Digressions&Impressions

How Did Kepler discover the Ellipse?

Yesterday, as we were ambling our way through Prague on a lovely late Summer evening, Jousef Moural, pointed me to a church barely visible behind scaffolding, the Italian Chapel of the Assumption of Our Lady. We stopped a few doors up in front of a plaque on Karlova street commemorating that Kepler lived there during his stay (1600-1612). On the authority of the late, great Renaissance scholar and historian of astronomy, Zdenek Horsky, he told me the following anecdote. I have not found it elsewhere on the internet, so I thought it worth sharing.

The chapel, which was completed just before Kepler arrived in Prague, has a dome. For nearly a decade Kepler passed by there as he was struggling with Tycho 's data before he recognized that the orbits were ellipses--something that does not just jump out of you from the Mars data. (Mars's orbit really is very close to a circle.)  The dome and the floor plan have, you guessed it, are elliptical, then an innovative architecture.

I'd like to think that sometimes when we are contemplating the starry heavens above, our beautiful even devote artifices can if not guide then inspire inquiry,  too.

 

Huygens and Newton on Beauty and Design (and Kant)

But such diversity and beauty of things is available on the other planets like our Earthly realm, surely they wouldn't lack a spectator! As the elegance and artful workmanship of the animals, and the colors and scents of the flowers seem to be made available for human admiration and delight, will there not be beings on these planets who [could] enjoy so many and so pleasing spectacles? ["Quod si igitur similis quaedam rerum varietas ac pulchritudo in caeteris planetis atque in Terra hac nostra viget, nunquid spectatore carebunt! an non ut animalium elegantia et artificiosa fabrica, florum colores atque odores ad hominum admirationem aut voluptatem comparata videntur, ita et in istis existent aliqui qui tantis spectaculis tamque jucundis fruantur."--Christiaan Huygens (ca 1689).

In the first edition of Newton's Principia (1686), God is mentioned only once, deep into the technical details of Book 3: ''Therefore God placed the planet at different distances from the sun so that each one might, according to the degree of density, enjoy a greater or smaller amount of heat from the sun'' (Book 3, proposition 8, corollary 5; quoted from the Whitman/Cohen translation, p. 814). This claim was removed in subsequent editions of the Principia, and Newton moved his natural theology -- without this particular argument -- to the new conclusion of the Principia, his General Scholium.

At least one person discerned the significance of Newton's remark in Book 3 of the Principia. As Bernard Cohen argues in his (1690) Discourse on Gravity, Huygens comments on proposition 8 that it showed what kind of gravity ''the inhabitants of Jupiter and Saturn would feel,'' (quoted from Cohen's long introduction to the translation of the Principia p. 219). We know that Huygens had empirical reasons to doubt Newton's argument for the inverse-square law as a universal quality of matter, but Huygens certainly accepted an inverse-square rule for celestial gravity that governed the planets.

As an aside, despite the fact that the argument was removed after the first editions, Kant, who knew his Huygens, also saw Newton's point: ''Newton, who established the density of some planets by calculation, thought that the cause of this relationship set according to the distance was to be found in the appropriateness of God's choice and in the fundamental motives of His final purpose, since the planets closer to the sun must endure more solar heat and those further away are to manage with a lower level of heat,'' (UNH, Part 2, section 2, 284–85 (271)).

Maria Cunitz, the greatest astronomer between Kepler and Huygens.

It remains here to forestall suspicion, for some will ask why it is that against the custom of all expert practitioners I have written the introduction in a two-fold idiom; and it will be suspected (for men are prone to suspicion) that either through eagerness for novelty or display of Latinity I seek after a little empty glory. To these I answer that I have done this neither heedlessly nor without careful thought, but persuaded by the encouragement of two weighty authorities, of which the first is LOVE OF FATHERLAND, the other NECESSITY itself. I believe it is unknown to no one that the German Nation abounds in those of abilities suited to astronomical practice although often lacking knowledge of Latin, to whom I do not see by what pretense of duty I, being of the German Nation, could refuse or take away the benefit of my labors since it is agreed by the opinion of foreigners also that the Fatherland claims a great part of our labors as its own. And we see that most other Nations publish their writings, in particular their discoveries, in the vernacular idiom familiar to them (German: in ihrer Muttersprache). But because this work, in as much as it is intended for the universal improvement of the republic of letters, should also be imparted to other nations not proficient in our idiom, necessity itself ordained to entrust this introduction to the Latin language as being more universal and familiar to most Nations. In addition, it is also to be feared, lest perhaps kidnappers (plagiarii)—for by the wickedness of our age such shamelessness has come about that very many are found who have no scruples to translate works of some note into another language, with the authors not knowing, not consulted, not willing, rather with their names entirely suppressed, and maliciously take credit for themselves—seizing this opportunity for conveyance in the open market of their own desire, ambition, and arrogance, expose for sale, enveloped in a veil of Latinity, this my authentic progeny, honorably and freely born and raised.-- Maria Cunitz’s Beneficent Urania (1650) translated by N.M. Swerdlow (2012), Urania Propitia, Tabulae Rudophinae faciles redditae a Maria Cunitia Beneficent Urania, the Adaptation of the Rudolphine Tables by Maria Cunitz 86-7.

Editing volumes can be ungrateful work; one is at the mercy of the often deplorable time-conscientiousness of others, and one must pray for their generosity in sharing their best work. One also relies on their integrity; I have had senior scholars recycle material from earlier publications without mention. But one of its great joys is learning the unexpected in nearby areas of scholarship. While editing a draft-paper by Rhonda Martens, "Newton's Introduction to Astronomy," on the significance of early Kepler (for the forthcoming Oxford Handbook to Isaac Newton, co-edited with Chris Smeenk). Martens writes: "Kepler's second law in particular was generally avoided by astronomers before Newton's Principia. Maria Cunitz (c.1604-­‐1664)5...approved of Kepler's work but used alternatives to Kepler's second law." The accompanying footnote reads: "Maria Cunitz is notable not only for her excellent tables, but also for achieving recognition despite her gender. Swerdlow (2012) has an excellent chapter on her." Made curious by Martens' comment and knowing from personal experience that Noel Swerdlow doesn't suffer fools lightly, I asked Swerdlow to send me his paper.