Here are a couple of experiments that anyone can do:
To begin either experiment, go to a site that provides long term
tidal predictions for lots of places on earth. (See, for
instance, <http://co-ops.nos.noaa.gov/tp4days_old.html> ) Choose a
place at random. Find the date and time of the highest high tide
(or the lowest low tide) during any given (usually) two week tidal
cycle.
Experiment 1: Move forward and find the date and time of the
subsequent highest high tide (or lowest low tide.) Usually this
will be about two weeks (half a "moonth") later, i.e., the time
between successive spring tides. Find the elapsed time between
the two events. You will almost certainly find that the elapsed
time is an integer times (12.42 +/- 0.06) hr. Convince yourself
that this is a highly meaningful result by, for instance, (a)
performing the analysis for many different sites, (b) noting that,
while the specific integer may vary, it is always the same as the
number of tidal cycles between the two events except that one must
account for the "missing tides" at those rare locations that
experience once a day tides, (c) considering the likelihood of
always being able to find an integer leading to such a precisely
defined time interval (i.e., with an uncertainty of only about 4
minutes) irrespective of whether or not that integer happened also
to be equal to the number of tidal cycles.
Experiment 2: Move forward one year and find the date and time of
the highest high tide (or lowest low tide) in approximately the
same two week period. Find the elapsed time between the two
events. You will almost certainly find that the elapsed time is
an integer times (12.421 +/- 0.001) hr. Convince yourself that
this is an even *more* meaningful result than that of experiment 1
by noting that the precision has increased by a factor of more
than 26 (i.e., the number of two week intervals in one year).
Finally note that half a mean lunar day is 12.421 hr and, in the
light of your experimental results, consider the likelihood that
this is an accident.