Instead of writing about LA, which I intended to do at some point soon, I'm going to link to Max Tegmark's latest paper which argues that the External Reality Hypothesis (the idea that there exists an external reality independent of human minds) implies what he calls the Mathematical Universe Hypothesis (that physical reality is entirely a mathematical structure). This is, in my opinion, the most powerful argument against the Copenhagen Interpretation of quantum mechanics (ie, antirealism) as opposed to the Many Worlds Interpretation (ie, realism). He goes into mathematical platonism, Godel incompleteness/undecidability, the halting problem, various multiverses, and the Simulation Argument (the idea that we're living in a computer simulation run by beings living in some other reality outside of our "Matrix"). Many of the points he makes, especially regarding the simulation argument, have been stuff I have also been thinking lately, and meaning to write down and explain. But since he's beat me to the punch, I'll just link to his paper rather than writing them out:

Tegmark: The Mathematical Universe

I do have a few more things (well, a lot more) to say on this besides what he says in this paper, and a few things I might have said slightly differently. But to write that out would delay my post on LA even further, which I don't want to do. So it'll have to wait.

I leave you with Tegmark's poetic closing two paragraphs:

"[The Mathematical Universe Hypothesis] is arguably extreme in the sense of being maximally offensive to human vanity. Since our earliest ancestors admired the stars, our human egos have suffered a series of blows. For starters, we are smaller than we thought. Eratosthenes showed that Earth was larger than millions of humans, and his Hellenic compatriots realized that the solar system was thousands of times larger still. yet for all its grandeur, our Sun turned out to be merely one rather ordinary star among hundreds of billions in a galaxy that in turn is merely one of billions in our observable universe, the spherical region from which light has had time to reach us during the 14 billion years since our big bang. Then there are more (perhaps infinitely many) such regions. Our lives are small temporally as well as spatially: if this 14 billion year cosmic history were scaled to one year, then 100,000 years of human history would be 4 minutes and a 100 year life would be 0.2 seconds. Further deflating our hubris, we have learned that we are not that special either. Darwin taught us that we are animals, Freud taught us that we are irrational, machines now outpower us, and just last year, Deep Fritz outsmarted our Chess champion Vladimir Kramnik. Adding insult to injury, cosmologists have found that we are not even made out of the majority substance. The MUH brings this human demotion to its logical extreme: not only is the Level IV Multiverse larger still, but even the languages, the notions and the common cultural heritage that we have evolved is dismissed as 'baggage', stripped of any fundamental status for describing the ultimate reality."

"The most compelling argument against the MUH hinges on such emotional issues: it arguably feels counterintuitive and disturbing. On the other hand, placing humility over vanity has proven a more fruitful approach to physics, as emphasized by Copernicus, Galileo, and Darwin. Moreover, if MUH is true, then it constitutes great news for science, allowing the possibility that an elegant unification of physics, mathematics, and computer science will one day allow us humans to understand our reality even more deeply than many dreamed would be possible."

- Current Mood: working

## Comments

dankamongmenonhavareallyexplain the "unreasonable effectiveness" problem? It's one thing to say that anything that exists independently of the human mind must have some mathematical description, but it's another entirely to think that that mathematical description is simple and contains solvable or easily approximated limits that we can understand. Does he go on to address questions like this?spoonlessThe symmetry issue seems very similar to what you're asking, and may or may not be the same thing. But I think that's the closest he comes to addressing the point you're wondering about.

onhavaIn other words, if we didn't live at such a highly symmetric point in the multiverse, the laws would look too chaotic and random for intelligent life to have figured out enough about its environment to survive.That's a pretty striking claim. Complex life demands a simple environment? I guess I kind of buy it, though; if some living thing can't compute whether a fast-moving object is going to hit it or not, it's probably going to be in trouble. But doesn't it sound surprising? I wouldn't have thought the resolution to Wigner's question could be anthropic, but that's more or less what this is.

spoonlessComplex life demands a simple environment?

Here's another way to say it...

Complexity isn't equivalent to randomness (consider a vast universe filled with pure random noise... in a sense, it ends up being homogeneous and "unintresting" everywhere). Consider what mathematicians mean when they say they've found something with a "rich structure" or "interesting structure". They don't mean that it has no symmetries; nor do they mean that it's so symmetric as to be trivial. There has to be a sort of balance between the two in order to get the kind of complexity that does "interesting" things... and I'd imagine that's exactly the sort of complexity needed to create intelligent life.

Also consider what happens when you get near a critical point in statistical mechanics... suddenly, you get universal scaling relation, extra symmetries, and all sorts of neat things showing up. If the system is too cold, then it's too simple; if it's too hot, then it's too random and homogeneous. Near the critical point is where the interesting patterns we call "life" can flourish. This would explain, for instance, why our universe happens to be so close to a supersymmetric conformal fixed point.

onhavaOne thing you say confuses me, though: in what sense is our universe "close to a supersymmetric conformal fixed point"?

(This reminds me: have you ever noticed this paper? It seems slightly nutty but resonates with some of the [also nutty] things I've been thinking about lately.)

spoonlessin what sense is our universe "close to a supersymmetric conformal fixed point"?

What I had in mind was starting at our point in moduli space and moving to the nearby point where the cosmological constant is zero. If I'm not mistaken, the theory there has exact superconformal symmetry? Or maybe some of Banks' more speculative ideas are starting to mix together in my head with more widely agreed-upon results.

I probably should not have called it a "fixed point" as that would imply there is some distance you're taking to zero or infinity. But isn't any CFT a fixed point in some sense... as in, there is a way to get to it by starting with a theory that has some distance scale and taking it to zero?

This reminds me: have you ever noticed this paper?

No, but just looking at the abstract it sounds interesting. I mentioned above that you get "extra symmetries" at a critical point. But you also get enhanced gauged symmetry at a self T-dual point in string theory... a similarity I'd never thought of before. It doesn't mean they're necessarily connected, but that would be pretty crazy (in a good way) if they were!

onhavaWhat I had in mind was starting at our point in moduli space and moving to the nearby point where the cosmological constant is zero. If I'm not mistaken, the theory there has exact superconformal symmetry?It certainly doesn't have to be true; there are infinite moduli spaces of SUSY theories that arise from string theory, and only very special points on these are superconformal. (I assume you mean the low-energy field theory; no perturbative string theory is conformal, because there's always the string scale.)

It does sound Banksian, though, since he suggests (for reasons I don't completely understand) that our vacuum is a small perturbation of an

isolatedsupersymmetric theory with zero cosmological constant (i.e. one with no associated moduli space). I guess such a point probably is superconformal?But you also get enhanced gauged symmetry at a self T-dual point in string theory... a similarity I'd never thought of before. It doesn't mean they're necessarily connected, but that would be pretty crazy (in a good way) if they were!Well, what is certainly true is that if you have a duality acting on one variable and you consider a flow in that variable, any self-dual point is a fixed point of the flow. So if for some reason cosmology (or some other abstract flow on the moduli space) was changing some radius and

onlythat radius, the self T-dual point would be a fixed point (not necessarily an attractive one). But since string constructions depend on many more variables, it's not so clear to me what relationship self-dual points and fixed points of some flow should have. I guess self-dual points should probably still be fixed points, but the more directions you have to go in on your moduli space, the more likely it is that the fixed point is only a saddle and you will get driven away from it. (The trouble is that the subspace where you flow into a saddle generally has a lower dimension.)Given what Ooguri and Vafa have to say about the geometry of the string theory moduli space, it seems unlikely that any picture of simply flowing along the moduli space to the right vacuum would make sense. They even suggest that geodesic flow might be ergodic.

Faraggi seems to be motivated more by some strange reformulation of quantum mechanics than by the idea of some flow driving to the fixed point, though.

onhavademoivrespoonlessdemoivreStill, the voice-over actor is good, the sound track is good and, for what it is, the animation is good--not up to contest standards, I think, but definitely something to be proud of for a two-week hack job between disparate departments. When I can, I'll post it.

demoivrespoonlessdemoivreYeah, you could say I'm stoked.

spoonless(Deleted comment)spoonlessI guess there's often a conflict between doing something that is popular right now and doing something you truly find interesting. I think a little of both is a good approach. Although in the long run, you're probably right... doing what you want is more important.

So where did you run into Max Tegmark?

(Deleted comment)(Deleted comment)spoonlessFor me, cosmology is mainly interesting because it gives us a way to test particle physics which is (in my opinion) where all the really fundamental foundational questions lie. In other words, I see the early universe as interesting primarily because it's the only time when things got hot enough to where low energy physics breaks down... something that would be too expensive to build an accelerator to do. But I'm aware that some (maybe most) cosmologists see things kind of in reverse. From things you've said, I gather that you're one of those who sees things in reverse from me, and that's fine... if that's where I thought the interesting questions were, I'd do the same thing.

(Deleted comment)spoonlessthis is something that lee and i regularly whine about other people not agreeing with

I would agree with you that the boundries between cosmology and particle physics are getting less and less clear. And anyone who studies quantum gravity should certainly be familiar with both, as it involves both. But would lee smolin say that "cosmology is about everything"? That's really the part I disagree with the most. I would say cosmology is about gravity, and particle physics is about everything else... which is starting to include gravity too :)

spoonlessex_memepr0gI think that it's pretty sobering to think about that...I find the universe staggering myself.