My Hypercube

In E8 you got Dalston, Mare Street, London Fields and even bits of Shoreditch. It's the kind of place where the girls wear denim short-shorts even when it rains (pairing with a kitsch raincoat of course.) It's the kind of place where cultures are supposed to smash together to birth sparkling creativity. Yes, truly one of the coolest postcodes in Britain. There's just one thing slightly cooler than this haven of the hip. Yup, that thing above is also E8. It's a 248-dimensional hypercube.

Allow me to stretch your mind. A hypercube, essentially represents the algebraic basis of a cube in different dimensions. A hypercube in 1 dimension (n1) has 2 vertices linked to 1 other, basically a line. A 2 dimension hypercube (n2) has 4 vertices connected to 2 others; a square. And a 3 dimension hypercube has 8 vertices linked to 3 others; a cube. All the connections must be at opposites and right angles to all the other connections. Here's a diagram of the first few:

Innit' pretty and perfect? You can keep going with the same basic formula. Using the 2 to the power of the number of dimensions to figure out the number of vertices (2, 4, 8, 16 etc.). Easy. Only it starts to fall apart after a while, things go wrong and the forms don't work, the right angles can't be held etc. etc. All very erm... "mathy". Anyway, at 248 dimensions it all briefly clicks back into place for some reason. This is called the Exceptional Simple Lie E8 Group. There's too much to go into here. Most of it I don't want to go into since I'm not sure and I don't want to put my foot in it with some militant mathematicians.

But, my point enters here. (You probably could have skipped the bit above but they are nice diagrams I suppose, well done you.) A theoretical physicist, also known as an extreme sports fanatic and firm believer in the 'balance' of life turned it into a Theory Of Everything.

(Gasp here.)

Extreme sports aside, Antony Garrett Lisi is taken quite seriously in theoretical physics so when he published An Exceptionally Simple Theory Of Everything in 2007 a lot of people sat up and paid attention. He showed that it might be possible to unite gravity and string theory (the wet dream of all theoretical physicists) using the E8 group.

Not sure how, still don't get it. As far as I can tell, you take the 248-dimensional super structure, imagine it as a wobbly 2-dimensional sheet and at every point (of which there are infinite) place a sphere. The interactions of these spheres define the universe. I think.

Sounds nuts and it probably is. The point is, that in the light of a theory that might possibly unite the behaviour of the entire observable universe in a flawless mathematical form, Shoreditch pretty much sucks.