There is a view, to which I subscribe, that a lot of innovation and creativity comes from the combination of worldly wisdom, perspective, accumulating existing ideas, failures from multiple disciplines, amongst other things. These ideas — sometimes consciously and sometimes unconsciously tossed around in our head — combine into something new. This is part of the reason that creativity and innovation is hard. You can’t just pick up a single book or thread of knowledge and have it deliver results.
This beautiful Steve Jobs quote sums it up nicely.
“Creativity is just connecting things. When you ask creative people how they did something, they feel a little guilty because they didn’t really do it, they just saw something. It seemed obvious to them after a while.”
In 1945 Jacques S. Hadamard surveyed mathematicians to determine their mental processes at work by posing a series of questions to them and later published his results in An Essay on the Psychology of Invention in the Mathematical Field.
It would be very helpful for the purpose of psychological investigation to know what internal or mental images, what kind of “internal words” mathematicians make use of; whether they are motor, auditory, visual, or mixed, depending on the subject which they are studying.
Especially in research thought, do the mental pictures or internal words present themselves in the full consciousness or in the fringe-consciousness …?
Einstein’s response to the French mathematician, found in his Ideas and Opinions, shows the physicist’s mind at work and the value of “combinatory play.”
My Dear Colleague:
In the following, I am trying to answer in brief your questions as well as I am able. I am not satisfied myself with those answers and I am willing to answer more questions if you believe this could be of any advantage for the very interesting and difficult work you have undertaken.
(A) The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be “voluntarily” reproduced and combined.
There is, of course, a certain connection between those elements and relevant logical concepts. It is also clear that the desire to arrive finally at logically connected concepts is the emotional basis of this rather vague play with the above-mentioned elements. But taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought — before there is any connection with logical construction in words or other kinds of signs which can be communicated to others.
(B) The above-mentioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will.
(C) According to what has been said, the play with the mentioned elements is aimed to be analogous to certain logical connections one is searching for.
(D) Visual and motor. In a stage when words intervene at all, they are, in my case, purely auditive, but they interfere only in a secondary stage, as already mentioned.
(E) It seems to me that what you call full consciousness is a limit case which can never be fully accomplished. This seems to me connected with the fact called the narrowness of consciousness (Enge des Bewusstseins).
Remark: Professor Max Wertheimer has tried to investigate the distinction between mere associating or combining of reproducible elements and between understanding (organisches Begreifen); I cannot judge how far his psychological analysis catches the essential point.
Ideas and Opinions is worth reading and re-reading.