E8 and the Semantic Web

A link to this video can be found at http://www.youtube.com/watch?v=bgB3GrcyutU


A link to this video can be found at http://www.youtube.com/watch?v=n_KsaOu3LBs

Last blog we imagined the "googleverse": ideas that have shapes and patterns across spacetime, and how this is another way of describing the concept of memes.

Some ideas seem to spring from nowhere, spread instantaneously, then eventually be overtaken by other ideas. The way of imagining reality that we've been playing with here says there is a universe of spimes (things that have a shape in spacetime, which is made of energy and matter), memes (ideas and patterns that have a shape in spacetime), and life (the interference pattern that happens when memes and spimes interact).

The imagining-the-tenth-dimension meme, then, has survived and flourished not because it's the scientifically approved Theory of Everything, but because it's a mind-expanding way of holding in your mind what most people would have thought is unimaginable - the underlying fabric of reality. Like other visualization tools, it has its strengths and weaknesses, but it's still a fun way of getting people started thinking about those "really big picture" ideas.

As I've described it, the tenth dimension is equivalent to the unobserved fields of quantum mechanics, and the ninth dimension can contain the ways of beginning to organize those fields that can't be expressed as physical matter: the "really big picture memes" that express a preference for one way of organizing reality over another, but which are too broad or too contradictory to create a physical expression. This means that according to my way of visualizing reality, the 8th dimension would be the highest dimension for a reality to spring from.

http://www.arxiv.org/abs/0711.0770

Now we have Garrett Lisi, who is creating a huge stir in the physics world with a new proposal for a Theory of Everything that uses "E8" - a complex, eight-dimensional pattern with 248 points. Here's a youtube animation demonstrating some of the rotations that can happen within an E8 construct:



As visually appealing as this animation is, its implications are startling: Lisi has demonstrated that there is a way to place the various forces and elementary particles (including their possible quantum spin values)on E8's 248 points. Rotating Lisi's model in various ways reveals the explanation for a variety of interactions, some of which (like the clustering of quarks into families of three) are natural outcomes from this structure. Some points in his model are currently occupied by particles which have been theorized but which have yet to be seen, and there is some hope that the Large Hadron Collider in Switzerland may reveal some of those particles when it goes online next year.

Whether this theory proves the existence of higher dimensions or not is open to interpretation - Lisi himself says this geometric pattern, although it is based upon an 8 dimensional construct, could be fully realized within our 4D spacetime without requiring additional dimensions. In an article in this week's New Scientist magazine, string theorist Sabine Hossenfelder (of the Perimeter Institute for Theoretical Physics) points out that this could be complimentary to string theory, which she says also uses E8 to describe the Calabi-Yau manifold, the higher-dimensional shape that string theory says our universe is derived from.

As Einstein liked to say, our description of the universe should be "as simple as possible, but no simpler". That's why the idea that our entire 4D universe can be defined from a geometric projection like the one seen in the above video is so appealing. But whether our 4D universe is a lower-dimensional shadow cast by higher-dimensional patterns, or whether those higher dimensions are imaginary because we can't ever see them may really be nothing more than two different ways of thinking about the same idea.

Last blog we also looked at the idea that there is an acceleration happening in our world, as ideas seem to spread faster and faster. Tim Berners-Lee's Semantic Web project is a great example of the tools that are arising now to help keep us all from being buried under a sea of rapidly rising and falling memes, which threaten to become an incomprehensible and overwhelming white noise. Perhaps E8 and the Semantic Web will become useful as ways to organize and rotate through the information of the world?

As simple as E8 may be, I've been trying to visualize something even simpler here. Personally, I have long been a fan of the idea of helix shapes derived from stacked dodecahedrons, and the implied six degrees of separation concept within that idea.
I was surprised to learn from the article I'm referring to in New Scientist magazine, then, that Garrett Lisi has also been using G2 rotations, a hexagon-based system which is a subset of E8. Apparently G2 can be used, for instance, to describe the relationship between quarks, antiquarks, and gluons.

If the Semantic Web eventually allows us to understand the googleverse of ideas as being derived from the interrelationship of Just Six Things, will we have passed the threshold of "simple as possible but not simpler"? It's an interesting exercise: try to come up with the six categories under which you should be able to put everything about your life and everything you know. If the Semantic Web could ultimately be used to connect together our knowledge into something as simple as that, we would really have reached a seemingly impossible goal. But even E8 as an overlay might be a very useful tool in our desire to keep the accelerating meme-space we are swimming through from becoming too much to fathom.

Enjoy the journey,

Rob Bryanton

PS - for a more hands-on experience of where the Semantic Web could take us, sign up for an account at Twine.com.