Hammersley: Crystals


“We deal with atoms and bonds: a bond is a (perhaps directed) path between two atoms. An n-stepped walk is an ordered connected path along n consecutive bonds, each step being in the permitted direction of a bond (if the bond in question is directed) and starting from the atom reached by the previous step (if any). Wn(A) denotes a typical n-stepped walk starting from an atom A. A walk is self-avoiding if it visits no atom more than once. Sn(A) denotes a self-avoiding Wn(A). Two walks are distinct if they do not utilize the same set of bonds, with due regard to order. fA(n, r) denotes the number of distinct Wn(A), each of which can be broken into r or fewer self-avoiding subwalks. In particular we write fA(n) =fA(n, 1) for the number of distinct Sn(A). Two atoms A and B are outlike if fA(n) = fB{n) for all n. An outlike class is a class of pairwise outlike atoms. A crystal is an infinite set of atoms and bonds satisfying the three postulates” (p. 642) #Hammersley #atom #bond #walk #crystal

Hammersley, John M., Percolation processes. II. The Connective Constant, in: Mathematical Proceedings of the Cambridge Philosophical Society 53 (1957), 642–645.

Prigogine/Stengers: The Laws of Fate (foedera fati)


„As Serres points out, the infinite fall provides a model on which to base our con­ception of the natural genesis of the disturbance that causes things to be born. If the vertical fall were not disturbed ‚with­out reason‘ by the clinamen, which leads to encounters and associations between uniformly falling atoms, no nature could be created; all that would be reproduced would be the repeti­tive connection between equivalent causes and effects gov­erned by the laws of fate (foedera fati).“ (p. 303) #Prigogine #Stengers #Serres #NaturalGenesis #clinamen #atom #LawsOfFate

Prigogine, Ilya/Stengers, Isabelle, Order Out of Chaos. Man’s New Dialogue With Nature. New York City: Bantam 1984.

Serres: Das Atom unserer Beziehungen


„Das parasitäre Verhältnis ist intersubjektiv. Es ist das Atom unserer Beziehungen.“ (p. 19) #Serres #Parasit #Atom #Beziehung

Serres, Michel, Der Parasit; übersetzt von Michael Bischoff. Frankfurt/M.: Suhrkamp 1981. 391 S., ISBN 978-3-518-07581-4.