Ellen MacArthur wrote:

Thanks for the explanation. So what's the difference between the
rule of 12ths and the rule of thirds. In the rule of thirds the first
two hours it goes down 1/4 which is the same as your 3/12th. The
second two hours it goes down 1/2 which is the same as your 6/12th
and the third two hours it goes down 1/4 which is the same as your
3/12th. See I got it right in spite of myself.

It's based on the pretty-much universal fact that the time for the tide to
change from high to low water, and vice-versa, is pretty close to six hours.
Since we humans deal with time in chunks of one hour, the question we ask
is: "how much does the tide change in one hour?". Since the smallest
fraction is one twelfth, just before and just after slack water, it's
natural to refer to the tidal change during other hours in terms of the same
denominator. One twelfth in the first hour leads us to express the change
during the second as two twelfths, etc.

Also, the larger the time slot, the greater the granularity. Imagine you're
waiting for the tide to rise enough to clear a sandbar. The rule of thirds
would have you waiting in chunks of two hours before you sail. The rule of
12ths would keep you at anchor for chunks of one hour. Of course, plot the
heights on a graph over time, and you can pinpoint your departure time
(rather, the time at which you can safely cross the sandbar) much more
finely.

Whilst your 'rule of thirds' (which, incidentally, isn't exclusive to
photography, but is a general principle used in many forms of visual art)
may be mathematically correct at its junctures, it doesn't fit with how
people think of time (ie, we think in days of 24 hours, not days of 12
bi-hours).


--
Capt Scumbalino