There are many definitions of duality in mathematics so I am not entirely clear on 6. For example the notion of duals from category theory has already been very

There are many definitions of duality in mathematics so I am not entirely clear on 6. For example the notion of duals from category theory has already been very helpful in understanding or developing many algorithms. In fact a generous viewing will allow for even enterprise software in the form of LINQ and Observables to have made use of duals in their development. I am neither clear on 7. I wish I knew what he meant about MaxEnt in particular, there's a lot of neat explorations from the connections between entropy and learning. But specific to what I interpret as a better Occam's Razor, my vote will have to go to Marcus Hutter as the person who is currently doing the most interesting work in that area. Specifically his work on approximating universal priors. Schmidhuber also has interesting stuff on complexity, search for his talks - they're great.