The subject of TEDGlobal 2009 held in Oxford this week was the Substance of Things Unseen. My talk, given in the section Curious and Curiouser on Wednesday, attempted to illustrate how mathematics is a powerful language to allow us to get access to things unseen. In particular, symmetry is superficially about something visual, something seen. We say a face is symmetrical because we can see that the left side is a mirror of the right side. But how can we "see" that two walls in the Alhambra for example have the same group of symmetries although they visually look very different. The power of mathematics is to be able to "see" an abstract entity underlying the object. It's like the concept of number. Do you ever "see" the number 5? No. You see visual representations of the number 5. This is the power of the language of symmetry that the French revolutionary Evariste Galois developed at the beginning of the 19th century. It allows us to articulate why two objects have the same symmetries although they visually look very diffferent.
It also has the power to prove when we have seen examples of all the symmetries possible. In the Alhambra for example, mathematicians proved that there are only 17 different groups of symmetries possible on a two dimensional wall. There are many more than 17 different wall designs across the palace but they are all examples of one of these 17 symmetry groups. For example, these two walls look very different. But the language of symmetry allows us to explain why the underlying symmetries are exactly the same:
This allows us to explore the symmetries of things seen. But the real power of mathematics is to create symmetries of things unseen. My work concerns creating symmetrical objects that exist beyond our three dimensional visual world. Only with the power of mathematical language can we "see" in 4, 5 even infinite dimensional space.
To celebrate TEDGlobal 2009 I constructed a new symmetrical object that cannot be seen but using mathematical language can be explored and played with. It was won in a competition I ran during my 18 minute talk by another of the TED speakers astronomer Andrea Ghez.
TED blog entry about my talk
Twitter Snapshot: Marcus du Sautoy on symmetry
Groups for Charity If you want your own "unseen" symmetrical object, then a donation through my FirstGiving page to the charity CommonHope will get your name on a new mathematical shape.
