Alan Turing Quotes

Sometimes it is the people no one imagines anything of, who do the things that no one can imagine

We do not wish to penalise the machine for its inability to shine in beauty competitions, nor to penalise a man for losing in a race against an aeroplane. The conditions of our game make these disabilities irrelevant.

To each computable sequence there corresponds at least one description number, while to no description number does there correspond more than one computable sequence. The computable sequences and numbers are therefore enumerable.

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.

The machine is supplied with a "tape" (the analogue of paper) running through it, and divided into sections (called "squares") each capable of bearing a "symbol".

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two faculties, which we may call intuition and ingenuity.
... In pre-Gödel times it was thought by some that all the intuitive judgements of mathematics could be replaced by a finite number of rules. The necessity for intuition would then be entirely eliminated.
In our discussions, however, we have gone to the opposite extreme and eliminated not intuition but ingenuity, and this in spite of the fact that our aim has been in much the same direction.

Sometimes it's the very people who no one imagines anything of who do the things no one can imagine.

We are not asking whether all digital computers would do well in the game nor whether the computers at present available would do well, but whether there are imaginable computers which would do well.

For some purposes we might use machines (choice... or c-machines) whose motion is only partially determined by the configuration... When such a machine reaches... ambiguous configurations, it cannot go on until some arbitrary choice has been made by an external operator. This would be the case if we were using machines to deal with axiomatic systems.

Sometimes it is the people no one can imagine anything of who do the things no one can imagine.

Sometimes it is the people who no one imagined anything of who do the things that no one can imagine

[...] Queste difficoltà possono essere risolte nel modo migliore facendo buon viso a cattivo gioco. I ritardi possono essere tollerati accettandoli ed elaborando una scansione temporale che li preveda. Si può poi tollerare una certa imprecisione nella risposta pensando in termini di <>. Così invece di dire: <>, noi diremo: <>. Le varie classi devono essere del tutto distinte e ben lontane dal sovrapporsi, cioé - topologicamente parlando - potremmo dire che devono avere tra loro una distanza finita. Con una decisione del genere avremo introdotto una ben definita divisione del lavoro tra il matematico e l'ingegnere, che permetterà a ognuno dei due di andare avanti senza preoccuparsi se le sue assunzioni siano in accordo con quelle dell'altro.

Presumably the child-brain is something like a note-book as one buys it from the stationer's. Rather little mechanism, and lots of blank sheets.

Can machines think?"... The new form of the problem can be described in terms of a game which we call the 'imitation game." It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart from the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A." The interrogator is allowed to put questions to A and B... We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?"

The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are particularly subject. This is the assumption that as soon as a fact is presented to a mind all consequences of that fact spring into the mind simultaneously with it. It is a very useful assumption under many circumstances, but one too easily forgets that it is false. A natural consequence of doing so is that one then assumes that there is no virtue in the mere working out of consequences from data and general principles.