Creative combinatorics is the subject of this blog as well as this blog is a way to explore this subject through creative combinatorics. So feel free to browse through using the categories or tags on the right or use the contents page which gives a short systematic overview.

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Many people view arts and sciences as being different because sciences yield objective answers to problems whereas arts produce subjective experiences I argue that art and science are on a continuum in which artists work with possible worlds whereas scientists are constrained to working in this world. But sometimes perceiving this world differently is the key to making discoveries. Thus, arts and sciences are on a continuum in which artistic thinking produces possibilities that scientists can evaluate for efficacy here and now. Not surprisingly, then, many of the most innovative scientists have had avocations in the arts, and some of the most innovative artists have had avocations in the sciences. These polymaths have often written or spoken about how their arts involvments have benefitted their scientific creativity and may provide a model for fostering a more innovative education.

Robert Root-Bernstein: The art of innovation: polymthas and universality of the creative process, in: Larisa V. Shavinia (Ed.): The International Handbook of Innovation. Oxford: Elsevier, 2003. PP. 267-278.

He argues that “artistic scientists and engineers have more image-ination, musically talented
ones duet (do it) better, and the verbally inclined have the skills to become pundits. Seriously.” (p. 270), and cited (on p. 268) Ostwald who “produced a large body of work on scientific genius that validated the polymath hypothesis”.

This supported by J. Rogers Hollingsworth who argued that:

the wider the range of experience and knowledge of the scientist, the more fields of science his/her work are likely to influence and the greater the importance with which it will be perceived. (p. 140)

J. Rogers Hollingsworth, “High Cognitive Complexity and the Making of Major Scientific Discoveries,” in Arnaud Sales and Marcel Fournier, eds., Knowledge, Communication and Creativity. (London and Thousand Oaks, California: Sage Publications, 2007). pp. 129-155.

Ostwald is mentioned here in a table of “Twentieth-century scientists who made major discoveries and were also quite active in music, art, writing, crafts and politics” (pp. 142-144)

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1. Petrowski, Mary Jane: Creativity research: Implications for teaching, learning and thinking, in:
   Reference services review 28 (2000) 304-312
2. Barry Eaglestone, Nigel Ford, Luy J. Brwon, Adrian Moore: Information systems and creativity : an emprical study, in: Journal of Documentation 63 (2007) 443-464
3. Vandenbosch, B., Fay, S. and Saatçioglu, A.: “Where Ideas Come From: A Systemic View Of Inquiry,” in: Sprouts: Working Papers on Information Environments. Systems and Organizations, Volume 1 (2001) 2, 109-131.

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One example is the work of Dean Keith Simonton:

• Presentation with the title Scientific creativity as a combinatorial process: The chance baseline. (“Milieus of Creativity” symposium at Villa Bosch Studio, Heidelberg, 2006.
• Paper with the title “Scientific creativity as constrained stochastic behavior: the integration of product, person, and process perspectives.” Psychological Bulletin 129(2003) 4, 475-94

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There is a science, the Theory of Combinations, which gives the rules by which, in given elements or characteristics, the kind and number of the possible groups can be found. The theory of combinations enables us to obtain a complete table and survey of all possible complex conceptswhich can be formed from given simple ones (whether they be really elementary concepts, or only relatively so) . When in any field of science the fundamental concepts have been combined in this manner, a complete survey can be had of all the possible parts of this science by means of the theory of combinations (p.71).

Thus combinatory schematization serves not only to bring the existing content of science into such order that each single thing has its assigned place, but the groups which have thereby been found to be vacant, to which as yet nothing of experience corresponds, also point to the places in which science can be completed by new discoveries (p.73).

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• Wilhelm Ostwald, ‘The art of discovery. Making discoveries by rule’, Scientific American Supplement 70, no. 1807 (1910), 123-124.

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“Combinatorics doesn’t replace productive imagination only, but is superior to it!”

So creativity included for Ostwald not only “productive imagination” but also “combinatorics”. From his view ideas and discoveries are often only “a novel combination of existing components”. Newly-discovered facts in scientific research also has to be combined with diverse existing facts to create new insights. His idea on creativity corresponds with modern views concerning an alternative exposure to copyright and intellectual property within the “Creative Commons” licences: “Share, reuse, and remix – legal” (http://creativecommons.org).

Wilhelm Ostwald (1929). Combinatorics and productive imagination (Kombinatorik und schaffende Phantasie. In: Forschen und Nutzen: Wilhelm Ostwald zur wissenschaftlichen Arbeit (pp. 28-30). Berlin: Akademie-Verlag, 1978.

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