> analog clocks are modeled around the idea that the time is circular because that's the natural cycle of day and night
This is not supported by evidence. For one, it would make a 24 hour dial make more sense than a 12 hour one. For two, many early non-discrete clocks took the form of parallax observation or liquid flows and were not inherently circular.
hourglasses and other similar devices are for keeping discrete times, not continuous times like in
"it cooks in half of that"
but they are circular inherently, when the top half falls to the bottom, we flip them and the cycle restarts.
analog clocks started as 24 hours historically [1]. the division of days in 24 equal segments was well know since ancient history, we still use base 60 to measure time because that's what babylonians used when they invented time keeping and started counting days in a year (360 of them, in base 60)
If you limit the set of "analog clocks" to 24-hour dials, then yes, you have proven a tautology. If you look at the overall history of time device user interfaces then circular displays don't seem like such a slam dunk. I'll point you to Al Muradi of 1200's Spain again who often uses little doors or other time indicators.
there are bizarre incantations of everything throughout history
Almuradi clock is still a *solar* clock hence it only works when the light rays hit it, so like a meridian, it can't show the full 24 hours rotation. in fact it's an half circle, because the earth rotates around the sun, the only approximation you can get is circular, of course there are meridians that do not display hours on an arc of circumference, but that's simply a design choice.
But at that time the fact that a day was of 24 hours was a long well known fact.
the point is that if your planet rotates around a star, the first thing beings living there would notice are the repeating patterns generated by light rays. Which are most probably shadows creating something like a circle (or an oval)
>Almuradi clock is still a solar clock hence it only works when the light rays hit it
No, Almuradi's works are powered by water and moved by gears. At least one used light to illuminate particular numbers, but the optical aperture was moved by gears.
>Which are most probably shadows creating something like a circle (or an oval)
During the course of the day the shadows make a half circle at best. Over the course of a year the end point at the same time of day makes an uneven figure eight, known as the analemma. At no point is there a circle or an ellipse.
Passive solar timekeeping has its limitations and the next phase of development was the water clock.
These simple water clocks, which were of the outflow type, were stone vessels with sloping sides that allowed water to drip at a nearly constant rate from a small hole near the bottom. There were twelve separate columns with consistently spaced markings on the inside to measure the passage of "hours" as the water level reached them. The columns were for each of the twelve months to allow for the variations of the seasonal hours. These clocks were used by priests to determine the time at night so that the temple rites and sacrifices could be performed at the correct hour. [0]
If anything the circular three hand clock is a pragmatic method of indictors based on the method of power control. Looking at the Antikytheria mechanism for example, the back side shows a deep understanding of how the different cycles of time measures interact.
Going back to the original topic of "an alien digital clock written in alien language," to the degree that we could comprehend on what basis they kept time a time communication rooted in a sidereal period cannot be a given since the aliens might come from a tidally locked planet or one like Mercury which "rotates on its axis exactly three times for every two revolutions it makes around the Sun."[2] Even if they just used the Unix epoch time would look linear and relative; not circular.
Iirc historically the day was first split into 12 parts with sundials, and only later was the night also split into 12 parts. Maybe thats where the 2x12 comes from. I guess another benefit is that it's simply less cluttered with 12 divisions.
This is not supported by evidence. For one, it would make a 24 hour dial make more sense than a 12 hour one. For two, many early non-discrete clocks took the form of parallax observation or liquid flows and were not inherently circular.
https://muslimheritage.com/the-clocks-of-al-muradi/
https://en.wikipedia.org/wiki/History_of_timekeeping_devices