Posted on Wednesday 15 November 2006
The life and work of Johannes Kepler straddles the transition
in science from mediaeval to modern. He was one of the most
outstanding
mathematicians of his day and yet his work eventually helped to fatally
undermine the entire field of mathematical astronomy, a mediaeval
dicipline which ultimately derived from Aristotle and which sought to
describe the
heavens purely in abstract terms based on compounds of uniform circular
motions.
Kepler worked within this tradition but became so
convinced of
the
fundamental truth of the Copernican model that he explored a vast array of mathematical approaches
in order to demonstrate its superiority to geocentrism. This ultimately
led him to discover his famous three laws of motion which were in the hands of Isaac Newton many years later to transform
astronomy from being merely predictive into a science with
unprecedented explanatory power.
But along the path his mathematical explorations led him down a number
of wrong turns and blind alleys. The most delightful and aesthetically
pleasing of these is, in my opinion, his polyhedra model of the solar
system, the one incidentally which inspired the most praise from his
contemporaries but was also completely and utterly wrong.
The above excerpt comes from the George Hart's exquisite Virtual Polyhedra : The Encyclopedia of Polyhedra site. Be sure to also visit the sections of Da Vinci and Pacioli (who were also collaborators on surely the classiest mathematics textbook ever). Another interesting section is the enigma of the Neolithic Polyhedra found in Scotland.The outer sphere is that of Saturn; inside it is the sphere of Jupiter. Kepler made two prototypes in colored paper hoping to have it fabricated in silver. His original plan was that it would also function as a punchbowl dispensing assorted beverages.Kepler proposed that the distance relationships between the six planets known at that time could be understood in terms of the five Platonic solids. His 1596 book, Mysterium Cosmographicum, proposed the model illustrated below, in which one Platonic solid fits between each pair of planetary spheres. (Note the use of Leonardo's style of open faces.)
The image at right is a closeup of the spheres of inner planets, Mercury, Venus, Earth, and Mars. This is a beautiful astronomical model. For example, it explains why there are only six planets: How could there be a seventh planet, when Euclid proved that there are only five Platonic solids! Of course, the model is completely false, the interplanetary distances it predicts are not sufficiently accurate, and Kepler was scientist enough to accept this eventually. But it an excellent example of how truth and beauty are not always equivalent.
