Brain puzzlers like these have been tickling the minds of humanity for thousands of years, made popular by artists like M.C. Escher - and now by computer programming and graphic artists worldwide.

But as a language-oriented individual (who has been anything but mathematically-minded), allow me to discuss linguistic self reference: Sentences and word definitions that devour themselves!

Sentences - or even lone words - can be a paradoxical loop, easily blowing your mind as easily as any Escher artwork could! For example...

The Liar Paradox:
This sentence is false.

or

Words that exist only to describe themselves:
sesquipedalian (a long word or person who uses long words)
T.L.A. (three letter acronym)

So which came first? The chicken or the egg? The top or bottom drawing hand? The acronym or the definition of the acronym?

Just so you know that programmers and mathematicians don't have all the fun. Linguists can rock a great self-referential paradox as well as the next nerd.

http://image.examiner.com/images/blog/wysiwyg/image/egg-chick.jpg

My personal take on self reference is that it is the point where math, science, linguistics, and art reach the absolute boundaries of their own existence. Running the infinite loop a few times in our minds - whether we're tracing the pattern of the drawing hands, or analyzing the sense of T.L.A. - teaches our brains the concept of futility.

I've always considered that there actually is a movie that broke it down to a very basic and understandable level - "War Games", the Matthew Broderick movie from 1983, in which a supercomputer must "learn" the futility of nuclear war, just as it can discover the futility of playing Tic Tac Toe. Only when the computer learns there is no winning, there is no end, then the world is saved from destruction. It has to recognize a looping pattern. It has to recognize that defense leads to offense leads to defense leads to offense.

And in many ways, that's the exact same concept that Escher embodies with his drawing hands. There's no start, there's no end, there's no winning, there's no definition. It's all one big lesson in futility.

http://www.worstpreviews.com/images/wargames2.gif

When I saw your question (or should I say brain teaser?) I immediately pictures the infinity symbol (or Ouroboros).

For me self reference is described at its best - in its paradoxical form - by something that defies the our common sense. It serves a purpose, at least a philosophical one, as to challenge us to think beyond the restraints of what is known to us.

If you don't know it, you would love the book Godel, Escher and Bach. The whole book is about self-reference, recursion, "strange loops" an how these ideas play an important part in understanding the mind, articificial intelligence and the nature of mathematics.

The book, on Wikipedia and Amazon:

http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach

http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567

A detailed review:

http://tal.forum2.org/geb

Video lectures from MIT, courtesy of MIT OpenCourseWare.

http://ocw.mit.edu/OcwWeb/hs/geb/VideoLectures/

Enjoy!

Recursion is fascinating because it occurs nature. Much of our early science was based on the direct observation of nature. These observations were brought in our culture through art and music with the discovery of Fibonacci numbers and the Golden Mean. The ratios and proportions derived from these numbers were used extensively because they are pleasing to the eye and ear. It is only natural that you are drawn to it because it surrounds you.

To answer the art question, I believe it is the hand on the left was started first because Escher was left handed.

I found this insightful bit about "Jim Carrey, Existential Cipher" at the site:
Infinite Recursion.
http://jsbangs.wordpress.com/tag/funny/

I also thought this gif was funny! Enjoy.
http://www.gifbin.com/982288