Regarding Objective Reality, E₈, and string theory (part II)

An article in the New York Times describes E₈ as “some sort of curvy, torus type of thing” and states twice that it has 57 dimensions.  The Wikipedia article on E₈ contains 2800 words, but after reading them I now know even less: E₈ seems to have only eight dimensions, or is it 248, or perhaps 696,729,600?  The number 57 does not appear there, but only in a catsup article.  They do show a nice Tinker-Toy picture, but obviously it captures very little of E₈’s hyperdimensional grandeur.

The problem is that I pre-announced a post about E₈, but I have no idea what that word *means* to mathematicians.  If I am to write an entire essay about a word that I don't understand, then I must be either a PHB or a linguist.  I actually have half a bachelor's degree in linguistics, so hopefully it will be okay if my hair isn't quite pointy enough for this essay.

So what does E₈ have to do with Objective Reality?  That’s a hard question.  Let's start with an easier one: is E₈ *alive*?  Think about that for a moment.  Does that sound like the silliest question you've heard all day?  It's completely outside the Overton window of socially-acceptable questions.  What kind of Commie-pinko-moonbat loonie would even ask such a thing?  Let's review the range of answers:

• Western Civ: No, because E₈ was not “born” and cannot “die”.  It does not eat, reproduce, or evolve.
• Anishinaabe (the Great Lakes Indians): Yes, because there are questions you can answer by studying E₈.
• Brain science: Maybe, because we don't have a clear idea yet what the word “alive” actually means in terms of brain activation.  Some research suggests that the superior temporal sulcus is active when analyzing situations that Western Civ would say are “dead” while the Anishinaabe would say “alive”.
• Furry: Yes, because the word E₈ can be drawn as a face-in-profile with a goatee.  Add some stick-figure arms and legs and you can make a dancing cartoon that sings about the philosophy of science in rhyming couplets.
• Dictionary: Yes (senses 2 and 5) or no (senses 3 and 4) or begs the question (sense 1) or cupcake sauerbraten tarball (sense 6).

Well, that clears things up nicely, doesn't it?  We can now confidently conclude that philosophy is a method for turning wrong answers into a continuing stream of research grants. 

On to our next question: does E₈ *exist*?  Philosophers have made lots of money on this one!  (Bonus question: define “alive” and “exists” so that God has both properties but rainbow-pooping unicorns have neither.)  Let us review the isms that philosophers have come up with:

• Nominalism: No, the word E₈ exists but the concept it refers to is imaginary.
• Idealism: No, because only consciousness exists, not the things that we are conscious of.
• Intuitionism: No, because only the natural numbers were created by God; everything else is man’s work.
• Formalism: Begs the question because math is just a game and has nothing to do with the real world.
• Logicism: Begs the question because math is just a sub-branch of logic so go ask the logicians.
• Platonism: Sort of, but the E₈ that you or I know about is just a shadow of the real E₈ whose grandeur is beyond any ape’s ability to appreciate.
• Social constructivism: Yes because E₈ is something that mathematicians talk about.
• Empiricism: Yes because it was discovered rather than invented.
• Realism: Yes, but only if E₈ describes string theory and string theory describes Objective Reality.

Well, *now* we're getting somewhere!  So if E₈ is needed to describe string theory and string theory is needed to describe Objective Reality and Mathematical Realism is the correct philosophy THEN WE WIN!

There's an article called An Exceptionally Simple Theory of Everything that was apparently never published in an official journal.  It was written by “surfer and theoretical physicist” A. Garrett Lisi.  BTW, the phrase “exceptionally simple” is a pun referring to E₈, not a measure of the theory’s conceptual difficulty!  The Wikipedia article has an animation, one frame of which I am showing to the right.  Note the multiple occurrences of the “Star of David” motif, hiding in plain sight within this physics theory, thus proving that Rabbinic Judaism is the only correct religion.

Anyway, Lisi’s theory shows how each of the 248 symmetries of E₈ can be thought of as corresponding to one of the 248 subatomic particles (including 22 that are yet to be discovered).  Many mathematician-physicists think that it would be sooo kewl if this theory turns out to be correct, although Gödel told us 80 years ago that there cannot be a “theory of everything” because every theory of the universe must be incomplete, inconsistent, trivial, and/or obsolete.  So why do they even bother?

Since I haven't completely run this topic into the ground, expect a (part III) at some point.