Details sometimes make the difference between science
and scholastic games. As Ted Davis pointed out, Kepler's
720 derived from the days of the year (360) on the Mesopotamian
calendar (both in the Bible and in Babylonia). Of course,
this is incorrect, but it is only off by 5 days per year, so it
can be ignored until it becomes a problem for farmers; then
they add a leap month.
We use 365.25 days per year, adding a leap day every
4 years. Of course, this is incorrect, but it is only off a few
minutes per year, so we add a leap day every 400 years
to adjust for this.
Of course, this is incorrect, because there are variations in
the length of the day, on the order of milliseconds per day,
which include both periodic variations and stochastic variations
due to the internal motion of liquid metal inside the earth, the
perturbations of the planets, etc.
The same thing can be said of the angular size of the
sun and moon. They vary considerably, so that sometimes
we have an annular eclipse.
As I mentioned yesterday, I think one of the most significant
episodes in the history of science was when Kepler noted
Tycho's 8 minutes of arc deviation in the orbit of Mars from a
perfect circle, and he accepted this as true, rather than
dismissing it as experimental error. This led him to reject the
perfect circle in favor of an ellipse, thus ushering in a new
empirical approach to nature. I said "the data forced him" to
the new view. This is a philosophically-laden statement.
In general, we have made remarkable success in science by
trying not to impose restrictions on what we can observe,
and let the data lead us to 'new facts'. Some say that this
is impossible, that all data are 'theory-laden', but I think that
history shows otherwise. No one still believes that the planets
must move in perfect circles, despite the centuries of allegiance
to this theory of the perfection of the heavens (a 'nova' also
was reported by Tycho; this should not happen in a perfect
(Incidentally, that is why I can't say that evolution is impossible.
How can I dictate a priori what life can and cannot do?)
Physical numerology survives today, but in a new form. Since
things like the earth and planets are now seen to be 'analog'
systems with variable and irrational numerical relationships,
this approach had to be abandoned. In order to do numerology,
one has to have numbers, that is -- integers. Fortunately for
the numerologists, physics obliged by discovering quantum
mechanics, in which integers once again prevail.
In the 20th century, there was first speculation that the fine
structure constant might be an integer fraction, 1/137. Now that
the data are better, this turns out to be false. Dirac was fond of
something like numerology, making a lot out of the prevalence
for the ratio 10^40 among various force constants. And then
the fractional charge was discovered, and it turned out to be
1/3! Wow, three again!
Here's another recent "three" item that appeared in the Washington
Post, Aug. 22, 1999. I will leave you with this:
A Biblical Garden
"The new analysis presented at the 16th International Botanical
Congress ... also comes to the jarring conclusion that there
are three separate plant kingdoms rather than one, as most
high school students are taught today." ["Scientists Find Three
Plant Kingdoms Instead of 1 in Revised Family Tree", front page,
So I opened my old science book to Genesis 1:11 and read:
"And God said, Let the earth bring forth grass, the herb yielding
seed, and the fruit tree yielding fruit after his kind, whose seed
is in itself, upon the earth; and it was so."
Three kinds of plants, just as the Bible says. Amazing. Do you
suppose someone knew something way back then?
-- Carlton E. Blake, McLean [VA]"