The table you have never used

Put a straight stick upright in level ground. As the morning goes on, the sun climbs and its shadow gets shorter. In the afternoon the sun sinks and the shadow gets longer again. So the length of the shadow tells you roughly what time it is, and it costs nothing.

Old Indian books turned that into a table, using units you carry around with you.

The smallest unit is the width of one finger, called an angula, about two centimetres. Twelve of them make a span, the distance from your thumb tip to your little finger tip on a spread hand.

Twelve is the important number. A measuring stick was made twelve finger-widths tall. Its shadow was then counted in the same finger-widths. Stick and ruler were both parts of a hand.

An old Sanskrit book on running a state, the Arthashastra, uses this to cut the daylight into eight parts. It gives four shadow lengths for the morning: 36 finger-widths, then 12, then four, then none at all, which it calls midday. After midday the same four lengths come back in reverse as the shadow grows the other way.

One of those marks is easy and exact. When the shadow is the same length as the stick, the sun is exactly 45 degrees up, halfway between the horizon and straight overhead. That is true anywhere, on any day.

The others are rougher. The "no shadow" mark only happens between the tropics, and only on two days a year. Near sunrise and sunset the shadow stretches very fast, so those readings are unreliable.

Here is the check anyone can do. Note the time when the morning shadow equals the stick. Note the time when the shadow is at its shortest, which is your local noon. Note the time when the afternoon shadow equals the stick again. Local noon should land halfway between the other two. And it will almost certainly not be twelve o'clock on your phone, for reasons to do with clocks rather than with the sky.