http://www.withoutatraceroute.com/2008/10/rome-the-eternal-city/ Time to live. Sat, 06 Sep 2014 18:43:23 +0000 hourly 1 http://wordpress.org/?v=4.0 http://www.withoutatraceroute.com/2008/10/rome-the-eternal-city/comment-page-1/#comment-103 Mon, 20 Oct 2008 21:06:16 +0000 http://www.withoutatraceroute.com/?p=1234#comment-103 Viewing non-Euclidean geometry as a fundamental shift in human thinking–akin to giving up the Earth as the center of the universe–is interesting. Most people would not be willing to even entertain the notion of parallel lines meeting. How many people can have been shaken-up? In math and science, it probably is earthshaking, as you say. Perhaps the biggest significance is the thinking required to come to non-Euclidean geometry: If we can’t prove parallel lines never meet, then let’s build a geometry where they do and see if there are paradoxes barring the geometry. This is crystaline logic in and of itself, but even more intriguing when the lack of internal paradoxes demonstrates we have been making unjustified assumptions. A new world dawns for those willing to explore.

]]>