The Geometry of Irregular Forms: Introduction

It's been two weeks since I posted my last update. I'm still here.

Last week I saw the play Arcadia by Tom Stoppard. Stoppard, with Terry Gilliam of Monty Python, co-wrote the screenplay for the movie Brazil (one of my favorites). That alone sets an expectation for genius. And just last night, the Broadway production of his trilogy The Coast of Utopia won the Tony award for best play.

I enjoyed Arcadia, even if it is not perfect. I'm still trying to figure out why some of the characters were even necessary (the mute child, for instance). But I was interested in how Stoppard works in some mathematics and science and uses some of the same themes as The Coast of Utopia dealing with the conflict between the Enlightenment of the 18th century and the Romanticism of the 19th century. Enlightenment philosophers, building on the discoveries of Galileo and Newton, thought that all problems, and all questions about how the world worked, could be solved by the application of reason. This was a great step forward from earlier periods dominated by superstitious thinking -- when women were being burned as witches, and lightning was seen as a sign of God's wrath. However, it became clear that not everything that happens in the world is as deterministic as a simple equation. Arcadia contains a tale of modern chaos theory being developed -- and then forgotten -- in the early 19th century as a synthesis of both Romanticism and the Enlightenment, even before such pioneers in the field as Sir Arthur Cayley were born.

One of the characters in Arcadia wrote a book titled The Geometry of Irregular Forms (which exists only in the play). I can't make any promises -- this is merely a blog, after all -- but I'll try to do a series of postings on this subject: the geometry of irregular forms.