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 of its measurements could be deduced. I take from Newcomb, in Popular Astronomy, that, in Kepler's view, there was a 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.(1) 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 the precise moments of eclipses are very much to be desired."(2) 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.(3) 65 observations, in the [69/70] 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.(4)
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 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 eighth and 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.(5)
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, [70/71] 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.(6) 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, [71/72] 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.(7) 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.(8) 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.(9) Astronomers have pointed to the sky, and there has been nothing; one of them pointed in four directions at once, and four times [72/73] over, there was nothing; and many times when they have not pointed at all, there has been something.(10)
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 it may be said that he invented, or discovered, analytic geometry; only patriotically do Englishmen say that Newton invented, or discovered, the infinitesimal calculus.(11) 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.(12) 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.(13)
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 [73/74] 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.(14) 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.
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 [74/75] 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 probably 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 interspaced 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 ratiocinations 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 the system, but the crotch of quandary.
7. "And thus in our days Sir Isaak Newton walking in his gardens had the first thought of his system of gravitation, upon seeing an apple falling from a tree." Voltaire. Ulla Kölving, ed. The
English Essays of 1727. Vol. 3B of The Complete Works of Voltaire. Oxford: University of Oxford, 1996, 372-3. Voltaire. W.H. Barber, and, Ulla Kölving, eds. Eléments de la Philosophie de Newton. Vol. 15 of The Complete Works of Voltaire. Oxford: University of Oxford, 1992; 34,
8. "If it is not an occult quality then, so Leibniz maintained, `the attraction of bodies, properly so-called, is a miraculous thing.' According to Leibniz, such attraction at a distance was unacceptable, being `inexplicable, unintelligible, precarious, groundless and unexampled.' Like so many of his contemporaries, Leibniz was much happier explaining the motion of the planets in terms of vortices in a Cartesian aether, and had such a theory been worked out in detail with the success of Newton's, there can be little doubt as to which would have prevailed." A significant difference between Newton's theory of gravitation and that of Einstein is that Newton's identifies gravitational forces as "attractions," whereas Einstein's is "indifferent as between attraction and repulsion." John D. North. The Measure of the Universe. Oxford: Clarendon Press, 1965; 25, 67.
9. Barnard discovered Amalthea, (satellite 5), in 1892, by visual observation; Perrine discovered Himalia and Elara, (satellites 6 and 7), in 1904; Melotte discovered Pasiphae, (satellite 8) in 1908; and, Nicholson discovered Sinope, (satellite 9), in 1914. Four more satellites, (Lysithea, Carme, Ananke, and Leda), were discovered from 1938 to 1974; and, three more satellites, (Metis, Adrastea, and Thebe), were discovered by the Voyageur 1 and 2 spacecraft in 1979. After Barnard's Amalthea, the next eight satellites were all discovered from examinations of photographic plates. Amalthea and the Galilean satellites, (or "regular satellites"), follow spin-orbit coupling and are mutually perturbed by "the puzzling Laplace resonance." The orbits of the remaining satellites are "located at relative distances from Jupiter similar to those of the terrestrial planets from the sun," but these "irregular satellites" are characterized differently. "With the exception of Himalia, and perhaps Elara (J7), the outer satellites are difficult objects to observe photoelectrically because of their faintness and their poorly defined ephemerides." D. Morrison and, J.A. Burns. "The Jovian satellites." Tom Gehrels, ed. Jupiter. Tucson, Arizona: University of Arizona Press, 1976; 993-5, 1026. Jeffrey K. Wagner. Introduction to the Solar System. Toronto: Saunders College Publishing, 1991; 290-2, A.16.
10. William H. Pickering was one of the astronomers with a tendency to point to many hypothetical planets, some of which he identified as "O," "P," "S," "T," and "U." William H. Pickering. "The next planet beyond Neptune." Popular Astronomy, 36 (1928): 143-65, 218-21. William H. Pickering. "The three outer planets beyond Neptune." Popular Astronomy, 36 (1928): 417-24. William H. Pickering. "Planet O." Popular Astronomy, 37 (1929): 135-8. William H. Pickering. "Planet P. Comet 1930 III, Wilk, number 590." Popular Astronomy, 39 (1931): 321-3. William H. Pickering. "Planet P, its orbit, position, and magnitude. Planets S and T." Popular Astronomy, 39 (1931): 385-98. William H. Pickering. "Planet U, and the orbits of Saturn and Jupiter." Popular Astronomy, 40 (1932): 69-88. William H. Pickering. "First report on the search for Planet P." Popular Astronomy, 40 (1932): 351-4.
11. Florian Cajori. A History of Mathematics. New York: Macmillan and Co., 1894; 185-6, 200, 220-36. Newton's invention of infinitesimal calculus was disputed by those who sought to give credit to Fermat, (by Lagrange and Laplace), and to Leibniz, (who first published its notation and rules, but who did little to explain them); and, Cajori states its invention "was not so much an individual discovery as the grand result of a succession of discoveries by different minds."
12. Oliver Lodge. Pioneers of Science. London: Macmillan and Co., 1893, 151-5.
13. "Even as late as 1730 the Paris Academy of Sciences awarded a prize to an essay on the planetary motions by John Bernoulli, written on Descartes' principles, giving second place to a Newtonian essay." Peter Doig. A Concise History of Astronomy. London: Chapman & Hall, 1950, 88. John D. North. The Measure of the Universe. Oxford: Clarendon Press, 1965, 25. Jean Bernoulli (I), (not Bernouli), was also identified as John Bernoulli; and, the date of this award, according to Newcomb, was 1732. Simon Newcomb. Popular Astronomy. 2nd ed. London: Macmillan and Co., 80-1.
14. Isaac Newton. Observations upon the Prophecies of Daniel, and the Apocalypse of St. John. London: J. Darby and T. Browne, 1733; ch. 7, 74-89, "Of the eleventh horn of Daniel's fourth Beast," and, ch. 8, 90-114, "Of the power of the eleventh horn of Daniel's fourth Beast." Newton attempted, by mathematical reckoning, to recognize the true nature of the prophecy and to show that the horns of the fourth beast represented the Roman Empire and the Roman Catholic Church, as Antichrist. Like other anti-papists, Newton chose to ignore many commentators who had identified the horns as successive kings, either Ptolemies or Seleucids, and most specifically Antiochus Epiphanes, who had persecuted the Jews during the Maccabean era. Louis Trenchard More. Isaac Newton: A Biography. New York: Charles Scribner's Sons, 1934, 625-9. John J. Collins. Daniel: A Commentary on the Book of Daniel. Minneapolis: Fortress Press, 1993; 112-23, 274-324.