Re: Can Events of Zero Probability Happen?

On Jan 15, 4:08 pm, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On Tue, 15 Jan 2008 02:36:45 -0600, Robert Israel



<isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> writes:

On Sun, 13 Jan 2008 21:37:23 -0800 (PST), Shubee <e.Shu...@xxxxxxxxx>
wrote:

On Jan 12, 10:05 am, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx>
wrote:

_If_ you're interested in resolving the difference between
you and the physicist you'd ask what I suggested you
ask and see what he says. Because it's possible that
he'd have no problem with "choose a real between 0 and
1 at random", and in that case you could explain why
he's simply _wrong_ about the impossibility of events
of probability zero happening.

Sure, on the face of it, it seems possible to reason with a physicist
that believes that conceptualizing events that occur with zero
probability is unfathomable. The problem is, he explicitly said that
even an event of incredibly small probability can't happen.

First, if he said that why didn't you say so? There's a big difference
between that and saying that events of zero probability can't happen.

Second, again you should simply ask him a question. First ask him for
an epsilon > 0 such that an event of probability < epsilon can't
happen. Second, calculate an N such that 2^(-N) < epsilon.
Third, ask him to flip a coin N times and tell you what sequences
of heads and tails resulted. Then point out that the probability
of that sequence of heads and tails is < epsilon.

Of course, if he's clever he'll take epsilon so small that he won't be
able to flip a coin N times.

Third, no he _didn't_ say that! He said "Probabilities this low
are generally taken to mean the event could not have happened."
That's _true_.

Yes it is. Suppose I tell you that I was watching a glass
of water the other day, and with no outside energy applied
it just happened that half of it froze solid while the other
half boiled away. Would you believe me?

You'd need a heck of a lot of coin flips to get a probability that small.

That doesn't answer the question. Would you believe me if I said
that happened?

Of course not. But that's because of my assessment of the
probabilities of
1) the event actually happening
2) you either lying or hallucinating.

I also might not believe you in situations where you assert
something that is clearly not impossible (e.g. if you were
trying to sell me something).

Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada


.

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