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already been announced by my comrades, who had crossed another part of the river, as dead and drowned.”

3
    A Source of Great Fear
    K ircher was “received and restored” in Neuss “to the tremendous joy of all.” After three days of rest, and another several hours of hiking on rutted, frozen roads, the young men finally walked wide-eyed through the gates of Cologne, a center of trade along the Rhine that had once rivaled Paris in size, sophistication, culture, and learning. A sovereign and heavily fortified “free city” within the Holy Roman Empire, Cologne laid claim to forty thousand citizens, an entire army of its own, one hundred fifty churches, and the world’s largest incomplete cathedral: building had begun almost four hundred years before Kircher’s arrival, but no work had been done for almost a century. Construction wouldn’t resume for another two hundred years. A couple of streets away from the site of this unfinished Gothic mountain, as many as fifteen hundred students took classes at the Jesuit college.
    Within this more urban setting, Kircher went on with his course in philosophy. Now he was the country boy in worn-out shoes, known or whispered to have barely escaped martyrdom at the hands of the Insane Bishop. He was still extremely pious, and still pretending to be a dimwit, but he wouldn’t be able to pass himself off that way much longer.
    Kircher and other Jesuit scholastics read Aristotle’s works in Greek and discussed them in Latin. They also took general instruction in mathematics, a strange part, on the face of it, of a philosophy program meant to prepare them for theology and the priesthood—especially since mathematics had traditionally been viewed with condescension by natural philosophers and theologians alike. Mathematics could be used to measure and describe, and it had many practical applications, but it couldn’t
explain
, in the opinion of natural philosophers, the way natural philosophy could. It had nothing to say about the causes or the natures or the essences of things, only about, as one historian put it, the “superficial quantitative properties” of things, properties regarded by philosophers as incidental. Mathematicians were bean counters, and their instruments (astrolabes, quadrants, protractors, plumb levels, calipers, magnetic compasses) just made for better bean counting.
    But the reputation of mathematics as a field of study had improved a great deal in the sixteenth century. New translations of works by Archimedes of Syracuse on floating bodies and mechanics gave engineering its own seemingly infallible ancient authority. Mathematics included four traditional academic subjects: arithmetic, geometry, astronomy, and music (basically the study of harmonics). But it also encompassed mechanics, engineering, optics, surveyorship, and astrology. People in positions of power cared more and more about math as applied to architecture and construction, shipbuilding and navigation, mapmaking, fortification, armament, ballistics, and so on. And one Jesuit in particular had exerted himself to elevate the role of mathematics within the order. He was born Christoph Klau, in Bamberg, but his Latinized name was Christopher Clavius, and many of his contemporaries referred to him as the Euclid of his time.
    Based at the prestigious Collegio Romano, the Jesuit college in Rome, from early in his priesthood until he died in 1612 (when Kircher was about ten), Clavius published works on astronomy, geometry, the construction of sundials, and algebra, a relatively new field in the West. He was among the first to use a dot or point as a decimal separator, parentheses to enclose calculations within an expression, and an
x
for variables. Most memorably, he recalculated the calendar year at the request of Pope Gregory XIII. The Julian calendar, put into use by Julius Caesar more than fifteen hundred years before, had been slipping to the point