Through the Looking Glass

"Why, sometimes I've believed as many as six impossible things before breakfast."
-- Lewis Carroll (Alice In Wonderland)

I love it when disparate mathy things I stumble across over a couple of days start bouncing off one-another in my head....

First, let me point readers to this per-usual great response today from Keith Devlin to a NY Times piece I had referenced here a couple days back (about Common Core):
http://devlinsangle.blogspot.com/2014/07/the-power-of-dots.html
(DO NOT miss this post... whatever side of the issues you're on!)

...Next, a h/t to Vi Hart for introducing me to the YouTube channel of "Looking Glass Universe":

https://www.youtube.com/channel/UCFk__1iexL3T5gvGcMpeHNA

Vi mentioned it for its excellent short vids on physics topics, but there are also some more strictly math videos as well, including the below, wonderful treatment of one of my favorite, mind-boggling, math puzzles/conundrums (...Keith Devlin writes above that "understanding structure... requires human insight. It is not trivial and it is difficult" -- I think this video possibly captures that in 3 minutes):



And finally, the above video, in turn, led me to recall a brief posting from a couple days back on the exquisite "Painter's Paradox" of Gabriel's Horn (another lovely mind-bender):

http://tinyurl.com/qhqphpa

The sudden inter-meshing (cross-fertilization, if-you-will, in my mind) of Gabriel's Horn, the diagonal paradox, and Dr. Devlin's emphasis on structure, pattern, and insight/creativity (...which can make the seemingly impossible, possible), was for me, a beautiful thing!...