Replication is Recursion; or, Lambda: the Biological Imperative

Abstract

There is a striking visual symmetry between the 'paradoxical combinator' (which implements recursion in the mathematical theory of computation) and the biological replication fork (which implements reproduction in the living cell). Can this mean anything? Living organisms are information processors – the genome encodes instructions for the process of life much as computer programs encode instructions for a computer. Replication in biological systems is intuitively similar to recursion in computational systems. The following discussion will present enough of the mathematics to allow biologists to make sense of the symmetries in the logo. Mathematicians will learn nothing new about biology, but may be encouraged to look at biological processes from a new perspective.