Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

A AppendixA.1 From Copernicus to Newton - A Historical Example for theRole of Observation on ModelingIt can be seen as the birth date of the modern science era, when NicolausCopernicus (* 19th February 1473 in Thorn; † 24th May 1543in Frauenburg) based on observations of himself and others, withoutmodern instruments like telescopes, developed a model of the planetarymotion around the sun. His work that took him centuries of hislife, and published by him at the year of his death, constituted theheliocentric system in contradiction to the geocentric system. In thegeocentric system the earth was thought as the center of the worldorbited by the sun and the planets, while in the heliocentric systemthe sun is thought as the center that is orbited by the planets. ThoughNicolaus Copernicus the heliocentric system already was introduced by the Greek naturalphilosopher Aristarchus of Samos, it was Copernicus who initiallyprovided a mathematical model it.Since the basis of the model by Copernicus is the circular path of the planets around the sun, hismodel possesses quantitative failures. Later Kepler delivered a model with his famous three rulesgrounding on elliptic orbits, and for this reason is in a better agreement with observation.In the comparison between the two models on the same problem becomesmanifest the role of observation on model development. It wasan extraordinary lucky coincidence for Johannes Kepler to have theobservation data that was accumulated by Tycho Brahe.Tycho Brahe, born Tyge Ottesen Brahe (* 14th December 1546 inSchonen; † 24th October 1601 in Prague) was a danish nobleman,and maybe one of the most outstanding astronomer of all times. Onehas to keep in mind that Brahe was the last great astronomer of thepre-telescope era, the era in which positions of planets and fixed starswere measured by instruments such as the quadrant. NeverthelessBrahe was able to accumulate data of such precision (accurate to thearc minute, or 1/30 the width of the full moon) and such quantity thathis achievement for the modern sciences is immense.Tycho BraheMore or less one can say that Brahe was the prototype of a scientificobserver. The accuracy of his observations were tremendous for his lifetime and he has influencedthe ideal of the modern science that was obeyed by the following generations of scientists, namely99