Archive for G2

Evidence of Extropy is in the Building.

Posted in Building with tags , , , , , , , on March 8, 2009 by Wizzy

Wizzy keeps building geometric objects of more and more intricacy and complexity.  Wizzy’s building is therefore necessarily Extropic.

6672 prim E8 Polytope

6672 prim E8 Polytope

This is my latest project.  A 6672 prim E8 Polytope.  This one is more representative of the E8 than any of my previous attempts.  It took several attempts to successfully rez this object, and even so the sim creaked and groaned.

This particular rotation of the E8 Polytope is important because it shows *all* 240 of the vertices.  Each vertice can be seen above as a meeting of edge struts.

From this angle, we can see a clear hole on this axis going straight down through the object.  When flattened down to two dimensions this object would look this:

The 2D graph commonly recognized as the E8 Polytope

The 2D graph commonly recognized as the E8 Polytope

This 2D version has 240 recognizable vertices or nodes.  If Second Life had less perspective programmed into our view, from this axis or view we could see the object like this.

Some of you might wonder why I am so obviously obsessed with this object.  It is considered to be the most beautiful and elegant geometric object known to mathematicians.  That alone is probably reason enough…

But as I proceed with this obsession, at each step I learn more and more.  I gain a more intuitive grasp of what this thing is all about.  Each new discovery is a wonder and a joy.

Another axis of symmetry reveals itself

Another axis of symmetry reveals itself

Where do I go from here?

The direction of higher complexity leads from the eighth dimension up to all 248 dimensions of the E8 Group.

The direction of lower complexity leads downward to the G2.  The cube-like, hexagonal symmetry of the G2 lends itself to demonstrations of how quarks and the strong force relate.

Next stop, G2.