Tidal Heights & The Rule of 12ths 

Great question. How would we use 6? Would we divide the clock face up into 6 instead of the usual 12? So at 1 o'clock 1/6 of the tidal range has been reached, at 2 o'clock another 2/6, and at 3 o'clock another 3/6. 3 o'clock marks high water and is halfway round this clock. But we have no indication that the water flow speed, the rate at which the height changes, has been falling by then, even though height itself has still been rising. On the other hand 1/12, 2/12, 3/12, 3/12, 2/12, 1/12 does show this has happened by 6, halfway round a 12 segment face. OK, so let's decompose 6 into rising and falling fractions just as 12 was in the vid. This could be 1/6, 2/6, 2/6,1/6. At 1 o'clock 1/6 of the TR is reached, at 2 another 2/6, at 3 another 2/6, at 4 another 1/6. Now we do have high water after falling speed. Trouble is 4 o'clock is past the halfway mark, and seems to mean that low water will be correspondingly past the 6 o'clock mark at the top of the clock. Nothing wrong with that necessarily I guess, but it wouldn't be as neat and straightforward as starting with low water at the top and passing through high halfway round as with our 12 segmented face. 12 decomposes into the palindromic rise-fall sequence 1 2 3 3 2 1, and 6 into 1 2 2 1. But the number of whole number digits into which 12 decomposes like this is 6, and 12 is two 6's, one 6 for rise and one for fall. However the 4 digits into which 6 decomposes is greater than half 6. Is 12 (and its multiples) the only number with this property? If so, it may be the reason why 12 was chosen for clock faces in the first place, maybe by some maritime civilisation.

If 6 - then, for example, you would have to say that the tide has risen 0.5 of a 6th in the first hour (instead of 1/12th) and in the 3rd hour, instead of saying the tide has risen 3/12ths you would have to say it has risen 1.5 6ths. You can divide the 6 hours of tide anyway that suits but 12 is the only whole number that works (making the dreaded maths easier), hence the rule of 12ths. GREAT EXPLANATION. There are other ways to explain this but this is the best I can find. Thank you very much Mick, lots of effort, hats off, best explanation, will steal (with credit). Much appreciated.