Re: Ask any human to choice a number between 0 - 0xFFFFFFFF

In article <1169561746.772966.19450@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, "Pubkeybreaker" <Robert_silverman@xxxxxxxxxxxx> writes:

Dennis Yurichev wrote:
Hi.
If my question is not appropriate for sci.crypt, please drop me a note
about where I can ask.
Consider some software asking different users for a hexadecimal number
between 0 - 0xFFFFFFFF.
Is there any done research in statistical (and psychological) field on
what numbers used more often and less often, except of obvious numbers
like 0x11111111, 0x12345678, et cetera.

I don't know the answer to the question.

I do know, however, that regardless of whom you ask, the answer you
will get had probability 0 of being selected.......

I'll see your pedant point and raise you one.

No. You don't know that. Because you are wrong about it.

Even if one takes the sample space here as uncountable, nobody said that
the distribution over the sample space is uniform or even characterized
by a continuous cumulative PDF.

In any case, the sample space is not uncountable. It's countable.
The only responsive answers can be conveyed as finite text strings.

And even if we stretch that point and allow respondents to point with
their finger to a point on a hexadecimal ruler and interpret that
result as an infinite precision real number (measurement error, anyone?),
we still have to deal with the fact that a significant number of
human beings are going to answer "00000000" or "12345678" rendering
the probability of those responses strictly positive.

I realize of course, that I am being somewhat obtuse, but I want to
point out
the importance of being careful in specifying the problem. Your
question
said "number" and not 'integer'.

For a number drawn at random in [0, 0xFFFFFFFF], the probability that
it
has a finite representation is 0.

We're not talking about numbers drawn at random though, are we?

I select the number 973FAC1E.E9000173625FFA27......

You haven't selected a number. What is the rest of its hexadecimal
expansion? Is it constructed by a deterministic rule?

If so, the sample space in question is countable.
If not, it's not clear that your answer is responsive.

Do not say "number" when you mean "integer".

In psychological exercises the wording is part of the problem. Saying
integer instead of number changes the problem. Using a technical term
where a simpler term will do isn't always appropriate.
.

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