"The whole process of thinking
is still very mysterious to us,
but I believe that the attempt to make a thinking machine
will be of great help
in understanding how we ourselves think."
From a 1951 BBC radio lecture
by Alan Turing
The paper that became the background to the idea of the Turing machine,
"On Computable Numbers, with an Application to the Entscheidungsproblem"
The halting problem that Turing dealt with here was, among the many concerns about the certainty of mathematics, the question of whether one could know in advance, with certainty, whether a given calculation, when carried out according to a fixed procedure, would eventually finish and yield an answer, or not.
Through the paper, Turing concluded that one cannot know. And in the process of arriving at this conclusion, he gained the insight that became the Turing machine.
In the paper, Turing predicted that the kinds of work a very simple machine could do would be capable of expressing many complex calculations and data-processing tasks as well.
Turning that around, this is to say that any number of seemingly extremely complex and difficult tasks - if you break them down minutely into the simplest of units and lay them out -
can also be processed as a collection of operations that an extremely simple device, like a universal Turing machine, can perform.
This can be seen as a kind of LEGO-module construction. In the end, you put together minimal modules that consider extensibility, and on top of those modules you can assemble a wide range of things. In a way, it is a very common-sense concept.
And of course, this concept can also be put to use in understanding the knowledge, cognition, thinking, language, and behavior of all sorts of complex and varied human beings. Because we have at our disposal the lever of mathematics (especially calculus, vectors, and matrices) - the criterion that they prefer enormously and to which they consciously try to align themselves.
Prediction is calculus, language is a vector, vision is a matrix... and so on.
The idea of the universal Turing machine also lends weight to the thought that the logic of mathematics - the cleanest and best-organized form of human knowledge - can be expressed by a machine that simply repeats very simple operations.
It gives the impression that, in the end, human intelligence and wisdom can be expressed as objects that move simply according to a few patterns, once you keep breaking them down.
And this impression can become a clue that draws out a different way of thinking about what knowledge, intelligence, human thought, and human ability really are. Turing himself often used this approach when dealing with the problem of artificial intelligence.
