Tuesday, March 1, 2011

Dave Richeson's Double Torus Clothesline Trick

  • Claymation! Who doesn't like claymation?

From David Richeson's weblog "Division by Zero", here, and his book: Euler's Gem (strongly recommended).

BTW, Today, March 1, is World Maths Day 2011 Click here, thanks Pat B.

OK, that was freaky, now try some of the links that show up at the end of the YouTube video. Topology is COOL, man!

"Euler's Gem" is about Algebraic Topology, and Richeson's exposition is simply beautiful. He certainly doesn't patronize the reader, since he has actual equations sprinkled throughout the book, nor does he make the John Q. Intelligent Layman Taxpayer (ahem) feel like an idiot either as one might feel when reading Weinberg's or Penrose's excellent books on Math Phys (although to be fair to Steve Weinberg and Sir Roger, those are textbook-grade books), assuming Math Phys is new to you.

There are a fair amount of illustrations as well, 99.9% of them clear except Fig. 17.3 on page 175 that inspired the above video. Other than that, it seems the proper balance between prose, equations, and illustrations.

Well, I didn't mean this to turn into a review of Dave's book so much to alert that there is a real gem on the bookshelves at your local bookstore that goes by the name of "Euler's Gem" and it's well worth the $$$.

Speaking of which, I'm a bit depressed that my local Borders bookstore is closing. Borders has filed Chapter 11 bankruptcy papers, and this is sad indeed. Amazon is to blame I reckon more so than the fact that less than half of Americans read as much as one book per year. I think the day of the bookstore is fading away. Ah, well, progress. What can you do, Shrug.

In any event, the Borders in question is having a closeout sale so loaded with my Borders Bucks I was able to purchase the extremely beautiful The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics by Clifford A. Pickover for eight dollars, which along with Dave Richeson's book and The Princeton Companion to Mathematics and the new book by Yau and Nadis should keep me busy for the next year. ;-)

A Double Torus made from a Single Super Silly String (soon to be revealed at the sLHC in s2020)


gus said...

OK -- that didn't help much. I would really like to see how the double torus trick works. I can't understand it from his book and the claymation, although it is cute, does not really help much.

Would somebody please explain this so that even I canunderstand it (if possible).


Steven Colyer said...

Good question, Gus! I must admit I had to watch that video twice (that is to say watch the "trick" 4 times) before I "got" it.

I'm not happy I missed it the first 3 times, since I'm not a dummy. However, from Psychology, I remember studying "Cognitive dissonance", aka "lying to one's self" aka "rationalization."

That is to say, the human brain is unhappy when we perceive something that makes no sense based on our practical experience, so we have a tendency to process what we see into something understandable, if at all. Donuts do not REALLY transform into coffee cups, do they?

Topology is wonderful to me because it's weird, but even I have to "suppress disbelief" when I see something outside my normal real-world ken. Try looking at the video a couple more times. If Dave wants to do a followup video, I would suggest putting rings and lines on the parts that transform, and/or do it again in slow motion.

Which reminds me, unlike the ancient days of videotape, You Tube doesn't have "slow-motion." Are we going backwards?