Re: Significance of numbers: Kepler and 720: waxing eloquent

George Murphy (
Thu, 09 Sep 1999 15:51:29 -0400

Ted Davis wrote:
> 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
> scientist?
> :-)

& of course there is a well known proof that there is no uninteresting number.
1 is obviously interesting because it's first &c. 2 is the first even number. 3 is the
first odd prime &c. Now suppose that n is the first uninteresting number. That very
fact makes it interesting. _Reductio ad absurdum_ - which, by the way, summarizes in a
fairly transparent code the value of numerological interpretations of the Bible, the
universe, &c.

George L. Murphy