Feeling is One Thing, Knowing Another On July 9, 1595, a young professor of mathematics at the seminary in Graz, Austria, was struck by a flash of insight that would change the world. On the blackboard he had inscribed a circle within an equilateral triangle, and inscribed it within another larger circle. Suddenly it occurred to him that if he inscribed a square within the inner circle, and another circle within the square, the distances between the circles would be comparable to the distances between the orbits of the planets Saturn, Jupiter, and Mars. He pursued the matter further in his private study, but found that by inscribing further polygons and circles within each other, he could not in fact re-create the ratios between the orbits of the six planets known at that time (Mercury, Venus, Earth, Mars, Jupiter, and Saturn). But what if he tried something similar in three dimensions? The ancient Greek geometer Euclid had proved in his Elements that there are only five regular solids - convex polyhedrons composed of congruent regular polygons. Could it be the case that each of the six planets occupied a sphere containing one of Euclids regular solids? The young mathematician believed it was simply too much of a coincidence that there should be six planets and five regular solids. After all, God could not design a universe that was less than perfect. He was to spend the rest of his life vindicating this one moment of profound clarity. In the process, he redefined astronomy and paved the way for Newtons Principia. His name was Johannes Kepler. Kepler stood astride the medieval and modern worlds. Like modern astronomers, and unlike Copernicus, Kepler was intent on developing a cosmology that was both physically plausible and which fit the observed data as closely as possible. But like so many other medieval thinkers, he believed that the True understanding of the universe would reflect the perfection of God, as that perfection was defined by the ancient Greek philosophers from Pythagoras to Plato to Aristotle. Thanks to Keplers dogged insistence on squaring this circle, he at last hit upon his Three Laws of Planetary Motion, which together with the work of Galileo and Newton ushered in the modern age, and a lasting split between science and religion. Kepler first published his theory of the relationship between the regular solids and the orbits of the heavenly bodies in a small book, the Mysterium Cosmographicum. In that book, [w]e had the privilege of witnessing one of the rare recorded instances of a false inspiration, a supreme hoax of the Socratic daimon, the inner voice that speaks with such infallible, intuitive certainty to the deluded mind. That unforgettable moment before the figure on the blackboard carried the same inner conviction as Archimedes Eureka or Newtons flash of insight about the falling apple. Questions Presented 1) Do you believe that when we experience the kind of flash of insight that Kepler and others experienced, that this is because we are tapping into some objective Truth, or are we simply having a subjective experience that happens, by virtue of our minds training and preparation, to more or less coincide with some regularity of the world? 2) Koestler describes Kepler as an astronomical analogue to Columbus. Like Columbus, Kepler discovered his America, believing it was India. Do you think it is fair to say of someone that (s)he discovered X if (s)he never appreciated that it was X? What degree of recognition does it take to say of someone that (s)he discovered X? Would (s)he have to appreciate all the implications of the discovery that we appreciate now? What if our own knowledge is deficient, as future researchers may (indeed almost certainly will) discover? (further reading: The Sleepwalkers, by Arthur Koestler) (images: Keplers diagrams of his celestial system)
Posted on: Fri, 26 Dec 2014 00:36:47 +0000
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