mrb_bk brought up this wonderful quote today.
What good are impossibility results, anyway? They don’t seem very useful at first, since they don’t allow computers to do anything they couldn’t previously.
Most obviously, impossibility results tell you when you should stop trying to devise or improve an algorithm. This information can be useful both for theoretical research and for systems development work.
It is probably true that most systems developers, even when confronted with the proved impossibility of what they’re trying to do, will still keep trying to do it. This doesn’t necessarily mean that they are obstinate, but rather that they have some flexibility in their goals. E.g., if they can’t accomplish something absolutely, maybe they can settle for a solution that works with “sufficiently high probability”. In such a case, the effect of the impossibility result might be to make a systems developer clarify his/her claims about what the system accomplishes.
–The inimitable Nancy Lynch, in A Hundred Impossibility Proofs for Distributed Computing
This information is very useful for theoretical studies.