Does time depend on the sun or does the sun depend on time?

If the time on your clock doesn't agree with the position of the sun, you know the sun is correct and you change the clock. If it disagrees with the sun again the next day, you figure out that the clock is broke, and you discard it and get a better one.

The sun keeps doing what it's doing. It doesn't know or care what your clock says. The sun is what you use to set your clock by, and to decide how fast or slow your clock should run ... i.e. exactly once (or twice) around every time the sun goes once around.

______________________

The above is true only in a 'folk' sense. In fact, Universal Time (UTC) is a system developed to overcome some of the problems with solar time. Without getting into every detail, solar time is different from clock time. Days reckoned in solar time are not of equal length. In other words, the time between transits of the sun on two consecutive days will not always be precisely 24 hours. This is because the orbit of the sun is eliptical, causing earth's orbital velocity to change over the course of a year. Our system of 24 hours comes from a complex calculation of the 'average' day based on the exact length of a year. In fact, the sun is 'wrong' most of the time. Our more precise reckoning of time is essential especially today, with the sophisticated communications and gps systems that we have. They wouldn't even exist if we had to deal with solar time. For an interesting approach, look up and study the "analemma", or anything dealing with Greenwich Mean Time, UTC, or Civil Time.

___________________________

All true. However, returning to the original question, the fact remains that the need to measure and quantify time is of human invention, and is one upon which the sun in no way depends.