Monday, August 20, 2012

On Infinities

Kurt Godel realized that there were limits to Mathematics (as shown by his Incompleteness Theorem) and he was wiling in part to accept these. However at the same time a part of him hoped that he could access intuitive knowledge through logic. His quest to do so eventually caused his life to spiral out of control ending in the unfortunate circumstances of his death. A genius he stretched the limits of rationality but could not access with the same conviction what lay beyond it.
Georg Cantor took Mathematics into regions nobody has dared to venture. However he found a world that surpassed the limits of human logic and like a sailor drawn by the songs of a siren was adversely eventually engulfed by its illusiveness.

All of this makes me wonder: Are there certain truths that we are just not supposed to know?
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