Friday, October 8, 2010

Zeno's Paradoxes

I don't remember blogging about them...But they are quite an interesting way to fire you up into logical thinking and the border between mathematics and philosophy. I think a paradox lies at the heart of that, really...It starts out in mathematics and ends in philosophy. A lot of math does that.

Take the time to read more on this set of ancient paradoxes [that demonstrate the wonders in simple actions] on Wikipedia here...My favorite is the dichotomy problem!

Sometime I'm going to reach the exact half of this post [in word count]; perhaps I already did. If I did, then I must have covered a quarter of it earlier. If I had then I must have covered one-eighth of it earlier; if I did I must have covered one-sixteenth of it earlier and so on...Which means by the end of this post; I would have finished doing a seemingly finite task (in terms of time) in a number of infinite sub-tasks. 'How can that be possible?' is the question the dichotomy problem asks.

Some other things I've been reading into just today that may also be of interest [if you're a fan of hashing and hashing algorithms]:
The Birthday Problem
Merkle-Damgard Construction.

If you have any advice to start me up in the right direction when it comes to learning more about hashing algorithms, methods and programming, I'd appreciate the information!

God bless and check this if you have not already.

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