Password Impossible

I have have a terrible sense of Deja Vu about that picture but then again if any picture should evoke such a feeling then it would be this which as the commenter on the link page says clearly references the whole film. This is then in turn referenced by the stargate sequence in Contact where the timing of the events that Ellie Arroway experiences are blurred by the distortions she experiences.

Well that was interesting but not what I wanted to mention. I overheard someone commenting on the complexity of a password requirement and while I fully support the complexity of passwords, I began wondering if it was possible to define minimum password requirements which would be be impossible to adhere to. Leave aside for the moment the fact that if this ever occurred then no valid passwords would ever get created and therefore no one would access the system behind them. Of course if the spec said four letters, two numbers and one special character and then limited the length to six characters you would be scuppered but I was thinking of other restrictions - no dictionary words, no sequences of the same character etc. All this made me think of the formulae in Godel, Escher, Bach which I have not looked at for so long that I cannot now link them to any reality at all. It also reminds me of the record guaranteed to break any deck it was played on and in turn has turned on a flag in my head about a strange mathematician who mentioned what seemed a non sequitur in the recent Horizon programme about infinity vis. there is no such thing as infinity - numbers, he states, get very large, much larger than any of the stupidly colossal numbers we have defined - a Googol is peanuts compared to Graham's Number - but do in fact end at some point and revert to zero. This was mentioned and then forgotten - the guy suggesting it popped up like some wizard, stated his idea and vanished with no comment about it again. And where madmen lead I follow.