The relevant types of non-linear forms of causal action linking successive, "observable" points in an economic, or related process, are of the form expressed by such types of transcendental functions. Walking a student through the steps by which Kepler trascended the errors of Copernicus and Brahe, in the discovery of the principle of universal gravitation, introduces the habits of creative thinkign which it is indispensable that we must develop further for grasping the practical meaning of the dynamic form of "non-linear" functions as a replacement for intrinsically defective mechanistic method of the type commonly employed in statistical economic studies today.
What is astronomy? What are the foundations of its practice, and which difficulties present themselves when the motion of the stars is taken up? Kepler takes up the basics of astronomy in chapter 1, and indicates a very particular question he will tackle: whether to use the "mean" or the "apparent sun" in taking observations. More on that soon. Before answering that question, Kepler demands of himself a proof of the equivalence of the three main planetary hypotheses of his day: those of the anti-science liar Ptolemy, the heliocentric (almost!) Copernicus, and the great observer Tycho Brahe. This he takes up in a few parts, one on the overall equivalence of epicycles and eccentrics, the results of which can be seen in animated form here. The particular question of Copernicus's rejection of Ptolemy's equant and his use of a double epicycle in its stead is here. The recently discovered Lunatic model is also presented, as it would surely have been by Kepler had he the opportunity to be acquainted with Claudius Lunarius.
After all this demonstration of the equivalence of seemingly thoroughly different planetary models, one might consider astronomy a lost cause: apparently no matter what you do, it's all the same, kind of like equivalence of Nazi-Communism under Synarchy. But! before you become too worked up, learn what Kepler has to say about something knowable in astronomy! The mean and apparent suns! Kepler firmly believes that actual bodies should be considered in astronomical work, rather than fake points, like the center of the orbit of the earth, which Copernicus said was actually the center of the universe! This is accomplished in chapters 5 (first inequality) and 6 (second inequality). Kepler is able to prove that astronomy is knowable, rather than an infinitude of ultimately equivalent geometrical models.
Selected quotes and data from Ptolemy and Copernicus are included as well.
Beginings of Astronomy
Equivalence of Hypotheses
Kepler's change from mean (fake) to apparent (true) observations
What are the mean and apparent suns ? ! ? !