Wilhelm Ostwald's combinatorics as a link between information and form
Library Trends, (2012)DOI: 10.1353/lib.2012.0041
Zusammenfassung
The combinatorial thinking of the chemist and Nobel laureate Wilhelm Ostwald grew out of his activities in chemistry and was further developed in his philosophy of nature. Ostwald used combinatorics as an analogous, creative, and interdisciplinary way of thinking in areas like knowledge organization and in his theory of colors and forms. His work marginally influenced art movements like the German Werkbund, the Dutch De Stijl, and the Bauhaus. Ostwald’s activities and his use of spatial analogies such as bridge, net, or pyramid can be viewed as support for a relation between information—or “in-formation,” or Bildung (education, formation)—and form. Introduction Combinatorics as a part of mathematics is concerned with the counting of objects and with the determination of possible arrangements of objects, which may or may not be distinguishable. Their sequence may or may not have consequences (Gowers, 2008, pp. 6–7). Combinatorics was seen as part of logic by Ramon Llull in the thirteenth century. For Leibniz, combinatorics was an ars inveniendi. It included the idea of creating knowledge mechanically through a machine (Knobloch, 2004, p. 80) and the combination of conceptual elements independently of their meaning (Krämer, 1988, p. 89). In the tradition of Llull and Leibniz, the German chemist and Nobel laureate Wilhelm Ostwald (born in 1853 in Riga, Latvia; died in 1932 in Leipzig, Germany) wrote: “Combinatorics doesn’t only replace productive imagination, but is superior to it!” (Ostwald, 1978, p. 29).1 Ostwald, one of the founders and organizers of the discipline “physical chemistry” at the end of the nineteenth century (Deltete, 2008; Ertl, 2009; Kim, 2008), worked from 1887 until 1906 as a professor in Leipzig and received the 1909 Nobel Prize in Chemistry for his work on catalysis, LIBRARY TRENDS, Vol. 61, No. 2, 2012 (“Information and Space: Analogies and Metaphors,” edited by Wouter Van Acker and Pieter Uyttenhove), pp. 286–303. © 2012 The Board of Trustees, University of Illinois 287 ostwald’s combinatorics /hapke equilibria, and rates of chemical reactions. Especially after his early retirement, he developed broad and multifaceted interests in philosophy (of nature), history (of science), and painting, color theory, and the international organization of scholarly work. The search for harmony and order in combination with his energetic imperative (“Do not waste energy, but convert it into a more useful form”) was a foundation of all Ostwald’s activities. In later years he developed a theory of forms to explain beauty and harmony, which can also play a role when conducting scholarly research in chemistry and other disciplines (Schummer, MacLennan, & Taylor, 2009). Although Ostwald saw mathematics as a foundation for the unity of science, he never contributed to the mathematical subdiscipline “combinatorics” itself. Nevertheless, Ostwald has been considered one of the discoverers of logic (Ziche, 2008), which he saw as more constitutive for other sciences than for mathematics. As will be discuseed, Ostwald used the mathematical tool “combinatorics” in his work far beyond chemistry, often in a metaphorical way or as an educational tool, as a form of representation and teaching of knowledge.2 Thus, combinatorics works in different disciplines as an analogous or similar method of thinking. Combinatorics: From Chemistry to Philosophy of Science Ostwald’s combinatorial thinking was influenced by his experience as a catalytic chemist. In his student years, he was impressed by the fact that it was possible to calculate the number of isometric substances in advance through combinatorics (Ostwald, 2003, p. 52). Chemistry has been described as a “combinatorial art” (Laszlo, 1999, p. 234) or as “combinatorial by essence” (Laszlo, 2001, p. 270). Today, the subfield “combinatorial chemistry” uses combinatorial methods as a form of selection to discover new molecules. The use of the term “library” in this context gives a first link between combinatorics and information: “Central to modern combinatorial practice in chemistry is the generation at some intermediate stage of a large set of molecules” (Hoffmann, 2001, p. 3337), which is called a “library.” In his “philosophy of nature,” his philosophy of science, Ostwald looked for an empiric foundation of mathematics and the sciences. For Hauser (1951, p. 492), Ostwald’s “greatest contribution to science and education was not the discovery of how to form oxides of nitrogen by passing a mixture of air and ammonia over a platinum catalyst . . . , but rather the emphasis he always placed in his writings and lectures on the need of the young generation’s acquiring at least a basic knowledge of what he called ‘basic philosophy.’ ” The formation of concepts should occur out of experience. Typically a chemist, Ostwald aimed for an “elementary table of concepts,” men288 library trends/fall 2012 tioning Gottfried Wilhelm Leibniz, who named this the “foundational problem of logic and philosophy of science” (Ostwald, 1911b). Then these concepts could be composed like chemical elements or compounds through systematic combination: “But we can easily make manifold arbitrary combinations of concepts from different experiences, since our memory freely places them at our disposal, and from such a combination we can form a new concept” (Ostwald, 1911a, p.18). For Ostwald, philosophy had the task to find the “general” issues of the specific sciences—like his physical chemistry within the whole chemistry. He viewed this as necessary also because of the “overload with new scholarly work and publications” Hochflut neuer wissenschaftlicher Arbeit (Ostwald, 1912b, p. 107). There was a need for Ostwald to reflect about general foundations of a discipline because otherwise it would not be possible to cope with information overload. Ostwald proposed a “science of order,” calling it “Mathetics,” as the basis of an arrangement of the sciences orientated on the hierarchical model from Auguste Comte, which Ostwald called the “pyramid of sciences” (Ostwald, 1929). Every lower discipline functions here as a foundation or auxiliary science for the upper ones. Upper disciplines have foundations in all disciplines below. “We see that . . . we can actually dispose of all ideas, each in its own place, and that a systematic arrangement of all conceivable and possible sciences, in the order of narrowing range and increasing content of the ideas, gives us the certainty of logically encompassing all human thought and hence all the human sciences possible” (Ostwald, 1912c, p. 814). With sentences like this, Ostwald influenced the development of the “Bibliographic Classification” of the librarian Henry Evelyn Bliss. Bliss (1929, p. 393) described Ostwald’s order of the sciences in the following way (in reverse order to fig. 1): I. Formal Sciences. Main concept: order. Logic, or the science of the Manifold. Mathematics, or the science of Quantity. Geometry, or the science of Space. Phoronomy, or the science of Motion. II. Physical Science. Main concept: energy. Mechanics.