Drawing the Urpflanze : Goethe, Arber, Grothendieck

Discovering the high diversity of plants in Italian gardens, Goethe coined the term Urpflanze (1817, primordial, archetypal plant). Agnes Arber (1950) describes this notion as "an intellectual basis for vegetable morphology", "under which all plant forms might be brought together". This Urpflanze was drawn by two botanists, Turpin in 1837 and Schleiden in 1843. Arber qualifies the first picture as a botanist's nightmare, and both drawings of being absurd, because of their wish to make an archetype visible. Goethe's concept is indeed both a real experience and an ideal mental construct, and might therefore not be representable as such. The Goethean concept is discussed through plant individuality, the history of botany, representation and sensory approaches of plant. Parallels are made between Goethe's Urpflanze concept and topology, a branch of mathematics, and in particular with two concepts developed by the mathematician Alexander Grothendieck: motives and topos. Both Goethe and Grothendieck were concerned about uniting multiplicity and emphasizing the connexion of knowledge and experience. Both the poet and scientist and the mathematician and political ecologist, in different times, advocate for paying a close attention to the diversity of life, and to its defence.