A friend of mine (who wishes to remain anonymous on the web) pointed me to Leslie Lamport's unpublished paper on Buridan's principle and expressed her disagreement over the following statement:

[I]f the ball is positioned randomly, random vibrations are as likely to keep it from falling off as to cause it to fall.

I would love to know what “randomly” means here, since we're evidently constrained to placing the ball on the edge of the knife. Does it mean “not symmetrically about it”? In any case, I agree that random vibrations will not keep the ball on the knife's edge: it seems highly unlikely that the effect of a first de-stabilizing impulse on the ball will be subsequently countervailed by a sequence of corrective impulses that keeps the ball on the knife's edge, and even more unlikely that this continues indefinitely.

So, while I grant that it's possible for the ball to remain on the knife's edge in the presence of random vibrations, I also think it's unlikely that it will. Unless we've misunderstood what Leslie is saying here, it seems plausible that this claim about the "ball on a knife's edge" is partly responsible for the paper's rejection, as it is bound to trip most physicists' wires.