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Monday, June 3, 2013

Cantor's Paradise…

Keith Devlin's latest "Devlin's Angle" blogpost was inspired (in part) by his moderation of the World Science Festival panel (shown in my May 31 post):


He muses about whether the "study of infinity – in particular the hierarchy of larger infinities that Cantor bequeathed to us – would ever have any practical applications." (...and he thinks likely, not).

Part of what makes Cantor's work so eternally interesting is the huge divergence of opinion about it from his very own time. As Devlin writes, "Reactions to Cantor’s revolutionary new ideas ranged from outraged condemnation to fulsome praise." And these completely opposed viewpoints came from individuals equally-well-established and respected in the field. One of the paradoxical aspects of infinity is the equal ease with which it may be discussed in either direction: i.e., the infinitely large or the infinitesimally small. In any event, it was David Hilbert who eventually coined the term "Cantor's Paradise" for the new Cantorian thought that did slowly take hold.

Even so, still today, "infinity" can be such a difficult concept to grasp, that Cantor's ideas remain a frequent target of attacks by "crackpots" of the sort Mark Chu-Carroll often hears from:


In other news... the 99th Carnival of Mathematics is now up at Wild About Math blog for your delectation:


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