Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.
Science is a differential equation. Religion is a boundary condition.
If a machine is expected to be infallible, it cannot also be intelligent.
We may hope that machines will eventually compete with men in all purely intellectual fields.
No, I’m not interested in developing a powerful brain. All I’m after is just a mediocre brain, something like the President of the American Telephone and Telegraph Company.
The idea behind digital computers may be explained by saying that these machines are intended to carry out any operations which could be done by a human computer.
Machines take me by surprise with great frequency.
We are not interested in the fact that the brain has the consistency of cold porridge.
Unless in communicating with it one says exactly what one means, trouble is bound to result.
The original question, ‘Can machines think?’ I believe to be too meaningless to deserve discussion.
I’m afraid that the following syllogism may be used by some in the future. Turing believes machines think Turing lies with men Therefore machines do not think Yours in distress, Alan.
My little computer said such a funny thing this morning.
Instead of trying to produce a programme to simulate the adult mind, why not rather try to produce one which simulates the child’s? If this were then subjected to an appropriate course of education one would obtain the adult brain.
Instruction tables will have to be made up by mathematicians with computing experience and perhaps a certain puzzle-solving ability. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself.
Those who can imagine anything, can create the impossible.
The isolated man does not develop any intellectual power. It is necessary for him to be immersed in an environment of other men, whose techniques he absorbs during the first twenty years of his life. He may then perhaps do a little research of his own and make a very few discoveries which are passed on to other men. From this point of view the search for new techniques must be regarded as carried out by the human community as a whole, rather than by individuals.
It is possible to invent a single machine which can be used to compute any computable sequence.
The popular view that scientists proceed inexorably from well-established fact to well-established fact, never being influenced by any unproved conjecture, is quite mistaken. Provided it is made clear which are proved facts and which are conjectures, no harm can result. Conjectures are of great importance since they suggest useful lines of research.
It is not possible to produce a set of rules purporting to describe what a man should do in every conceivable set of circumstances.
The works and customs of mankind do not seem to be very suitable material to which to apply scientific induction.