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•76 The 100 Greatest Business Ideas of All Time

Idea 44 – Turing’s table of behaviour

‘Bernard of Chartres used to say that we are like dwarfs on the shoulders of
giants, so that we can see more than they, and things at greater distance, not by
virtue of any sharpness of sight on our part, or any physical distinction but be-
cause we are carried high and raised up by their giant size.’

John of Salisbury, 1159

Alan Turing, who is generally credited with the invention of the basics behind the
digital computer, can justly claim to be one of the giants on whose shoulders stand
many others. He developed his concept of a table of behaviour in the mid-1930s as
his contribution to a question posed by the mathematician David Hilbert.

The question was ‘Is mathematics decidable?’ Was there a definite method which,
when applied, in principle, to any assertion, could be guaranteed to give a correct
decision as to whether the assertion was true or false. The answer that Turing came
up with was ‘Yes, by a mechanical process.’

He searched for an ‘automatic machine’ that would require no human inter-
vention. It must be capable of reading a mathematical assertion and eventually writ-
ing a decision as to whether the assertion could be proven or not.

This led to the table of behaviour. Turing saw it as a tape marked off into
squares. The tape was definite, but of unlimited length. The tape passes by what
Turing called a scanner at a fixed point, which is capable of reading whether each
square contains a 1 or is blank. The machine is capable also of writing 1 into a blank
square and returning a square containing 1 to blank by erasing it.

A limited number of ‘configurations’ is then required for the machine to be able
to do calculations. You can think of configurations by thinking of a typewriter with
two configurations: upper and lower case.

It requires only four configurations, to move the tape right or left, write 1 or
erase 1, to carry out additions.

So, from that teasingly simple basis the rest is history.