Category Archives: book promotion

Hypatia, the lady philosopher/mathematician/astronomer

Sometimes writing about history is hard. At the beginning of this project, I’d envisioned a fun and slightly wacky tour through Western Civilization presented by a fun and slightly wacky uncle. The story of human beings is often violent and cruel, though. Human beings are flawed creatures. There are parts of civilization’s history that make me heartsick.

I want to tell you about a glorious and brilliant woman who lived in Alexandria, Egypt in the 4th century ad. Her name is Hypatia. She was the daughter of a philosopher and mathematician, and she became a philosopher and mathematician herself. Hypatia was lovely to look at, but her intellect was what made her irresistible. I became interested in her when I read that if she hadn’t outright invented the astrolabe, at the least she played an big part in developing it.

Hypatia helped her dad expand Ptolemy’s work on astronomy. She eventually did her own scholarly work on the stars and the geocentric model of the universe. It might have been she who came up with the idea of ‘flattening’ the spheres to create the star-map that is central to the astrolabe’s design (this is my own conjecture).

Hypatia was also a philosopher. Her philosophy was Neo-Platonism, which adapts Plato’s ideas about what makes the world tick. Hypatia was a gifted teacher. She often gave lectures in the agora (Greek for public square) about philosophy, astronomy, and her many intellectual interests. At that time Alexandria was boiling with religious trouble. Christians and Jews battled with each other and with philosophers who rejected a belief in God. The Roman Empire was in its last days, about to split into East and West. Politics absolutely played a part in the violent clashes between religion and philosophy.

I’m sorry and ashamed to tell you that a mob of Christians ambushed Hypatia, and murdered her. It’s nearly impossible for me to believe that these were followers of Jesus. But it happened. They behaved as a mob—the very opposite of civilization—and murdered a woman for promoting a philosophy that rejects Christianity.

You can read more about Hypatia here and here. There’s a movie about her, too.  Here’s a review—caution: some violence.  (I have a quibble with History Buff’s conclusion that, because of Christianity, scholarship was discouraged in the Dark Ages. Beginning with Charlemagne, the Holy Roman Empire fostered a culture of learning that was encouraged in the monasteries. Monks copied books by hand—the books from the Greek philosophers that had been translated into Arabic, which the monks then translated into Latin. See How The Irish Saved Civilization by Thomas Cahill.)

Title type for my groundbreaking soon-to-be bestseller

Fooling around with lettering. It needs a little tweaking. Some strokes ought to be heavier, maybe. I’m trying to hold onto the energy of my sketch. I’m not sure if I like this yet. Let it sit for a while.

And it doesn’t need batteries

If you read my last astrolabe post and swung by one of the links you can find there, you’ll have seen that these astrolabes work like a charm. As well as telling time, an astrolabe can be used for surveying and navigation. Of course, it wouldn’t work at all without Ptolemy’s accurate mapping of the sky.

The astrolabe was used for centuries before clocks came along. Even after clocks it was used for predicting when sunup or sundown would occur. This was important in the Muslim world, where the faithful need to pray at exact times, like sunup. The Koran says that it’s sunup when it’s light enough to tell the difference between a black thread and a white thread, but an astrolabe tells you when sunup will happen beforehand—by looking at the stars.

Notice that around the rim of the astrolabe the circle is divided into 24 hours of the day. Each hour takes up 15 degrees of the 360-degree circle. If you’ve been following this blog for the past year, you’ll remember the Sumerians came up with that idea—a 360-degree circle uses the Base 60 system of counting. This is an example of using distance to calculate time. In this instance, not miles traveled but degrees around a circle. The hours are distributed equally along the circle of Earth’s horizon.

Back to the beginning of The Western Civ User’s Guide to Time & Space

Hey, what time is it?

We’ve talked about telling time with sundials and water clocks and hourglasses. Those things are a headache to carry around. Mechanical clocks, like a pendulum clock, wouldn’t be invented until 1637. What if you’re traveling around in ad 800—how do you know what time it is?

One way to tell time was this fantastic little device called an astrolabe.

This sketch is based on a beautiful antique brass astrolabe.

Wherever you happen to be, if you can see the Sun or the stars, you can tell the time if you’re carrying an astrolabe with you. The main feature of an astrolabe is a flat map of the sky—with the stars and planets on a grid. The grid—called a climate—shows the sky as it appears in your part of the world. It’s circular and fits into a circular frame, called the mater (Latin for ‘mother’). On top of the climate is the rete (Latin for ‘net’), an openwork circular plate with pointers that you can line up to point at the Sun or a specific star on the climate. On top of that is a sighter—a straight arrow kind of piece. All these spin on the same axis. You pick a star, adjust the rete to point at your star on the climate, and hold up the astrolabe and sight the actual star along the sighter. When the sighter lines up with the star, you can read the time with remarkable accuracy. Here’s a video showing how it’s done. This guy even made his own astrolabe. And here’s more.

Here’s a website that explains how to use an astrolabe and even gives you pdfs you can download and print to make your own.

Wait—I thought *I* was the center of the universe

The orb in the center of this contraption is the Earth.

The idea of multiple nesting spheres—each sphere tracking a ‘wandering star’ or planet; the fixed stars; and the motions of the Sun and Moon—is kind of complicated. Astronomers built models of the geocentric universe to try to explain it. These are called armillary spheres.

They were usually made out of brass. Here’s one you can build out of cardboard.

Even though Earth isn’t the center of the universe, the model still works for locating positions of stars as we see them from Earth. Not only was Ptolemy’s data useful for knowing where the stars are and tracking them, but we can also predict where they will be tomorrow or next year. It became possible to know exactly when the Sun will rise and set years in the future. Astronomers could predict eclipses of the Sun or Moon. You can accurately tell the time based on Ptolemy’s data. It was a pain in the neck to carry an armillary sphere around, though. Something more compact was needed.

This is NOT an armillary sphere. It’s an armadillo sphere. Just in case it turns out armadillos are the center of the universe.

https://www.thoughtco.com/armillary-spheres-and-what-they-got-wrong-1991234

Back to the beginning of The Western Civ User’s Guide to Time & Space

How they got all the planets inside that building I’ll never know

If you’re lucky enough to live near a planetarium, you should go see one of their shows.

As Ptolemy worked out the positions of the stars on a big sphere, he imagined smaller spheres that account for the movement of the Sun and the planets— operating like separate, smaller gears in a giant clock. The amazing thing is, even though Earth isn’t the center of the universe, Ptolemy’s geocentric model is still accurate. Weird, huh? If you ever visit a planetarium, you’ll sit in a round room with a domed ceiling above. At the bottom of the dome, all around the room, is the horizon. The night sky is projected onto the dome with all the fixed stars in their places—they rotate around, just like the real night sky. The planets are also projected onto the dome. The planet projectors operate on a separate gear system exactly like the spheres Ptolemy had proposed.

A rough sketch of a planetarium projector.

Here’s some interesting info about planetarium projectors. 

Here’s a listing of planetariums so you can find one near you.

Every little star in the sky

An azimuth compass shows 360° starting with 0/360°at due North.

Who wants to talk about Ptolemy some more? I told you about how people back then thought Earth was at the center of the universe and all the stars and planets revolve around her. This is called the geocentric model. The geocentric model has the stars on a humongous sphere. Good ol’ Ptolemy calculated the positions of all the stars and planets in the sky. He mapped exactly their azimuth and altitude.

Imagine you’re standing outside on a clear night and can see all the way to the edge of the sky—no trees or buildings in the way. That’s Earth’s horizon (we usually don’t see the horizon unless we’re in a flat desert or a big lake or ocean). You’re standing in the middle of a big circle, the base of a big dome. Directly above your head is the zenith, the center of the dome above. You can use a compass to find the direction of a star’s position—that’s its azimuth.

Using a cross-staff to find a star’s altitude.

You’ll need another device to figure how high that star is from the horizon—you work out the angle with your eyeball being the center point, the horizon at zero and the zenith at 90 degrees. A cross-staff is something Ptolemy may have used. You sight along the staff and point it in the star’s direction. Move the crossbar until it touches the horizon at the bottom and the star at the top. The position of the crossbar on the staff marks the angle of the star’s altitude.

Back to the beginning of The Western Civ User’s Guide to Time & Space

Charlemagne & Pope Leo III from yesterday

Here’s the painting I did yesterday. Still a bit rough; needs some tightening up. Charles’ right hand doesn’t look like it’s holding the hilt of that sword. I have to figure out how to mount my camera (phone) so it’s not in the way when I paint. I kept bumping into it.

Charlemagne & Pope Leo timelapse

Here’s a little painting—you can watch as it gets painted. https://www.instagram.com/p/B3-HCj-gCVs/

It’s an image for this post.  Enjoy!

Ptolemy—why not take Ptolemy?

Ptolemy showing his geocentric model of the universe. That’s Earth in the middle.

We’re coming up on the Middle Ages, everybody! The Roman Empire has become the Holy Roman Empire—we’re still working on creating individual countries out of the territories of various tribes. The Christian Church has become a stabilizing institution. With Charlemagne’s help, religious centers—like monasteries—are also places of learning. Alcuin of York (Charlemagne’s right-hand man) designed an easier-to-read way of writing using capital letters and small letters instead of ALL CAPS!

Life isn’t easy for regular peasants, which is most people. It’s hard to make a living on a farm. Some people head to the towns to learn a trade. Sanitation isn’t so great and the bubonic plague is always just around the corner. It will be centuries before anyone figures out that plague is carried by fleas.

It usually takes a long time for civilizations to accept new ideas. Even after Eratosthanes showed the Earth to be round, many people thought she was flat. Both educated and uneducated people believed that the Earth was the center of the universe and the Sun, planets and stars revolved around her. They thought of the universe as a giant sphere—a ball—with planets and stars stuck onto it. This sphere would be like clear glass. The word for this idea is geocentricgeo is a Greek word for Earth, centric means smack dab in the middle.

We get this idea from an astronomer named Ptolemy (TOE-leh-mee), who lived in Alexandria, Egypt (100-170 ad, we think). He improved on the basic geocentric idea. Ptolemy used math to place the stars in fixed positions on this big sphere. He observed that the planets didn’t stay fixed on the sphere, though, so they were called wandering stars and got their own smaller spheres that fit inside the big one. The Sun made its own orbit, a circle, called an ecliptic.

Here’s Billie Holiday singing “All of Me.”

Back to the beginning of The Western Civ User’s Guide to Time & Space

https://www.britannica.com/biography/Ptolemy
https://www.teachastronomy.com/textbook/The-Copernican-Revolution/Ptolemy-and-the-Geocentric-Model/