To relate this to extremal black holes, we regard the exceptional Jordan algebra as a twenty-seven dimensional vector space over Z. This is the charge space for d=5 N=2 magical sugra, where the trace inner product takes values in Z (charge quantization). The off-diagonal octonion integers span twenty-four dimensions over Z, forming a charge lattice, from which the black hole can take its values. This twenty-four dimensional charge lattice is likely related to the Leech lattice via halving-sets.

]]>*closely tied to the concept of information entropy*

Yes, kneemo, this is where the fancy new higher monads come in. Funny, I had a research proposal along these lines a couple of years ago, but nobody thought it was worth worrying about. Oh, well.

To me, this is all just a part of **Mach’s Principle** for inertia, which is at the heart of causality. The right monads will form a ‘causal diamond’ for idempotent swapping structures. On one side of the diamond is Entropy and on the other is Information. The Entropy is about ‘looking outward’ (the arrow of time) whereas information gathering requires probing things more closely. But one must not mistake all this for the simple SpaceTime duality that crops up, because these monads are prior to everything else, including space etc.