I learned some truly amazing things at the workshop on [Biological and Bio-inspired Information Theory](http://www.birs.ca/events/2014/5-day-workshops/14w5170).
The first big thing was Nafthali Tishby's program to develop a principled approach to biology and intelligence using a combination of
* partially observed Markov decision processes,
* Bayesian networks,
* rate-distortion theory (a branch of information theory)
* Bellman's equation (from control theory).
For some details, read [my blog article](http://johncarlosbaez.wordpress.com/2014/10/30/sensing-and-acting-under-information-constraints/). Very briefly, the idea is that
> _organisms store and process information about their past to make decisions to achieve goals in the future, and optimizing this process must take into account the price for information storage and processing_.
This idea is sort of obvious... and oversimplified: reality is more complex. But the important part is that Tishby and his colleagues have the mathematical tools to study this idea quantitatively by writing software and proving theorems! It's not just chat, it's math.
I think there's a huge amount left to be done here - and that's fine: this is the kind of ambitious synthesis I want to be involved in! If "green mathematics" ever succeeds, it will have to include ideas like this (and much more).
So, I'm going to steer my research in this direction. It's not hard, because I'm already working on control theory, Markov processes and information theory, trying to fit them together in a unified whole.
That's the _first_ big thing.