Bell’s Number, the Interactome, and a Peek at a Monumental Problem for Evolution

If you ever wondered how the biological world could have arisen from random events and a few simple natural laws then you might be interested in a recent paper introducing some basic, fundamental problems confronting evolutionary theory. For whereas man-made machines may have a great number of components, these machines are specifically designed to limit the number of interactions. The components only interact with a small number of other components and a matrix describing these interactions would be very sparse. Not so for many biological systems. The paper shows that the magnitude of the interactome—the sum total of all interactions in systems such as the nervous system—is on the order of Bell’s number, which scales faster than exponentially. Indeed, for n discrete components, the logarithm of Bell’s number is n[log(n) – 1].  Read more