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This question already has an answer here:

Early civilizations have noticed the passage of time through heavenly bodies periodically crossing the sky. With this information, they adapted according to the seasons- especially in agriculture.

This is quite confusing in my tidally-locked world (which- for convenience- is able to support life). The night-side could measure the year by observing the stars, the twilight-side experiences the sun dipping and rising on the horizon in varying degrees plus they have the growth of vegetation as reference.

Then comes the day-side that live at the edges of the sub-solar "eye". I decided their culture would be close to primitive but not savage. Living in perpetual daylight, how would they perceive time? Would they even have such concept? I suppose they can have the availability of specific trade items from the twilight-side as reference. (There's also the issue of the circadian clock, but that's a topic for another time. Let's just assume these people have 'adapted' to their environment.)

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marked as duplicate by L.Dutch, MichaelK, Ash, Frostfyre, Mołot Sep 25 '17 at 13:07

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In general, people have told time in two ways. They've done it linearly, and they've done it cyclically. Which one is used at any point in time is really more a matter of convenience than anything else.

The key question you should ask yourself is what would your culture want to measure? What drives your culture to need a measure of time? With those questions, you start to capture how they would approach time. For example, if your people subsisted heavily on fruit, the time it takes a fruit to spoil might be important. One might start to talk of meeting in the time it takes for 3 fruit to spoil, one after another.

There will always be one important cyclical measure of time: the passing of generations. We are born, we grow up, we grow old, and we die. This cycle will always be important, even in a sun-facing society. It is likely to spawn the need to measure time in a cyclical way.

There's also animals that can create a sense of time. Consider the cicada. It has two sub-species that come out in 13 and 17 year cycles. These are very noticeable events, where the land is cluttered with insects. Of course, these species are Earth bound, and thus operate on seasonal cycles, but your animals may need cyclical patterns just like the humans do. I could see a cicada-like creature which "borrows" the seasonal patterns from the night-side and brings them over to the day.

Finally, consider that they might not measure time in even increments. The passage of time might not need to be marked in even seconds or minutes. Time might be defined by when you get hungry (and thus you eat), or when you get tired (so you sleep), or when you go... well... (thank you Forrest Gump). The idea that time needs to be measured so terribly evenly is rather new. In fact, most of our obsession with precision didn't occur until the industrial era.

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The day-night cycle would be absent for obvious reasons, but the year cycle may still occur like on earth due to the weather (as orbit still would have some aphelion and perihelion). Also, keep in mind that the fixed dates of holidays we have in our culture is strictly connected with the fact we have such precise calendar. Even if some holidays seem to move (like Easter) it is only due to historical differences between lunar and solar calendars. Yet there are cultures where there is no common calendar and events are defined more ad hoc. So maybe you can introduce some cast of shamans/priests who call to make holiday when society seemingly needs it?

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Physical processes could be used to measure the passage of time such as water or sand falling through a narrow channel, the amount of time it took to walk between fixed land marks, regular eruptions from geysers and regular animal behaviour such as hibernation or migration. Human and animal bodies also include a number of rough and ready embedded “clocks” such as heart beats, the circadian clock, female Oestrus and the growth of offspring to a particular height. Plant growth would also provide another mechanism.

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