Significance of numbers: Kepler and 720: waxing eloquent

Ted Davis (
Thu, 09 Sep 1999 15:34:08 -0400

If we want to place significance on numbers, let's consider Kepler's
argument for the significance of 720 in the archetypal design of the
universe (this is his term, "Archetypal," and it seems appropriate), more
significant than these alleged biblical things since it would be plain to
all, at least to all who follow his line of reasoning. :-)

Most important is the fact that both the sun and the moon take up exactly
the same angular size when seen from the earth: this is why eclipses of the
sun are possible! Without eclipses of both the sun and the moon, it would
not have been possible, Kepler points out, for the ancients or the moderns
to have calculated the distances to the sun and the moon, and thus the
astronomical unit (he was a Copernican). He relies here on the calculation
of Aristarchus, which called for observations including some taken from
solar and lunar eclipses. And this makes it possible for us to get the
dimensions of the cosmos generally, etc.

Now it happens that the sun and moon each subtend about half a degree of
arc in the sky, or 1/720 of a circle. NO, it doesn't "happen" that this is
so, it was part of the creator's intention. "We must seek the archetypal
cause," but "there is no geometrical cause for the division of a circle into
720 parts". But there is a harmonic cause--and we must remember that Kepler
considered the harmonies of the world as his greatest discovery--to wit,
that "the least number which offers itself in determining all the parts of
the monochord and in setting up the twofold scale of the octave, ie in the
minor and major mode--I say that this number is 720, as was shown in the
Harmonies of the World." (I lack space to develop this here and won't
respond to inquiries; go look for yourself at the Epitome of Copernican
Astronomy, Book IV, and the relevant parts of the Harmony.)

720 is divisible by
1,2,3,4,5,6,8,9,10,12,15,18,20,24,36,40,45,48,60,72,80,90, etc. Surely a
remarkable number for God to pick. As Kepler says, God chose this number to
scale the universe "both on account of the number itself," and "also on
account of the eclipses of the sun, a spectacle ordained by the Creator in
order that the speculative creatures should thereby be taught concerning the
rationale of the course of the stars. And teaching would be done most
rightly if the semidiameters of the sun and moon were to appear equal at the
greatest distance of each." He refers to conclusions that follow from this
as "a wonderful concord of probabilities."

Now, let's be honest, folks, which would YOU rather read: Kepler's
profoundly beautiful conception of the universe, expressed thusly, or the
deafeningly dull prose that editors of modern scientific journals impose on
(often) equally unimaginative authors. Now, perhaps, there is a fuller
understanding of why I decided to become an historian rather than a


Ted Davis