/lit/ - Literature

>The apodictic nature of geometry stands against the fallibility of intuition— a passage in Galileo’s Dialogue Concerning the Two Chief World Systems reveals the striving for a methodological certitude that is not affected by the vicissitudes of human error and judgment:

>If this point of which we dispute were some point of law, or other part of the studies called the humanities, wherein there is neither truth nor falsehood, we might give sufficient credit to the acuteness of wit, readiness of answers, and the greater accomplishment of writers, and hope that he who is most proficient in these will make his reason more probable and plausible. But the conclusions of natural science are true and necessary, and the judgment of man has nothing to do with them.

>Einstein was not unjustified, then, in his assessment of the advance of geometry in Europe. In fact, if we look at the history of cosmology from its mythical origins up to modem astronomy, via Claudius Ptolemy, Copernicus, Tycho Brahe, Kepler, and Newton, at every stage it is fundamentally a geometrical question. Even Einstein’s theory of general relativity which identifies gravity with the curvature of four-dimensional space-time, is fundamentally a geometrical theory (albeit no longer a Euclidean one).

>But rather than limiting ourselves to geometry as a mathematical subject, let us take the question further by connecting it with the question of time. It seems to me that the relation between time and geometry/space is fundamental to the Western concept of technics and its further development into efficient mnemotechnical systems. In posing the question in this way, we will shift from abstraction to idealisation— that is, from mental abstraction to idealisation in externalised geometrical forms. Idealisation has to be distinguished from ideation, which still concerns theoretical abstraction in thought— for example, we can think of a triangle (e.g. ideation), but the apodictic nature of the triangle becomes common to all when it is externalised (e.g. drawn).

>Idealisation in this sense thus involves an exteriorization, whether through writing or drawing. My reasoning on the relation between geometry, time, and technics can be summarised as follows: (1) geometry demands and allows the spatialization of time, which involves (2) exteriorization and idealization through technical means, (3) geometrical apodicticity allows logical inferences as well as the mechanization of casual relations, and (4) the technical objects and technical systems made possible on the basis of such mechanisation in turn participate in the constitution of temporality: experience, history, historicity.

>This interconnection or accommodation of all created things to each other, and each to all the others, brings it about that each simple substance has relations that express all the others, and consequently, that each simple substance is a perpetual, living mirror of the universe.

― Gottfried Wilhelm Leibniz, Monadology