You might also soon hear about his friend mentioned in the article, Brandyn. He's working on a problem that is just as important as ToE. They had a running joke: who would find ToE first, Garrent by math and thinking or Brandyn by inventing AI that would do it for him.
Hey Joe thanks for reminding me of jaanix again. I seem to remember it being reviewed in HN a long while ago. Looking at it again the sig/noise is pretty good. Is the site pulling HackerNews from RSS?
My knowledge of mathematics is dwarfed by anybody with a higher degree in the subject, and Algebra (the abstract kind, not the kind with lots of letters) was my worst subject, but part of me is a bit pleased that E8 might be related to an important bit of physics. It's a rather interesting structure, although not 'the largest' as the article claims, as there are some which (if I recall correctly), reach into million-dimensionality.
E8 also has some interesting properties relating to symmetry, so I'm not surprised that it gets used in physics. It's just a pity that the universe couldn't be related to A4, or A8, because I can actually grasp what's happening in those groups.
Even if he's wrong, it goes to show that stepping outside the mainstream can often times be the only way to starting out on a novel, and potentially revolutionary, approach.
E8 is an exceptional Lie group (ie a group that is also a manifold, hence in particular infinite). You seem to be mixing it up with the exceptional finite simple groups. Wikipedia explains.
No. Even though particle physics gets all the media attention, theories like this (and string theory for that matter), are shallow in comparison to statistical mechanics and thermodynamics.
It's exciting to find out what the smallest building blocks look like, but all the real structure in the universe arise from the interactions... and statistical mechanics addresses the interactions at all scales.
Modifications to our understanding of the smallest scales will trickle up to stat mech and thermo, but statistical mechanics is the true heart of physics.
I find that blog post characteristic of what's wrong with academia. Lisi's obviously not a nutjob, and obviously not an idiot, and he's treated with contempt for proposing a big idea that might be wrong; might even be spectacularly wrong. Academia as a whole would usually rather see people get back in line and go on solving irrelevant problems. I found it encouraging that in the originally linked article that he at least did find some people in the scientific community that would treat him with a modicum of respect even if it was just in taking the time to explain why his theory doesn't fit the bill.
Sure, but boring and correct isn't a whole lot more interesting, and academia seems to produce a seemingly endless stream of such in my field of expertise. Many of the breakthroughs would have seemed naïve prior to having become dominant. Incidentally, some of my most productive research while in college was sparked by reading a paper that was patently wrong, but off-kilter enough to get me to look into some previously unexplored corners for new models.
From the link: "the overlap between the set of people who know some group theory and those who are (still) interested in giving Lisi’s “Theory of Everything” a passing thought is empty."
This also an older post back from when Lisi's paper first came out: http://www.math.columbia.edu/~woit/wordpress/?p=617 Again, I don't really know too much about this stuff, but it should be interesting to anyone who'd like to get to the bottom of how credible the paper is.
I don't remember where I read it, nor the exact wording, but there is a quote that is perfect for this. It went something like this, "Godel proved incompleteness. Anyone who thinks there is a theory of everything laughs in the face of Godel."
My point is that physics does not exist in a vacuum. It is built up from observational data found in nature and taken from experiments. If mathematics can't come to complete truth (Godel has proven this), then there is no hope for a theory of everything in something that uses mathematics as its language.
That's complete nonsense. There's nothing about Godel's theorem that says the physical rules of the universe can't be described. You're babbling religiously.
"A small number of scientists claim that Gödel's incompleteness theorem proves that any attempt to construct a TOE is bound to fail. Gödel's theorem states that any non-trivial mathematical theory that has a finite description is either inconsistent or incomplete."
That's from the Wiki, FWIW. I'm not big on using Wiki as a source.
"Babbling religiously" is right on the line in my opinion. It makes you sound like an arrogant jerk. If you have problems with the content of the comment, state your case in neutral terms.
Learn to live with other people's ambiguity and looseness in phrasing. Then perhaps they'll be more forgiving of yours. (Downmod)
You appear to misunderstand the meaning of the terms "inconsistent" and "incomplete" in the context of Gödel's theorem.
"Inconsistent": There is at least one statement within the system that can be proved both true and false.
"Incomplete": There is at least one statement within the system that is true, but cannot be proved to be true within the system.
Since Gödel's theorem applies to formal systems in mathematics, it does not say anything about the possibility or impossibility of constructing a "complete" (whatever that means) mathematical description of our reality.
What about it? All Godel's incompleteness theorem says is that there will be open questions about a universe describable by finitely many rules. The laws of physics don't need to provide answers to questions about whether computers in its universe will halt or whether planetary systems are stable.
What do you mean "the laws of physics don't need to provide answers to whether planetary systems are stable"? Since when are planetary systems outside of physics?
Your sentence "All Godel's incompleteness theorems says is that there will be open questions about a universe describable by finitely many rules" shows right there that there cannot be a theory of everything. How can you have a theory of everything yet still have open questions? That means that you have not answered everything.
It's my understanding that a theory of everything describes the rules by which the universe operates. It doesn't say anything about emergent properties of these rules.
For example, if everything in the universe obeyed Newtonian mechanics, I would say that Newtonian mechanics was a theory of everything. You would say that it isn't.
Technically, a "Theory of Everything" in physics is just a theory that relates the four known forces in the universe: gravity, electromagnatism, strong nuclear, and weak nuclear. The latter three (I believe) have already been unified. It's a "theory of everything" because it describes every force in the universe.
That of course does not imply that the theory of everything automatically gets you a complete description of the universe. Even in the context of a single force, it can be difficult/impossible to come up with a closed form solution for how many different objects interact subject to that force. For example, the behavior of gravity is really well understood but that doesn't mean that we can come up with straightforward, closed form solutions for the n-body problem of a bunch of stars interacting with each other's gravitational pulls in space.
One counterexample for you: Conway's game of life has finite number of rules but you can construct universal turing machine with it that will have formally undecidable behaviour.
Godel showed (and guys tell me if I mess this up) that formal self-consistent systems have both statements that are true that cannot be proven and false statements that cannot disproved. In other words, complete systems are incomplete.
This does not mean that complete systems cannot model reality to a high degree -- there's no reason why a ToE could pop out from some rotation or transmutation of mathematics. It just means there would be parts of it that would be incomplete -- the model itself could have a very high degree of fidelity.
When applied to higher math and physics, this is another way of saying "you don't know what you don't know" ie, the models can work perfectly across all observation space and still be true to Godel.
"Theory of Everything" is not a theory for everything, literally. It is just a catchphrase used by physicists to mean a theory that encompasses the "Standard Model" (which describes particle physics) with General Relativity and gravitation, thus describing the whole physical universe (which, in the physicists narrow mind, is everything). So Godel has nothing to do with this.
You can have a theory of everything that is incomplete. There are no problems with that. And that's what people is looking for... ToE doesn't mean "a complete theory of physics", in the logical meaning of complete.
Well leaving aside Godel, I think one can have a theory of everything that has, as Rumsfeld would say, "known unknowns", i.e., a theory of everything which "manages" in some way unknown parameters. Like infinities in quantum field theory go away by the nature of string theory's elimination of arbitrarily small distances. Anyway. I think I'm keeping my money on string theory, but an interesting thought nonetheless!
If you read a bit of Wolfram, he asks a provocative question: suppose the universe is, in fact, discrete and not continuous. If this is the case, and I think that's non-controversial now, then it may be that Sir Newton took us way down the wrong road with his discovery of the integral. We've been doing continuous math-type things with a universe that simply does not work that way. The integral was simply a cheat -- a numbers game that looked as true to reality as we could possibly verify at the time.
So we're working with known unknowns. That is, the integral works so well in most everything we do we're comfortable where it falls apart -- right around ToE, probably. But if we went belly-up as far back as Newton, where to start to fix it? I know I'm sounding like a shill for NKS now, but I _did_ find it had some really interesting ideas. In a computational universe, we could have really simple physics that lead to incredibly complex and non-intuitive results.
I didn't think the question of continuous versus discontinuous universes has ever really been resolved in a convincing way. Do you have any references?
No references and I may be going down the wrong path here, but wasn't there some relatively recent activity with respect to the quantization of space, with the Planck length being the minimal quantum?:
http://www.scienceandresearchdevelopmentinstitute.com/planck...
As far as I know the question is completely theoretical: we haven't been able to use the idea to produce any predictions which we might use to measure whether the universe is this way or isn't.
Also, that linked paper seems to be nothing other than numerology. It is interesting that the numbers are so close, but that could be a pure coincidence.
Numerolgy, hilarious. I have to use that one someday, hope you don't mind. At any rate, I meant to post a Smolin paper on LQG that posited quantized space,
and if I recall there was supposed to be some data coming in from an observatory that could lend some weight to the theory (back in 2005?).
You might also soon hear about his friend mentioned in the article, Brandyn. He's working on a problem that is just as important as ToE. They had a running joke: who would find ToE first, Garrent by math and thinking or Brandyn by inventing AI that would do it for him.