Process and Calculus

[Anonymous No.17428560]

When did you realize that the fundamental theorem of calculus corresponds to a metaphysical first principle, and that this principle is the foundation of both the work of Bergson and Whitehead and was the catalyst of the scientific revolution?

https://www.religion-online.org/article/bergson-mathematics-and-creativity/

>Originally the calculus was established by using, not the concept of a function but that of a limit, and of the notion of "convergence" to a limit. To the beginner the notion of convergence to a limit, with its sense of endless approximation, may appear clumsy or counterintuitive, as if one were being required to "corner" velocity or acceleration or area by endlessly patching together ever smaller (or, in the case of the integral, larger) bits of time or space. In fact, if the "bits" are understood not as ad hoc increments but as parts of a series, and if the series are allowed to converge, the sought-for quantities suddenly appear as if by magic. In the calculus the student discovers a new way of thinking, one which is both dynamic and supple.

>It is interesting, and a bit puzzling, that this new way of thinking did not emerge until the seventeenth century. Greek mathematicians had worked out many of the concepts necessary to it. Yet they seem to have halted at the entrance. One major problem lay in their unwillingness to accept change on its own terms. According to Morris Kline, the problem was both mathematical and cultural:

>Another characteristic of Greek mathematics runs through the culture. Euclidean geometry is static. The properties of changing figures are not investigated. . , rather, the figures are given in their entirety and studied as is. The restful atmosphere of the Greek temple reflects this theme. Mind and spirit are at peace there."

[Anonymous No.17428564]

>In the terms of another historian of mathematics, Salomon Bochner, there is simply an immense gap between modern "analytical variability" and "Greek stationarity." Bergson could have added a second "static" limitation of Aristotle’s thought in this regard: his refusal to countenance kineseos kinesis (motion of motion)." Motion of motion, is of course, the definition of acceleration. Bochner asserts "Aristotle’s statement . . . ‘There cannot be motion of motion or becoming of becoming or in general change of change’ is a devastating self-indictment of Greek rational thinking at its root"

>This sketch of some basic concepts of the calculus and of factors involved in its creation is intended neither a complete outline nor as a technical account It is intended, rather, to set the stage for Bergson’s appropriation of the calculus as fundamental to his metaphysics and epistemology; Bergson believed that the calculus represented (and furthered) a profound shift in understanding, one which made modern science possible. This shift involved both increased linguistic precision (mathematical precision) and a deepening sense of change -- of mobility of all kinds. A renewed scientific and philosophical effort is necessary, he believed, to take account of it.

Likewise, the fundamental theorem of calculus is all over Whitehead's work: https://imgur.com/a/ZtLDYJT

>Two inseparable notions therefore constitute the foundational insight of Whitehead's process philosophy: the permanence of value achieved and the ongoingness of value achievement. To construct a metaphysical scheme capable of elucidating the implications of these notions was his purpose in writing PR.