Two problems are discussed. The first is whether there has been time for evolution by natural selection to have occurred. The concept of a "protein space" is introduced, and it is shown that a fundamental inequality, concerning the proportion of all amino acid sequences which form functional proteins, must be satisfied if evolution is to occur. The second is whether there is any biological law (analogous to the second law) which enables us to put a time arrow on evolutionary processes. It is argued that Fisher's "fundamental theorem of natural selection" does not meet this need.