>From: Norman Samish [mailto:[EMAIL PROTECTED]
>Sent: Monday, June 27, 2005 4:33 AM
>Subject: Re: Have all possible events occurred?
>>>Norman Samish writes: Stathis, when you say "if you believe that
>>>everything possible exists" are you implying that everything possible need
>>>NOT exist (thus refuting Tegmark)? Wouldn't this mean that space-time was
>>>not infinite? What hypothesis could explain finite space-time?
>>Brent Meeker writes: Spacetime could be infinite without "everything
>>possible" existing. It might even depend on how you define "possible".
>>Are all real numbers "possible"?
>Norman Samish writes:
>Brent, to me this is cryptic. Can you enlarge on what you mean? Your
>statement seems to contradict what I've read, more than once; "In infinite
>space and time, anything that can occur must occur, not only once but an
>infinite number of times." I don't know the author or source, but I've
>assumed this is a mathematical truism. Am I wrong?
It's certainly not a mathematical truism. It might follow from certain
conceptions of quantum mechanics; but I haven't seen any explicit derivation of
that. There's nothing to prevent the universe from being infinite in both
space and time and yet be almost completely empty, or filled with only photons,
or repeating periodically, or various other possibilities if you are willing to
count as "possible" different spontaneous symmetry breaking of the fundamental
>As for "Are all real numbers 'possible'?" According to the definitions I
>use, the answer, of course, is yes. I obviously do not understand the point
>you are trying to make.
Different sets have different cardinality. The cardinality of real numbers is
greater than that of integers. The cardinality of functions over space is
greater than the cardinality of points in space. So what's the cardinality of