Wulf Rossmann

Kepler’s Grail

The new teacher for Mathematics of the Province arrived in Gratz in April 1594, at the age of 23. He thought himself a poor pedagogue because, as he explains in his self-analysis, whenever he go excited, which was most of the time, he 'burst into speech without having the time to weigh whether he was saying the right thing'. His 'enthusiasm and eagerness is harmful, and an obstacle to him, because it continually leads him into digressions, because he always thinks of new words and new subjects, new ways of expressing or proving his point, or even of altering the plan of his lecture or holding back what he intended to say. On these grounds his lectures are tiring, or at any rate perplexing and not intelligible.' The fault, he explains, lies in his peculiar kind of memory which makes him promptly forget everything he is not interested in, but which is quite wonderful in relating one idea to another.

The one administrative duty which he secretly enjoyed was the publication of an annual calendar of astrological forecasts. He thus started his administrative career with the publication of calendars and ended it as Court Astrologer of the Duke of Wallenstein. He did it for a living, with his tongue in his cheek, and called astrology 'a sortilegous monkey-play’. ‘A mind accustomed to mathematical deduction, when confronted with the faulty foundations of astrology resists a long, long time, like an obstinate mule, until compelled by beating and curses to put his foot into the puddle.'

A year after his arrival in Gratz, more precisely on 9 July 1595 he was drawing a figure on the blackboard for his class when an idea suddenly struck him with such force that he felt he was holding the secret of creation in his hand. The idea was to stack the five perfect solids in space, inner sphere on outer sphere, so that the resulting six spheres for the six planets will ‘put the true and correct model of the world before the eyes’. 'It is amazing! (Kepler informs us) although I had as yet no clear idea of the order in which the perfect solids had to be arranged, I nevertheless succeeded in arranging them so happily that later on, when I checked the matter over, I had nothing to alter'. During the next six months he worked feverishly on A Forerunner to Cosmographical Treatises, containing the Mysterium Cosmographicum of the admirable proportions between the Heavenly Orbits and the true and proper reasons for their Numbers, Magnitudes, and Periodic Motion, by Johannes Kepler, Mathematicus of the Illustrious Estates of Styria.

By February 1596 the rough draft of the book was complete and Kepler wrote to Frederick, Duke of Württemberg, to whom he explained his idea in a letter : 'The Almighty granted me last summer a major inventum in astronomy, after lengthy toil and diligence; which whole work and demonstration thereof can be fittingly and gracefully represented by a drinking cup of an ell in diameter which then would be a true an genuine likeness of the world and model of the creation insofar as human reason may fathom.' The Duke wrote in the margin of Kepler's letter 'Let him first make a model of copper.' But Kepler had no money to make a copper model, as he resentfully conveyed to the Duke in his next letter; instead he settled down to the Herculean task of making a paper model. When the monster was finished he sent it to the Duke, apologizing for its clumsiness and huge dimensions. The correspondence went on for another two years; then the subject was at last mercifully forgotten. As he later confessed, it was 'a childish and fatal craving for the favour of princes' that had driven him to Frederick's court.

Postscript. An older but no wiser Kepler proudly refers to some minor discoveries in his later works, but there is not single mention of his immortal three Laws, which every schoolboy associates with his name. A hundred years later the illustrious inventor of the Calculus of Fluxions thought he understood Kepler's Laws. No more mysterium but principia mathematica! proclaimed the secret dabbler in alchemy and apocalypse, from shoulders of giants, as he said.