Between manifold and completeness – Wilhelm Ostwald on mathematics and form

For the chemist and Nobel laureate Wilhelm Ostwald, mathematics became something like an overall concept for his philosophy of science. Mathematics as a basis of his pyramid of sciences and for the unity of all sciences led him to aim, typical for a chemist, for an “elementary table of concepts”. Ostwald applied mathematical thinking and here especially combinatorics in areas like his philosophy of nature, like creativity as well as like his theory of colors and forms. In addition this paper discusses the use of the term 'manifold' which was very popular also outside mathematics around 1900. František Wald used this term in the sense of a model whose dimensions had to fit the dimensions of described phenomena. Wilhelm Ostwald took over this notion in his lecture at the 1904 St. Louis Congress. Another term, especially used by Ostwald when discussing stoichiometric laws, 'Restlosigkeit' – its English translation 'completeness' is also used in mathematics – played an important role within another of Ostwald’s activities: the foundation of an "International Institute for the Organization of Intellectual Work", "Die Brücke The Bridge", also called "World Brain" by Ostwald. This institute tried to build a comprehensive encyclopedia on sheets of standardized formats so to improve and organize scholarly information and communication. All this may contribute to explain a hidden tradition of “in-formation” in chemistry (trans-formation) which is also visible in the fact that so many information pioneers in the 20th century were educated as chemists.