If you're a fan of Alan Turing, and interested in the work at Bletchley Park
on the Enigma decryption, and also interested in models of perception and models
of learning, then this
paper will bring it all together for you -- *Banburismus and the Brain:
Decoding the Relationship between Sensory Stimuli, Decisions, and Reward*,
by Joshua Gold and Michael Shadlen.

I've felt for a long time that the "Banburismus" stuff deserves more attention, both on its own terms and in its relationship to the birth of information theory. One reason for the neglect is that its details were classified until a few years ago. Also, Turing never had a chance to write about the general principles of Banburismus because he was busy with other things in the few years before his death, and previous descriptions of the work either focus on the cryptanalytic details or present the general ideas without enough mathematical substance to tell you how to apply them. Gold and Shadlen do a great job of explaining the general principles and why they're important, while also grounding the ideas in enough specifics for you to implement them if you want to. And they also show how to use this perspective to frame research questions about the neuroscience of perception!

There is still an untold story about the relationship between Turing's Banburismus work and the birth of Shannon's information theory. Most of the story will probably never be told, since all the people involved are dead, and there are probably no relevant documents. Turing spent a few months at Bell Labs in 1942-43, as the British representative on a team working out a method for encrypted voice communication, which was implemented in a system that Churchill and Roosevelt used for transatlantic conversations. Given what Turing and Shannon were like, I bet that the Banburismus stuff came up. I don't mean to take anything away from Shannon -- he was clearly one of the most important and original thinkers of the 20th century -- but it's nice to think that Turing had a hand in the origins of the mathematics of information as well as the mathematics of computation.

It's too bad that Gold and Shadlen's paper didn't come out before Neal Stephenson
wrote *Cryptonomicon*, since
its theme would be excellent source of dramatic metaphors. Stephenson's novels
tends to nucleate around odd bits of intellectual history. Wilkin's
"philosophical character" in *Quicksilver*; Julian
Jayne's "bicameral mind" theories (about which more later...) in *The Big U* and *Snowcrash*;
the Enigma decryption in Cryptonomicon.

There's another indirect literary spin-off from Turing's visit to Bell Labs. Stalin was very jealous of the vocoder, and set mathematicians and electrical engineers to work in a prison-camp laboratory to try to create one for him. One of the prisoners working on this project was Aleksandr Isaevich Solzhenitsyn, and his experiences there later became the back-drop to his novel *The First Circle*.