The notion of doing geometry with a 360-degree circle had been around for a long time because it divided so well. A sundial marks the passage of time by drawing a circle, so the two ideas naturally went hand in hand. (Also note the mystical number 12 fits very nicely into a 360-degree circle.)
It’s important for science to have a universal standard so that experiments can be reproduced and recipes followed everywhere. In normal life, people could accept the measurement of a “yard” being “about as long as your arm,” or an hour being “about this much time,” and they rarely needed a measurement more precise than those. But science needs a more strict definition.
My old physics textbook tells me the original scientific definition of a “second” was 1/86,400 of a mean solar day, but it doesn’t tell me who came up with that. It sounds like something Copernicus or Galileo could have taken a stab at, probably Newton and his crowd, certainly. Once people figured out how to work with individual atoms, science was able to come with a really precise definition. The current definition of a second has to do with the amount of time it takes for a cesium atom to decay from one energy state to another. I guess that’s something people are able to measure with great accuracy and ease. Anyway, that’s what an “atomic clock” is.
You might be interested to know that things like the meter have similar scientific definitions. I think the meter is the measure of so many waves of a certain kind of laser light shot through a certain kind of gas. This is, again, apparently something scientists can count with ease. I can’t.
In the “What Might Have Been” department, when the metric system was formally adopted during the Age of Reason, the revolutionary French government also proposed a 400-degree circle with right angles of 100 degrees. They also proposed a standardized calendar with 30-day months and 10-day weeks. Both of those ideas make logical sense, but they didn’t catch on.
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