In Mathematics, a number of advances were made: Francis Pellos of Nice invented the decimal point in 1492. Thomas Harriot, the astronomer who discovered sunspots, created what are now the standard symbols used in algebra. John Napier of Scotland invented logarithms, which in turn permitted William Oughtred to develop the slide rule - which could be considered a simple analog computer - in 1622. Descartes himself invented analytic geometry.

Biology and medicine also had a few breakthroughs: Paracelsus (Theophrastus Bombastus von Hohenheim was his real name! 1493-1541) recognized that life was based on chemical and physical sources, and should be explained thus. In 1553, Michael Servetus - the same one that Calvin had burned at the stake in Geneva - discovered pulmonary circulation. William Harvey (1578-1657), physician to King James I and King Charles I (and Francis Bacon, below), explained the circulation of the blood for the first time. He also promoted the idea that every animal comes from an egg - in an age when spontaneous generation of flies was the established belief.

Instrumentation drove much of the progress in science. The compound microscope was invented in 1595 by Zacharias Janssen of Middleburg in Holland. The telescope was invented by his neighbor, a German named Hans Lippershey in 1608. Galileo invented a thermometer in 1603, and his student Evangelista Torricelli invented the barometer in 1643.

[A note: Glass lenses had been around for some time. "Reading stones" (magnifying glasses) exist that date from 1000 ad in Venice. Roger Bacon suggested the principle of reading spectacles in 1264, and the first spectacles show up in Florence, Italy, around 1280. A nobleman named Amati is suggested as a possible inventor. They were considered a near miracle by the elderly of the time. On the other hand, spectacles for the near-sighted only show up in the 1500's (on the nose of Pope Leo, no less!), and bifocals have to wait for Ben Franklin to invent them in the 1780s.]

And then there were the great astronomers! Nicholas Copernicus of Poland (1473-1543) introduced the heliocentric solar system. The church, of course, asked why would God not put us - his special creation - in the center? How can this be reconciled with scripture? And doesn’t this conflict with direct experience?

Johannes Kepler 1571-1630 added the laws of planetary motion, i.e. that they have elliptic, not circular, paths. Note that this implies something less than perfection - certainly not what God would do, even if he did put the sun in the center!

If astronomers were having a hard time with the church, heaven forbid you elaborated on Copernicus: Giordano Bruno (1548-1600), of Nola near Naples, believed in an infinite universe without center, with innumerable earths traveling around innumerable suns, each with plants and animals and people. And he was a pantheist. Pantheism is the belief that God is found throughout nature, that he is, in fact, identical with the universe. When people say “God is in everything and everyone,” they are in fact making a pantheist statement that could have gotten them killed until fairly recently! He had a particularly powerful effect on Spinoza, whom we will discuss in the next chapter.

After a brief stint as a Dominican monk, he wandered around the cities of Europe until a Venetian aristocrat invited him to return. That same aristocrat turned him in to the Inquisition in 1592. He was imprisoned for eight years, but refused to recant. Finally, on February 17, 1600, he was burned at the stake in the Square of the Flowers in Rome, naked and with a nail through his tongue. In 1889, a statue of him was erected in that same square, and his death commemorated by free-thinkers world-wide every year since.