 Henri Poincaré (1854/1912), French mathematician, physicist, astronomer, philosopher of science and eminent popularizer of scientific knowledge, was the last great sage of the 19th century and the first great scientist of the 20th. Godfather of the Theory of Relativity and twelve-time nominee for the Nobel Prize (which he never won), he wrote about his thoughts on creativity and the mental processes that generate creative intuitions in the 1906 book Science and Method, a collection of essays on scientific methodology written with extraordinary clarity.
His references to creativity are brief, yet they manage to provide a very clear idea of the topic, to the extent that the resulting definition of creativity is perhaps the most satisfying of the many that been offered till now:
«A new result has value, if any, when, by establishing connections between elements that are known but until then dispersed and apparently unrelated to one another, order is immediately created where chaos seemed to reign [...] Inventing consists exclusively in constructing not useless combinations but useful ones, which are a distinct minority. Inventing means discerning, choosing [...] among all the combinations that can be made, with the most fertile being those formed by elements drawn from distantly related fields. This is not to say that in order to invent, one need only put together the most unrelated objects, for the majority of such combinations would be utterly sterile. But some of them, though rare, will be the most fertile of all.
[...] What is most striking is the phenomenon behind these sudden illuminations, the manifest sign of the long unconscious process that precedes them [...]. A propos the conditions under which this unconscious process unfolds, there is another point worth making: it is impossible, and would in any case remain sterile, if not preceded and followed by a period of conscious effort.
Sudden inspirations [...] never happen without a number of days of voluntary effort which seems at the time completely futile [...]. Among the myriad combinations that the subliminal self has unconsciously formed, nearly all are useless and devoid of interest, and it is for precisely this reason that they exercise no influence on the aesthetic sensibility – the conscious mind will never even know them. Only a handful of these combinations are harmonious, useful and beautiful». (Jules Henri Poincaré, from Science and Method)
Poincaré speaks of creativity as the ability to unite pre-existing elements in new combinations that are useful, and he further states that the intuitive criterion for recognizing the usefulness of these new combinations is “that they are beautiful”. Clearly he is not talking about beauty in a purely aesthetic sense, but rather about something to do with the ‘elegance’ to which mathematicians often refer: harmony, economy of signs, the correspondence between process and functional purpose.
Poincaré’s definition is equally valid for the arts and sciences. He identifies the phenomenon of creativity, speaks of what it consists (a “production of new and useful combinations”) and how to arrive at them (through a process that calls for “the union of pre-existing elements”). He also lays out the premises, conditions and results of the process.
• Premises: Nothing can be created from nothing (creativity starts with “pre-existing elements”, something that is already there)
• Conditions: One needs a specific ability (to unite elements) that can be applied to any field or argument, and this must in turn be united with the ability to select from among all the available elements those that will best fit together. The ability to intelligently select has itself four aspects:
1. Skill: In order to identify elements, you need to know them. (Pasteur: “Chance favors the prepared mind”.)
2. Intuition (and perhaps instinct as well): This allows you to make a choice that will likely work, even when it isn’t possible to exhaustively evaluate the complexity of all the variables.
3. Experience: Cultivates intuition and sharpens instinct.
4. Determination: Creativity proceeds by trial and error, and can therefore be tiring and frustrating (Thomas Edison: “Genius is one per cent inspiration and ninety-nine per cent perspiration. Accordingly, a ‘genius’ is often merely a talented person who has done all of his or her homework”)
• Results: There is a first prerequisite (the combinations produced must be new), and there is another for establishing whether the new combinations have creative value (i.e. that in addition to being new, they are also useful).
The categories of ‘new’ and ‘useful’ explain the essence of the creative act, which is to transcend existing rules (the ‘new’) to establish a better rule that can be shared (the ‘useful’).
In sum, Poincaré lays down a simple, general principle – one that mathematicians know very well – that distills the multiformity of possible creative acts into the formula:
C = n + u
Creativity is essentially the product of a quantity of ‘new’ and a quantity of ‘useful’. These quantities can vary from little to much, and this is why some forms or expressions of creativity seem to us intuitively more relevant than others, particularly when their newness or usefulness – or both – are truly great.
In any case, newness and usefulness must both be present, for in the total absence of either we cannot define an idea as ‘creative’.
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