Friday, December 12, 2014

Continuities with the past

I take comfort in the idea that the language I speak goes all the way back to the beginning of language, just like my genome has that sort of continuity with the past. When I think about it, my genome did not follow the same path as my language, because I don't speak Russian. I do speak French. English is my native language but not my native genome.
Update: and every one of my ancestors survived!

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, 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 esst 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.

Sunday, December 7, 2014

More about false positives

This feels like a similar topic to the previous post: If someone asks me if such-and-such is correct and I can only answer in terms of good or bad (e.g. my mouth is full and I can give a "thumbs up" but cannot say "correct") then I say "good" as a substitute for "correct". The good/bad axis and the correct/incorrect axis are neither orthogonal nor co-linear.

Saturday, December 6, 2014

Was that a blue bird? Ignoring observations during classification

I have a little story that illustrates possible approaches to handling false positives in a classification system with limited alternative categories. 

Driving in Bedford a small bird with a rust-red underbelly flies past the car and I get a brief (.3 sec?) glimpse.

Analysis: It was too small to be a blue bird and there are no birds that small around here with rust-red breasts. 
  • If the bird had been a bit bigger it could have been a blue bird or, even bigger, it could have been a robin.
  • If it wasn't really red then it could have been a Junco or sparrow.
  • If it was an accidental European bird, it might be one of those
  • If I misjudged size as well as position of the red color, it  could have been a Towhee or Catbird.
No small birds like that? Maybe the bird was a bit larger than I thought. For some reason I am more willing to dismiss a magnitude observation than a color one. Anyway, the mind obviously tries to loosen the observed 'measurements'; doubting each, in turn, in order to fit to a broader set of categories.