In reply to the member who seemed upset about my comments about the complex multiplication not reducing to real operations, I have to say a few things. 1. There's no room for indicating that a member is old-fashioned in my opinion. In any case, I won't waste time replying to such a person in the future after two occurrences of that behavior. 2. A positive or neutral orientation is the most easily detected part of reading somebody's internet or email postings, and I don't reply to people with negative orientations after two occurrences of that behavior. 3. The real and complex fields are NOT ISOMORPHIC, and the two- dimensional Euclidean plane regarded as a vector space R2 over the real field is not algebraically isomorphic to the complex plane over the complex field because R2 has no complex multiplication. This is not old-fashioned - it is upper division algebra. 4. The positive part of what I said in my previous posting is the part that is obscured by readers' anger: Rare Event Theory is the only way that I know of to get partially around the difficulty of item 3. Osher Doctorow