A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Brad Morris
Date: 2017 Apr 30, 14:43 -0400
Brad Morris, you asked:
"Yet Newton's Principia 1st ed is 1687. How can there be a calculus application prior to the publication of Principia?"
While Newton, and Liebniz simultaneously, revolutionized the mathematical material that we have called "calculus" ever since, they didn't invent it. They built on centuries of prior work. That earlier work is not pre-calculus. It is genuinely part of the history of differential and integral calculus and recognized as such by historians of science and mathematics today. Math suffers from the same "cartoon history" problem that afflicts many technical subjects including, of course, celestial navigation. It's useful pedagogically to provide a shortened, polite society, highly linear, formally "logical" history to engineering and science students, but unfortunately these are pseudo-histories. The real thing is messy, non-linear, political, and even mystical --affected by highly illogical and frequently "un-scientific" beliefs and prejudices. For a basic introduction to the pre-Newtonian history of calculus, try the Wikipedia page on the History of Calculus.
A major problem with pedagogy that employs "cartoon histories" is that they lead to a type of social confirmation bias that creates a comforting lore version of history that's at odds with real history. In navigation, for example, if everyone is taught that Bowditch's Navigator was a revolutionary book that dramatically changed the way that navigators did lunars, then of course any "crowd" of navigators discussing history will nod their heads approvingly when such words are uttered, because it's something that "everyone knows". It is the "lore" of navigation.
Disclaimer: I don't know what it's in that book that's up for auction, of course, and I am only addressing the question as posed here.