Ancient doesn’t mean stupid. Ancients were every bit as intelligent as moderns, capable of observation, critical thinking, drawing conclusions and projecting logic. And just like moderns, some were as smart as dirt.
Unlike today, the cycles of the sun, moon and stars were critical to harvest and survival. When one’s life depends on it, one concentrates hard.
A day is pretty easy to figure out, scratch a mark for each one. The position of the sun is also easy to figure out, scratch a mark on a rock. in a year or so, you can interpolate that a year is 365 days. Do it for another year to check your work.
Leap years take more than a year or two to figure out, after a few cycles you realize that an extra day keeps sneaking in. If you have a society which keeps records (scratches on rocks), and a class to maintain and interpret (shamans perhaps), then over a century or so, one can begin to track and interpret the anomalies. Moderns could do the same thing, except we are normally distracted by angry birds and tik-toks.
Fortunately we have a class of folks who specialize in observations, recordings, interpretations of data and projections of logic. Those are scientists, mathematicians, librarians, engineers, doctors, etc.
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