C. An extension of our basic intuition
We may then ask whether we cannot, by a refinement of our geometric intuition, furnish our scientific investigation with a stock of ideas and procedures subtle enough to give satisfactory qualitative representations to partial phenomena. It is necessary to emphasize one point: we can now present qualitative results in a rigorous way, thanks to recent progress in topology and differential analysis, for we know how to define a form and can determine whether two functions have or have not the same form or topological type. We therefore endeavour in the program outlined here to free our intuition from three-dimensional experience and to use much more general, richer, dynamical concepts, which will in fact be independent of the configuration spaces. In particular, the dimension of the space and the number of degrees of freedom of the local system are quite arbitrary - in fact, the universal model of the process is embedded in an infinite-dimensional space. This is obviously necessary; there is no doubt that the closer the study approaches the infinitesimal, the more degrees of freedom are needed, so that all qualitative representation of microscopic phenomena will require the use of an infinite-dimensional function space.
One essential feature of our use of local models is that it implies nothing about the "ultimate nature of reality"; even if this is ever revealed by analysis complicated beyond description, only a part of its manifestation, the so-called observables, are finally relevant to the macroscopic description of the system. The phase space of our dynamical model is defined using only these observables and without reference to any more-or-less chaotic underlying structures.
To each partial system, relatively independent of the environment, we assign a local model that accounts qualitatively and, in the best cases, quantitatively for its behaviour. But we cannot hope, a priori, to integrate all these local models into a global system. If it were possible to make such a synthesis, man could justifiably say that he knew the ultimate nature of reality, for there could exist no better global model. For myself, I think that this would be extravagant pretension; the era of grand cosmic synthesis ended, very probably, with general relativity, and it is most doubtful that anybody will restart it, nor would it seem to be useful to attempt to do so.