Pseudo heart of a phantom thing—it is Keplerism, pulsating with Sir
Isaac Newton’s regularizations.
If triangulation can not be depended upon accurately to measure distance
greater than a mile or two between objects and observers, the aspects of
Keplerism that depend upon triangulation should be of no more concern to
us than two pins in a cushion 180 miles away: nevertheless so affected
by something like seasickness are we by the wobbling deductions of the
conventionalists that we shall have direct treatment, or independent
expressions, whenever we can have, or seem to have, them. Kepler saw a
planetary system, and he felt that, if that system could be formulated
in terms of proportionality, by discovering one of the relations
quantitatively, all its measurements could be deduced. I take from
Newcomb, in _Popular Astronomy_, that, in Kepler’s view, there was
system in the arrangement and motions of the four little traitors that
sneak around Jupiter; that Kepler, with no suspicions of these little
betrayers, reasoned that this central body and its accompaniments were a
representation, upon a small scale, of the solar system, as a whole.
Kepler found that the cubes of mean distances of neighboring satellites
of Jupiter, divided by the squares of their times, gave the same
quotients. He reasoned that the same relations subsisted among planets,
if the solar system be only an enlargement of the Jovian system.
_Observatory_, December, 1920: “The discordances between theory and
observation (as to the motions of Jupiter’s satellites) are of such
magnitude that continued observations of their precise moments of
eclipses are very much to be desired.” In the Report of the Jupiter
Section of the British Astronomical Society (_Mems. B. A. A._, 8-83) is
a comparison between observed times and calculated times of these
satellites. 65 observations, in the year 1899, are listed. In one
instance prediction and observation agree. Many differences of 3 or 4
minutes are noted, and there are differences of 5 or 6 minutes.
Kepler formulated his law of proportionality between times and distances
of Jupiter’s satellites without knowing what the times are. It should be
noted that the observations in the year 1899 took into consideration
fluctuations that were discovered by Roemer, long after Kepler’s time.
Just for the sake of having something that looks like opposition, let us
try to think that Kepler was miraculously right anyway. Then, if
something that may resemble Kepler’s Third Law does subsist in the
Jovian satellites that were known to Kepler, by what resemblance to
logicality can that proportionality extend to the whole solar system, if
a solar system can be supposed?
In the year 1892, a fifth satellite of Jupiter was discovered. Maybe it
would conform to Kepler’s law, if anybody could find out accurately in
what time the faint speck does revolve. The sixth and the seventh
satellites of Jupiter revolve so eccentrically that, in line of sight,
their orbits intersect. Their distances are subject to very great
variations; but, inasmuch as it might be said that their mean distances
do conform to Kepler’s Third Law, or would, if anybody could find out
what their mean distances are, we go on to the others. The eight and the
ninth conform to nothing that can be asserted. If one of them goes
around in one orbit at one time, the next time around it goes in some
other orbit, and in some other plane. Inasmuch then as Kepler’s Third
Law, deduced from the system of Jupiter’s satellites, can not be thought
to extend even within that minor system, one’s thoughts stray into
wondering what two pins in a cushion in Louisville, Ky., look like from
somewhere up in the Bronx, rather than to dwell any more upon extension
of any such pseudo-proportionality to the supposed solar system, as a
whole.
It seems that in many of Kepler’s demonstrations was this failure to
have grounds for a starting-point, before extending his reasoning. He
taught the doctrine of the music of the spheres, and assigned bass
voices to Saturn and Jupiter, then tenor to Mars, contralto to the
female planet, and soprano, or falsetto, rather, to little Mercury. And
that is all very well and consistently worked out in detail, and it does
seem reasonable that, if ponderous, if not lumpy, Jupiter, does sing
bass, the other planets join in, according to sex and huskiness—however,
one does feel dissatisfied.
We have dealt with Newcomb’s account. But other conventionalists say
that Kepler worked out his Third Law by triangulation upon Venus and
Mercury, when at greatest elongation, “finding” that the relation
between Mercury and Venus is the same as the relation between Venus and
this earth. If, according to conventionalists, there was no “proof” that
this earth moves, in Kepler’s time, Kepler started by assuming that this
earth moves between Venus and Mars; he assumed that the distance of
Venus from the sun, at greatest elongation, represents mean distance; he
assumed that observations upon Mercury indicated Mercury’s orbit, an
orbit that to this day defies analysis. However, for the sake of seeming
to have opposition, we shall try to think that Kepler’s data did give
him material for the formulation of his law. His data were chiefly the
observations of Tycho Brahé. But, by the very same data, Tycho had
demonstrated that this earth does not move between Venus and Mars; that
this earth is stationary. That stoutest of conventionalists, but at the
same time seeming colleague of ours, Richard Proctor, says that Tycho
Brahé’s system was consistent with all data. I have never heard of an
astronomer who denies this. Then the heart of modern astronomy is not
Keplerism, but is one diversion of data that beat for such a monstrosity
as something like Siamese Twins, serving both Keplerism and the Tychonic
system. I fear that some of our attempts to find opposition are not very
successful.
So far, this mediæval doctrine, restricting to times and distances,
though for all I know the planets sing proportionately as well as move
proportionately, has data to interpret or to misinterpret. But, when it
comes to extending Kepler’s Third Law to the exterior planets, I have
never read of any means that Kepler had of determining their
proportional distances. He simply said that Mars and Jupiter and Saturn
were at distances that proportionalized with their times. He argued,
reasonably enough, perhaps, that the slower-moving planets are the
remoter, but that has nothing to do with proportional remoteness.
This is the pseudo heart of phantom astronomy.
To it Sir Isaac Newton gave a seeming of coherence.
I suspect that it was not by chance that the story of an apple should so
importantly appear in two mythologies. The story of Newton and the apple
was first told by Voltaire. One has suspicions of Voltaire’s meanings.
Suppose Newton did see an apple fall to the ground, and was so inspired,
or victimized, into conceiving in terms of universal attraction. But had
he tried to take a bone away from a dog, he would have had another
impression, and would have been quite as well justified in explaining in
terms of universal repulsion. If, as to all inter-acting things,
electric, biologic, psychologic, economic, sociologic, magnetic, chemic,
as well as canine, repulsion is as much of a determinant as is
attraction, the Law of Gravitation, which is an attempt to explain in
terms of attraction only, is as false as would be dogmas upon all other
subjects if couched in terms of attraction only. So it is that the law
of gravitation has been a rule of chagrin and fiasco. So, perhaps
accepting, or passionately believing in every symbol of it, a Dr. Adams
calculates that the Leonids will appear in November, 1899—but chagrin
and fiasco—the Leonids do not appear. The planet Neptune was not
discovered mathematically, because, though it was in the year 1846,
somewhere near the position of the formula, in the year 1836 or 1856, it
would have been nowhere near the orbit calculated by Leverrier and
Adams. Some time ago, against the clamor that a Trans-Uranian planet had
been discovered mathematically, it was our suggestion that, if this be
not a myth, let the astronomer now discover the Trans-Neptunian planet
mathematically. That there is no such mathematics, in the face of any
number of learned treatises, is far more strikingly betrayed by those
shining little misfortunes, the satellites of Jupiter. Satellite after
satellite of Jupiter was discovered, but by accident or by observation,
and not once by calculation: never were the perturbations of the earlier
known satellites made the material for deducing the positions of other
satellites. Astronomers have pointed to the sky, and there has been
nothing; one of them pointed in four directions at once, and four times
over, there was nothing; and many times when they have not pointed at
all, there has been something.
Apples fall to the ground, and dogs growl, if their bones are taken
away: also flowers bloom in the spring, and a trodden worm turns.
Nevertheless strong is the delusion that there is gravitational
astronomy, and the great power of the Law of Gravitation, in popular
respectfulness, is that it is mathematically expressed. According to my
view, one might as well say that it is fetishly expressed. Descartes was
as great a mathematician as Newton: veritably enough may it be said that
he invented, or discovered, analytic geometry; only patriotically do
Englishmen say that Newton invented, or discovered, the infinitesimal
calculus. Descartes, too, formulated a law of the planets and not by a
symbol was he less bewildering and convincing to the faithful, but his
law was not in terms of gravitation, but in terms of vorticose motion.
In the year 1732, the French Academy awarded a prize to John Bernouli,
for his magnificent mathematical demonstration, which was as
unintelligible as anybody’s. Bernouli, too, formulated, or said he
formulated, planetary inter-actions, as mathematically as any of his
hypnotized admirers could have desired: it, too, was not gravitational.
The fault that I find with a great deal of mathematics in astronomy is
the fault that I should find in architecture, if a temple, or a
skyscraper, were supposed to prove something. Pure mathematics is
architecture: it has no more place in astronomy than has the Parthenon.
It is the arbitrary: it will not spoil a line nor dent a surface for a
datum. There is a faint uniformity in every chaos: in discolorations on
an old wall, anybody can see recognizable appearances; in such a mixture
a mathematician will see squares and circles and triangles. If he would
merely elaborate triangles and not apply his diagrams to theories upon
the old wall itself, his constructions would be as harmless as poetry.
In our metaphysics, unity can not, of course, be the related. A
mathematical expression of unity can not, except approximately, apply to
a planet, which is not final, but is part of something.
Sir Isaac Newton lived long ago. Every thought in his mind was a
reflection of his era. To appraise his mind at all comprehensively,
consider his works in general. For some other instances of his love of
numbers, see, in his book upon the Prophecies of Daniel, his
determinations upon the eleventh horn of Daniel’s fourth animal. If that
demonstration be not very acceptable nowadays, some of his other works
may now be archaic. For all I know Jupiter may sing bass, either
smoothly or lumpily, and for all I know there may be some formulable
ratio between an eleventh horn of a fourth animal and some other
quantity: I complain against the dogmas that have solidified out of the
vaporings of such minds, but I suppose I am not very substantial,
myself. Upon general principles, I say that we take no ships of the time
of Newton for models for the ships of today, and build and transport in
ways that are magnificently, or perhaps disastrously, different, but
that, at any rate, are not the same; and that the principles of biology
and chemistry and all the other sciences, except astronomy, are not what
they were in Newton’s time, whether every one of them is a delusion or
not. My complaint is that the still mediæval science of astronomy holds
back alone in a general appearance of advancement, even though there
probably never has been real advancement.
There is something else to be said upon Keplerism and Newtonism. It is a
squirm. I fear me that our experiences have sophisticated us. We have
noted the division in Keplerism, by which, like everything else that we
have examined, it is as truly interpretable one way as it is another
way.
The squirm:
To lose all sense of decency and value of data, but to be agreeable; but
to be like everybody else, and intend to turn our agreeableness to
profit;
To agree with the astronomers that Kepler’s three laws are, not
absolutely true, of course, but are approximations, and that the planets
do move, as in Keplerian doctrine they are said to move—but then to
require only one demonstration that this earth is one of the planets;
To admire Newton’s _Principia_ from the beginning to the end of it,
having, like almost all other admirers, never even seen a copy of it; to
accept every theorem in it, without having the slightest notion what any
one of them means; to accept that moving bodies do obey the laws of
motion, and must move in one of the conic sections—but then to require
only one demonstration that this earth is a moving body.
Kepler’s three laws are popularly supposed to demonstrate that this
earth moves around the sun. This is a mistake. There is something wrong
with everything that is popular. As was said, by us, before, accept that
this earth is stationary, and Kepler’s doctrines apply equally well to a
sun around which proportionately inter-spaced planets move in ellipses,
the whole system moving around a central and stationary earth. All
observations upon the motions of heavenly bodies are in accord with this
interpretation of Kepler’s laws. Then as to nothing but a quandary,
which means that this earth is stationary, or which means that this
earth is not stationary, just as one pleases, Sir Isaac Newton selected,
or pleased himself and others. Without one datum, without one little
indication more convincing one way than the other, he preferred to think
that this earth is one of the moving planets. To this degree had he the
“profundity” that we read about. He wrote no books upon the first and
second horns of his dilemma: he simply disregarded the dilemma.
To anybody who may be controversially inclined, I offer simplification.
He may feel at a disadvantage against batteries of integrals and
bombardments of quaternions, transcendental functions, conics, and all
the other stores of an astronomer’s munitions—
Admire them. Accept that they do apply to the bodies that move around
the sun. Require one demonstration that this earth is one of those
bodies. For treatment of any such “demonstration,” see our disquisition,
or our ratiociations upon the Three Abstrusities, or our intolerably
painful attempts to write seriously upon the Three Abstrusities.
We began with three screams from an exhilarated mathematician. We have
had some doubtful adventures, trying hard to pretend that monsters, or
little difficulties, did really oppose us. We have reached, not the
heart of a system, but the crotch of quandary.