### Why 12?

Can I take this opportunity to air my theory about why clock faces are divided into 12? Your observation about the 123 theme is a starting point.

Tides. Let’s define an hour as the time by which 1/12 of the tidal range is reached starting at low water. The next hour will see another 2/12 added to the height, and the third hour another 3/12, followed by another 3/12 at the end of the fourth hour. After that the speed of tidal flow and rise in height begins to diminish, with 2/12 added with the fifth hour and 1/12 again by the end of the sixth hour at which point we have high tide. The process then reverses until we get back to low water again.

The rise and fall in flow speed is represented by the sequence 123321 which sums to 12. Other numbers, such as 20 can be similarly partitioned (12344321), but 12 is also 2 (1 for rise + 1 for fall) times the number of digits in the sequence. No other number, except of course integer multiples of 12, partitions in precisely these two ways.

I suggest that comes into why early maritime civilisations would have chosen 12 as the number by which to divide such clock faces as they had, in deciding when to set sail or enter port day or night, thus originating the so-called “rule of twelths”, still in use today. In addition, the length of an hour defined in tidal terms, whatever the divisor, would have been invariant with respect to season, and also to tidal range (that is from spring to neap and from port to port).