Tim May writes: > I want to give a solid example of a time-varying set and how it relates > to possible worlds (and even to MWI). > > Consider that cat being chased by the dog. > > Is the cat in the world in which he will escape the dog or is in the > world in which the dog catches him? > ... > In the other approaches, the Boolean "cat is in one world or in other > world" is replaced by a time-varying set: > > -- "We don't yet know which world the cat is in, or which world we are > in along with the cat, but in a few minutes we'll know for sure." (And > everyone will agree on this...there will be no disagreement amongst > honest observers as to whether got away or got caught by the dog.)
Future uncertainty is familiar to us, but one of the things that the many universe model introduces is past uncertainty. There is a sense in which the past is not unique and determined. My mental state is consistent with many macroscopically distinct pasts. My brain and my mind hold only a certain amount of information. Vastly more information than that has existed in my past light cone, the history of the universe which has led up to me. My brain is therefore very probably consistent with a great many past histories, each of which will lead to a brain, a mind and a mental state which is indistinguishable from that which I am now experiencing. From my first-person perspective, the past is indeterminate in much the same way as the future is, although to a lesser degree. And I think it is likely that some of these histories may be macroscopically distinct to a dramatic degree. It's even possible that there could be Earths with different sets of inhabitants, different cities, different historical events and I could be existing in many of these Earths with exactly the same mental state I experience today. Who is the head of the Chamber of Commerce of Gary, Indiana? It's possible that this question is actually indeterminate for me, that I may in a sense span universes where this has different answers. Of course I could do some research and find the answer, and then my mental states would diverge in a process somewhat analogous to the splitting of the MWI. But until then, from my first person perspective, there is no unique answer. Generally, when I learn information, my possible worlds diverge, and when I forget information, my possible worlds merge. Life seems to be a matter of forgetting almost as fast as we learn, so the set of possible worlds would have a very dynamic structure of different streams constantly diverging and merging. Hal