The division of the hour into 60 minutes, and then the minute into 60 seconds, is not the result of an arbitrary choice. It stems from an arithmetic logic developed in ancient Mesopotamia, subsequently transmitted to the Greeks, and then to modern Europe. Understanding this chain of transmission allows us to grasp why our watches still display a dial inherited from vanished civilizations today. <\/p>\n\n
Before addressing minutes, we must go back to the 24-hour day, the authorship of which belongs to the Egyptians. According to Sara J. Schechner, curator of scientific instruments at Harvard, the Egyptians identified 36 stars known as “decans,” about 12 of which were visible each night. They thus divided the night into 12 periods, then applied the same division to the day. The first known Egyptian sundial dates from around 1500 BCE, but similar instruments likely existed as early as the third millennium BCE. This 24-hour system then passed to the Babylonians, and later to the Greeks. <\/p>\n\n
The subdivision of the hour into 60 minutes is of Mesopotamian\u2014not Egyptian\u2014origin. Jo Ellen Barnett, in Time’s Pendulum<\/em>, explains that Mesopotamian mathematics did not have fractions in the modern sense of the term. To bypass this limitation, the Mesopotamians favored whole numbers offering the greatest number of exact divisors. The number 60 is divisible without a remainder by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30, totaling ten integer divisors. The number 100, by comparison, has only seven. A third of an hour is exactly 20 minutes in base 60; in base 100, one would have to write 33.33 minutes, which a system without fractions cannot process. <\/p>\n\n The same reasoning extends to the second. A day consists of 24 \u00d7 60 \u00d7 60 = 86,400 seconds\u2014a figure that stems directly from the cascade of divisions by 60 inherited from the Babylonians. As highlighted in an analysis published by Hodinkee on the history of the second, the Babylonians also used advanced geometric shapes to calculate agricultural surface areas, which testifies to a level of genuine mathematical sophistication rather than a simple practical convention. <\/p>\n\n Herodotus explicitly mentions that the Greeks inherited this system of hours and minutes from the Mesopotamians. From Greece, the transmission to Europe was direct: Greco-Roman culture constitutes the intellectual foundation of the medieval West, and the mechanical clockmakers of the 14th century\u2014who built the first weight-driven escapement movements\u2014adopted the temporal framework inherited from Antiquity without modification. <\/p>\n\n The French Revolution did attempt to impose decimal time: 10-hour dials, 100-minute hours, and 100-second minutes. This system was officially adopted in 1793 but abandoned by 1795 due to a lack of popular support. More recently, Swatch launched “Internet Time” in 1998, which divided the day into 1,000 units called “beats.” The brand has since stopped producing watches in this format. These two failures illustrate the robustness of the sexagesimal convention: it is deeply integrated into tools, habits, and infrastructure. <\/p>\n\n Every analog watch dial mechanically reproduces this logic: 60 graduations for minutes and seconds, and 12 hours for a half-turn of the dial. Deadbeat seconds movements (deadbeat seconds<\/em>), which display the second through discrete jumps from one graduation to the next, make this division particularly visible. The movement literally counts 60 impulses to complete one full rotation of the second hand. <\/p>\n\n The division into 60 minutes is not an arbitrary convention frozen by inertia: it is based on a real arithmetic property of the number 60, identified and exploited by Mesopotamian mathematicians who did not have fractions. This origin explains why all replacement attempts\u2014whether from a political revolution or a multinational watch company\u2014have failed against a system whose internal consistency is difficult to match. For a collector or a watchmaker, every graduation on a watch dial is, in this sense, a direct vestige of a mathematical decision made over three millennia ago. <\/p>\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" A millennia-old convention with precise mathematical roots The division of the hour into 60 minutes, and then the minute into 60 seconds, is not the result of an arbitrary choice. It stems from an arithmetic logic developed in ancient Mesopotamia, subsequently transmitted to the Greeks, and then to modern Europe. Understanding this chain of transmission […]<\/p>\n","protected":false},"author":1,"featured_media":1771,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1773","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-non-categorise"],"yoast_head":"\nThe sexagesimal system also applies to seconds<\/h3>\n\n
\n\nThe transmission of the system to our watches<\/h2>\n\n
Herodotus attests to the transfer to Greece<\/h3>\n\n
Attempts at disruption have failed<\/h3>\n\n
Base 60 remains present in contemporary watchmaking<\/h3>\n\n
\n\nWhat this implies in practice<\/h2>\n\n