where he talks about all of his four levels of the multiverse. It's quite entertaining to read. I have previously written why I think the mathematical universe hypothesis is

*we*(i.e. human beings) don't know anything except maths without 'human baggage' it doesn't follow from this it is the only thing there can be. Call it The Principle of Finite Imagination: The capacity of the human brain is finite. It is very possible that we simply aren't able to understand 'what' the universe is or why it works how it works. For my general problems with reality, see comments to the Block Universe.

But anyway, despite my disliking of its content, Tegmark's paper is as courageous as entertaining and bestowed this photo series upon you. If I have to read that

Tegmark has pursued this work despite some risk to his career. It took four tries before he could get an early version of the mathematical universe hypothesis published, and when the article finally appeared, an older colleague warned that his “crackpot ideas” could damage his reputation.

and

Q: Right from the start you tried to get this radical idea of yours published. Were you worried about whether it would affect your career?

A: I anticipated problems and did not submit until I had accepted a postdoctoral appointment at Princeton University [...]

it sounds to me like there's something really wrong with the academic system. If young people are afraid of pursuing their interests because it might damage their career this is likely to result in a self-reinforcing deviation of the topics that are investigated from those that are considered interesting. How can you expect science to work under these circumstances?

## 47 comments:

Is it really so bad that younger researchers can't work on whatever they want. For every crazy idea that works out, there are ten that don't, and (1) if you know what is good for your career, you really shouldn't work on them until after you have tenure, and (2) maturity is supposed to improve your judgment, and so presumably* you will have a better chance of choosing the right crazy idea later in your career.

* I'm not totally convinced of this.

Hi Peter,

This was not what I said. I see there is reasons not to pay every young person for doing whatever crosses his/her mind, but if he has to be afraid of damaging his reputation with (openly) pursuing unconventional ideas, that's an atmosphere which I don't think is beneficial to progress. Best,

B.

Having to listen to people on the religious right here in the US I think that it is very important, in fact imperative, that young researchers not be able to "work on whatever they want". They darn well better have to take a risk and bet their career, and get stepped on if they do goofy stuff. The alternative is to be overrun by creationists and their ilk.

That is much more damaging to scientific progress.

Markk,

Unconventional doesn't mean dropping the scientific method. But yes, unfortunately, there are apparently a lot of people out there who believe being unconventional is sufficient for being a genius, but the inconvenient truth is it's neither sufficient nor necessary. As Peter pointed out "for every crazy idea that works out there are ten that don't" (I'd have made that a hundred if not more), but one must at least have the education to figure out what works and what doesn't. Best,

B.

Professional management views discovery as unquantifiable risk. It is unfundable (failure) or insubordination (success). Central micromanagement cannot work. Decisions belong in the trenches where problems are real, options are few, and young warriors are fearless.

The NSF costs $(US)5+ billion/year. Bush the Lesser's Middle East adventurism costs $5+ billion/week. The 2008 US corn crop will be down by half. The planet will starve as managers get performance bonuses.

Hi Bee,

“The capacity of the human brain is finite.”

Perhaps, but currently the average human being use about 5% of it. Anyway it is long way to go. Apparently at Princeton University they use the upper bound of 1%.

Regards, Dany.

(Off topic answer)

Dany, this 5% or 10% of the brain thing is a myth.

Yes, this must be a myth. Nature is running with the absolute minimum energy necessary to sustain life; it would never create or preserve something that is not used and the examples are countless.

Dear Rikard,

“This 5% or 10% of the brain thing is a myth.”

I admit my ignorance in that topic. I have no idea who B.Radford is (U.Geller however is a citizen of my country and the general consensus treat him clown). My statement is based on the knowledge of Network Topology and Mesh network in particular. I also have experience in dynamical development of the communication networks. In private conversations with brain scientists I never met disagreement with that statement.

Regards, Dany.

Bee:...written why I think the mathematical universe hypothesis is nonsense unjustified,Ah, this is a good sign to me(changing it from nonsense to unjustified) that You are almost getting the point of what Tegmark was doing. :)

Scientists Get Glimpse of First Moments After Beginning of Timeby DENNIS OVERBYE"If this holds up to the test of time, it's a real landmark," said Max Tegmark, a cosmologist and cosmic microwave expert at M.I.T. "I really feel like the universe has given up one more clue," he said.See:If it's Not a Soccer Ball What is it?-Thursday, March 16, 2006Why I support, even though of a layman category, as it was sometime ago, and with current verifications was able to finally convince somebody of the relevance of mathematics (as a decomposable limits[

self evident])even though it is an abstraction, it is married to what is happening with science. Our Cosmos.Sean's current post in regards to his "lopsided universe" is a case in point. You had to know what the WMAP represented, and what it was doing.

Getting to the PoincarĂ© Conjecture entailed a whole lot of "geometrical understanding." If you did not know of "this history" how would you have known that such abstractions could lead you to see the universe with what had always existed? The mathematics "was not invented," it was discovered, and to discover it, means that it had always had to be there.

Hi Plato,

I never said that mathematics is not relevant. Gee, I studied mathematics. What I am saying is simply that it might be a language to describe nature better than words, but there's no knowing there isn't another language beyond maths that we don't even remotely anticipate right now. Shortly after spoken language was invented, I am sure people thought that's the greatest thing to describe nature ever, and they didn't expect there to be something like maths that is infinitely more precise. So how are we to know in 10,000 years from now there won't be some other description better than maths?

Best,

B.

Dear Giotis,

“Nature is running with the absolute minimum energy necessary to sustain life; it would never create or preserve something that is not used and the examples are countless.”

I am envy you actively participating in running Nature project. Please transmit my best regards to God. You also will make us happy telling what TOE is.

Regards, Dany.

P.S. What about my coccyx?

Bee,

To speak about philosophy of science, mathematics is a wonderful thing as it bring wholeness to the endeavours and incorporates the logic that is needed, yet, recognizes the human potential needed to delve into what is required of science.

Recognizing the value of nature and sitting with it under the guise of "an umbrella" is to recognize that nature is very close to what needs to be discover within our own selves. That going to a indecomposable limit is to recognize where this exists within you.

Tegmark:So I developed this Dr. Jekyll/Mr. Hyde strategy where officially, whenever I applied for jobs, I put forth my mainstream work. And then quietly, on the side, I pursued more philosophical interests.”You recognized how unfortunate it is that one could have dual personalities, and wonder indeed why such protection is necessary under the virtues and values and requirements of science, while there are human beings who pursue the ultimate questions, who are still credible people.:)

Bee:So how are we to know in 10,000 years from now there won't be some other description better than maths?WE are evolving with the science where the last question leaves off. Human Ingenuity is part and parcel of this quest to understand and we had to recognize where this leaves off.

In a quiet country setting, or by a stream, this is conducive for reasons that influence the very nature of who we are, to "settle the air for a brain wave" that is conducive to moving our positions to where this question leaves off.

Holding it, is like sending this off into the "wild blue yonder" and coming back with insights into what the discoveries are to meant to convey.

Without that question/position you could not have never advanced any ideas. Yet, those ideas exist all around, and just need to be plucked from that air:)

Mathematics is getting closer inside to that indecomposable you. As you journey inwards, you are journeying outwards.

Bee,

Even if there's not an atmosphere of opposition to non-conventional research, there are good reasons for not openly pursuing crazy ideas. I can easily see people saying, with regard to a hiring decision, "he's the guy who works on crazy ideas that never get anywhere; we should hire somebody more productive," even without deliberate attempts to squelch non-conventional research. Hopefully, once you have a bunch of good non-crazy articles published, working on crazy ideas will not damage your reputation, and you might even be lucky enough to work on a crazy idea that turns out to be correct.

I agree deliberate attempts to squelch non-conventional research indeed produce a bad atmosphere.

Hi Dany,

Yes you are right, i forgot. I will rephrase:

God said:

"I have programmed nature to run with the absolute minimum energy necessary to sustain life; it would never preserve something that is not used."

I think we are ok now.

Regards

Hi Peter,

What is good talking math is that you must talk literally. Let talk literally at least when we are doing science. Then the place for the individual with crazy ideas is at bedlam and not at the Department of the Theoretical Physics.

Regards, Dany.

P.S. Talking math not literally is not a math.

Hi Giotis,

“I think we are ok now.”

Sorry, I still have two problems:

1)You didn’t explain from where you know what God said;

2)You didn’t answer my question about coccyx.

Regards, Dany.

Hi Rikard,

Thanks for the link. I always suspected this to be a myth. You might want to check out this though ;-)

Best,

B.

Hi Danny

1)You didn’t explain from where you know what God said;

I use 100% of my brain.

2)You didn’t answer my question about coccyx.

God said:

"Your coccyx has a usage. Check your Wikipedia"

Regards

I find Tegmark's sort of ideas (the idea is called "modal realism," similar to musings of Frank Tipler but w/o the extra baggage of the latter) to be fascinating, but many ironies apply. First of all, saying that "the universe is just math" isn't a verifiable statement in empirical terms if it's actually true! Let me explain: if there was no way to say what ought to be different in behavior or observation, a MR supporter must appeal to fundamental but metaphysical arguments. Those are arguments such as, "How can you logically define the difference between 'really existing as stuff' versus just being a platonic model?" I consider such arguments logically impeccable in context and on the face of it, but the real world is ickier than that.

Well, are there actual differences? I wish I could say, definitely so, but there are suggestive arguments against. First, "real" quantum style randomness cannot be modeled by a mathematical process. It is incredible that Tegmark would overlook this, but apparently he did. Math is

deterministic. The results are what they have to be, and any "randomness" in output of such functions and structures involves "cheating" such as using pseudo-random "random number generators." They require an operator to seed the process with something like a number to get digits of a root out of, etc. It is a contrived action, it can't come naturally and unaided out of the math itself. (IOW, you can't design a mathematical function which actually produces "random numbers" by itself, you have to help it along. Just *calling* a function a "random variable" is a construct, not an actual generator of same.)The way in which ensembles of muons or etc. decay is not supposed to be like contrived RND functions, it is supposed to express randomness in endlessly divisible form. So, members of each remaining portion of the muons has the same chance of decaying as if they had just formed. How can a mathematical structure manage that without contrivance? Who or what would be seeding the RND generators, especially absurd inside a "structureless fundamental particle"?

Randomness

per seisn't the only problem, consider also the wave function. We don't even know how to model what happens to the wave when an observation forces a collapse, so how can the universe "be" math if math can't even coherently describe what waves do throughout their entire span?The alternative is to reference "descriptions" and just forget about laws. There is a "block universe" of the events that happened, and only an appearance of laws since we just happen to be able to form in a universe that seems to have regularity? (This is not the same as universes with different laws, since laws are still laws even if they can vary.) But in such an unstructured scenario, there would be all kinds of little variations that would give things away (maybe electrons wouldn't all have the same mass, etc, and that's just one little divergence.) IOW, there are many more slightly variant logically possible worlds than there are tidy ones, so our Bayesian chance of finding ourselves in a tidy one (even after filtering down to habitable worlds) is vanishingly small. But we do live in a tidy world. Hence the universe has real lawful "virtus", not just a happenstance of one math option versus another. It is not "made of math."

tyrannogenius

Neil, your definition of mathematics is too restrictive. Mathematics is just an abstract representation - if we've got a fundamentally random process (quantum) we can say we will define it by a random variable. That's maths. I can then use that in my statistical analysis or whatever maths I want to do. You're being too restrictive, and I think you're missing Tegmark's real point.

I think his real point is "If you say that the physical world is separate from the mathematical world, then how, precisely, are you going to specify what that difference is?" And I don't think it's possible to do that (I see you ask the question yourself:

"How can you logically define the difference between 'really existing as stuff' versus just being a platonic model?").For a start, we don't seem to have definition of what a physically real object is - we just define physically real objects in terms of other physically real objects (e.g.,

"I know the apple is real because I can hold it in my hand"). If we really were in a mathematical universe then we would not be able to tell because every (mathematical) object would be defined only in terms of other (mathematical) objects.You're very certain and sure of yourself:

"The universe is not "made of math."Er ... how do you know? Have you performed an experiment to determine the nature of the reality around us and found it is not mathematical? What "reality criteria" or "reality test" did you use? I'm not saying I think Tegmark is right, but I don't see how he can be disproved or falsified.Neil:First, "real" quantum style randomness cannot be modelled by a mathematical process.I always refer to Ramanujan in this context because it helps one to see that what was "unreliable in the process of a consciousness," one's dreaming, could have a foundational basis to it, although camouflaged by the insanity of events, actually releases complex mathematic formula.

It is no easy effort to map a position for the "philosophy of mathematics" to be extolled in it's diverse forms, without understanding from which it can arise.

This is in no way a view that Tegmark espouses, as far as I can tell, yet, his platonic search for meaning to the light, is very real to me:)

I think the first step we have to take before we can say "The universe is/is not mathematical" is to provide a clearcut and unequivocal answer to the two questions "What is physical reality?" and "What is mathematics?"

And as we haven't yet answered those two questions adequately, any argument over "The universe is/is not mathematical" seems rather pointless!

Andrew, I suppose you see the irony that if Tegmark's supposition can't be verified/falsified, that it is "meaningless" so what is his point in believing it? Or does he just mean, we don't know how to express the difference? It's a matter of ultimate metaphysics. One reason I don't think the universe is math, is the subjective nature of experience. I (like e.g. Roger Penrose) don't think it can be modeled by math entire (although some things, like much of all thought process, can be.)

Finally, I already explained why "random variables" don't actually work to produce the particular results themselves, they are just about the overall statistics. You can't create a function that will actually produce the hits, the unpredictable sequences themselves. Think about it.

Hi Bee,

I see the discussion has drifted from what your point was onto whether Tegmarks’s theory is the be all and end all. To tell you the truth from the hard ball science perspective as to ask what does it help us predict I don’t believe he has such an intention for it. I think as I do he sees it more as a metaphysical or philosophical anchor to aid pursuing notions that turn into things that are a little more objective and testable.

It has always been a compliant of mine that physics in particular has become far too vacuous in this regard. That is besides those like Einstein, Bohm, Penrose and a few others that admit to having things that guide and focus their direction there are and have been few others. Sure they all talk about the maths, symmetry, economies, conservation and so forth yet nervously skirt around them as to what they might truly represent to be.

So should we consider this 9-5 theoretical physics? I think not. Should it be considered perhaps to have utility as to serve more as a stronger scent in following the trail? I would say most definitely? I also agree with his timing for it’s always better to demonstrate you are familiar with the terrain before you seriously suggest a different direction.

So as it stands is it enough for places such as PI or others to set up a department to explore it further? I’d say most likely not. On the other hand Is it something perhaps other theorists should take into their considerations when looking at things more generally? I would say most definitely. Well it does appear that at least the sadly late and certainly great Prof. Wheeler would share my humble opinion.

Best,

Phil

I wonder if John Baez might jump in here and explain about the topology of the universe?

What does the Poincare conjecture have to do with the shape of space?

Any relevance to our universe? Anyone for that matter?

Hi Giotis,

“I use 100% of my brain.”

We call that in physics – saturation. Be careful, you should leave space for new knowledge and ideas (not necessary crazy).

Regards, Dany.

Neil said;

"I suppose you see the irony that if Tegmark's supposition can't be verified/falsified, that it is 'meaningless' so what is his point in believing it?"I can see where you're coming from, but it's not really right to call it 'meaningless'. The argument is that if a theory cannot be falsified then it should not really be considered a part of science. It's the old "multiverse" argument all over again. But maybe that just reveals a weakness in the scientific process, not a weakness in the theory?Going back to your point about random variables, again I see where you're coming from by saying that you could never reproduce a fundamentally random sequence using a mathematical function. However, I still feel that if you define your mathematical system to include random variables (instead of fixed values such as 1, 2, 3, etc.) then there's no problem. The problem arises from our limited conception of maths, thinking it can only deal with fixed values and not values that are fundamentally random. Ok, so using that method you could never then reproduce an identical second universe from the same mathematical model (written on paper, for example) because of the fundamental randomness involved, but it could produce a single-shot random universe (such as the one in which we live). So I don't see that all this necessarily implies that the universe is not mathematical.

What a f***king waste of time!

No one should be offended, the above is a mathematical statement that describes some universe (ask Tegmark!)

Sorry if this has already been pointed out, but maybe people want to hear Max Tegmark sing his relativity song on Youtube.

Well if anyone is still around ... Just what would a "mathematical description" of our universe specify, anyway? How could it be "particle locations and velocities" since that is not allowed as a precise spec. OK, then "the wave function" - but that doesn't specify the collapses, the localizations themselves. Even if you say, there are multiple universes each having different patterns of collapse hits, the hits in any universe need to be described. Just what would a description of a real tomato involve, IOW, if "the universe is a mathematical description"? No locations, even of nuclei of atoms, or yes, but then how well specified?

Within Tegmark's mathematical universe, time stands still at its top level, while time flows throughout its lower levels. But to me, a universe where time doesn't flow is a universe without physics. And a universe (mathematical or otherwise) without physics isn't reality; it's fantasy. So the top level of Tegmark's mathematical universe, IMO, is nothing more than fantasy.

I simply remark that I do not understand in any sense what you mean by saying humans had a

finite brain, this obviously pre-supposes some sort of natural bijection between thoughts and 'the number of neurons' or.. the number of interconnections between neurons etc., possibly one should be little bit clearer at this point? I always am delighted by the fact, how stereotyped the 'intuition for reality' seems to be that scientifically active physicists can have: the number of eigenfunctions of the Hamilton operator for the hydrogen atom, this is 1 electron + 1 proton is already infinite, the harmonic oscillator has an infinite spectrum etc., but the human brain, which consists, I will not guess this, but ofenoughprotons and electrons etc. is 'finite'. Do thoughts leave your brain entangled with a group of electrons and photons, does knew knowledge mechanically kick out the previous, or what exactly is the underlying model of your thesis?Just one word to the Tegmark-debate: it is indeed, at least from my point of view, quite serious to observe the entanglement of 'recreational' philosophy performed by physicists and, as a tendency, regressive ideas about science (the multiverse etc.), there was good reason to separate scientific spheres: philosophy is not a compensational enterprise for physicists in total lack of rigorous ideas, on the other hand physics is not a field for philosophers without firm backgrounds in the natural sciences. Both tendencies became observable since quite a while and it is interesting to note that both converge to some of the most irrational ideas which were produced in fundamental physics since possibly more than eighty years. I could add at this point a list of 'sociologic' correlations to this development but it is quite clear that a mixture of 'Groessenwahn' (sorry for this typically teutonic expression), lack of knowledge of classical philosophical discourse and some pseudo-religious ambitions which may be possibly traced to Bush and his 'war on terror' and a general tendency of western societies to compensate for their (since 9/11, at least) self-diagnosed 'lack of religiousness' are involved, but I dispense myself now from submitting further depressive comments..(and, of course is the universe 'mathematical' but these are long-known trivialities that I would never ask anyone to get payed for).

I can't help but think this piece is going to simply degenerate into pointless semantic quibbling.

If I read Tegmark the way I think he means, i'd say what he says is trivially true and borderline tautological. Physics is described in the language of mathematics, almost by definition, and presumably being interested in fundamental physics means writing down all the laws that generate all observable and experimental results to be found in the universe.

Most of us believe such a theory will be found one day and exists, and therefore this will show that the universe is mathematical by definition.

Now since this doesnt actually help us (proffessionals) do anything differently, I'll leave it to the layman and philosophers to mangle the meaning into a nice stream of fog, endless redefinitions and equivocation.

-Haelfix

Re: Neil's randomness argument, Tegmark is a proponent of the multiverse, in which there is no randomness, just the appearance of randomness in any particular world-line. Taken as an undivided whole, the multiverse is perfectly deterministic.

I think the more interesting question is to look at the implications of incompleteness with respect to any statement about the universe being mathematical. Another way of looking at incompleteness is to say that "any formal self-referential axiomatic system has an infinite number of axioms"... this would imply that the multiverse is truly infinite (i.e. infinite in all the ways for it to be possibly infinite in). Definitely well into the realms of mysticism at this point, but it does allow for all points of view to co-exist.

Hi Haelfix,

“Physics is described in the language of mathematics, almost by definition”

Y.Neeman liked to say:

“God choose to be mathematician.”

How about that?

Regards, Dany.

Hi Andreas,

I simply remark that I do not understand in any sense what you mean by saying humans had a finite brain,Well, I just came across Lubos truly lovely piece where he explains he can't make sense out of my criticism on Tegmark's paper, and doesn't understand either what I mean with finite imagination. First, if you read what I wrote, and not what Lubos thinks I wrote, you'll notice that I said "The capacity of the human brain is finite". That's meant to say the amount of input a human brain can, in a finite amount of time, process and convert into output is finite. We might be far off from reaching this limit, but it's a very real limit unless we attempt to design our own evolution.

But besides this, it is quite ironic that Lubos totally didn't get what I said. He goes on explaining how complicated mathematical structures can be grasped by the human brain and counts neurons, whereas I was saying that what we might not (yet?) be able to imagine is there is something beyond maths. Call it the level 5 universe. He very nicely demonstrates his finite imagination.

While I'm at it, everything else he says about what I allegedly care or don't care about, or what I rate other people's work by is complete bullshit. I hope he at least has fun with it.

Best,

B.

Hi Haelfix,

If I read Tegmark the way I think he means, i'd say what he says is trivially true and borderline tautological. Physics is described in the language of mathematics, almost by definition, and presumably being interested in fundamental physics means writing down all the laws that generate all observable and experimental results to be found in the universe.Just that Tegmark writes down also all the laws that generate all kind of unobservable results not to be found in our universe, but in other parts of the 4 level multiverse that's inaccessible for us. Besides this, yes, his argument for the Mathematical Universe Hypothesis is tautological, as I've argued in the mentioned previous post. Scroll down, you will find he left a comment somewhere, read my reply and I think you will understand the problem. Best,

B.

I hesitate to get into this, for the aforementioned reasons. I expect we don't disagree except maybe on unfalsifiable statements, which will probably reduce to semantic differences regardless.

But when Tegmark asks for an example, I don't really think you answered the question.

Suppose for instance an alien civilization lives in some inflating bubble different than ours, with different fundamental parameters in their laws of physics. Does it stand to reason that they won't be able to describe their physics with their own mathematics? Also that whatever language they use to describe it, admits no homomorphism to statements in our own mathematical language?

I suspect that no, it doesn't stand to reason.

A concrete example is the classification of finite groups. Its very hard to imagine another race that doesn't have a similar concept. These things are fixed in a sense by mathematics.

So in a sense, *if* (by hypothesis) there is some sort of symmetry in the fundamental laws in the alien universe, then they will invariably write down something that looks like what we might be familiar with.

Thats just one specific example. But you see the gist I hope, and how it can be generalized.

I think rebutters of my criticism of Tegmark re randomness don't appreciate the fullness of the problem. It isn't just about generating a bunch of "hits" from a wave, yes we can just have every possible combination represented somewhere (kind of like the set of all possible dice tosses within a range of tries and conditions, etc.) But the bigger deal is, the nature of the "compressions" to a small space after an observation. Just what is the nature of that, what does being seen "as a particle" consist of, what description tells us what it is. The probability is just an abstraction about "how many" there are as a statistical spread. That's why I asked about a tomato, not just patterns of scintillations in terms of the abstract math of their distribution.

Clarification and then a rest: We know, we can't specify in classical form positions as function of time. If you then say, "oh, the wave functions are what's real" then you have the problem that we can't actually map out the WFs according to most QM (projection postulate, and what no-cloning theorems and quantum information limitations are supposed to "protect", like knowing the full polarization state of a single photon.)

Sure, you can

stipulatea WF in a mathematical model, but what are the WFs really as they happen naturally? We don't have *them* to work with from measuring, just our model WFs that correspond to the degree we need for experiments. Remember too that the WF contracts after a measurement, and then starts evolving again - you can't just say, all possible patterns of "hits" are represented in innumerable multiple worlds, because in any one world-pattern we need the new compacted WF to continue the evolution under the Schroedinger equation, true?BTW, I will post soon in my blog, of how we could perhaps measure the polarization of a single photon (in part, at least.) It's like a "weak measurement."

Hi Anonymous,

No, I didn't give an example. What I was trying to say is merely that my, your, our all inability to give an example doesn't prove anything. You can just define mathematics as whatever describes nature, then nature is always described by mathematics, but there's nothing to learn from that. With every other definition, or even in the absence of a definition, there is no basis on which to draw that conclusion. Thus, it remains a hypothesis. One can build on this hypothesis and play with it. I don't think this will get us anywhere, but that wasn't my problem with Tegmark's paper. My problem was that he argued this would be a necessary consequence, which is a conclusion that just doesn't apply. Best,

B.

once you realize that mathematical structures may contain life - and from the perspective of that life their universe is as “real” as ours - it begs the question: why is ours “real” and theirs “fake”?

answer: narcissism.

Yes qarl that's a good question. But everyone should be aware of the implications of modal realism. If every "mathematical description" exists (you can't just have "lawful" ones, i.e. describable by smooth functions, for then matrices etc. would be rule out) then all the cartoon worlds, simulacra or whatever of the Road Runner cartoons, the Wizard of Oz, Sherlock Holmes, Dilber, whatever, "exist" and are as real as we are. (I mean of course, various versions with more complete distributions of the same sort of characters and objects, not the vague impression of "the story" as we can imagine from a collection of drawings etc.) Are you prepared to live with that mess?

I have written a longer comment on the mathematical universe here (my blog).

Maybe you want to check it out :-) (it was too long to include it here)

Someone follow up this comment (even if it's just Bee) so that I know someone read it. This is a very old post, but

Max Tegmark's popular book on his mathematical-universe theorywill be available soon.Post a Comment