We locked a bunch of astronomers in a room and you’ll never believe what happened next!

Roman astronomers trying to get the lunar and solar cycles to match up. I threw a couple of Sun-worshiping Druid priestesses in there, too.

A big headache with ancient calendars is that they had to be constantly updated to make them agree with the movements of both the Moon and the Sun. Months are based on the Moon’s cycles. Years are based on Earth’s orbit around the Sun. ‘Calendae’—we say ‘calends’—is a Latin word for ‘first day of the month.’ ‘Ides’ is the day in the middle of each month. Astronomers (scientists who study the stars and planets) would first determine the ides (when the moon will be full) for each month and calculate the rest of each lunar cycle/month from there. It is a tricky business to get the twelve cycles of the Moon to work out to be the same amount of time the Earth orbits the Sun.

Archimedes and his odometer

Archimedes was a Greek mathematician who specialized in measuring space. He was certain that there must be a way to accurately measure how much space is in a circle—area—or how much space is in a sphere or a cylinder—volume (he figured out how to measure volume when he noticed that a certain amount of water spilled out when he got into a bath tub). Archimedes was influenced by other great mathematicians, like Pythagorus and Euclid.

Archimedes invented many wonderful machines, like a screw for drawing up water, or catapults that were used to fight off invading navies. Although we don’t have his plans for it, Archimedes is said to have invented a way to measure distance. This machine is called an odometer.

Archimedes’ odometer operated on the idea that every time a wheel goes around, it travels its own circumference. The odometer adds up those circumferences and marks when the wheel has traveled a mile. In our last post, we showed how a standard Roman chariot wheel goes around 42 times to travel a mile.

We know about Archimedes’ odometer because the Roman military engineer Marcus Vitruvius Pollio (80–70 bc – 15 bc), or Vitruvius for short, wrote about it in his 10-volume book De Architectura. Engineers build stuff. As the Roman Empire expanded, the army took along a corps of engineers to build fortifications; siege engines; bridges; tunnels; aqueducts to provide water; and roads. These engineers did such a good job that you can still find Roman bridges, aqueducts and roads today.

Emperor Caesar Augustus wanted to know exactly how big the empire was and decreed that mile markers should be put up along the newly-built roads. Vitruvius decided to build Archimedes’ odometer to accurately measure the miles.

We only know what Vitruvius’ odometer looked like from a fanciful drawing. We don’t know exactly how it worked. Some people, including Leonardo da Vinci, have come up with some pretty good guesses about how it worked. You can see Leonardo’s drawings here—plus, you can even download plans if you’d like to build one yourself! Now that’s cool.

We do know that every time the chariot wheel goes completely around, it moves other gears. The other gears are set up to mark a mile at the 42nd revolution of the chariot wheel. The trick is gear ratio—meaning some gears are bigger, some gears have more teeth. If the gear on the drive shaft has only one tooth and the gear holding the marbles has 42, the marble-gear moves 1/42 of a revolution every time the chariot wheel goes completely around. At the 42nd revolution, a hole with a marble lines up with a hole underneath the gear and the marble drops into a bucket. Each dropped marble represents one mile traveled.



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Who doesn’t like π?

Pi, or π, is a letter from the Greek alphabet used by mathematicians. π signifies this weird number: 3.14159265359… or 3.14 for short. It is the ratio of a circle’s circumference to its diameter. Circumference is how big around a circle is. The diameter is how wide a circle is from side to side if you draw a line through its center. Diameter x 3.14 = circumference. This is true of any circle, no matter how big or small.

MrNystrom has a great video about how to think about π.

Pi has been around for 4000 years, but Archimedes of Syracuse (287–212 bc) was the first mathematician to calculate π accurately.


Archimedes came up with his best ideas in the bath tub.

So back to the Romans. If you want to measure miles across the Roman Empire, how would you do it? Counting steps and paces as you march along isn’t very accurate—it’s too easy to lose count. What if you used a circle—like a wheel? I mentioned that chariot wheels were made a standard size, like many things in the Roman Empire.


A chariot wheel is 4 feet across at its widest point—that’s the diameter. Let’s calculate a chariot wheel’s circumference—how big around the wheel is. You can calculate the circumference by multiplying its diameter by π. π = 3.14. Four feet x 3.14 = 12.56 feet.

Now, there are 5280 feet in one mile. 5280 divided by 12.56 = 42 revolutions of the chariot wheel. All we have to do now is count every time the wheel goes around. At 42 times, we’ll know we’ve reached a mile.

Counting how many times a chariot wheel goes around still seems like a big pain in the neck, doesn’t it? Archimedes thought so, too.

Side note: March 14, 3/14, is known as π Day. On π Day a grocery store in my town sells pies for $3.14.

pie day559

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Measuring long distances

The Romans were geniuses at organization. The way they organized their government and army/navy is how they could maintain such a huge empire. The Romans found that standardization really helped—from soldiers’ armor to the width of a chariot wheel to money to constructing roads.

Good roads are important to a maintain a huge empire, especially for moving armies quickly from one place to another. It’s vital to know exact distances, too, if you are planning a big march with thousands of soldiers. We know that one Roman mile is 1,000 passus—paces—or 5,000 gradus—steps. The problem is, it’s too easy to lose count of all those steps. How do you measure a mile and know for sure you didn’t lose count?

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Measuring distance in Rome

The Romans borrowed religion, art, architecture and literature from the people they conquered to make a hodge-podge, eclectic culture for themselves. Mostly they borrowed from the Greeks—the Greek gods got Latin names. Ares (the god of war) became Mars. Zeus became Jupiter, Hera became Juno, Poseidon became Neptune, Aphrodite became Venus.

The Romans also borrowed technology. They measured distance the same way the Egyptians and Greeks did, by using parts of a typical grown man for standardized units.

finger—digitus (1/16 of a pes)
thumb-joint—uncia (inch, 1/12 of a pes)
four fingers—palmus (1/4 of a pes)
foot—pes (plural: pedes)
one step—gradus (2.5 pedes)
pace—passus (5 pedes)

For longer distances, a mile (mille passus) was 1000 passus or 5000 pedes. (I hope I’m getting the plurals right—https://en.wiktionary.org/wiki/passus)

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The last king of Rome

Lucius Tarquinius and his Superbus

Lucius Tarquinius Superbus (died 495 BC) was the legendary seventh and final king of Rome, reigning from 535 BC until the popular uprising in 509 BC that led to the establishment of the Roman Republic. He is commonly known as Tarquin the Proud, from his cognomen Superbus (Latin for “proud, arrogant, lofty”).
—from Wikipedia


Gaius Julius Caesar

Romulus was the first of seven kings to rule Rome. In 509 bc the last king was tossed out and a republic was created. A republic is where citizens elect representatives to govern them (like how the United States government works). SPQR is an abbreviation for Latin Senatus Populusque Romanus which means ‘The Senate and People of Rome.’

The elected representatives were called a senate. Once in a while some military emergency would come up, and the senate would appoint one guy to be caesar (pronounced KY-zar, means dictator). He was given absolute power. It was meant to be a temporary arrangement. Cincinnatus is remembered for leaving his farm to become caesar and take over the military—he whupped the invading armies then 2 weeks later gave power back to the senate and returned to his farm.

The republic lasted until 45 bc when a Roman general, Gaius Julius, declared himself caesar and began expanding Rome into an empire by conquering territory around the Mediterranean. The Roman Empire eventually reached as far north as England, east into Iran, south into Africa and west to the western edges of France and Morocco. Julius’ nephew, Octavian, became Augustus Caesar—Rome’s first emperor.

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Puppy training

Just some sketches. Something softer and more idyllic than my take on the Etruscan statue in the last post. I’m imagining Lupa Capitolina teaching the boys how to become wolves.


Got milk?

According to the story, here’s how Rome got started: twin baby boys named Romulus and Remus (whose dad was Mars, the god of war) were abandoned in the wilderness of what we now call Italy. A friendly she-wolf discovered the boys and raised them as her own pups. She taught them survival skills, like how to bark at the moon and scratch your ear using your hind paw.

Eventually they grew up and founded a town where they’d been abandoned. It was a perfect spot: on the Tiber river, easy access to the sea, smack in the middle of Italy which is smack in the middle of the Mediterranean Sea. But boys will be boys and these brothers quarreled, argued and fought (they were sons of the god of war, remember). During their most bloody fight, Romulus killed Remus. Romulus took over the town and named it after himself—Rome.

The future!

Can you see into the future? Thinking in linear time allows us to think about the future. It’s not easy, of course. People do use a timeline to plan projects and life goals, so that they can make them happen. In fact, I’m using a timeline for this project—writing this history which I plan to make into a book. Do you think about what you’ll be doing in 5 years? Successful people plan for the future. Holy cow, I sound like I’m selling life insurance.

The Torah (what Christians call the Old Testament), with its timeline of many generations of Jews, was read by ordinary people and changed the way ordinary people think about time and themselves.

In the Torah, ordinary people became important. Religious stories of other cultures were about gods and goddesses. Mortal beings had supporting roles in those stories, like when the mortal Paris judged a goddess beauty contest, or the gods created Enkidu to hang out with the semi-divine Gilgamesh. You don’t get a sense that the gods and mortals have a destiny together, because the stories don’t talk about a future. On the other hand, the stories in the Torah are about ordinary mortals who share a past and future with one God. When ordinary mortals—everybody, us—see ourselves as part of a destiny, the way we think about ourselves is changed. A person with a future, a destiny, has free-will and the mindset to break free of a cycle. You can see how a person with the inheritance of generations of history—aligned with God’s—has more free-will than the person who lives only in a cycle, the now, the present.