TITLE: Patterns and Motives AUTHOR: Eugene Wallingford DATE: November 23, 2016 3:17 PM DESC: ----- BODY: This week, I read a cool article that covered a lot of ground: Feynman diagrams, experiments at the Large Hadron Collider, algebraic geometry, pendulums, and periods. This paragraph even made me think about software:
That same answer -- the unique thing at the center of all these cohomology theories -- was what Grothendieck called a "motive". "In music it means a recurring theme. For Grothendieck a motive was something which is coming again and again in different forms, but it's really the same," said Pierre Cartier, a mathematician at the Institute of Advanced Scientific Studies outside Paris and a former colleague of Grothendieck's.
Something that comes again and again in different forms but is really the same thing... That sounds like a design pattern. Software patterns are quite different than numeric periods in algebra and geometry, but the idea feels familiar. The analogy to music feels familiar, too. The article then says:
Motives are in a sense the fundamental building blocks of polynomial equations, in the same way that prime factors are the elemental pieces of larger numbers.
This is how I have often thought of elementary design patterns in software: as the elemental particles out of which all software is constructed. I'd like to think these thoughts again more actively in my programming languages course, when my students and I begin to learn and do functional programming. -----