We can demonstrate more forcibly that any such statement would be unjustified.
For suppose we could be sure of finding such laws if they existed. Then given
a discrete-state machine it should certainly be possible to discover by
observation sufficient about it to predict its future behaviour, and this
within a reasonable time, say a thousand years. But this does not seem to be
the case. I have set up on the Manchester computer a small programme using
only 1,000 units of storage, whereby the machine supplied with one sixteen-
figure number replies with another within two seconds. I would defy anyone to
learn from these replies sufficient about the programme to be able to predict
any replies to untried values.
This is possibly one of the first examples of a pseudorandom function as we understand the term today. I would love to know what Turing's function was, and how breakable it would be with today's techniques.