Tegmark's Mathematical Universe


by Chronos
Tags: mathematical, tegmark, universe
Chronos
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Nov28-07, 12:35 AM
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Max Tegmark has interesting, if controversial ideas about cosmology. I read this paper today and was intrigued. Any comments?

http://arxiv.org/abs/0704.0646
The Mathematical Universe
Authors: Max Tegmark (MIT)
(Submitted on 5 Apr 2007 (v1), last revised 8 Oct 2007 (this version, v2))
Abstract: I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.

I reflexively dismiss this idea because it appear untestable, but, he makes a compelling argument this objection may be illusory. The symmetry breaking thing really intrigues me. The apparently broken symmetries could be restored in parallel universes. I find that idea strangely attractive.
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marcus
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Nov28-07, 01:12 AM
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Quote Quote by Chronos View Post
... the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. ...


I reflexively dismiss this idea ...
Didn't you realize?
Tegmark himself is an abstract mathematical structure.

They used to hang out at Schraft's on Park Avenue and 53rd street, eating abstract mathematical icecream, but recently they have been duplicating themselves and gradually infiltrating Think Tanks and Major Universities.
Chronos
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Nov28-07, 01:29 AM
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Hilarious, marcus. His posits on the brain thing were amusing. His reasoning, however, was interesting. I think he made a case that Godel's 'incompleteness' conjecture is not bullet proof.

Coin
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Nov28-07, 01:35 AM
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Tegmark's Mathematical Universe


I think Tegmark's idea is really interesting, but as I see it it is fundamentally not a scientific idea. It is a philosophical idea. I don't think we can ever use it to draw useful conclusions except in a philosophical sense.

The one obvious, useful conclusion that I'm aware of which comes out of Tegmark's idea-- "we should expect the ultimate laws of our universe to have a description which is simple, in the k-information theory sense"-- one could perhaps reach in other ways without specifically positing Tegmark's whole mathematical multiverse.

I'm a little confused where Godel comes in. I may try to read that paper later and see if I have anything to say on that particular point.
Ben Niehoff
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Nov28-07, 01:54 AM
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If the "true physical laws" (whatever they are) have a finite mathematical description, and these laws encompass all of the possible phenomena of reality, then the idea that reality is a mathematical abstraction is tautologically true (it would, after all, be isomorphic to a mathematical abstraction, which is good enough as far as any sensible philosophical definition of "is"). As such, this idea is both fascinating and meaningless at the same time.

The other possibility is that reality admits no finite mathematical description, which means there are ultimately no fixed rules; but it does mean physicists won't be out of a job any time soon.

In either case, this is the stuff of philosophy, not physics.
Fra
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Nov28-07, 02:19 AM
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Perhaps I misunderstand what he means but I skimmed this paper before and when I read the paper my impression is that his constructs and the ERH somehow has the purpose of justifying a reductionist approach.

My main objection is that the birds view as he calls it, might not fit into a frog projection due to information capacity limits. So doesn't that miss see point?

He seems to look for a bird view, so that he can explain the frog view? But I consider myself the frog in this context, not the bird. I can "try to be a bird" but my nature probabyl limits me?

Imagine that the the "size of the view" is constrained by the information capacity of the observer. Certainly the environment can be used to extent the information storage, but then it can hardly be immediately available because we ran into the issue of information content vs compression vs processing. And if we reduce this into "computing" and "decoding", that is fine, but then what's the different from normal "learning"?

I like parts of the paper, but I don't think I share his apparent philosophy of science.

Edit: I think I said this in another thread, but relative to say an atom in a lab, a human + the lab could probably fairly well satisfy the requirements for a birds view, informationwise. But relative to a remote object in space, or on the cosmological scale I am nothing but a tiny frog.

/Fredrik
staf9
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Nov28-07, 05:23 PM
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That seems like borderline philosophy to me
Chronos
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Nov28-07, 11:10 PM
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Philosophy relies on logic, an often useful instrument in the 'tool box' of science. Mathematics is merely a more rigorous extension of logic. I'm pretty firmly attached to the idea the universe must be mathematically consistent. I perceive Tegmark has framed a persuasive argument to this effect. But, I'm also attached to information theory as a powerful tool in understanding the universe.
Fra
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Nov29-07, 12:35 AM
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For example, tegemarks seems to distinguish between apparently random and "true random".

In terms of information exchange - what is the difference until the "algorithm is cracked"?

How _long time_ does it take to "crack an algorithm"? In the general case?

The question is then, how can a definition be made _in time_, that doesn't incorporate a specualtion about future findings? If it can't be made, then again - what's the difference?

/Fredrik
marcus
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Nov29-07, 01:22 AM
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Quote Quote by staf9 View Post
That seems like borderline philosophy to me
Borderline seems right. But could it be borderline something else?
marcus
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Nov29-07, 01:36 AM
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Seriously, I agree with Coin's comment, at least the second part:

Quote Quote by Coin View Post
I think Tegmark's idea is really interesting, but as I see it it is fundamentally not a scientific idea. It is a philosophical idea. I don't think we can ever use it to draw useful conclusions except in a philosophical sense...
Chronos mentioned this in the original post. Untestability even in principle, the implication being that it doesnt fall within the domain of empirical science.

Probably there should be a thread discussing Tegmark mathematical universe idea in the Philosophy forum. Maybe there is one already. Did anyone check?

edit: I checked in Philosophy
http://www.physicsforums.com/forumdisplay.php?f=112
and they don't have a Tegmark thread, at least so far.
Fra
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Nov29-07, 02:34 AM
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A general forum question: Maybe I haven't seen the feature yet, but is there somewhere a "list of all posts (in any section)" since the last time visiting the forum?

Becase it could be that an interesting post is put under an "odd topic". For example, I would not a priori expect physics related dicussions under philosophy - which means I don't even look there. Philosophy is such a wide topic ranging almost from psychology to science. IMO, philosophy is not a sensible topic on it's own. Rather one usually refers to something more specific, for example the _philosophy of science_. IMO someone who thinks the _philosophy of science_ (not philosophy in general) is irrelevant to science should think again ;)

This probably has the effect that one has to place the post, where it's most likely to be read by the intended group of readers, which gets wrong? If there was such a think as a list of new posts (listing the subjects) it would be easier to find interesting things regardless of where it's posted?

Is there such a feature on here that I missed? Anyone else missing this?

/Fredrik
Fra
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Nov29-07, 03:03 AM
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I guess I didn't look very hard because I thought it wasn't there :) I found the feature.

/Fredrik
Count Iblis
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#14
Nov29-07, 11:16 AM
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Didn't you realize?
Tegmark himself is an abstract mathematical structure.
Indeed, we are all programs/algorithms run by a brain, therefore we are universes in our own right that happen to be simulated in this universe (described by the Standard Model + GR). This idea provides us with a better way to think about a whole host of philosophical ideas and bring them back into the realm of physics/mathematics.

E.g. what are qualia (i.e. if I see the color blue, then what is this color blue I'm seeing)? What else could they be than events in the universe simulated by the brain?

Tegmark writes in his articles about his idea that the fundamental problem is to come up with a measure over the space of all mathematical models. I think that it is unavoidable that the measure is some function of the Kolmogorov complexity of the model such that more complex models are assigned a low measure.

This then leads to extremely complex universes like us that need trillions of arbitrary parameters to define finding themselves being simulated in simple universes instead of finding themself in their own universe.
setAI
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#15
Nov29-07, 11:53 AM
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IMO the MUH is not nearly as important and vital as the CUH- this is a fundamental issue of the ontology of existence- what existence is and what can be

I said in another thread: I am a proponent of something like Max Tegmark's Computable Universe Hypothesis which states that Reality is defined by computable causal systems and that only computable structures 'exist'- or more precisely computability IS existence- since only causal structures with logical/consistent/computable relations and rules can provide the medium of isotropic space and time for which a world and it's history could be physically expressed as real-

Chronos
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Nov29-07, 11:46 PM
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Agreed, setAI. The CUH is the more fundamental issue. A causal universe [which ours appears to be] must yield logically consistent experimental results. It is otherwise difficult to imagine how our univere has persisted for so long. This concept may not be inherently predictive, but has utility in eliminating untenable solutions.
Fra
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Nov30-07, 12:50 AM
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Quote Quote by Count Iblis View Post
Tegmark writes in his articles about his idea that the fundamental problem is to come up with a measure over the space of all mathematical models. I think that it is unavoidable that the measure is some function of the Kolmogorov complexity of the model such that more complex models are assigned a low measure.
I agree completely with this.

The way I envisions this, the reason for this constraint is that the probabilities are conditional and they must be formulated in terms of something the obserever can relate to. And if we think that the encoding capacity of an observer is generally not infinite this implies two things:

1) Overly complex things are automatically assigned a low measure, and this is an explicit realisation of occams razor or thta simplicivy is a virtue. It ultimately boils down to fitness. A overly complex model is not as fit because it adapts poorly.

2) The limiting relational capcity of the observer implies that there are bound to be limits to what he can predict. He knows what he knows, but it's not possible to assign bounds on what you don't know. However, there is also no reason to make assumptions on what you don't know. So as long as there is no negative feedback due to this ignorance forcing the observer to remodel, the ignorance of the observer could be stable.

This is a fundamental key in my own thinking.

/Fredrik
Chronos
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Dec3-07, 01:57 AM
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Just a side note - the paper was submitted to 'GR-QC' [of Arxiv], not 'physics.hist-ph'.


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