On Sat, May 1, 2010 at 7:37 PM, Brent Meeker <meeke...@dslextreme.com> wrote:
> Sure we can, because part of the meaning of "random", the very thing that
> lost us the information, includes each square having the same measure for
> being one of the numbers.  If, for example, we said let all the "1"s come
> first - in which case we can't hit any "not-1"s, that would be inconsistent
> with saying we didn't have any information.

We have two things here.  Random.  And infinite.

Three things actually.  My random aim.  An infinite row of squares.
And each square's randomly assigned number lying between 1 and 6.

If, due to the nature of infinity, there are the same number of 1's
and not-1's, then I'd expect the probability of hitting a 1 to be

But, there are also the same number of 1's and even numbers.

And the same number of evens and odds.

And the same number of 1's and 2's.

And the same number of 2's and not-2's.

AND...I have the *random* aim of the dart that I'm throwing at the
row.  So it's not a question of saying which number is likely to be
next in a sequence.  Rather, the question is which number am I likely
to hit on this infinite row of squares.

SO, I think we have zero information that we can use to base our
probability calculation on.  Because of the counting issues introduced
by the infinity combined with the lack of pattern.  There is no usable

All we can say for sure is that we won't ever hit a 7.  Ha!

We could say something about the probability in the case where the
numbers followed a repeating pattern.  There we only had one random
variable...my aim.  And we had definite information...the repeating
pattern.  Actually the infinite aspect in that case didn't add

So, I think the eternal recurrence Boltzmann brain scenario is more
similar to the random aim at an infinite grid of randomly arranged

> My personal view is the probability is a mathematical tool something like
> linear algebra.  It's useful precisely because it has different
> interpretations.  Here's the introductory paragraph I wrote for a course for
> engineers I taught years ago.  If you'd like can send you the rest of the
> hand-out off-line:

By all means, send it my way!  I'll give it a gander.  More
information is better!

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