“[W]e presented a System of the World in which an active principle, the Xon, generates Space and Time by ‚occurring‘ in a substrate made up of i-points bearing no geometric relations of distance or proximity with each other—in brief, which do not constitute a continuum.” (p. 1427) #Auffray #Xon #space #time #continuum
“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
“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
„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
„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