Heh. It was kind of noted in the OP and broken down in other posts (see ultrafilter’s), but since no one’s made the point explicitly, let me: the “exceptionally simple” in the title is just a pun, based on the fact that there are technical math terms “exceptional” and “simple” which apply to E8. Even if the author thought his theory wasn’t really all that straightforward, who would pass up the opportunity for that title?
While attempting to digest this nugget of information, my wife (who’s a mathmatician) cruised by and said I should never trust an ultrafilter: after all, if one has an ultrafilter handy then any bounded sequence will converge! Even sequences like 1,-1, 1, -1,… that I thought don’t have a limit – now they have ultralimits!
I dunno what that means really, but she certainly cracked herself up saying that. She cryptically went on to say that ultrafilters can be very handy (tipping me off that your handle is a mathematical set theory term). Also that she really likes your layman’s summary of what E8 is.
This guy says he’s a crackpot.
http://motls.blogspot.com/2007/11/exceptionally-simple-theory-of.html
Okay, ths thread is whooshing so far over my head like a 747 from Chicago on its way to Frankfurt, but could I ask our learned math and physics types two questions:
So E8 is the largest of simple exception Lie spaces, correct? Is this simply the largest one to have been discovered or is it possible that larger versions of this type of space have yet to be discovered by aspiring mathematicians?
Finally, isn’t the fact that this was found in the largest of these types of spaces just a bit problematic in terms of its likelihood of being correct or its predictive ability? That is, presumably the currently discovered particles, “fit” into this Lie set in a slightly inexact manner. Presumably there’s some level of experimental error in every known aspect of every particle. For instance, we don’t know the exact weight of an electron or quark, etc., do we? So, is it not somewhat more likely that the size and complexity of the E8 Lie set would be more accomodating to fitting our currently known phyisics into it?
Does that argument make any sense?
The simple Lie groups have been completely classified and are completely known. Four infinite classes and exactly five exceptions.
Incidentally, the simple finite groups (finite, but no differentiable structure) have been completely classified too. At least, so it is thought. There are 15 infinite classes (many of which have two independent parameters and so, in some sense are doubly infinite) and exactly 26 exceptions, of which the largest, the so-called monster, has over 10^54 elements, but only, i think it is, 194 conjugacy classes. (This means that there is a set of 194 elements such that every element is conjugate to one of the 194, meaning that it is essentially indistinguishable from it. The proof, if it is correct, of this claim, is said to occupy 15,000 pages.
A propos the sequence 1,-1,1,-1,1-1,… what does it converge to modulo an ultrafilter? Well, the answer is that it must converge to 1 or converge to -1, depending on the ultrafilter chosen. If the ultrafilter contains the even integers, it converges to 1 and if it contains the odd integers, then to -1.
Ah yes, so it was. I guess when I read it, I did not equate “this big pretty spirograph thing” with the toy. When I finally saw the diagram, I’d forgotten the description.
I don’t know anything about anything, but from my recent rounds of the Internet, I gather Luboš Motl is infamous within the physics community as, while a genuine scientist, also a prickly character who is very, very dogmatic in his support of string theory, and unbecomingly harshly dismissive of anyone he perceives as presenting any opposition to it.
But, like I said, I don’t know anything about anything, so hopefully others who do can either add to or refute that.
Allow me to attempt a defense of ultrafilter’s honor. Presumably, your wife is not particularly distrustful of principal ultrafilters (given a principal ultrafilter, the resulting “ultralimits” are those obtained by just saying “The ‘ultralimit’ of a sequence is always its kth value”, for some constant index k. Silly but harmless.). As for nonprincipal (a.k.a., free) ultrafilters, well… at least in this context of sequences of reals, let it be noted that, given the existence of a single free ultrafilter, it follows that “The sequence S converges to the value r relative to some free ultrafilter” if and only if “The sequence S has an infinite subsequence which converges to the value r”. So it seems fair to take “The sequence S has an infinite subsequence which converges to the value r” as an accurate generalization of free ultrafilter convergence of sequences of reals to even those contexts where one does not accept the existence of free ultrafilters. So, for fairness’s sake, if your wife is going to never trust an ultrafilter on these grounds, she should never trust an infinite subsequence either (every bounded sequence of reals has an infinite convergent subsequence).
Of course, there may not be a unique limit of infinite subsequences; but, then, there isn’t a unique ultralimit either, to the extent that there isn’t a unique free ultrafilter to choose.
Okay I saw the Youtube video and that’s very cool. Is it a low-res version of the .mov file in the link above? Cos that no worky for me. 
It says I don’t have the right compressor, but doesn’t tell me which is the right compressor, or how to get it.
If E8 is indeed the structure of elementary particles and forces for our universe, does this have any cosmological significance? Does it suggest what alternative physics hypothetical alternate universes might have?
From that post:
Could someone knowledgable answer these two questions:
- Is the author correct that Lisi does this in his paper?
- Is the author correct that there’s something wrong with doing this?
-Kris
A good book that covers some stuff about groups and physics is “Symmetry and the Monster” by Mark Ronan. There are a lot of people working on using the Monster to build a TOE. So that someone publishes a paper on it is not at all surprising.
Note that around 1920 something, a nice group based model was proposed that was beautiful. However, it predicted the decay of protons (IIRC). Experiments were done, no decay detected. Oh well. (My Goolge-fu is weak. Sorry if I can’t recall the details.) (A lot of other, more modern GUTs also predict proton decay, which is one of the major ongoing issues with models of this type.)
So this might turn out the same. Or not.
(If there really is a confusion about units, then that definitely kills it. But someone will come along with a better model using the Monster soon enough.)
John Locke, is that you? I knew this whole thing sounded like it was from a *Lost *episode. How does this relate to the Valennzetti equation?
You might be thinking of Kaluza-Klein theories, originally developed to unify electromagnetism with gravity. Of course, the 1920s were the infancy of quantum particle physics, so there’s a gap of a few decades (and two new fundamental forces) between the KK proposal and its extensions to particle physics. I don’t really know anything about these, so I don’t know what they predict about proton decay.
The idea of proton decay is actually a selling point in many GUTs, being part of an asymmetry used to explain the matter-antimatter asymmetry observed in nature (at least in our local neighborhood). The problem is that (as you say) it hasn’t been observed, and so the bounds on proton lifetime keep going up as the detectors get larger, ruling out more and more GUTs.
Lubos Motl is pretty well known to be, um, unconstrained in his dialogue, so you should take that into consideration when reading his blog. There is a lot of discussion at the Backreaction blog, following Bee’s post on the paper, including posts by both Lisi and Motl. The answer to (1) appears to be “yes”; as for (2), Lisi maintains that this is OK, while Motl considers it sheer lunacy. I’m not qualified to judge between them.
Well yeah, so much is obvious just from reading Motl’s post itself. 
I think the argument I mentioned in my question was the only actual argument in the post. The rest was character assassination.
-FrL-
I’m fascinated that the mathematical and scientific world is actually this enamored with a Spirograph.
If he’s actually adding together such disparate sorts of objects (I still haven’t had time to read the paper), then at the very least he had better be prepared to define exactly what this “addition” operation is that he’s using, because it bears a significant lack of resemblance to anything commonly considered addition.
On the question from last page about the falsifiability of strings, there’s a reason I refer to it as “string model” instead of “string theory”. It isn’t yet a theory, nor does it look likely to become a theory any time soon, and calling it such dilutes the meaning of the term as applied to genuine theories. String model is at present an interesting toy, but it is not any more than that.
That Spirograph is only a 2-d shadow of the 248-d object the E8 Lie Group represents: you can never see this object, only it’s lower dimensional shadow as the higher dimensions “rotate” to highlight certain interconnected nodes.
From the backreaction.org link given a few posts back, I gather that Lisi’s answer to this question has something to do with something called a “BRST extended connection.”
-FrL-