According to the model we have from Boethius, the fourth and final mathematical art is astronomy. Like the other three arts (arithmetic, geometry, and music), the practice of astronomy can be traced back as far as we have documentation. In fact, in some regard, it goes all the way back to Adam, who was given the sun, moon, and stars “for signs and seasons, and for days and years.” How much Adam discovered or knew about the workings of the sun, moon, and stars, we don’t know (I like to think he knew much more than we do!), but as far as written records go, we can read ancient astronomical math at least as old as the Babylonian civilization.
Astronomy has always posed a particularly tricky problem for mathematicians: the heavenly bodies are too far away to measure with a ruler! How can you know how far away the stars are, or how far away they are from each other, if you’re much too far away to measure them yourself? The Babylonians already had a system in their day, and it’s the same one many mathematicians still use today: the degree system.
Now, degrees can’t measure distance, but they can measure how much you have to rotate your pointed finger to get from one star or planet to another. And the amount of rotation is what degrees are all about. Around 150 B.C., the Babylonians decided to base the degree system on the twelve main constellations in their zodiac (picture the twelve positions on the clock). Then they divided each of those 12 sections into 30 degrees, making a full circle equivalent to 360 degrees. Coincidentally, the Greeks decided on the same system around this time. With this tool, there was a way to consistently measure the spinning paths of objects in the sky.
But how to measure actual distances from those degrees? That’s where Hipparchus comes in. He was a Greek astronomer, and he is recognized today as being the inventor of a very notorious branch of math: trigonometry. It can get quite complicated (just ask our Advanced Math students!), but at its core, the idea of trigonometry is very simple. If you have a section of a circle (like you would trace in the sky with your finger from one star to another), a little trigonometry can tell you how far it would be from the first star to the second in a straight line. With trigonometry, there is indeed a way to measure distances far outside of our reach. For over a thousand years, with the help of other famous Greeks like Menelaus and Ptolemy, trigonometry (with some geometry) became the backbone of astronomy. Even today, trigonometry is essential to astronomy, helping us make calculations for things like planetary motion or space flight.
As time moved on, and people began making extreme voyages across oceans, astronomy became a chief concern for governments conducting explorations. The stars were what navigators used to calculate their position on earth, and these calculations needed to be incredibly precise. Since the stars are so far away, even the slightest error in measurement or calculation could result in anchoring hundreds of miles away from where you intended to sail. This meant that one of the large goals of mathematicians in the 15th and 16th centuries was to improve methods of trigonometry and to improve the working model of the solar system. In the 15th century, Nicolas Copernicus famously theorized that the sun, not the earth, was at the center of the solar system. A century later, Johannes Kepler (a Lutheran!) showed that the planets orbit in ellipses (squished circles) rather than perfect circles. By the next century, Isaac Newton had completed his three laws of motion which we still use today, and which beautifully and masterfully explained Kepler’s model of the universe using calculus. Even now, although navigation is not a large problem anymore, discoveries continue to be made about the workings of the heavens.
The great thing about astronomy is that, on the one hand, it is beautifully complex. A student can do astronomy through geometry and trigonometry like the Greeks, or through calculus like Newton. There’s so much complexity yet to be uncovered. On the other hand, astronomy is beautifully simple. Rigorous paper-and-pencil calculations can’t replace the utter magnificence of the night sky. Astronomy pulls our gaze away from ourselves and out to the entirety of God’s creation; and for that reason, astronomy helps us see—probably more than any other mathematical art can—that the heavens do indeed declare the glory of God.
In Christ,
Mr. Hahn
