Being at LIDS for more than three and a half years, I have picked up some knowledge of information theory. In 1999 and 2000, I played the tuba in The F-M Land Band, a Dixieland band, alongside a bunch of friends from high school: Jason Smucny (clarinet), Steve Keller (saxophone), James Ahern (trumpet), John Downer (trumpet), Paul Arras (trombone), and Dave Chalenski (drums).
Why do I mention these things? LIDS alumni gave talks this week about information theory and music.
The main point of Sahai's talk was that, along with probability of error, the energy per bit required to encode and decode should be the critical parameter in a digital communication system. He analyzed various decoders, including iterative, message-passing decoders in terms of energy consumed per bit, assuming that certain operations use a certain amount of energy. The main point of Dabby's talk was that chaos theory can be used to generate variations of musical pieces. Given a piece of music and a recurrence plot of a chaotic system, a new piece of music can be created by substituting tones in the original piece according the the recurrence plot, but keeping the rhythm, dynamics, and everything else the same.
Dabby mentioned that her ideas could potentially be applied to other types of sequences involving context, such as dance. Now that I have thought about it more, I would ask: how about the genome? Variation and recurrence plots show up in genomics as well. Just as some of her technique-produced variations do not sound pleasing, some genetic variations are unfit to survive. Mutation and natural selection might result in the evolution of life, but where does the original life come from? The original musical piece to which the chaotic variation was applied sprang from the creativity of a composer, but it is not clear what the analog is for life, or for that matter, what is life?
According to Schrödinger and others, the characteristic of life is that life reduces entropy. Thermodynamic entropy and information entropy have a long history of being the same and being different. Sahai's research makes energy the common currency for communication systems. Decoding a received message involves a computation which uses energy. The energy usage might be necessary due to Landauer's principle (which I was introduced to by Lav, and which he was introduced to by Sanjoy, I believe).
With all this talk of information theory, music, and life, I am starting to venture into Two Famous Papers territory. A jolt of the Land Band's renditions of Sidewalks of New York and When The Saints Go Marching In might bring me back to "exciting and important problems."