Consider this: adding 8 to a number is really the same as adding 1 eight times. Multiplying by 3 is equivalent to adding 3 of the same. So multiplying can be reduced to adding 1 the right number of times! Which makes one wonder how much of mathematics (or perhaps thought!) can be reduced to a counting procedure?

Back in 1673 the mathematician Gottfried Wilhelm von Leibniz used these ideas to predict the mechanisation of arithmetic and by 1871 another mathematician, Charles Babbage, had produced a blueprint of a machine (involving cogs like an old fashioned watch) that could multiply and divide 250 digit numbers to 100 decimal places. Unfortunately in those days the engineers didn’t have the tools to build it!

The technology was not much more advanced in 1936 when the mathematician Alan Turing dreamed up his imaginary ‘Turing machine’. At the basic level Turing's machine could simply count (in base 2). But Turing understood that for instance multiplying by two, then taking the square root can be achieved through an algorithm (or program) or a series of logical steps which reduce the operation to counting.

By the 1940s technology started to catch up and during World War II computers became an essential tool (in particular for the atomic bomb project). Von Neumann and others at Los Alamos pioneered new approaches modelled on the workings of the brain. Today mathematicians keep pushing back the boundaries, developing networks and even self reproducing computers. The University of Queensland’s parallel computer…….

New questions in computing arise all the time: can these networks (or perhaps the internet itself) evolve like an organism?

For more see Darwin among the machines by George Dyson.