Talk:Geometric algebra

Deferential Geometry

Something I stumbled onto, that I feel is "somehow" related to geometric algebra, is Garrett Lisi's "An Exceptionally Simple Theory of Everything."

His notes on Deferential Geometry are above my head, and why he calls it 'deferential' I don't know. Still, I find the theory appealing, as it is a geometric interpretation of physical reality, much like Clifford algebra / Geometric Algebra applied to Dewey Larson's Reciprocal System of Theory. It's neatly summarised by Mitchell Porter:

The paper’s title is a pun on the mathematical nomenclature; E8 is an “exceptional” “simple” group, simple meaning that it lacks a certain type of internal structure, and exceptional meaning that it’s one of a handful of simple groups which fall outside the infinite families to which all the others belong. I suppose it’s also a reference to the unified theories of recent decades; Lisi wants to do without unverified innovations like supersymmetry and extra dimensions. A theory of everything can be simple, so long as its implications are sufficiently complex. Since most things that exist are regarded as already explained by existing physics, for most physicists the attempt to explain “everything” reduces to explaining, or at least completing, the existing fundamental theories. Everything else is just applied science and historical contingency.

I want to agree with Lisi simply because he disagrees with String Theory. The theory is broken-down for the non-expert a bit more in an interview on Wired:

Freelance physicist A. Garrett Lisi made headlines last year when he published his "Exceptionally Simple Theory of Everything" to an online wiki. The theory purports to be a blueprint of the universe, showing how all of the particles and forces of the universe are connected. Lisi, who is speaking at the TED conference in Monterey, California this week, rejects string theory -- currently the dominant model of the universe. Instead, his unification theory places all known particles and the four fundamental forces of nature (electromagnetic, the strong force, the weak force and gravity) onto an exceptionally complex 248-point mathematical model known as E8 that was formulated in the late 19th century. Lisi's schema uses 228 points of the model, with 20 points left over for what he predicts will belong to 20 as-yet-undiscovered particles. His theory met with enthusiastic media coverage, but to date, the scientific community has been far more skeptical about the validity of Lisi's model. Lisi left academia after obtaining his Ph.D. in 1999, and since then has been working odd jobs to support himself while spending the rest of his time working on physics, surfing and snowboarding. Wired.com interviewed him by e-mail before his appearance. Wired: Your entire career has been focused, in essence, on your rejection of string theory. What do you have against strings and extra dimensions? Garrett Lisi: It's more accurate to say my career (or, often, lack of one) has been focused on doing what I wanted. There are a lot of good things about string theory, and it's great that some people want to work on it. But, to me, it seemed too disconnected from real particle physics and gravitation. It seemed unlikely that many of these string constructions could ever be experimentally tested, or connected up with the real world. So I set off to follow my own interests.

More interesting discussion on PhysForum, also mostly over my head.