Tuesday, November 20, 2012

A Little Geekery

The last few days have been pretty depressing to write, and to read, I'm sure.  I want sitemeter to give me a "slitmeter" - how many people read my stuff and slit their wrists.  So I want to write about  something more fun tonight.

Most people know the art of M.C. Escher, a 20th century Dutch artist known for his mathematically inspired drawings, many of which depict impossible objects.  A famous example is Belvedere, drawn in 1958 and shown here:
At first glance, this looks perfectly normal.  Then you notice that the columns that start in the front actually end at the back and vice versa.  Some of his drawings are impossible.  Look closely at the people on the stairs in Relativity:
Some Escher drawings, a Penrose Triangle for example, can be made into real objects by using forced perspective: they look the way Escher drew them only when viewed from one very specific angle.

Professor Gershon Elber at Israel's Technion Institute of Technology has studied the drawings and developed ways to actually make models of these.  See his ‘Escher for Real‘ project at the Computer Science Department.  Dr. Elber has created a video that has garnered a massive following.


EDIT 2050 EST:  I forgot the link to "It's A 3D World" - lots of good stuff to look at there!


  1. Just loved that video - thank you so much for posting it. Wouldn't it be great to have that model sitting on your coffee table and be able to look at and hold it everyday?

    Phyllis (N/W Jersey)

    1. Seriously!

      Makes me think I need to make a 3D printer. The cheap hobbyist kits aren't super expensive. At least, not like the professional boxes.

  2. Programming a 3-D printer to do an Escher would be quite a feat.

  3. The second drawing reminds me of dealing with the government...

  4. There is a great book called "Goedel, Escher, Bach" that has stories about those people and the fun math around their stuff.

    Bach is quite fractal.

    The Escher stuff reminds me of half diminished 7th chords, where the chord can connect two different keys by becoming re-defined by the new key. But that's more Wagner or Beethoven or even jazz, than Bach.

    1. "Goedel, Escher, Bach" is a book I remember seeing a lot of when it came out (1980?) and not much since then. Never got around to reading it, but always meant to. Always a 2nd or 3rd priority.

      Your last statement kinda puzzles me, though. I need to go listen to some diminished 7th chords and try to make sense of it.

      I'm at that awkward stage. I know too many chords to be a rock musician, but not enough to be a jazz musician.