RE: Is the universe computable

From: Kory Heath <kory.heath.domain.name.hidden>
Date: Tue, 20 Jan 2004 23:01:14 -0500

At 1/21/04, David Barrett-Lennard wrote:
>This allows us to say the probability that an integer is even is 0.5, or
>the probability that an integer is a perfect square is 0.

But can't you use this same logic to show that the cardinality of the even
integers is half that of the cardinality of the total set of integers? Or
to show that there are twice as many odd integers as there are integers
evenly divisible by four? In other words, how can we talk about probability
without implicitly talking about the cardinality of a subset relative to
the cardinality of one of its supersets?

I'm not denying that your procedure "works", in the sense of actually
generating some number that a sequence of probabilities converges to. The
question is, what does this number actually mean? I'm suspicious of the
idea that the resulting number actually represents the probability we're
looking for. Indeed, what possible sense can it make to say that the
probability that an integer is a perfect square is *zero*?

-- Kory
Received on Tue Jan 20 2004 - 23:04:34 PST