Tag Archives: technology

Little Dennis


At the Council of Nicaea a lot of things were agreed upon. One thing the western and eastern halves of the Roman Empire could not agree on was when Easter should be celebrated. Each half—western and eastern—celebrated on a different date. This went on for a long time until finally in ad 525 an expert was called in. Dionysius Exiguus (his name means ‘Little Dennis’) was a scholarly monk who got the job of figuring out exactly when the Christian holy day of Easter should occur every year.

Dionysius decided to go back and find when the first Easter occurred. Jesus’ resurrection happened during the Jewish Passover—Pesach. The Jewish calendar relies on the motions of the Moon and Earth’s orbit around the Sun. Using some incredibly complicated astronomical calculations, he was able to arrive at the original date.

Dionysius realized once he’d found the date of Jesus’ resurrection, he could then figure out when Jesus was born. Jesus was 33 years old when He was crucified, so Dionysius counted back 33 years from the first Easter to get the year of Jesus’ birth.

In the past, years had been named after whoever was the imperial consul at the time. Dionysius decided it was time to change that. He named the years after Jesus, the Christian Savior. So the years beginning with Jesus’ birth are numbered and called Anno Domini (ad for short)—Latin for ‘the year of our Lord.’

By the way, Dionysius reckoned that Easter should occur on the first Sunday following the 14th day of the lunar cycle—the full moon—that falls on or after the spring equinox.

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


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

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

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)

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

How to build a better water clock

Ctesibius of Alexandria. Believe it or not, this guy’s dad was a barber.

If you’ve been following this blog, you’ll remember that a couple of posts ago I ranted about how Egyptian water-clocks seemed impractical and I didn’t see how they could even function as clocks at all.

Well, apparently back around 270 bc, an inventor named Ctesibius (Teh-SEE-bee-us) of Alexandria thought the same thing. He identified two problems:

One) The water-clock wasn’t a clock, but rather a timer. It only worked while there was water in it.

Two) The water came out of the bung-hole at the bottom at different rates of speed: quickly when the jar was full, slowly as it grew empty. That’s because the weight of the water on top pushed down on the water that was escaping—less water, less pressure, slower dripping of water. That made it unreliable for keeping time.

So how did Ctesibius fix these problems? Well, he figured in order to keep constant pressure on the hole at the bottom, the water clock should always be full. So he set up a second jar of water to keep the first one filled. The second jar had a hole at the bottom that leaked water into the first jar.

THEN, a third, empty jar was placed under the first jar. Instead of telling the time by how much water had leaked out, this empty jar told time by how much water had leaked into it.

Ctesibius even made a float to put into the empty jar. As the water level rose, an arrow—attached to the float—pointed to the hour.

A tip of the hat to Heidi K. for sending me a link to this video!

Egyptian sundials


An Egyptian lady catching some rays from Ra.

Let’s travel west from Sumer, away from the MidEast, along the northern coast of Africa to Egypt. About 1,000 years after civilization was up and running in the Tigris-Euphrates valley, the Egyptians got started on their civilization which thrived from 3100 bc to 332 bc. Like the Sumerians, Egyptians depended on a river—the Nile—and a system of irrigation to water their crops to keep the economy going. Their writing system was hieroglyphics—symbols that represented sounds, or ideas, or things. Their government was monarchical—they had a single ruler, called a Pharaoh. The Egyptians worshiped a pantheon—which means a bunch of gods and demi-gods. The Pharaoh was worshiped as a god, too.

The Sumerian culture must have influenced the Egyptians somewhat. The Egyptians divided the day into two halves, each having 12 hours—twelve is an easy Base Sixty number. The Egyptians are thought to have invented the sundial. The earliest example of a sundial has 12 hours marked using lines on a semi-circle, 15° apart.



A fragment of a limestone sundial. The gnomon goes into the hole at top.


This sundial is a half-bowl cut out of a block of stone.

A sundial is a simple way to measure the passage of the Sun. There’s a post (called a gnomon, pronouced NOM-ON) sticking up from a flat, horizontal surface. Lines are drawn on the flat surface, radiating out from the gnomon. When the Sun is shining, the gnomon casts a shadow on the lines. Each line represents the passage of an hour.

The Egyptians built huge obelisks—big stone monuments. These were sundials, too. The obelisk cast a shadow on the ground, which was marked for every hour. As the Sun moved across the sky, the shadow would move along the dial, showing the time. Of course, sundials only work when there’s daylight. How did they tell time at night?