Brahe, Kepler, and the “Multi-Legged Cow Problem”



Kepler’s Geometer God and the “Multi-Legged Cow Problem”

( Johannes Kepler (1571-1630)

• 1589-94: University of Tubingen (a Lutheran school)

• Michael Maestlin as teacher

• Wittenberg interpretation not completely “fictionalist”

( By the 1580’s, two distinct traditions of interpreting Copernicus:

|Conservative |Radical |

|E.g.: Melanchthon, Reinhold |E.g: Maestlin, Rheticus |

|“Demonstration of the fact” |“Demonstration of the reasoned fact” |

|Reasoning from effects to causes |Reasoning from causes to effects |

|a posteriori |a priori |

|Specifies a possible cause in explaining an effect |Specifies an actual and unique cause of that effect |

|The traditional view that astronomy was limited to a posteriori |The ideal of true, causal knowledge (Aristotelian) |

|explanations only | |

( Historical irony: Radical Copernicans claimed the Heliocentric theory satisfied the ancient Aristotelian ideal of true knowledge

( Lutherans ( Atheism = Skepticism about attaining knowledge

( Knowledge of God’s providential plan a must

• But can such knowledge be obtained through astronomy?

( ‘No’, say anti-Copernicans (especially Catholics, including Jesuit

mathematicians)

( ‘No’, say conservative (Wittenberg, Protestant) Copernicans

( Astronomy cannot decide between geometrically

equivalent systems (only higher disciplines could do so)

( ‘Yes’, say the radical Copernicans (Wittenberg Protestants, some

Catholics (especially mathematicians))

( Kepler’s assumptions: “God as a geometer’

1. A priori demonstration is possible with Copernican astronomy

2. The Lutheran idea of providential design

3. Doctrine of “natural light”

Kepler’s Mysterium Cosmographicum (1596)

( What was God’s motive and plan for creating the universe?

( Central Questions: the number, the size and the motion of the orbs

( Why just 6 planets?

( A geometer God constructed the world using the 5 Platonic solids

( God is a Copernican. Why?

( Anima Motrix (motive soul) moves planets (decreases with distance)

( Brahe to Prague, 1599. Kepler leaves (Catholic) Graz in 1600 to work for Brahe. Brahe dies in 1601, leaving his observational records to Kepler.

( Imperial Mathematician

( “War with Mars”

Kepler’s Astronomia Nova (1609)

|The 1st Law |The 2nd Law |

| | |

|The planets move in elliptical orbits with the sun at one focus |The line through each planet to the sun sweeps out equal areas in |

| |equal times (law of areas) |

( Join Math & Physics: a physical reason for planetary motion?

( William Gilbert, De Magnate (1600)

( From anima motrix to vis motrix (motive force)

( Decreases proportionately with distance from the Sun

( Inverse-distance speed law ≠ law of areas

Kepler’s later work

( Epitome of Copernican Astronomy (3 vols., 1617-21)

( Applied the ‘laws’ to the other planets

( Harmony of the World (1619)

( The 3rd Law: The squares of the planets periods are

proportional to the cubes of their mean

distances from the sun

( (T1/T2)2 = (R1/R2)3

( The status of the “Laws”?

( Cartesians could ignore them as irrelevant, because they had

their own physical mechanism (Vortex theory)

( Post 1687, Newton argues for the incompatibility of Kepler’s

laws with the Vortex theory, but their compatibility (as

empirical conjectures) with his own inertial physics

( ‘Laws’ not impersonal, but part of God’s plan

( Bennett: hind-sight made them significant

Kepler: the actual v. the apparent

( Seek actual trajectories of planets, not just calculation aids

( E.g.: Franciscus Patricius said true paths are what we immediately

observe with our visual senses (Aristotelian)

( Kepler’s response: “Philosophizing astronomers” separate the actual from the apparent:

“Patricius philosophizes in such a way that whosoever listens to him cannot move a foot without creating a miracle . . . Once some friends of mine were looking through the window glass at the cows grazing in the meadows beneath the walls; a spider hung in front of the window, obstructing and not separating the distance between it and a bull directly before it, thus declaring its mockery of us. The miracle was a multi-legged cow. Clearly, Patricius’ wisdom was not greater when he contended that, as the planets appear to us amongst the fixed stars, so in fact their courses pass through them.”

Apologia Tychonis contra Ursum (1600), I, 240

( Summary:

( Kepler united astronomy & physics

( The concept of an ‘orbit’

( Kepler’s aesthetic sense that heliocentrism must be true was related to the baroque movement and political centralization in Europe (see Lecture 8, page 5)

-----------------------

[pic]

[pic]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download