Abstract
Recent advances in design theory help clarify the logic, forms and conditions of generativity. In particular, the formal model of forcing predicts that high-level generativity (so-called generic generativity) can only be reached if the knowledge structure meets the ‘splitting condition’. We test this hypothesis for the case of Bauhaus (1919–1933), where we can expect strong generativity and where we have access to the structures of knowledge provided by teaching. We analyse teaching at Bauhaus by focusing on the courses of Itten and Klee. We show that these courses aimed to increase students’ creative design capabilities by providing the students with methods of building a knowledge base with two critical features: (1) a knowledge structure that is characterized by non-determinism and non-modularity and (2) a design process that helps students progressively ‘superimpose’ languages on the object. From the results of the study, we confirm the hypothesis deduced from design theory; we reveal unexpected conditions on the knowledge structure required for generativity and show that the structure is different from the knowledge structure and design process of engineering systematic design and show that the conditions required for generativity, which can appear as a limit on generativity, can also be positively interpreted. The example of Bauhaus shows that enabling a splitting condition is a powerful way to increase designers’ generativity.
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Notes
As suggested by an anonymous reviewer (whom we warmly thank), we provide here complementary references on forcing—these sources explore forcing historically: {Kanamori 2008 #3191; Moore 1988 #3192}; the reader can also refer to {Chow 2009 #3193}. {Dickman 2013 #3194} is a case study of creativity in science applied to the discovery of Forcing.
In forcing theory, one uses interchangeably the terms “forcing constraint” and “forcing condition”. In this paper, we favour the term “forcing constraint” to avoid confusion with the “splitting condition” that will be presented below.
Demonstration (see Jech 2002, exercise 14.6, p. 223): Suppose that G is in M and consider \( D = Q\backslash G \). For any p in Q, the splitting condition implies that there are q and q′ that refine p and are incompatible; one of the two is therefore not in G and thus is in D. Hence, any condition of Q is refined by an element of D. Hence, D is dense. Therefore, G is not generic.
Demonstration (see Jech 2002, p. 203): Let D 1, D 2… be the dense subsets of Q. Let \( p_{0} = p^{*} \), a constraint in Q. For each n, let p n be such that p n < p n−1 and p n is in D n . The set \( G = \{ q \in P/q > p_{n} \;{\text{for}}\;{\text{some}}\;n \in N\} \) is then a generic filter acting on Q and \( p^{*} \) is in G.
Demonstration: If Q is non-splitting, then there exists p0 such that whatever q and q′ are refining p 0, and there is r such that r < q and r < q′. We show that if p 0 is in G, then G refines all conditions stronger than p 0. We want to show that, whatever q < p 0, there is r in G that refines q. To this end, we introduce D q = {p in Q/p is not refined by p 0 or p < q}. D q is dense: for every p in Q, either p is not refined by p 0 and it is in D q or p < p 0; we know that q < p 0 and Q is non-splitting, and hence, there is r < p and r < q. D q is therefore dense. G therefore intersects D q . Hence, for every q that refines p 0, there is an r in D q . Moreover, we know that p 0 is in G, and hence, r in D q necessarily refines p 0. Therefore, every constraint stronger than p 0 is refined by a constraint in G. Hence, every constraint stronger than p 0 is in G. Hence, G is determined by p 0. Note that the splitting condition is sufficient but not necessary. A non-splitting knowledge base Q can be used to create a generic filter G not in M, which is a consequence of the theorem above that states that G must “avoid” all p 0 where modularity or determinism begins.
They sponsored lectures, exhibitions (Köln 1914), and publications (Werkbund Jahrbücher), helped found a museum of applied arts and were involved in Dürerbund-Werkbund Genossenschaft (publishing a catalogue of exemplary mass-produced goods 1915), linked to Werkstättenbewegung (Riemerschmid, Naumann). In parallel, they made great efforts to establish a theoretical basis, and Werkbund was a forum for discussion, with a wide cultural, economic, social and political audience.
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Le Masson, P., Hatchuel, A. & Weil, B. Design theory at Bauhaus: teaching “splitting” knowledge. Res Eng Design 27, 91–115 (2016). https://doi.org/10.1007/s00163-015-0206-z
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DOI: https://doi.org/10.1007/s00163-015-0206-z