Galileo's New Toy

The night of 7 January, 1610, in Padua, Venetian Republic, a 45-year-old mathematics professor opened his window and peered at the sky through an optical instrument he had built some six months earlier. This professor´s name was Galileo Galilei and the instrument was the telescope, known at the time as a "spyglass."
By the time Galileo came across the spyglass in 1609 the instrument had been known for some time as a peculiar toy sold in marketplaces in the Netherlands, France and England. Nobody knows who invented it. It is most likely one of those inventions that "are in the air" and which several people hit upon serendipitously and almost simultaneously. One Hans Lippershey, spectacle-maker from Middelburg, had applied for a patent to the States General of the Netherlands and tried to sell the instrument to the government by pointing out its possible military applications.
Galileo was a skillful constructor of scientific instruments, and once he had seen a spyglass he was quick to grasp the principles involved. He immediately set to work on an instrument which made distant objects appear to be three times closer than they really were. Some time later, he pushed contemporary technology to the limit by building a telescope ten times as powerful as the first one.
Realizing, as Lippershey had, the strategic potential of the spyglass, Galileo subsequently arranged a demonstration for the Venetian authorities. Later he wrote:
"Very many were the patricians and senators who, although aged, have more than once climbed the stairs of the highest campanili of Venice, to detect sails and vessels on the sea, so far away that coming under full sail toward the harbor, two hours or more passed before they could be seen without my spyglass."
As a consequence of this demonstration, Galileo´s salary was doubled and he was granted a lifelong professorial appointment at Padua.
Six months later, Galileo took his best telescope and trained it on the night sky. It was a stroke of genius. Today, one can hardly think of anything more natural to do with a telescope than to point it at the sky, but we must remember that at the time, although Nicolaus Copernicus had published his views about a sun-centered cosmos more than 60 years before, the sky was still held to be divine and pristine, a place of purity as opposed to earthly corruption. Many centuries before, Aristotle claimed that the stars and planets, including the sun and moon, were celestial emmanations that moved around the earth attached to crystal spheres and surrounded by a transparent substance called aether. Looking at the sky, therefore, meant peering into the abode of God. Galileo was treading unchartered and dangerous territory.
What he saw with his telescope during the Winter of 1610 confirmed what he had known for a long time, but had been cautious not to maintain openly --that Aristotle had been dead wrong about the nature of the stars and planets. The moon did not have a polished surface, as the Greek philosopher had said, but was instead deeply scarred with craters, crevasses and mountains, like the earth. The telescope revealed countless stars that were not visible to the unaided eye, and showed that Venus has phases like the moon, which is only possible if it orbits the sun and not the earth. But what stunned him the most was the discovery of four previously undetected "stars" in the vicinity of Jupiter. It gradually became clear that they were circling the planet. This demolished an old objection to the Copernican system in which the earth moved around the sun like the wandering stars, namely, that the moon could not possibly revolve around the earth if the earth itself revolved around the sun.
Galileo´s telescopic findings, which he wasted no time in publishing, changed humankind´s picture of the universe.

Kepler's Most Beautiful Idea

Johannes Kepler, the 17th-century astronomer credited with discovering that the planets’ paths around the sun are ellipses, was teaching geometry to a bunch of bored kids in Graz, Austria, when he was suddenly struck by the most beautiful idea he would ever have.
Six planets were known at the time --Mercury, Venus, Earth, Mars, Jupiter, and Saturn. Their orbits, which Kepler still believed were circles, placed them at certain distances from the sun. Why six planets? Why those particular distances? Kepler wondered. In the true spirit of modern science, he was confident that the distances of the planets were governed by some sort of mathematical law.
It is a well known geometrical fact that if you wish to construct solid, three-dimensional bodies whose sides are regular polygons (polygons whose sides are all the same length), try as you might, you will end up with no more than five such bodies. This result is a geometrical theorem --in 3D space there exist five and only five regular, or “Pythagorean,” solids. It has nothing to do with the state of our mathematical knowledge or our technological prowess. Like the statement that parallel lines meet at infinity, the existence of no more than five regular solids is an inescapable property of three-dimensional flat space.
Kepler’s idea was this: there are only six planets because there are only five regular solids and if we put these solids one inside the other in a nested pattern, the spheres defining the boundaries where an inner solid touches the next one out have radii which are in the same proportion as the distances of the planets. Kepler called this hypothesis the Mysterium Cosmographicum . It was beautiful in its geometrical simplicity and awe-inspiring in its depth of implication (the existence of god the mathematician). It rang true. But it was not.
Kepler tried hard to make the nested regular solids match the distances of the planets, but to no avail. He had based his calculations on figures obtained by Copernicus seventy years earlier. Perhaps more accurate measurements of the distances might show them to fit his elegant scheme?
The greatest observational astronomer of the age, Tycho Brahe, had performed such measurements. When Kepler got hold of the data after Tycho’s death he was disappointed. In the end --and in view of Galileo’s subsequent discovery of Jupiter’s four large moons, which the Mysterium could not possibly accomodate-- Kepler reluctantly abandoned his pet theory. It took courage, but Kepler was imbued with “the will to find out” as opposed to “the will to believe”. He was skeptical even of his own ideas.
Skepticism is essential in science. It prevents us from foisting our emotions on the universe, and thus helps us to study verifiable facts with a cool head. Gullibility readily accepts claims that may seem satisfying on grounds of personal taste or convenience, but that all too often are simply not true. The Argentinean philosopher of science Mario Bunge wrote:
Scientific knowledge is sometimes unpleasant. It often contradicts the classics; occasionally tortures common sense and humiliates intuition. Lastly, it may prove convenient for some, but not for others. The hallmark of scientific knowledge is that it is verifiable.
Personal taste, appeals to authority, and even democracy (like in deciding by popular vote which one of several contending hypotheses is true) have no place in science. Science is about discovering objective facts whose truth does not depend on who champions or opposes them. As the French mathematician Henri Poincaré said: “The sole source of truth is experiment. Only it can teach us something new; only it can give us certainty.”