manaster at manaster at
Mon Feb 8 20:14:50 UTC 1999

Brian is exactly right on both points.  Re the second
one, there is a common fallacy here which I think
has been addressed in some of my joint work with
Baxter and Hitchcock, namely, people think that the
"expected" value is somehow guaranteed to be th
one you find, e.g., that if you toss a coin100 times
it will be precisely 50 heads and 50 tails, whereas
in fact it is quite likely that it will NOT be, and
it possible though not very likely that it could
be 0:100.  Much of the stuff that people publish
on probability in comp. lx. suffers from this fallacy.

On Fri, 5 Feb 1999, Brian M. Scott wrote:

> Patrick C. Ryan wrote:

> > What I find amazing is that you would think a "100% CORREKATION" does not
> > establish a cause and effect relationship.

> It obviously doesn't.  Imagine a large, square room whose sides are
> oriented east-west and north-south.  The floor of the room is blue in
> the northern half and red in the southern half.  The ceiling is blue in
> the eastern half and red in the western half.  A track runs through this
> room between the SW and NE corners.  Mounted on the track is an opaque
> cubical with a window in the ceiling and another in the floor.  You are
> riding in this cubical, which moves slowly but erratically back and
> forth along the track.  From time to time a buzzer sounds, the window in
> the floor opens momentarily, and, as it closes, the window in the
> ceiling opens.  You find that every time you see a blue (resp. red)
> floor, you also see a blue (resp. red) ceiling a moment later.  The
> correlation is perfect, but there is clearly no cause-and-effect
> relationship between the floor color and the ceiling color.

> > I can see why you prefer not to deal with mathematical models. If you have
> > 100 trials, and the same cause has the same effect, the probability of the
> > cause creating the same effect again is 100%. Not 99%. Not 98%. Infinity is
> > not a factor in this equation.

> No.  I flip a fair coin (the 'cause') 100 times and get tails (the
> 'effect') 100 times -- unlikely, but certainly possible.  The
> probability that I get tails on the 101-st toss is still 1/2, not 1.

> Brian M. Scott
> Dept. of Mathematics
> Cleveland State Univ.

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