Here’s the idea. Everyone likes to say that biology is all about information. There’s something true about this—just think about DNA. But what does this insight actually do for us, quantitatively speaking? To figure this out, we need to do some work.
Biology is also about things that make copies of themselves. So it makes sense to figure out how information theory is connected to the replicator equation—a simple model of population dynamics for self-replicating entities.
To see the connection, we need to use ‘relative information’: the information of one probability distribution relative to another, also known as the Kullback–Leibler divergence. Then everything pops into sharp focus.
It turns out that free energy—energy in forms that can actually be used, not just waste heat—is a special case of relative information Since the decrease of free energy is what drives chemical reactions, biochemistry is founded on relative information.
But there’s a lot more to it than this! Using relative information we can also see evolution as a learning process, fix the problems with Fisher’s fundamental theorem of natural selection, and more.
So this what I’ll talk about! You can see my slides here:
• John Baez, Biology as information dynamics.
but my talk will be videotaped, and it’ll eventually be put here:
• Stanford complexity group, YouTube.
You can already see lots of cool talks at this location!