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How did we come to divide the hour into 60 minutes and the minute into 60 seconds? These smaller divisions of time have been in practical use for only about 400 years, but they were vital to the advent of modern science.

For millennia, ancient civilizations looked to the sky to measure the big units of time. There's the year, which is the time it takes Earth to complete one orbit around the sun; the month, which is approximately how long it takes the moon to orbit our planet; the week, which is approximately the time between the four phases of the moon; and the day, which is the duration of one rotation of the Earth's on its axis.

Dividing the day was not so straightforward, though hours and minutes have their origins in traditions tracing back thousands of years.

## Number systems

The use of 60 began with the Sumerians who used different number systems. While you and I write numbers using base 10, or “decimal” this civilization used base 12 ("duodecimal") and base 60 ("sexigesimal"). It is not known exactly why they chose these systems, but there are a few theories:

- Many ancient cultures used the three segments of each finger to count to 12 on one hand, writes Georges Ifrah in his book, “The Universal History of Numbers” (Wiley, 2000; translated by David Bello). It is hypothesized 60 arose from using five fingers of one hand with the twelve segments of the other.
- Fewer fractions have repeating decimals (1/3 = 0.333…) when written in sexagesimal. This is particularly important because the Sumerians had no notion of repeating-digit fractions. In “An Introduction to the History of Algebra” (American Mathematical Society, 2009), author Jacques Sesiano describes a tablet that reads, “I don’t know the inverse of 7/6.”
- Twelve was an important number to the Sumerians, and later to the Egyptians. For example, it was the number of lunar cycles in a year and the number of constellations of the Zodiac. Day and night were each divided into 12 periods, and the 24-hour day was born.

Credit: Robert Coolman.

# Angles and ancient astronomy

In the 24th century B.C., the Sumerians were conquered by the Akkadians, who then fell to the Amorites, who rose to power and built the nation-state of Babylon, which peaked in the 18th century B.C. The Babylonians invented the degree and defined a circle as having 360 degrees. There are a couple of theories as to why they chose 360:

- The Babylonians understood a year as having close to 360 days; hence the sun "moves" along the ecliptic approximately 1 degree per day.
- The radius of a circle maps onto a circumscribed hexagon of six equilateral triangles, and thus a sixth of a circle forms a natural angle measure. In the numerals inherited from the Sumerians, a number’s sexagesimal value was inferred from context, so six was “spelled” the same way as 360.

Babylonian astronomers began cataloging stars in the 14th century B.C. Astronomy flourished as they developed a deep understanding of sun and moon cycles, and even predicted eclipses. Babylonian star catalogs served as the basis of astronomy for more than a thousand years despite the boom and bust of the Middle Assyrian Empire, the Neo-Assyrian Empire, the Neo-Babylonian Empire and the Achaemenid Empire.

## Off to Greece and Rome

The conquests of Alexander the Great between 335 and 324 B.C. helped spread Babylonian astronomy to Greece and India. Though the Greeks had their own numerals in base 10, Babylonian star catalogs created such a strong association between astronomy and the sexigesimal system that Greek (and later Roman) scholars kept using it. This association soon bled into navigation and trigonometry.

Following the discovery by Eratosthenes of Cyrene that the Earth is round, in the first century B.C., Hipparchus of Nicaea adapted degrees to quantify lines of longitude and latitude. Two centuries later in the Roman Empire, Ptolemy of Alexandria subdivided degree coordinates into 60ths (minutes) and 60ths of 60ths (seconds). This convention of “degrees, minutes and seconds” is still used today to plot locations on Earth as well as the positions of stars.

## To Arabia, Iberia and Greater Europe

Much of this knowledge was lost to Europe for several centuries after the fall of Rome in the fifth century A.D. The Islamic-Arabian empires inherited many Roman (and later Indian) ideas starting with the Rashidun Caliphate in the seventh century. Muslims scholars, after expanding on this knowledge greatly, reintroduced it to Europe in the eighth century through the Iberian Peninsula, which was then part of the Umayyad Caliphate.

The 10th-century Caliphate of Córdoba became very influential in transferring knowledge to medieval Christian scholars. Such works included many lost writings by Greek and Roman scholars, the invention of algebra by ninth-century Persian scholar Al-Khwārizmī, the Indian invention of numerals 0-9, and the invention of a symbol for zero by seventh-century Indian scholar Brahmagupta.

Medieval astronomers were first to apply sexigesimal values to time. The 11th-century Persian scholar Al-Bīrūnī tabulated times of new moons on specific dates in hours, 60ths (minutes), 60ths of 60ths (seconds), 60ths of 60ths of 60ths (thirds), and 60ths of 60ths of 60ths of 60ths (fourths). Full moons were tabulated using these same divisions by Christian scholar Roger Bacon in the 13th century.

# Minute hands

Minutes and seconds, however, were not used for everyday timekeeping for several centuries. Mechanical clocks first appeared in Europe during the late 14th century, but with only one hand, following the design of sundials and water clocks. Minutes and seconds were but hypothetical quantities of time. According to David S. Landes, in “Revolution in Time” (Belknap, 1983), astronomers of the 16th century began physically realizing minutes and seconds with the construction of improved clocks with minute and second hands in order to improve measurements of the sky. While sextants and quadrants (no telescopes yet) had long been used to quantify the heavens, due to the movements of the sky their accuracy was limited to how well a user knew the time.

Tycho Brahe was one such pioneer of using minutes and seconds, and was able to make measurements of unprecedented accuracy. Many of his measurements required him to know the time to within 8 seconds. In 1609, Johannes Kepler published his laws of planetary motion based on Brahe’s data. Seventy years later, Isaac Newton used these laws to develop his theory of gravitation; showing that terrestrial and celestial motions were governed by the same mathematical laws.

## Sumerian legacy

Today, 5,000 years after the Sumerians first began using 60, we divide our days by hours, minutes and seconds. In recent years, we have changed how the units are measured. No longer derived by dividing astronomical events into smaller parts, the second is now defined on the atomic level. Specifically, a second is the duration of 9,192,631,770 energy transitions of the cesium atom.

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