[darcs-users] Re: File name too long

[Peter Simons]

John Meacham writes:

 > collisions are not a concern. think about how big a
 > space of 160 bits is.

Right ... But you also have to think about how big the
_input_ space is!

The key to the answer is Algebra, not Combinatorics: A hash
function maps an infinite set to a finite set. Thus, it
cannot possibly be injective. Thus, collisions _must_ occur!

And the math is in perfect harmony with the world as we know
it. Reality doesn't give a damn about how unlikely something
is. Just because it isn't supposed to happen for the next
billion years, doesn't mean it won't happen in five minutes.
There _are_ people winning the lottery three times in a row.
And systematic collisions _were_ found in many hash
algorithms even years after their first publication.

Murphy's Law is mostly cited in humor, but it is a pure
mathematical truth: Tertium non datur. Either it impossible,
or it is possible. There is no such thing as "almost
impossible".

Peter