Grimmett: The Random-Cluster Model


“The random-cluster model as studied so far is random in space but not in time. There are a variety of ways of introducing time-dynamics into the model, and some good reasons for so doing. The principal reason is that, in our 3 + 1 dimensional universe, the time-evolution of processes is fundamental. It entails the concepts of equilibrium and convergence, of metastability, and of chaos. A rigorous theory of time-evolution in statistical mechanics is one of the major achievements of modern probability theory with which the names Dobrushin, Spitzer, and Liggett are easily associated.” (p. 222) #Grimmett #Random-ClusterModel #Space #Time #ProbabilityTheory

Grimmett, Geoffrey R., The Random-Cluster Model. With 37 Figures. Berlin/Heidelberg: Springer 2006. 377 S., ISBN 978-3-540-32890-2.

Olsen et al.: Times


“Primary times provide the grounds for secondary times. Primary times are relational. Secondary times are processual. Primary times are spatial, yet saturated with a ceaseless, liquid motion. Secondary times separate space and time.” (p. 156) #Olsen #Shanks #Webmoor #Witmore #time #space

Olsen, Bjørnar u. a., Archaeology. The Discipline of Things. Berkeley/Los Angeles/London: University of California Press 2012.

Dewar: Spacetime


„The key difference from Newtonian spacetime, then, is that there is no ‘persistence of space over time’: since there is no notion of a vector being ‘purely temporal’, we cannot say of two points in G0 that they differ by a purely temporal vector, and hence correspond to the same point of space at two different times. (By contrast, since we do have a notion of purely spatial vectors, we can say of two points of G0 that they differ by such a vector and hence correspond to two different points of space at the same time; this is precisely the relation that foliates G0.).“ (p. 55) #Dewar #spacetime

Dewar, Neil, Structure and Equivalence. Cambridge, UK: Cambridge University Press 2022, ISBN 978-1-108-82376-0.

Bühlmann: Communication


„A physics of mathematical communication challenges philosophy to welcome the concept of ‚mass‘ as a third in the fundamental order of physics, next to those of space and time.“ (p. 5) #Bühlmann #communication #mass #space #time

Bühlmann, Vera, Mathematics and Information in the Philosophy of Michel Serres (Michel Serres and Material Futures); herausgegeben von David Webb und Joanna Hodge. London: Bloomsbury Academic 2020. 238 S., ISBN 978-1-350-01976-8.

Mill: Number and Space


„In the laws of number, then, and in those of space, we recognize in the most unqualified manner, the rigorous universality of which we are in quest. Those laws have been in all ages the type of certainty, the standard of comparison for all inferior degrees of evidence. Their invariability is so perfect, that it renders us unable even to conceive any exception to them; and philosophers have been led, though (as I have endeavored to show) erroneously, to consider their evidence as lying not in experience, but in the original constitution of the intellect.“ (Chap. V, § 1) #Mill #number #space

Mill, John Stuart, A System of Logic, Ratiocinative and Inductive Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation. New York: Harper & Brothers 81882.