Armillary Spheres

The "wooden terrestrial spheres" mentioned here are what we now call "armillary spheres." An armillary is a spherical arrangement of rings designed to mimic the orbits of the sun and planets around the Earth—or around the Sun, depending on the prevailing theory at the time. If the Earth is the center, it is a Ptolemaic sphere; if the Sun is at the center, it is a Copernican sphere. China and Greece each invented them BCE. Hipparchus credited Eratosthenes (276 - 194BCE) as the inventor.

An early Christian philosopher, John Philoponus, wrote the earliest extant treatise on the armillary sphere and the astrolabe. The oldest example of one we have today dates to the 11th century.

Gerbert d'Aurillac (946 - 1003), who became Pope Sylvester II in 999, had brought the armillary sphere to Western Europe. He was also responsible for introducing Western Europe to the abacus, the Hindu-Arabic numeral system we use today, and (possibly) the mechanical clock.

Sylvester used the armillary sphere and sighting tubes to determine the definitive position of the pole star and to record measurements for the tropics and the equator. His work was improved upon in the Renaissance by Tycho Brahe (1546 - 1601). Public figures would have an armillary sphere incorporated into their portraits to indicate their wisdom and knowledge.

I've written about clocks before, but I don't recall learning that Gerbert d'Aurillac invented it. I want to check that out; I'll let you know what I find.

The Theory of Impetus

1582 woodcut demonstrating
impetus with artillery

Impetus is the force or energy with which a body started to move. The term itself entered the English language in the 17th century, but the concept was studied long before that.

Aristotle thought that, for an object in motion to continue to move, it must have a continuous force behind it. John Philoponus in the 6th century thought rather that the initial force was necessary and did not need anything else, but that the initial force would therefore be only temporary; hence an object in motion's observed tendency to slow and stop. Avicenna in the 11th century agreed with him, calling the phenomenon "projectile motion."

In the 12th century, an Islamic philosopher, Hibat Allah Abu'l-Barakat al-Baghdaadi, recognized (finally!) that the motive force diminishes with distance from the mover.

Jean Buridan, writing in French in the 14th century, called this force "impetus" (from Latin impetere, "to assail"), and even expressed it mathematically: impetus = weight x velocity. Even he, however, treated impetus as if it were momentum. Modern physics distinguishes the two thusly: impetus is the initial force behind a moving object, momentum is "the quantity of motion of a moving body." It seems universally understood by anyone who has ever thrown a ball that Aristotle's option of a continuous motivating force is simply quaint.

Buridan understood that there was resistance (such as the air) that caused the impetus to fade. There was a case, however, in which impetus did not have resistance. God, when putting the celestial spheres in motion, did so in a way that created infinite impetus so that they would (obviously!) never stop moving.

To which the medieval world replied: Thank Heavens.

Defeating Eternity

How long has the universe existed? Has it been around forever? Did it have a beginning? Could it have a beginning? These questions troubled the ancients.

Aristotle in his Physics tried to answer this through reason. Everything that comes into being does so from something that already exists; matter is made from matter, after all. The matter of the universe would have to come into being from some underlying matter; it couldn't come from nothing. For the matter of the universe to come into being, some matter must have existed before it. This statement is ridiculously self-contradictory, and therefore could not be taken seriously. The universe must have always existed.

Others supported Aristotle. Critolaus (c.200-c.118 BCE) couldn't believe that human beings would ever stop simply procreating into eternity. In the Early Medieval Period, Proclus (412-485) produced De Æternitate Mundi (On the Eternity of the World) with 18 proofs.

This belief was about to collide headlong with Christianity, however. The Bible makes it clear that there was a moment of Creation. That being the case, the universe cannot have been eternal.

John Philoponus (490-570) was a prolific and controversial writer who realized that Aristotle needed to be questioned on some things. Although he would be condemned after his death as heretical for interpreting the Trinity as three gods instead of one God, he was known in his lifetime for defending the Biblical necessity of a universe with a starting point. He wrote "Against Proclus" in which he challenged every one of Proclus' arguments. The basis for his argument is simple, and referred to now as the Traversal of the Infinite. If the existence of something relies on the existence of something else prior to it, then you need to account for the existence of the prior thing. That prior thing would rely on the existence of something before that, and so on. You have to have an infinite series of assumptions that something existed before the thing that came afterward, and never actually explain where any of the substances came from. The world could not possibly be infinite, and must have been created by a divine being.

Pre-Inertia

Expositio & questiones manuscript

Jean Buridan (c.1300-c.1361) was a University of Paris scholar who was not afraid to tackle some of the big scientific and philosophical issues of the day. That meant, in some cases, taking a critical look at one of the most revered figures in science and philosophy, Aristotle. Buridan, like William of Ockham (c.1288-c.1348),  believed in the observable reality around him, and believed that observation of the world was the key to understanding it. Challenging Aristotle could be risky, but as more and more scholars observed the world around them, they realized that Aristotle's theories needed amendment. He wrote Expositio & questiones (Expoition and questions) to analyze Aristotle's work.

For example, Aristotle believed that an object set in motion—let's say, a rock thrown by a human hand—continues to move after it has left the hand because there must be some continuous external force exerted on it. He theorized that, in the same way a hand swished through water creates little eddies and swirls in the water around it, so the rock's movement is continued by eddies and currents of the air. If there were no movement in the medium that helped carry the rock forward, he believed, the rock would stop its forward course (and presumable drop the the ground). The currents eventually faded, allowing the rock to end its forward flight.

Buridan was not satisfied with this. Building on the work of others (such as John Philoponus and Avicenna, both of whom deserve their own entries some day), he believed that there must be a property in the rock itself that accounts for its action once it has left the motive force of the hand. He called this property of the object impetus (from Latin impetere, literally "to rush toward, to attack").

The property or quality of impetus was clearly changeable. To hurl a heavy rock required you to give it more impetus than to hurl a pebble. Also, impetus was obviously used up over time, allowing the rock to cease its movement and fall. He also explained that a falling object gained impetus the longer it fell (are you paying attention, Galileo?). Unlike Aristotle, who believed that the medium of air in which the object moves helps it along, Buridan saw the air as resistance, causing the object to use up its impetus.

He expanded this theory by looking up. A question had bothered some philosophers for ages: why don't the planets slow down? Will they move forever? Buridan extrapolated his theory to say that a thrown rock in a vacuum would experience no resistance and its impetus would last indefinitely. If the planets were moving in a vacuum...

Well, actually, he couldn't go that far. He agreed with Aristotle that a vacuum couldn't exist in space, since there was no container to keep matter from rushing into the empty area. If above our atmosphere were filled with quintessence, however, Aristotle's "fifth element" that was pure, unchangeable, and frictionless, then the impetus imparted to the planets by whatever initial agency would continue to move forever! The idea of an eternal universe was supportable by science!