I have been learning to tell time.
For our D&D games, I have been researching how the heathen Anglo-Saxons told time. They used two calendars in parallel: the Julian calendar, which was an early draft of ours, and their own lunar calendar. Learning about them in enough detail to use them in our games has taught me how much I took for granted about how we tell time today.
Designing a calendar system is not easy. The different units by which we measure time do not divide into one another evenly, and we have no fixed frame of reference for measurement.
For example, what is a day?
One naive answer is twenty-four hours, but that turns out to be circular reasoning because an hour is defined as a fraction of a day, and has no other natural meaning. The day is the natural unit, but what is it?
A second naive answer is that it is the span of time from midnight one day to midnight the next, but this turns out to be the first answer in disguise. After all, when is midnight? It is a repeating point in time spaced out every twenty-four hours, which takes us back to an hour being an arbitrary fraction of a day, and back to the original question, what is a day?
A third naive answer is that it is the time from sunset one day to sunset the next, or from sunrise to sunrise. This captures an important element of the definition of a day, but not all of it. We do know the sun rising and setting is involved, but the time of sunrise and sunset ebbs and flows through the seasons, with the daylight longer in the summer and shorter in the winter. Yet we know the answer we are looking for describes something of approximately constant length throughout the year. This answer does not satisfy that criterion, but it does correctly identify that our definition is related to the relationship between the sun and the earth, particularly to the cycles of day and night. Any definition of a day that runs out of sync with the cycles of day and night cannot be right. So again I ask what is a day?
A fourth answer, a more astronomical answer, is one complete rotation of the planet Earth, but this turns out to be subtly inaccurate. What counts as a full rotation? If we watch the second hand move from 12 around back to 12 on a clock, we can see that we are thinking about a complete rotation as returning to the starting point on a fixed reference. We have no fixed reference for the Earth's rotation, but if we approximated one, say by using the stars, or by projecting an imaginary frame of reference on space around us, the answer is still wrong. The result of doing this would be that over the course of a year, midnight would rotate around through the day as the earth revolves around the sun. Midnight would sometimes be at night, sometimes at sunrise or sunset, sometimes during the day, gradually shifting with the seasons. This seemingly reasonable answer, which is the one given by all the people I know who think they are smart people, is mathematical and astronomical but false.
A more correct answer (but no promises) is that a day is slightly more than one complete rotation of the planet Earth. The line of the Earth's orbit around the sun is our guide to the length of a day. In the almost-day it takes for the Earth to spin completely around, the Earth has also moved just under one degree around its orbit line, changing the sun's position with respect to the Earth by one degree. For the times of day to stay stable, for example for midnight to remain in the middle of the night and noon to remain in the middle of the day, the start and end of each day must remain oriented toward the sun. Since during the course of one day the Earth's revolution around the sun changes its orientation by almost one degree, the Earth must rotate just a little bit more (almost one degree) than one complete rotation to compensate, to line back up with the orbit line and with the sun. That way, noon stays mid-day and midnight stays...well, you get the picture.
If this explanation does not make sense to you, ask me in the comments and I will explain it differently.
It is easy to explain what a day is with a picture but even with words it is pretty easy to explain. So why do we not explain it this way in first grade? Everyone should know what a day is. Why do even most intelligent people define it incorrectly?
Extra credit: Explain why a day is a about a degree more than one complete rotation instead of about a degree less. What would have to be different for a day to be about a degree less than a complete rotation?