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Well, I imagine you start out just putting a stick in the ground or something each day lined up with the sunrise. Then after 365 days you notice that the sun is rising in the same place you put the first stick.

You can discover all sorts of things that way. Noon, solstice and equinox, calender cycles (eg leap years), radius of the the earth, calendars. Combine it with water clocks, lunar observations, and tide measurements and you can discover all sorts of things to theorize about. Add straight edges and a compass and develop nomograms and slide rules and higher math. All with Stone Age technology.

It’s even an opportunity to develop the scientific method, but that’s a leap.

Unlike you and I with all the distractions of the modern world these people had nothing to do at night, no farming, no hunting, no TV, no books, so observing the heavens was where it was at. If you've ever spent a night at 12,000 ft on a mountain pass in Colorado you can't take your eyes off the star show. Many people made many observations and had their ways to communicate and share mutual knowledge. They created the scientific method of theory and confirmation by repeating the experiment before all the famous heroes western culture touts.

How were goats, horses, and dogs domesticated? It was these ancient peoples who gave us these extraordinary gifts that we have discounted for centuries. As Texas Fossil and I touched on earlier Fajada Butte in Choco Canyon Throws cold water on the sticks in the ground theory when it is an eighteen to nineteen year cycle of the moon risings. Those people had mathematics excellent communication, and a way to record observations for people who followed them and a great tradition of scientific intelligence. They might not align with our politics or religion, but they were pretty awesome in the results they got.