M theory reloaded
The history of the discovery of DNA is quite fascinating. It was heavily influenced by a little book that Schroedinger (yes, the physicist) wrote in the 1940s in Dublin, entitled simply What is life? It bothered Schroedinger a lot that the biologists had shown conclusively that the transfer of genetic information was dictated entirely by a certain mysterious molecular structure, because he knew that the rules that governed this information transfer were quantum mechanical, and yet he also knew that these complex molecules could not be explained by quantum mechanics. He argued that to truly understand it, we would need even newer physics.
Nowadays we know that DNA (and related) molecules like to knot themselves, and of course they are made of helical ribbons. But, hang on a minute, information transfer in quantum computation is also about knots and ribbons. Computer scientists know this very well. Could these two things be linked?
It shouldn't really be any surprise that a quantum theory of gravity has something to say about biology. After all, look how quantum mechanics affected chemistry. A few years ago I started to notice that a lot of neuroscientists and geneticists were talking about a notion of perception that was highly non-trivial in its vision of space. Somehow the mind creates its own reality. It sees what it wants to see.
In a decent Machian theory of quantum gravity one must likewise make sure that space does not really exist. The arrow of time is not laid out upon a general relativistic manifold, like an a priori worm, eating up any hope we might have of understanding the origin of mass.
So what is fundamental? Well, at least information transfer is clearly more fundamental than space. But what does transfer mean? Do I mean then to now? This is where category theory comes in. By simply drawing an arrow one does not presume that its interpretation should be as a movement in some god-given time. A diagram should represent precisely an experimental question, even a question such as what is the rest mass of the electron? We are quite used to this idea from Feynman diagrams in QFT. And indeed, operad theory is really a kind of advanced Feynman diagram calculus; a calculus that does algebra, geometry and logic all together.