quote frome the wikipedia article:http://en.wikipedia.org/wiki/E8_(mathematics)
"E8 has rank 8 and dimension 248 (as a manifold). The vectors of the root system are in eight dimensions and are specified later in this article. The Weyl group of E8, which acts as a symmetry group of the maximal torus by means of the conjugation operation from the whole group, is of order 696729600."
the only i can understand in this explanation is that it is a damn big mathematical group, dimension 246 huihuihui ( am i right when i say the base for this algebraic body is , this is a lot ..
i can adopt it to linear algebra, where dimension is defined as the number of lineary independent values of the (vector) group, e.g. x,y,z as 3d coordinates forms an algebraic
group (...even a body ) and you have 3 lineary independent base vektors ( (1,0,0) ( 0,1,0) and ( 0,0,1) with those three vectors, you can create every other member
of vectors belonging to that group, e.g.
1*(1,0,0)+2*(0,0,1)+3*(0,0,1) wouild form the vector ( 1,2,3 )
but i go bancrupt when thinking about 248 of those
no, i can not help you out on this ... can anyone else ?