From: Lee Daniel Crocker (lcrocker@mercury.colossus.net)
Date: Mon Mar 29 1999 - 11:25:45 MST
[Thought experiment about 20 numbered people]
>> Are you aware that this is the same reasoning that gives rise to
>> the Doomsday argument? Do you accept that argument? If not, why?
Not exactly. The problem is properly specified. What "gives rise"
to the Doomsday Argument is that it is not properly specified, so
one must make assumptions to fill in the gaps--and different people
make different assumptions.
For example, "probability" exists only as a relationship between
a set of events and a superset ("universe") of events. Both must
be specified for probability to have any meaning. In the problem
above, the universe of events is clear--you might be one of 20
given people. The subsets of events in whose probability we are
interested is well-defined too, so we can answer it. In the DA,
the universe of events is "all possible physical universes"--a
concept so ill-defined that one could write pages just on what
that means.
The second assumption, of course, is self-sampling. That too has
more problems in the DA than here, because in the DA we must make
some assumption about just what we are a sample of, whereas in the
problem above that's a given.
Finally, the "100!-th digit of pi" bit is irrelevant--it's no
different from a poker player using probability to determine the
proper bet on the next turned card, even though its identity is
already strictly determined by an earlier shuffle, although with
the slightly added twist that the frequency of digits is not
strictly random (but then again, neither is a shuffled deck of
cards).
-- Lee Daniel Crocker <lee@piclab.com> <http://www.piclab.com/lcrocker.html> "All inventions or works of authorship original to me, herein and past, are placed irrevocably in the public domain, and may be used or modified for any purpose, without permission, attribution, or notification."--LDC
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