Climax of the Scientific Revolution: Kepler to Newton

1. Climax of the Scientific Revolution: Kepler to Newton

2. Johannes Kepler (1571 - 1630)

3. Johannes Kepler (1571 - 1630) Studied astronomy at Tübingen – a first-generation student of the new Lutheran astronomical tradition • Copernicanism as a model  Copernicanism as reality

4. Johannes Kepler (1571 - 1630) New questions within Copernican theory: • How are the distances of the planets from the Sun established? • In the absence of real spheres and orbs: what determines the planet’s motions? • Why are there exactly 6 planets?

5. Johannes Kepler (1571 - 1630) MysteriumCosmographicum (1596) There were three things in particular about which I persistently sought the reasons why they were such and not otherwise:  the number, the size, and the motion of the circles....  In the beginning I attacked the business by numbers, and considered whether one circle was twice another, or three times, or four times, or whatever, and how far any one was separated from another according to Copernicus.  I wasted a great deal of time on that toil, as if at a game, since no agreement appeared either in the proportions themselves or in the differences; and I derived nothing of value from that except that I engraved deeply on my memory the distances which were published by Copernicus....  If God allotted motions to the spheres to correspond with their distances, I thought, similarly he made the distances themselves correspond with something....

6. The Conjunctions of Jupiter and Saturn (1570-1770) (Expected …)

8. Jupiter-Saturn conjunctions over 40 cycles generates this pattern. Kepler was struck by the emergence of what appeared to be a smaller circle inscribed within the larger original one.

9. Mysterium Cosmographicum(1596)

10. MysteriumCosmographicum(1596) Six planetary orbits are nested in five Platonic solids

11. Six planetary orbits are nested in five Platonic solids

12. “” MysteriumCosmographicum(1596) A claims about the planets: Six planetary orbits are nested in five Platonic solids Also a (Pythagorean) claim about knowledge: God created the world according to fundamental magnitudes; mathematics is the science of magnitudes; mathematics is qualified to establish physical truths.

13. “” MysteriumCosmographicum(1596) Kepler to his teacher Mästlin, Apr. 19, 1597: Then man will realize that God, who founded everything in the world according to the norm of quantity, also has endowed man with a mind which can comprehend these norms. For as the eye for color, the ear for musical sounds, so is the mind of man created for the perception not of any arbitrary entities, but rather of quantities; the mind comprehends a thing the more correctly the closer the thing approaches toward pure quantity as its origin.

14. “” MysteriumCosmographicum(1596) Kepler to Herwart von Hohenburg, Apr. 9, 1599: Those laws [which govern the material world] lie within the power of understanding of the human mind; God wanted us to perceive them when He created us in His image in order that we may take part in His own thoughts . . . . Our knowledge [of numbers and quantities] is of the same kind as God's, at least insofar as we can understand something of it in this mortal life.

15. MysteriumCosmographicum(1596) 1599: Tycho Brahe invites Kepler to Prague 1600: Kepler starts to study the data on Mars 1601: Tycho dies 1603:Kepler’s second law: “celestial bodies need not move at constant speeds:  planets move faster when they are closer to the Sun, slower when they are far away”

16. 1603:Kepler’s second law: “celestial bodies need not move at constant speeds:  planets move faster when they are closer to the Sun, slower when they are far away” Planets sweep out equal areas in equal times

17. 1603:Kepler’s FIRST law: “celestial bodies need not move in perfect circles” Kepler’s FIRST law: “planets move in elliptical orbits”

18. 1609

22. The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes:

23. Pythagorean claims about knowledge: Kepler to Herwart, Feb.10, 1605: I am much occupied with the investigation of the physical causes. My aim in this is to show that the celestial machine is to be likened not to a divine organism but rather to a clockwork . . . insofar as nearly all the manifold movements are carried out by means of a single, quite simple magnetic force, as in the case of a clockwork all motions [are caused] by a simple weight. Moreover I show how this physical conception is to be presented through calculation and geometry.

24. 1619

25. Harmonices Mundi (1619)

26. Harmonices Mundi (1619) • God the Creator played music, in like manner he taught Nature to play after his likeness -- that is to say, precisely that piece of music that he has played for her. Therefore it is the case that in music no natural soul of a human being wants to play with a septangle, nor will he enjoy such if this proportion is given to the voices, because God did not play with these figures.

27. 1627 Rudoplphine Tables

28. Isaac Newton(1643-1727)

29. Isaac Newton(1643-1727) 1664-1666 AnnusMirabilis Binomial, Calculus, Gravitation, Composition of Light

33. Isaac Newton (1642-1727) • Alchemy and Theology: • A corrected chronology of ancient kingdoms • Exegesis of Daniel’s Bookand Saint John’s Apocalypse • A reconstruction of a blueprint for the temple

34. Isaac Newton(1643-1727) 1671: The telescope

40. Preface: Rational Mechanics will be the science of motions resulting from any forces whatsoever, and of the forces required to produce any motions, accurately proposed and demonstrated [...] And therefore we offer this work as mathematical principles of philosophy. For all the difficulty of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of Nature, and then from these forces to demonstrate the other phenomena

41. Preface: I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to that or some truer method of philosophy.

42. Part 1: De motucorporum (On the motion of bodies): motion in the absence of any resisting medium. Part 2: motion through a resisting medium. Part 3: De mundi systemate (On the system of the world): an exposition of the consequences of universal gravitation, especially for astronomy. 

43. General Scholium (1713) Responses to criticism of the first edition Hypotheses non fingo Phenomena imply gravitational attraction; but they do not indicate the cause of this gravity. It is both unnecessary and improper to frame hypotheses of things not implied by the phenomena: such hypotheses "have no place in experimental philosophy", in contrast to the proper way in which "particular propositions are inferr'd from the phenomena and afterwards rendered general by induction"

44. General Scholium (1713) Responses to criticism of the first edition Hypotheses non fingo  A criticism of the vortex theory of planetary motions, of Descartes: it is incompatible with the highly eccentric orbits of comets, which carry them "through all parts of the heavens indifferently" Also: a theological argument. From the system of the world, Newton inferred the existence of a Lord God, along lines similar to what is sometimes called the argument from intelligent or purposive design.

45. Atheism is so senseless & odious to mankind that it never had many professors. Can it be by accident that all birds beasts & men have their right side & left side alike shaped (except in their bowels) & just two eyes & no more on either side the face & just two ears on either side the head & a nose with two holes & no more between the eyes & one mouth under the nose & either two fore leggs or two wings or two arms on the sholders & two leggs on the hipps one on either side & no more? Whence arises this uniformity in all their outward shapes but from the counsel & contrivance of an Author? Whence is it that the eyes of all sorts of living creatures are transparent to the very bottom & the only transparent members in the body, having on the outside an hard transparent skin, & within transparent juyces with a crystalline Lens in the middle & a pupil before the Lens all of them so truly shaped & fitted for vision, that no Artist can mend them? Did blind chance know that there was light & what was its refraction & fit the eys of all creatures after the most curious manner to make use of it? These & such like considerations always have & ever will prevail with man kind to believe that there is a being who made all things & has all things in his power & who is therfore to be feared.

46. Netwon’s Three Laws of Motion Every body perseveres in its state of being at rest or of moving uniformly straightforward except insofar as it is compelled to change its state by forces impressed The size of an acceleration is directly proportional to the force applied, and inversely proportional to the mass of the body. Further, the acceleration will take place in the same direction as the For every force applied to a body, there is an equal and oppositely directed force exerted in response. applied force.

48. Isaac Newton(1643-1727) Philosophiae Naturalis Principia Mathematica “Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power … I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses [hypotheses non fingo]; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy … To us it is enough that gravity does really exist, and acts according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.”

49. Isaac Newton(1643-1727) Philosophiae Naturalis Principia Mathematica “This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. This Being governs all things, not as the soul of the world, but as Lord over all; and on account of His dominion He is wont to be called Lord God.”

50. Isaac Newton(1643-1727) PhilosophiaeNaturalisPrincipia Mathematica:“… against notorious infidels …” When I wrote my book, I had an eye on principles that might help people considering belief in God. Nothing would make me happier than to see it used for that purpose.