Tag Archives: Base Sixty

Longitude doesn’t represent distance—there, I said it

In the last post I said I’d tell you how Eratosthanes knew how many degrees of longitude Benghazi is from Alexandria.

We know that lines or parallels of latitude are about 69 miles apart. Latitude measures degrees of two 90° quarter-circles, each starting at the Equator and ending at the poles. The Equator is 0° and the North & South poles are 90°.

Longitude measures time. Or to be more precise, longitude converts time into degrees of a 360° circle. “WHAT?” I hear you holler as you spring from your comfy chair. “Have you finally lost your marbles, Manders?”

Al-Biruni (973–1048), another one of those amazingly-accomplished scholars

Ptolemy’s geocentric vision of the universe reckoned that Earth doesn’t move—she is stationary while the heavens whirl around her. But a Persian scholar, Al-Biruni, thought that the Earth spins on her axis—just like the globe in your classroom. If that were true (and of course it is), you’ll realize that the Earth spins all the way around every day, every 24 hours.

I drew 24 sections on this sphere—for the 24 hours it takes for Earth to spin around on her axis. Each line is a meridian, a longitude line.

THAT CHANGES EVERYTHING! Mapmakers could divide the Earth’s surface into 24 units. Each unit would represent one hour. Each unit would also represent 15 degrees. Why? Because there are 360 degrees in a circle. 360 divided by 24 equals 15. Now I ask you, who was it who divided the day into two 12-hour halves? Who was it who came up with Base Sixty counting, which makes it so easy to divide 360 by 24? Who? WHO?

Thanks, Sumerians!

The Sumerians, that’s who! I love those guys!

Getting back to Eratosthanes’ experiment: if that lunar eclipse began at 12:36 am Alexandria time and midnight Benghazi time, Eratosthanes knew that Benghazi is 36 minutes west of Alexandria. The Earth rotates on her axis 360° every day, 15° every hour, and 1° every 4 minutes. So, 36 minutes difference in time from Alexandria to Benghazi ÷ 4 = 9 degrees of longitude. Thinking of a chunk of time as a chunk of a circle, Eratosthanes could confidently mark Benghazi’s longitude on a map.

https://www.britannica.com/biography/al-Biruni

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

Longitude

We don’t have Ptolemy’s original map. It’s one of those documents lost to history. Lucky for us there’s a copy made by monks centuries after Ptolemy shuffled off the ol’ mortal coil. I drew this version of Ptolemy’s map showing only the longitude lines. He drew them curved to give you the idea that the world is round.

So Eratosthanes and Ptolemy knew that the Earth was round. And it was relatively easy to locate the big latitudes like the Equator and Tropics. To find each degree of latitude was a little more difficult—you need to accurately sight the Sun or moon or a star. Eratosthanes located his latitude in Alexandria by measuring the angle of a shadow at noon of the solstice. After the astrolabe was invented mapmakers used that device to find their latitude.

Latitude lines are parallel, so each degree of latitude is about 69 miles from the next one. On the other hand, longitude lines travel from north to south poles. They join at the poles and are farthest apart from each other at the Equator. There are 360 degrees in a circle; the Earth is round; so there are 360 lines of longitude. If you’ve been following this history from a year ago, you remember that our pals the Sumerians came up with Base 60 method of counting—that’s why there are 360 degrees in a circle.

One of those longitude lines needs to be zero degrees. Which one? There’s no natural starting point for longitude (like the Equator is Point Zero for latitude). Eratosthanes started his system of longitude in Alexandria, where he lived. Alexandria—and every place due north or south of it—was zero degrees: the Alexandrian Prime Meridian. It was also 360 degrees, because it represented the beginning and end of a full circle.

So far, so good. Here’s the kicker, though: how do you measure longitude? How do you know where, say, 87° is on Earth in real life so you can put it on a map?

https://apps.lib.umn.edu/bell/map/PTO/GEO/place.html
https://www.britannica.com/biography/Ptolemy/Geographer

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

Egyptian calendar

An Egyptian man plows a furrow so the lady can sow seeds into it.

Both the Sumerians and Egyptians had economies that depended on agriculture—they grew crops for their food. If you ever planted tomatoes—or onions, or zucchini, or those two-ton pumpkins you see at the state fair—in a garden, you’ll have seen on the seed packages instructions about when to plant. If you plant your tomatoes too late, the fruit will never ripen in time before the first frost. This is why calendars are so important.

The Egyptians’ planting schedule was built around their river, the Nile. Every year the Nile would flood. After the floodwater receded, it left behind nutrient-rich silt that improved the soil. Egyptian farmers had to plant crops as soon as the Nile receded so they could harvest before the Nile flooded again.

By around 2450 bc the Egyptians had developed a calendar whose year was twelve months. Each month was thirty days long (12 x 30 = 360 days). The year was divided into three seasons—Inundation, when the Nile was flooded (Akhet), Emergence, time to plant the crops (Peret), and Harvest, time to gather the crops (Shemu)—of four months each, with five days added to the end of the year.

In case you hadn’t noticed, the Egyptian calendar used Base Sixty for counting the days. I’d like to think they sent a nice thank-you note to the Sumerians.

Egyptian sundials

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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.

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

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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?

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