  We present a mean field model for spin glasses with a natural notion of
distance built in, namely, the Edwards-Anderson model on the diluted
D-dimensional unit hypercube in the limit of large D. We show that finite D
effects are strongly dependent on the connectivity, being much smaller for a
fixed coordination number. We solve the non trivial problem of generating these
lattices. Afterwards, we numerically study the nonequilibrium dynamics of the
mean field spin glass. Our three main findings are: (i) the dynamics is ruled
by an infinite number of time-sectors, (ii) the aging dynamics consists on the
growth of coherent domains with a non vanishing surface-volume ratio, and (iii)
the propagator in Fourier space follows the p^4 law. We study as well finite D
effects in the nonequilibrium dynamics, finding that a naive finite size
scaling ansatz works surprisingly well.
