we remove from the information that part that we contributed to. The transforms, the integration, the mindset etc. Lots to strip away and QM and GR help us in that work.

Lorraine Mar 15 23:22

If you accept the quantum event as statistical ... then it is still maths? Determinism is traded for probability ... still maths!

Lorraine mar 16 00:14 ( Bo to ged !) 

Agree! Dead on the paper is the finished event and all summed up with an = sign. But look out the window and everything is moving and changing. Once on paper the time passing background is gone integrated into a time passed a.k.a. time duration. Want to understand the universe ? Keep the time running and go from there.

Marcel,