Coming of Age in the Milky Way Read Online Free PDF Page B

model, proposed four centuries before Ptolemy was born! Although we know today that one light-year is but a quarter of the distance to the nearest star, and less than one ten-billionth of the radius of the observable universe, Aristarchus’ model nonetheless represented a tremendous increase in the scale that the human mind had yet assigned to the cosmos. Had the world listened, we today would speak of an Aristarchian rather than a Copernican revolution in science, and cosmology might have been spared a millennium of delusion. Instead, the work of Aristarchus was all but forgotten; Seleucus the Babylonian championed the Aristarchian system a century later, but appears to have been lonely in his enthusiasm for it. Then came the paper triumph of Ptolemy’s shrunken, geocentric universe, and the world stood still.
    Writing “The Sand Reckoner” was one of the last acts of Archimedes’ life. He was living in his native Syracuse on the southeast coast of Sicily, a center of Greek civilization, and the city was besieged by the Roman general Marcus Claudius Marcellus. Though his last name means “martial” and he was nicknamed the Sword of Rome, Marcellus for all his mettle was getting nowhere in Syracuse. Credit for holding his army at bay went to the frightening machines of war that Archimedes had designed. Roman ships approachingthe city walls were seized in the jaws of giant Archimedean cranes, raised high into the air while the terrified marines aboard clung to the rails, then dashed on the rocks below. Troops attacking on foot were crushed by boulders rained down on them by Archimedean catapults. As Plutarch recounts the siege, the Romans soon were so chagrined that “if they did but see a little rope or a piece of wood from the wall, instantly crying out, that there it was again, Archimedes was about to let fly some engine at them, they turned their backs and fled.” 4
    “Who,” Marcellus asked in his frustration as the siege wore on, “is this Archimedes?”
    A good question. The world remembers him as the man who ran naked through the city streets shouting “Eureka” after having realized, while lowering himself into a bath, that he could measure the specific gravity of a gold crown (a gift to King Hieron, one that he suspected of being adulterated) by submerging it and weighing the amount of water it displaced. Remembered, too, is his invention of the Archimedes’ screw, still widely used to pump water today, and his fascination with levers and pulleys. “Give me a place to stand,” he is said to have boasted to King Hieron, “and I shall move the earth.” 5 The king requested a demonstration on a smaller scale. Archimedes commandeered a ship loaded with freight and passengers—one that normally would have required a gang of strong men to warp from the dock—and pulled the ship unassisted, employing a multiple pulley of his own design. The king, impressed, commissioned Archimedes to build the engines of war that were to hold off the Romans.
    Plutarch writes that although he was famous for his technological skills, Archimedes disdained “as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit,” preferring to concentrate upon pure mathematics. His passion for geometry, Plutarch adds,
    made him forget his food and neglect his person, to that degree that when he was occasionally carried by absolute violence to bathe, or have his body anointed, he used to trace geometrical figures in the ashes of the fire, and diagrams in the oil on his body, being in a state of entire preoccupation, and, in the truest sense, divine possession with his love and delight in science. 6
     
    Archimedes determined the value of pi to three decimal places, proved that the area of the surface of a sphere equals four times that of a circle of the same size (the rule of 4πr 2 ), and discovered that if a sphere is circumscribed within a cylinder, the ratio of their