On 1/10/2015 4:08 pm, Stathis Papaioannou wrote:
On 30 Sep 2015, at 10:10 PM, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
On 1/10/2015 12:44 am, Stathis Papaioannou wrote:
In an infinite random sequence of numbers it is possible that my
phone number appears once and never repeats, while other eight
digit sequences appear multiple times; but I wouldn't bet on it.
An infinite random sequence of digits has certain well-defined
probabilistic properties. In particular, ll digits are equally
likely, and all sequences of any particular length are equally
likely. If that were not so, the sequence would not be random. So
your phone number will occur many times. But this is not a good
analogy because it relies of the definition of a random sequence of
digits. We do not have any comparable uniformity definition for a
collection of universes.
A good guess is that the universe is infinite and every configuration
of atoms repeats. If it is not infinite then a given configuration may
not repeat. It could also be infinite but only some patterns repeat -
others do not. There might be infinite copies of Mars, but only one
Earth. That would be strange, but possible. That's what I thought you
were proposing to fill an infinite universe with.
Such would be a completely unevidenced guess -- no better than any
other. Even if the universe is infinite, there may be patterns (of zero
measure) which do not repeat. Your example of universe with many copies
of Mars but none of Earth is not really what I had in mind. The
evolution of complex structures such as galaxies, stars, planetary
systems, and the like depends on the initial conditions. You might not
get the necessary clumping, or dark matter might not be sufficiently
common to aid clumping, or ...... So you could get an infinite number of
repeats of uniformly rather dull universes, with only one with the
complex structure we see, sufficiently complex for suitable planets to
form, and for life to evolve on these. Much less intelligent life, or
copies of oddities like you and me!
Bruce
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