Tuesday, December 9, 2014

I was in the right place at the right time for moving frames

[A brief autobiographical note] I had the great good fortune to fall under the influence of the theory of moving frames that was brought to light by Frenet, Darboux, Cartan, Weyl, and others. My thesis adviser William Pohl was the student of SS Chern and Pohl claimed Chern was a student of Cartan. (This is not what the math "geneology" says, so perhaps it is wrong, or perhaps the relationship was different). 

I was always enamoured of the logarithm, especially the complex logarith, and I used to see how to define it using cut-and-paste methods that also work and generate other things like the Hopf bundle (which is a circle bundle over the torus, generated by puncturing the torus and sewing a cicle of circles into the wound, using circle as a group). It is especially nice to see these objects in terms of moving frames and sections of fiber bundles.

I got lucky and was perhaps first to notice that anatomical descriptions could be done in terms of anatomical frame standards, and I was definately lucky to be at a job where I invented a useful fiber bundle and was not able to publish it - which forced me to think of it in the abstract and develop a general form of classification: as a choice of sections of a fiber bundle induced by measurement of variants. To be able to shoehorn Berkeley's "esse est percipi" into the same mathematics as the logarithm is pretty sweet.

I just wish someone could understand what I am talking about. I am trying hard to write up "Best Model Classification" clearly. I hope to send it out by Christmas and let's hope it works out.
Update: 3 journal rejections later I am trying again and ready to try once more after that.

1 comment:

  1. I got it published in 2015 Journal of Pattern Rec. Research....phew!