The Shape of Code

We now know that the reproduction and growth of organisms is driven by DNA and proteins. The DNA contains the instructions which proteins execute.

If we travelled back in time, what arguments might we use to convince people that ‘our’ model for how organisms reproduced and grew was correct?

The General and Logical Theory of Automata is a talk given in 1948 by John von Neumann, four years before the discovery of the structure of DNA.

In this talk, von Neumann deduces from first principles:

• that the mechanism for organism reproduction must be digitally based, rather than analogue. His argument is based on error rates. The performance of the recently invented computers showed that it was possible for digital systems to return correct results for calculations requiring at least operations; while for analogue systems the signal/noise ratio is often , with to sometimes being possible.

  Prior to 1940s valve based electronic computers, relays were used to build what were essentially digital devices.

  Relays go back to the mid-1800s, which is when Boolean algebra was created. The Jacquard weaving loom takes us back to the start of the 1800s, but there is not yet any digital mathematics to cite,

• it is possible for a simple machine to build a much more complicated machine. Twelve years earlier, Turing had published his results around the universal capabilities of a Turing machine, i.e., Turing completeness, the ability of any Turing machine to perform any calculation that any other Turing machine can calculate.

  Turing completeness is a surprising result. An argument that it is possible for simple machines to build more complicated, prior to Turin, would have to rely on evidence such as ship building,

• a conceptual algorithm for a self-reproducing machine; this uses two Turing machines, and a mechanism for sequentially controlling operations.

A talk on automata obviously has to say something about organic computers, i.e., the brain. The von Neumann paper intermixes the discussion of neurons and reproduction. McCulloch, of McCulloch & Pitts neurons fame, was in the audience, as was the psychologist Karl Lashley, and neuroscientist Lorente de Nó. The recorded post talk discussion was mostly ‘brain’ oriented.