Reading documents on creativity "On the dynamics of creativity" By: Ben Goertzel, and many other authors on the subject, I was pointed at Henri Poincaré in relation to creativity. To find out something more about this mathematician and the relation with creativity, I read several extracts and summaries of his work. (It would be too difficult for me to read the complete work or some specific publications) 

At first I was primarily interested in the link with creativity, a relation which Poincaré had described in the publication "Science and Method", but later on there appeared to be a direct link with the artist Marcel Duchamp, especially with the work "La marieé mise à nu par ses célibataires, même" (The bride stripped bare by her bachelors, even). 
In the edition "A l'Infinitif", "la Boîte Blanche"( the White Box), Duchamp refered to Poincaré (two times he even mentions his name: but this could concern quotes from other publications) and several notes would seem to be closely related to the ideas of this mathematician. 

Linda Henderson and Craig Adcock, art historians at the University of Texas at Austin and resp. the University of Iowa , also wrote about the possible relation Poincaré - Duchamp. 

Adcock, C. [1984] "Conventionalism in Henri Poincaré and Marcel Duchamp." Art Journal 
Linda Dalrymple Henderson "The Fourth Dimension and Non-Euclidean Geometry in Modern Art" [1982]; "Duchamp in Context: Science and Technology in the Large Glass and Related Works" [1998]; "Marcel Duchamp's The King and Queen Surrounded by Swift Nudes (1912) and the Invisible World of Electrons" [1999]

Duchamp’s championing of the artist’s "special intuition" in interpreting the world in a certain extend paved the way for conceptual art. But what were the odds? 

Poincaré speculates that unconscious processes, between distinctive periods of active thought, continue to associate ideas, bringing fertile combinations to consciousness. Chosen by their aesthetic appeal, a creative mathematician would recognize the sudden whim or EUREKA, which could be the link - if not solution - for his problem. 

Within the speculation Duchamp was aware of this particular publishing, it could be possible that he decided to use his 'laziness' - periods of existential 'breathing' (i. e. a process of subconscious thinking) - to serve higher levels of creativity.  Duchamp had a special interest in the science of that time, the mathematician Riemann for example. In an interview he said: "Naturally, I never read seriously the works of Riemann because I would have been incapable of it" (MD), but he had a very real appreciation for Riemann’s mathematics. 

It's almost beyond doubt that Poincaré’s essay was known to Duchamp. The avant-garde artists - Duchamp in particular - of that time were keen on scientific and mathematical theory with exotic notions as four-dimensional and non-Euclidean geometries significantly in focus. The work "Marieé" (The Bride) shows evidence of his awareness with Poincaré’s work, the painting of which he claimed to be his first glimpse of the "fourth dimension". 

The link I see however, is not only aimed towards the possible inspiration through the notions of  non-Euclidean geometries, thermodynamics, electricity etc. (which must have been important sources for the notes from the "Green Box"), but mainly towards the unorthodox and special notions of creativity and the role of intuition Poincaré described in a number of publications.

during a period of apparent repose, but of unconscious work, some of them are detached from the wall and set in motion. They plough through space in all directions... like the gaseous molecules in the kinetic theory of gases. Their mutual collisions may then produce new combinations. (Science and Method) 

Poincaré describes habitual thinking as anchored in an inertial frame represented by the spatial metaphor of walls to which thoughts are hooked. He describes liberated thought as the product of entropic processes capable of spontaneous re-orderings once those thoughts are unhooked." 

"Clearly, Poincaré means to apply these physical references as tropes for thoughts swarming through the boundaries of conceptual systems. While he says that "My comparison is very crude, but I cannot well see how I could explain my thought in any other way" (Science and Method), he expects his readers to take this correspondence seriously. This tactic is especially fascinating since he implies that tropes constitute a linguistic limit to his ability to explain something crucial about his own thinking." 

"He seems to ascribe to these entropic thought-swarms the capacity to self-organize in a way that would make the return of those atom-thoughts to their original positions on the walls impossible. These swarms may indeed overwhelm their containing structures, may even require the reorganization of the sedentary structures of the walls themselves."  (Martin E. Rosenberg - Kettering University) 
 
In my view it's not so much the scientific merits of the insights of Poincaré and others, that could have been such important sources to the new and deviated approach to the making of works of art, but the very issue of creation, of the way of transforming conceptual spaces by a special state of mind: as if the fourth dimension is the conceptual space (within the mind) which have to be / can be "scanned" to obtain "flashes" (illuminations) of thought, all of this automatically, "given" as "objets trouve" (found objects: ready made thoughts) from the mind. 

Bergson continuously describes the emerging idea as an image: "one point, not so much a vision as a contact, contact furnishes an impulse, this impulse, a movement, a swirling kind of dust taking a particular form, becomes visible to our eyes through what it has collected along its way." (Henri Bergson - The Creative Mind) 

As such, it isn't in the realm of the verbal, but instead forms as a sort of translucent graphic that emanates from a "dust storm of knowledge". 

But all of the loose ends and snippets of thought had to be described to the proper mental structure to be applicable to his work. The (hard to visualize) scientific and technical notions of the surrounding world (including mathematics from Poincaré and Riemann for example, but also much less imaginative "machines" such as a coffee mill or chocolate grinder and water wheel) would have helped Duchamp to the visualization of all these notes. (which for the largest part - deliberately - haven't been worked-out in the piece of glass)

(which he once called visual / aesthetic indifference, but it is doubtful if he could sufficiently suppress impulses of aesthetic care: Duchamp can tell us: "the choice of these "readymades" was never dictated by aesthetic delectation", or that he suffered from "a reaction of visual indifference with at the same time a total absence of good or bad taste... in fact a complete anaesthesia" - it helps, but it's not conclusive.  If Duchamp was gifted in a visual creative manner, can he ignore impulses? He can react; might suspend - "delay" - them and challenge his self-control - the faculty to sublimate must have been one of his extraordinary characteristics)

Within this process of (re-)internalizing (both ideas, notions and objects) he tried to preserve the state in which "it came to him" as much as possible. This is why the form he chose to multiply the original "Green Box", was so meticulously carried out: 

"The limited edition of ninety-four notes, drawings, and photographs, printed in facsimile, using the same papers and the same inks or pencil leads, torn or snipped in precisely the same way as the originals, with the same crossings-out and corrections and abbreviations and unfinished thoughts" (Calvin Tomkins)

"---The creative act is not performed by the artist alone; the spectator brings the work in contact with the external world by deciphering and interpreting its inner qualifications and thus adds his (her) contribution to the creative act---." (MD) 

The fact Duchamp didn't talk to much about his motives and that he didn't care to explain his work, could be related to the manner in which his creativity revealed itself and became manifest in his work.

"Verbal learning physically affects and detracts from intuitive thinking". According to Laura Spinney, putting words to information will actually prevent the mind from being able to non consciously access that information again.  In her article, she quoted a researcher who studied this particular effect,  "verbalization has a very specific effect, it impairs judgement based on intuition." Within the brain, when certain areas related to vision are activated by a task, the focused electrical signals move outwards as multiple possibilities emerge.  If the verbal area of the brain is suddenly activated, it actually impedes this expansion because it employs the prefrontal cortex, known for shutting down other brain electrical activity." (Laura Spinney - "I had a Hunch...." New Scientist 1998) 

Intuition and sensation are pattern recognition processes.  The difference is that sensation focuses on the content of an in- or ex- ternal experience. Intuition focuses on the precursors of an experience or where an experience might lead. Descartes stated that sensory perception is not important to knowledge and intuition and that the intellect was the source of information. Immanuel Kant, on the other hand, introduced two types of intuition, sensory and pure. Sensory intuition had two pure forms that created a priori knowledge, space, which underlay all outer intuitions, and time, which underlay inner ones. Pure intuition, however, "unaided by the sense and moreover, constituting the very possibility of sense experiences, is for Kant the source of all synthetic a priori judgements."  For Kant, intuition was transcendental, beyond reason and mundane experience. (Paul Budnik -   Einstein's Revenge 1995)

As part of his work, Duchamp created fictional, quasi-scientific systems that he worked into his visual designs. Calling these playful systems "pataphysics", he used current scientific thinking of the time in a satiric way, making fun of rational, determinist systems and celebrating interesting new developments that cast doubt on traditional thinking.
---The word "pataphysics" was first introduced in 1893 by playwright Alfred Jarry who was attempting to create what he called a "science of imaginary solutions"--- (Pata or Quantum: Duchamp and the End of Determinist Physics - Jonathan Williams) 

This breaking down of assumptions concerning the predictable, rational behaviour of the world in Duchamp’s work and in the sciences share traits with the Dada movement. Rebelling against the rationalist social structures responsible for the devastating war, Dadaists attempted to create new languages for artistic (or even anti-artistic) expression. The Dada movement recognized the inadequacies of existing forms of expression to compass a real understanding of the changing world, and sought to destroy all rationalistic cultural norms in art. By satirizing, mimicking, and distorting the systems they attack, the Dadaists prove the inadequacies of their targets and point the way to the possibility of better forms. In a way, the Dada movement acted as a sort of social resistor, slowing down the cultural machinery of the time, helping to re-orient everyone in a different direction. 
 
Although Marcel Duchamp can't be classified as a member of the Dada movement (he didn't strongly refuse to be considered Dada-ist, but he wouldn't have accepted that he was subject to any movement or -ism) the activities of Dada were sympathetic to him and he certainly was interested in satirizing, mimicking, and distorting determinist systems; and here Henri Poincaré is fitting in too. 

"Poincaré's attitude toward the non-Euclidean geometries --- was that they were just as valid constructs for solving certain kinds of problems as the more traditional Euclidean descriptions that had been perceived to be eternal and unshakeable for over two centuries. He felt that scientific theories are only conventions used by scientists to describe the patterns they see in nature." (Pata or Quantum: Duchamp and the End of Determinist Physics - Jonathan Williams) 

Poincaré was in certain aspects the kindred spirit of Duchamp, especially in his views of personal / intellectual freedom and was - like Duchamp - a true individualist.

Anarchic Discipline 

Each individual has the right of full and complete freedom, 
as long as this doesn't obstruct the liberty of other people. 

Thinking must never be subjected, 
not to a dogma, 
not to a party, 
not to a passion, 
not to an interest, 
not to a prejudgement, 
nor to whatever what, 
but only to the facts itself, 

because subjection would mean 
the end of all thinking. 

"What he (Duchamp) was interested in above all was freedom - complete personal and intellectual and artistic freedom". (Calvin Tomkins) 

Concluding with the idea that it probably had not been the scientific merits of the theory of Poincaré which could have been appealing to Duchamp - partly because it was such a specialist matter, only fully comprehensible to progressive mathematicians and naturally because Duchamp said about the publications of Riemann "he never read it seriously because he would have been incapable to fully understand it" - but that it had been the particular attitude of Poincaré towards science and thinking in general (freedom), while the theory of course was very challenging, exciting and imagianitive, also to the average interested layman. 

The inspiration derived from the publication(s) of Poincaré had been one of creative theoretical nature and intuitively Duchamp got the sense of a new and radically different way of thinking: a fundamental shock in a common view of the world. The result of the inspiration was a radically different approach to creativity. 

Though Duchamp in fact coupled a conventional (classic) world view (Adcock) to the fantasy of a - from a to science still largely unexplored domain - extrasensory dimension, which is only logical and unavoidable, in the end it became a fundamentally different approach to art. Metaphors and classical imaginative mechanisms are from time immemorial the only means to treat particular advanced conceptions in a more general way. With this "translation" in fact part of the content gets mystified, even actually incorrect reproduced, which always has been cause of anxiety to scientists, but without this way of spreading - or rather "widen" - of insights, no matter how crooked sometimes, science would have been isolated from society and would have been deprived through the lack of a broad social basis. 

One could say that Duchamp mystified - viewed from a scientist - the ideas of Poincaré, but if he did, he did this out of pseudo-morphological scientific, poetic and aesthetic motives. He tried to place the "work of art" in an other dimension, but it had been merely a "hunch": an approximation. 

A tactic to test if there would be some point in the question whether Duchamp actually incorporated the very merits of science in his work and what it would mean if he did, is to turn the question around: if we would ask a scientist to give a definition of a work of art which would be in proportion to the scientific insights acquired in the 20th century, than the conclusion must be - provided that the particular scientist is as sensible as we would expect him to be - that it isn't the competence of (hard-)science to define what art is or that the secretion of works of art isn't his cup of tea (we didn't ask, but implied it in the question) Of course, in art and science, mutual inspiration could arise from ideas and the common joint of creativity, which is from time immemorial too, but lets face it: art and science are disciplines, specializations.

Although the idea of the "Homo Universalis", which became a matter of common knowledge through the work of Leonardo Da Vinci, of course stirs the imagination, in the work of Da Vinci as well as Duchamp however, the "brewing of ideas" in potential and an unmistakable expressive skill and craftsmanship, but none the less the raw non-elaborated and impracticable ideas - often unfinished, sometimes impossible - represent a very different practise than the one of argumentation and practical - reproducible - working models, as is the case with science. The common factor is one of a philosophical creative nature (ARTIS), but the comparison in social context (the working out and appliance of ideas) wouldn't have the slightest similarity, just because art and science are (or since the renaissance became) really different specializations.

Apart from the conclusions Linda Henderson and Craig Adcock reached in their publications, I'm not standing alone in the opinion that Henri Poincaré - specifically the publication "Science and Method" - could have been important to Duchamp. 

Recently a very active and informative source on the WEB about this relation has been esthablished by Rhonda Roland Shearer - who even organized a symposium about the subject, but unfortunately - in my view - got a bit carried away with it. Shearer and her team present a lot of amazing (preliminary) findings though...

Shearer directs the Art Science Research Laboratory in New York City, which is devoted to the scientific study of Duchamp's art. In November 1999, she hosted a symposium at Harvard called "Methods of Understanding in Art and Science: The Case of Duchamp and Poincaré."

N.B. - This short text about "the possible Influence of Jules Henri Poincaré on Marcel Duchamp" is not exhaustive and it is certainly by no means an attempt to be scientifically correct. (I'm no art historian, nor scientist)  It simply expands on the ideas and direction of ABANDON, while various opinions and ideas expressed here are subjective. 

[trans•••] - These small texts from Jules Henri Poincaré were (rather loosely) translated from French by me, because I couldn't find a sufficient translation to English in other sources.