Re: Small probabilities

Iain,
Here goes four for the day.

I agree that you did not intend my problem, but I don't think you can
quite get out of it. Your revision has A and B specified. There is no C.
One has to decide between A and B. But reality does not specify strict
alternatives. That is, you don't know that there is a B.

Where does one draw the line? If A and B are specified, we can be fairly
confident that an instance belongs in one rather than the other. But we
can't be certain. Unless we know relevant facts about A and B, we cannot
exclude either A+B or C. It looks to me as though you are thinking of A
Xor B, but even that does not necessarily exclude additional
possibilities.

On the other matter, I understand that you were being facetious. But
there is a great difference between "God, you got it wrong" and "God, I
don't understand." We tend toward the former because we're sure we're
that bright. We should rather go along with Job's "Though he slay me,
..." explicitly. With this a good question may be, "What did I
misunderstand of your intent?" Sometimes there seems to be no error, just
that God takes us from where we are. I recall painful situations where I
wondered "why?" but now I recognize, "That's why."
Dave

On Sat, 14 Jan 2006 21:21:25 +0000 Iain Strachan <igd.strachan@gmail.com>
writes:
Dave,

I think your argument that we know someone intelligent did something with
the chess pieces is not quite the point I was making. The argument is
whether someone designed the _position_ to be one that was arrivable
after a sequence of legal (though bizarre) moves, and that you could
deduce that exact sequence, or whether the position was arrived at by
some arbitrary random process. I gave the example of a child playing
with the pieces as toy soldiers. But, as you say, the child might put
the pieces on the corners of the squares. If a monkey had had a go at
it, many of the pieces might be lying on their sides. But let's make the
experiment more tight.

You have a computer program where you click a button on the screen and a
chess position is displayed. With 50% probability the computer generates
a position using random techniques. With 50% probability it loads up a
published retrograde analysis position. You look at the position on the
screen and you have to tell if it was the random position, or the
retrograde analysis position. I suppose you could say the non-puzzle was
also designed - someone had to write the computer program and design the
algorithm for the random number generator etc. But I'm talking about
detection of the way the chess position was designed - was there
intentionality behind it, to produce the puzzle, or was it a fluke of the
random number generator? I believe that if I did "solve the puzzle" I'd
deduce on the grounds of probability, that it wasn't the random number
generator that did it.

You say it's possible, though unlikely that the thoughtlessly generated
position would correspond to a valid retrograde analysis puzzle. But
where do you draw the line in the sand? Given quantum mechanics, just
about everything is possible though unlikely. In "Hitchhiker's Guide to
the Galaxy", Douglas Adams humourously explored this with the notion of
the "Infinite Improbability Drive" (driven as I recall by a Brownian
motion generator in the shape of a cup of tea). Such a drive could, for
example, cause all the molecules in a party hostess's dress to appear 1
metre to the right of where they should be. Such an event is possible,
though extremely unlikely. I'm guessing if you saw that you'd say it was
a supernatural miracle, even though it's possible.

Regards,
Iain
Received on Sat Jan 14 19:07:56 2006