← Is the Universe Actually Made of Math?

# Is the Universe Actually Made of Math? - Comments

Reminds me a bit of the old Doctor Who episode "Logopolis":

"The basis of matter is structure, the basis of structure is mathematics...There is no mathematics like Logopolitan mathematics, with that we can create matter."

An interesting theory, just rather hard to prove.

Permalink Wed, 18 Jun 2008 10:16:00 UTC | #185623

Permalink Wed, 18 Jun 2008 10:18:00 UTC | #185624

interesting. but Tegmark sounds more like a philosopher or a mystic.

pop quiz: without consciousness, would there be mathematics?

http://coolmel.typepad.com/iblog/2008/06/there-is-only-m.html

~C

Permalink Wed, 18 Jun 2008 10:27:00 UTC | #185627

Okay, reading this article just about fried my brain, but I just HAVE to try out my new found skill at block quoting.

Level III comes from a radical solution to the measurement problem proposed by a physicist named Hugh Everett back in the 1950s. [Everett left physics after completing his Ph.D. at PrinceÂton because of a lackluster response to his theories.] Everett said that every time a measurement is made, the universe splits off into parallel versions of itself. In one universe you see result A on the measuring device, but in another universe, a parallel version of you reads off result B. After the measurement, there are going to be two of you.

How can anyone put such a complex theory on the table for consideration and then, well, just walk away from the discussion. "Oh, the measuring split universe thing? Uhhh. Nevermind."

Permalink Wed, 18 Jun 2008 10:38:00 UTC | #185630

Permalink Wed, 18 Jun 2008 10:48:00 UTC | #185633

OK, well I am not a profsessor at MIT, so maybe I am just ignorant. HOWEVER:

I can't be the only one that thinks this just sounds like a bunch of meta-physical musings and nonsense centered on games with semantics, right?

Permalink Wed, 18 Jun 2008 11:01:00 UTC | #185638

I think Max Tegmark is one of the most exciting thinkers in physics. He is a highly reputable physicist with a young and active mind, and we need thinkers like him to challenge the status quo.

We should not dismiss lightly what he says. It is not games, it is someone with a deep understanding coming up with original thoughts.

Permalink Wed, 18 Jun 2008 11:09:00 UTC | #185641

Comment 12 by Janus

Thank you for posting this.

As far as I know, this is the only hypothesis that answers all three of the big cosmological questions (unlike the God hypothesis which merely dodges these questions):

1) Why is there something rather than nothing?

2) Why is the universe complex rather than simple?

3) Why does the universe appear to be fine-tuned?

To those calling it metaphysics, it's not metaphysics if it can be tested, even if that test can't be done anytime soon, and Tegmark does think that his hypothesis can be tested. I suggest you read his multiverse page:

http://space.mit.edu/home/tegmark/multiverse.html

It contains a link to his original article about the subject (in a pdf file) at the top of the page, and a FAQ.

Permalink Wed, 18 Jun 2008 11:32:00 UTC | #185654

Comment 13 by Janus

Here's an extract from the article mentioned in my previous post:

C. How a multiverse theory can be tested and falsified

Is a multiverse theory one of metaphysics rather than physics? As emphasized by Karl Popper, the distinction between the two is whether the theory is empirically testable and falsifiable. Containing unobservable entities does clearly not per se make a theory non-testable.

For instance, a theory stating that there are 666 parallel universes, all of which are devoid of oxygen makes the testable prediction that we should observe no oxygen here, and is therefore ruled out by observation.

As a more serious example, the Level I multiverse framework is routinely used to rule out theories in modern cosmology, although this is rarely spelled out explicitly. For instance, cosmic microwave background (CMB) observations have recently shown that space has almost no curvature. Hot and cold spots in CMB maps have a characteristic size that depends on the curvature of space, and the observed spots appear too large to be consistent with the previously popular "open universe" model.

However, the average spot size randomly varies slightly from one Hubble volume to another, so it is important to be statistically rigorous. When cosmologists say that the open universe model is ruled out at 99.9% confidence, they really mean that if the open universe model were true, then fewer than one out of every thousand Hubble volumes would show CMB spots as large as those we observe; therefore the entire model with all its infinitely many Hubble volumes is ruled out, even though we have of course only mapped the CMB in our own particular Hubble volume.

The lesson to learn from this example is that multiverse theories can be tested and falsified, but only if they predict what the ensemble of parallel universes is and specify a probability distribution (or more generally what mathematicians call a measure) over it. As we will see in Section VB, this measure problem can be quite serious and is still unsolved for some multiverse theories.

Tegmark then goes on to talk about the evidence for (and ways to falsify) all four levels of the multiverse over several pages, which I won't copy/paste here.

Permalink Wed, 18 Jun 2008 11:42:00 UTC | #185655

parallel universes of level III exist in an abstract mathematical structure called Hilbert space

Why not a Banach space or a locally convex space, or even a general topological space? Are these parallel universes subspaces of these Hilbert spaces? If so, then they must interest at the origin. What is the significance of that? Of course, they can't go into that here... it's only Discover.

I like these parallel universes theories, but I always come away wondering what they base their ideas on. My guess is that they are looking at some of the partial differential equations of mathematical physics and noticing (or guessing in many cases) that the solutions are not unique. However, it's a long leap from saying an equation has a non-unique solution to saying parallel universes might exist. (Perhaps I am missing part of their reasoning.) Certain equations in fluid mechanics have non-unique solutions (see the Taylor-Couette problem), but it would be a little far-fetched to then say, "Well the fluid actually flows in

*both*ways, each one in its own universe." This will not do very well. It's a fluid moving around, and our description of it is just a little under-determined. Often one only has to use a simple so called "entropy condition" (it's not exactly what you are thinking) to get the solution that exists in nature.

For those of you without much mathematical background, an analogous situation happens in the following. Suppose I am given the dimensions of a door frame as 3ft by 9ft (or say, 1m by 3 m). I want to calculate the length of the diagonal to see if I can fit my large 9.5ft tall (or say 3.2m tall) FSM painting in the doorway. I use the Pythagorean theorem (a^2 b^2=c^2) to solve for c=the length of the diagonal. To do this I have to take a square root. Don't for get that I get two solutions (the plus and the minus)! I get c=9.49ft (or say 3.16m) AND c= -9.49ft (or say -3.16m). Of course, I throw away the negative solution because we think of length as positive.

Here is the point: I DO NOT then posit something like "My equation also gives a negative length, therefore there

*probably is*another universe, where my door frame has a diagonal of negative length." This not only adds nothing useful, but it is intellectually profligate. Instead I simply need to understand that I have decided to describe my doorframe in two ways, using positive lengths, and then (in a slight abstraction) as a rectangle. Accounting for both of these ideas together gives me an answer that makes sense and doesn't need to posit additional universes.

Perhaps I am being a bit too simplistic, but I think to the contrary that physicists look at impressive equations like Einstien's field equations and the Shrodinger equation and forget that the same ideas present in much simpler equations shouldn't be forgotten when things become more complicated.

Finally, since Monty Python has already been invoked, I can't resist:

Ian Bamlett-

Really, to the average man on the street...

And now, we ask the man on the street:

First person: "I'm not a man."

Second person: "I'm not in the street."

Permalink Wed, 18 Jun 2008 11:56:00 UTC | #185664

Steve

I agree, Tegmark is brilliant, I love reading his work...he can really get one thinking about his ideas...

I first ran into his works when I was studying dark matter...great stuff.

Permalink Wed, 18 Jun 2008 12:01:00 UTC | #185666

zreroangel-

I agree, but remember that this is Discover magazine (the Maxim of science magazines), who waters down every article so that it is impossible for any ideas not to sound crack pot. (Imagine them doing an article on Einstein in 1905. They would spend the first half of the article taking about his funny hair and mustache, the next bit talking about how maybe time and space are 'woven together' in some funny way that involves the speed of light, and wrap up by saying how he is at odds with the scientific community. Everyone who read that article would miss the good stuff and think they were just reading about some quirky scientist.)

Janus-

Thanks for the links. I'll check them out. These might help answer some of my questions in my previous post. Still, I don't really see how we are supposed to observe something "outside" our universe. (I understand measure theory quite well, so if you respond, feel free to get technical.)

Permalink Wed, 18 Jun 2008 12:15:00 UTC | #185674

The title of this article reminds me when I was teaching math. You always get the "I hate math" comment from someone. And I would reply: "everything is mathematical, if anyone can give me an example that has nothing connected with math...they get 100 pts extra credit". First, the easy stuff, "My book" OK, your book has weight, dimensions, number of pages, and it's a MATH book, next." They would get harder, like music, then I'd have to explain why music is totally mathematical. Besides, look at Billy Joel, he turned his accounting over to his brother-in-law and the guy ripped off millions.

Is the universe actually made of math? Yep.

p.s. No one ever said "god". The answer of course would be 0 plus 0 = 0

Permalink Wed, 18 Jun 2008 12:17:00 UTC | #185677

Comment #195500 by Ian Bamlett: "Really, to the average man on the street, what is the difference between this level of abstract phyics and a theolgian debating how may angels can dance on the head of a pin?"

I can sympathize with this sentiment, but the problem is that if science doesn't offer answers to ultimate questions, religion will. To the average man on the street, being told that "God did it" is satisfying. They don't really care how many angels can dance on the head of a pin as long as they go to heaven after they die. The fact that their "ultimate answer" sidesteps the deep questions altogether is not apparent. The kind of speculations discussed in the interview are fine as long as they are somehow linked to reality before being proposed as actual facts. Hopefully, these ideas can be tested at some point in the future.

Permalink Wed, 18 Jun 2008 13:38:00 UTC | #185695

So, if I divide the universe by zero, will it blow up or turn into the letter 'E'?

Just tell me when it's safe...

Permalink Wed, 18 Jun 2008 13:39:00 UTC | #185696

Comment 20 by Forti

Permalink Wed, 18 Jun 2008 13:40:00 UTC | #185697

Doesn't the world of math seem independent of time? I know that there's something to the speed of light being related to the existence of time, but that doesn't seem to be a law of math. Why can't I break the speed of light in a mathematical equation?

Permalink Wed, 18 Jun 2008 13:47:00 UTC | #185700

Max has hit the nail on the head. If you're looking for a reason as to why anything exists at all, this is it. In fact, if anything, it's unavoidable. Brilliant brilliant stuff.

Permalink Wed, 18 Jun 2008 14:09:00 UTC | #185706

Comment 23 by Donald

Level III comes from a radical solution to the measurement problem proposed by a physicist named Hugh Everett back in the 1950s. [Everett left physics after completing his Ph.D. at PrinceÂton because of a lackluster response to his theories.] Everett said that every time a measurement is made, the universe splits off into parallel versions of itself. In one universe you see result A on the measuring device, but in another universe, a parallel version of you reads off result B. After the measurement, there are going to be two of you.It's much worse than that. It is only in certain specific, rather narrow, experimental situations that there are merely two outcomes to consider.

In general, every quantum collapse creates a colossal number of outcomes. Instead of two-slit experiments, diffraction is a much more typical example. Consider a photon aimed at a wide screen through a tiny hole Here the collapse of the photon can occur at any position on the screen. An almost inifinite number of outcomes. And this is for every quantum collapse. The universe must be splitting, not merely in two at each quantum collapse, but into a staggering number of universes, each one representing a different location for the collapse.

It doesn't stop there. Quantum collapse is governed by tight laws of probability. So these universes are not equiprobable - if they exist, their existence cannot be merely binary, exist or not exist, there has to be a probabilistic character embedded in their existence OR observers have to be OUTSIDE the universes, traversing them in a manner that obeys the probabilistic rules. So either existence is no longer binary, or we reintroduce a spiritual nature to "observers".

These problems destroy the advantage of Everett's theory IMO.

As for Tegmark's "theory", well.....

I think it's vacuous. I read http://arxiv.org/pdf/gr-qc/9704009

He begins that paper by presenting the question: "Is the physical world purely mathematical, or is mathematics merely a useful tool that approximately describes certain aspects of the physical world?" Very reasonable question. But a few sentences later he

*rules out!!*: "The physical world is not completely mathematical."!! from further discussion. So it is not surprising that 30 pages of obfuscation later he reaches a conclusion that our universe is a mathematical structure. It's a bit like theologians starting out with the idea that god must exist.

He completely ignores the possibility that he started by acknowledging - that the universe is not a mathematical entity, but is merely approximated by one. He completely ignores the different possibility that mathematics does not have an existence independent of our thought-structures, and the consequent possibility that the universe, even if susceptible to mathematical description, is not large enough to contain a complete and perfect model of itself.

Anyway, having restricted himself to theories that assume the universe is a mathematical structure, he ends up arguing that it is pointless to discuss whether mathematical structures which do not correspond to our universe have reality, because we could never know, and as we know

*our*mathematical structure exists (because we exist within it), we might as well say

*all*mathematical structures correspond to universes. (I simplify in the interests of parody, but I have conveyed the essence.)

Tegmark's "theory" reminds me strongly of St Anselm's ontological argument. Not so much true by virtue of its structure, but having the virtue of being so convoluted that it's not easy to see it's false.

I think Max Tegmark is one of the most exciting thinkers in physics. He is a highly reputable physicist with a young and active mind, and we need thinkers like him to challenge the status quo.Sadly, there is nothing to prevent highly intelligent people having nutty beliefs whether it's belief in the God of the Bible, or in the power of mathematics to create universes.

We should not dismiss lightly what he says. It is not games, it is someone with a deep understanding coming up with original thoughts. - Steve Zara

Permalink Wed, 18 Jun 2008 14:10:00 UTC | #185707

Permalink Wed, 18 Jun 2008 14:11:00 UTC | #185708

Hmmm. It seems that there are a couple of camps emerging. Some, like Donald, think Max has lost the plot big time. Some, like me and Steve, think Max is right on the money (I thought his paper - the arxiv one - was a work of genius!).

Having said that, I still haven't forgiven him for not replying to my fan mail ;-)

Permalink Wed, 18 Jun 2008 14:26:00 UTC | #185712

Permalink Wed, 18 Jun 2008 14:38:00 UTC | #185718

Comment 27 by acs

That made real sense to me. Kalam's argument from first cause is the most powerful in the Theists armoury, it requires us to examine how everything came to be. On that note, although we can explain everything from the Big Bang [or convergence of dimensions for you M Theory fans] it gives us little grasp of how those original singularities/elements came to be. This is perhaps a limitation of the human brain in relaiton to reaching backwards through time. Nonetheless, the mathematical model of the universe does answer this quandry, it allows us to recognise that the universe exists because it can. No other reasons required.

Permalink Wed, 18 Jun 2008 15:11:00 UTC | #185739

Um... I kinda lost it here:

"The question then becomes, what is the nature of this external reality?

If a reality exists independently of us, it must be free from the language that we use to describe it. There should be no human baggage.

I see where you're heading. Without these descriptors, we're left with only math.

The physicist Eugene Wigner wrote a famous essay in the 1960s called "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." In that essay he asked why nature is so accurately described by mathematics. The question did not start with him. As far back as Pythagoras in the ancient Greek era, there was the idea that the universe was built on mathematics. In the 17th century Galileo eloquently wrote that nature is a "grand book" that is "written in the language of mathematics." Then, of course, there was the great Greek philosopher Plato, who said the objects of mathematics really exist. "

So....

Basically,

Maths = Language

External Reality /= Language therefore

No External Reality!

OK Mr clever-clogs, go walk through that wall then! :-)

Permalink Wed, 18 Jun 2008 15:29:00 UTC | #185758

Hm. So, if I get the idea correctly, we exist simply because it is possible to construct a mathematical model of our universe - we are that model.

Here's where it gets interesting for Atheists: if it is possible to mathematically describe a model of a theistic universe, then one must exist.

Contrariwise, if a theistic universe can be shown to be mathematically impossible (which is to say, it is provable that no such model can be constructed), then there's no God anywhere, nohow.

The latter seem like it could a worthwhile pursuit - to attempt to mathematically describe systems with the properties required for theistic universes and perhaps even coming up with testable ideas concerning to properties of theistic universes (and I mean beyond Archibald MacLeish's "If God is Good He is not God, If God is God He is not Good").

Just having fun, mostly.

Permalink Wed, 18 Jun 2008 16:21:00 UTC | #185799

Well I also checked Tegmark's paper at arXiv.org, and I think the problem is not so much that it's nutty but that it's yet another variation of Plato's "ideal/perfect forms" metaphysics. Rare with cosmologists, until now, but you can only pray this from a mathematician's cold dead fingers. (Read Penrose's *The Emperor's New Mind* for a treat in that direction.)

Philosophy, ditto. There you thought it's been crushed beyond recognition, and again it rears its ugly little head---in, like, Taylor's *Sources of the Self*. And wouldn't you know it? Eight years later Taylor's awarded the Templeton Prize for, quote, progress towards research or discoveries about spiritual realities, unquote.

Sheesh.

And now for something completely different:

Sometimes it's quite comical. I will be thinking about the ultimate nature of reality and then my wife says, "Hey, you forgot to take out the trash." The big picture and the little picture just collide.

Sorry to say that, but this is about as funny as a '90s Garfield cartoon.

^_^J.

Permalink Wed, 18 Jun 2008 16:45:00 UTC | #185814

Comment 1 by IaninPA

Really, to the average man on the street, what is the difference between this level of abstract phyics and a theolgian debating how may angels can dance on the head of a pin?

Mind you, I suppose it is our ability to think such thoughts that makes us better than pond slime. Some of us that is. :-)

Permalink Wed, 18 Jun 2008 09:58:00 UTC | #185615