Why 3+1 metric rather than 4+0 or 2+2?

Why does the physical 4-dimensional space have a 3+1 signature rather than a 4+0 or a 2+2 for its metric? We give a simple explanation based largely on a group-theoretic argument a la Wigner. Applied to flat spaces of higher dimensions the same approach indicates that metrics with more than one time dimension are physically unacceptable because the corresponding irreducible unitary representations are infinite dimensional (besides the trivial representation).