I have heard that that when we get older, time, in a sense, speeds up. We are confronted less often with novel experiences or big changes in lifestyle, and so the days and the years blend into each other much more neatly. For kids, life is messier, with huge changes in circumstance happening regularly and thus making time take longer. There’s an episode of the TV show Star Trek: Voyager in which the characters interact with a planet where time moves much more quickly. The people in the slower time appear perfectly still to those experiencing faster time. As teachers, we are working with where whose lives are moving much more slowly than ours. The philosopher Henri Bergson claimed that the passage of time depends partly on the individual, and that our inner lives play a key role in that experience. Considering the dramatic and chaotic inner lives of secondary school students, who knows how fast or slow they are traveling.
I appreciated learning the history of second, particularly the part about how its length is now tied to a fundamental physical relationship. Scientists have redefined other key metrics in a similar way, including the kilogram (now based on Planck’s constant) and the meter (now measured using the speed of light). Moving these measurements away from definitions that may rely on the arbitrary whims of a dominant society to something more universal feels like progress.
The author seems confident that the Mesopotamian base-60 system emerged from the combination of two other number systems. Is this scenario so much more plausible than Sumerian bureaucrats standardizing and codifying a number system from above? The author thinks so, dismissing the latter possibility out-of-hand. I’m curious whether we have evidence from elsewhere of two or more number systems combining to form a joint system. Could we model this scenario and see how easy it is for a person using one number base to interact and come to an understanding with another individual using a different base? Does it “naturally” allow for the combination of the two systems? Sumeria and its civilizational inheritors are among the first agricultural, sedentary societies. Do different societal needs, modes of production, and hierarchies lead to different number systems? It seems like agricultural societies would benefit a lot from a number system that allows for the easy creation of fractions, as it would make measuring and comparing amounts of grain or other commodities easier.
Your question about whether base 60 could have been shaped by the practical needs of an agricultural society made me return to the MacTutor article. The article considers explanations involving weights, measures, and fractions, but it also warns us about constructing a logical explanation after the fact. I find that tension interesting: the divisibility of 60 clearly makes it useful for sharing and measuring quantities, but usefulness alone doesn’t tell us whether that is actually why the system developed.
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