Threads in the Tapestry of Physics


Sheldon Lee Glashow in Inference:

Quantitative science depends on measurement; measurements are expressed in numbers. Our number system is based on ten but some earlier systems were based on twenty—perhaps because our barefoot ancestors counted on their toes as well as on their fingers.4 Linguistic remnants, like eighty as four-score in English, firs in Danish and quatre-vingt in French, reveal their vigesimal ancestry, as did the once widely used Réaumur temperature scale, where the boiling point of water was set at 80 degrees. Many living languages, such as Mayan, Nahuatl, Georgian and Yoruba, retain heavily vigesimal counting schemes.

Computers, using simple yes-no binary numbers, are both digital and digitless.

Four millennia ago, our Sumerian and Babylonian antecedents favored 12 for the number of hours of daylight, signs of the zodiac, and months of the year. They also introduced the 360 degrees of the circle, and, for a while, used a year of that many days. Their number system was decimal from 1 to 59, but otherwise sexagesimal, using positive or negative powers of 60.5 It was a sophisticated choice.

In the measurement of time, early civilizations recognized three natural but incommensurate periods, each of which now has a precise meaning: 1) the solar year, the interval between successive vernal equinoxes, 2) the lunar month, that between successive new moons, and 3) the solar day, that between successive sunsets. The mean solar year is a few days more than 12 lunar months and a few hours more than 365 days. To deal with this issue the Sumerians came up with a remarkably accurate lunisolar calendar based on the near equality between 19 solar years and 235 lunar months. Their year consisted of 12 lunar months, one for each sign of the zodiac.

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