There should be an Olympic event to test human's ability to measure time intervals.
Each contestant receives a stopwatch. Tests are conducted in various environments, with different levels of information / actions available to competitors.
In these events they just have to click the timer to start, and then click it again later to end.
Whoever clicked the timer closest to the right time would win. There would be no special penalty for going over or under.
I would love to see what strategies participants invented for themselves.
Perhaps reciting a memorized speech? Or physical, repetitive motions - drumming a certain number of times on the table. Or writing out a memorized speech. Some might use their own heartbeat, or rate of breathing.
It would be very interesting also to compare the different strategies. Which types of activities let us measure time best while we're doing them?
Some contestants might try to use physical constants like gravity to help - calibrate their clocks based on how quickly a bouncing ball stops.
We shouldn't let people bring in clocks, but if they wanted to build one in the longer events, I guess they could. For this there would be another event - played in wilderness, over a time span of 10 years, in an area where there are no seasons?
In extremely long variants, the main problem is preserving the knowledge that a game is being played at all. If the task is to click a timer after 1000 years, how would you design a civilization to even have people who remember that winning this event is their goal?