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In Kepler's case the
situation was that his problem was to interpret a large body of data he
had managed to wrest away from Tycho's sons. He got Mars, and those were
the best data for his purposes. The data were taken by a man who had an
axe to grind: he had his own model of the universe. Kepler was hired to
interpret the data in that way even though Kepler himself was inclined
toward a different model. When Tycho unexpectedly died, Kepler's income
and those constraints ended simultaneously. He made off with his treasure
(I don't remember how he fed himself) and then spent a very long time
pondering the observations.
Leigh