On Prediction in
Science
In order to bring into proper focus the significance of correct
prediction in science, I offer at the start a short survey of the most
celebrated cases, and it is not by chance that almost all of them come
from the domain of astronomy. These cases are spectacular and, with one
or two exceptions, are well known.
The story of scientific “clairvoyance” in modern astronomy starts with
Johannes Kepler, a strange case and little known. When Galileo,
using the telescope he had built after the model of an instrument
invented by a Danish craftsman, discovered the satellites circling
Jupiter, Kepler became very eager to see the satellites himself
and begged in letters to have an instrument sent to Prague; Galileo
did not even answer him. Next, Galileo made two more discoveries, but
before publishing them in a book, he assured himself of priority by
composing cryptograms, not an uncommon procedure in those days:
statements written in Latin were deliberately reduced to the letters of
which the sentences were composed, or, if the author of the cryptogram
so wished, the letters were re-assembled to make a different sentence.
The second way was chosen by
Galileo when he thought he had discovered that Saturn is “a
triple” planet, having observed appendices on both sides of Saturn, but
not having discerned that they were but a ring around the planet, a
discovery reserved for Christian Huygens in 1659, half a century
later. Kepler tried to read the cryptogram of letters recombined
into a non-revealing sentence, but did not succeed. He offered as his
solution:
Of this, Arthur Koestler
in The Sleepwalkers (1959) wrote (p. 377):
“He [Kepler] accordingly
believed that Galileo had discovered two moons around Mars.”
But Galileo did not discover
them and they remained undiscovered for more than two hundred fifty
years. Strangely, Koestler passes over the incident without
expressing wonder at Kepler’s seeming prescience.
As I have shown in Worlds in Collision (“The Steeds of Mars” )
the poets Homer and Virgil knew of the trabants of Mars,
visualized as his steeds, named Deimos (Terror) and Phobos
(Rout). Kepler referred to the satellites of Mars as being “burning” or
“flaming” , the same way the ancients had referred to the steeds of
Mars.
Ancient lore preserved traditions from the time when Mars, Ares of the
Greeks, was followed and preceded by swiftly circling satellites with
their blazing manes.
“When Mars was very
close to the earth, its two trabants were visible. They
rushed in front of and around Mars; in the disturbances that took
place, they probably snatched some of Mars’ atmosphere, dispersed as
it was, and appeared with gleaming manes”
(Worlds in Collision, p.
230).
Next, Galileo made
the discovery that Venus shows phases, as the Moon does. This time he
secured his secret by locking it in a cryptogram of a mere collection of
letters—so many A’s, so many B’s, and so on. Kepler again tried
to read the cryptogram and came up with the sentence:
“Macula rufa in Jove est
gyratur mathem etc.” which in translation reads: “There is a red
spot in Jupiter which rotates mathematically.”
The wondrous thing is: how
could Kepler have known of the red spot in Jupiter, then not yet
discovered? It was discovered by J. D. Cassini in the 1660’s,
after the time of Kepler and Galileo. Kepler’s assumption that Galileo
had discovered a red spot in Jupiter amazes and defies every statistical
chance of being a mere guess. But the possibility is not excluded that
Kepler found the information in some Arab author or some other source,
possibly of Babylonian or Chinese origin. Kepler did not disclose what
the basis of his reference to the red spot of Jupiter was — he could not
have arrived at it either by logic and deduction or by sheer guesswork.
A scientific prediction must
follow from a theory as a logical consequence. Kepler had no
theory on that. It is asserted that the Chinese observed solar spots
many centuries before Galileo did with his telescope. Observing solar
spots, the ancients could have conceivably observed the Jovian red spot,
too. Jesuit scholars traveled in the early 17th century to
China to study Chinese achievements in astronomy.
Kepler was well versed in ancient writings, also knowledgeable in
medieval Arab authors; for instance, he quoted Arzachel to
support the view that in ancient times Babylon must have been situated
two and a half degrees more to the north, and this on the basis of the
data on the duration of the longest and shortest days in the year as
registered in ancient Babylon.1
Jonathan Swift, in his Gulliver’s Travels (1726) tells of
the astronomers of the imaginary land of the Laputans who asserted they
had discovered that the planet Mars has,
“two lesser stars, or
satellites, which revolve about Mars, whereof the innermost
is distant from the center of the primary planet exactly three of
[its] diameters, and the outermost Five; the former revolves in the
space of ten hours, and the latter in twenty-one-and-a-half; so that
the squares of their periodical times are very near in the same
proportion with the cubes of their distance from the center of Mars,
which evidently shows them to be governed by the same law of
gravitation that influences the other heavenly bodies.”
About this passage a
literature of no mean number of authors grew in the years after 1877,
when Asaph Hall, a New England carpenter turned astronomer,
discovered the two trabants of Mars. They are between five
and ten miles in diameter. They revolve on orbits close to their primary
and in very short times: actually the inner one, Phobos, makes
more than three revolutions in the time it takes Mars to complete
one rotation on its axis; and were there intelligent beings on Mars they
would need to count two different months according to the number of
satellites (this is no special case — Jupiter has twelve moons and
Saturn ten*), and also observe one moon ending its month three times in
one Martian day. It is a singular case in the solar system among the
natural satellites that a moon completes one revolution before its
primary finishes one rotation.
Swift ascribed to the Laputans some amazing
knowledge—actually he himself displayed, it is claimed, an unusual gift
of foreknowledge. The chorus of wonderment can be heard in the
evaluation of C. P. Olivier in his article “Mars” written
for the Encyclopedia Americana (1943):
“When it is noted how
very close Swift came to the truth, not only in merely
predicting two small moons but also the salient features of their
orbits, there seems little doubt that this is the most astounding
’prophecy’ of the past thousand years as to whose full authenticity
there is not a shadow of doubt.”
The passage in Kepler
is little known—Olivier, like other writers on the subject of Swift’s
divination, was unaware of it, and the case of Swift’s prophecy appears
astounding: the number of satellites, their close distances to the body
of the planet, and their swift revolutions are stated in a book printed
one hundred and fifty years to the year before the discovery of Asaph
Hall.
Let us examine the case. Swift, being an ecclesiastical dignitary
and a scholar, not just a satirist, could have learned of Kepler’s
passage about two satellites of Mars; he could also have learned of them
in Homer and Virgil where they are described in poetic
language (actually, Asaph Hall named the discovered satellites by
the very names the flaming trabants of Mars were known by from
Homer and Virgil); and it is also not inconceivable that Swift
learned of them in some old manuscript dating from the Middle Ages and
relating some ancient knowledge from Arabian, or Persian, or Hindu, or
Chinese sources. To this day an enormous number of medieval manuscripts
have not seen publication and in the days of Newton (Swift published
Gulliver’s Travels in the year Newton was to die), as we know from
Newton’s own studies in ancient lore, for every published tome there was
a multiplicity of unpublished classical, medieval, and Renaissance
texts.
That Swift knew Kepler’s laws, he himself gave testimony,
and this in the very passage that concerns us:
“. . . so that the
squares of their periodical times are very near in the same
proportion with the cubes of their distance from the center of Mars”
is the Third Law of Kepler.
But even if we assume that
Swift knew nothing apart from the laws of Kepler to make
his guess, how rare would be such a guess of the existence of two
Martian satellites and of their short orbits and periods? As to their
number, in 1726 there were known to exist: five satellites of Saturn,
four of Jupiter, one of Earth, and none of Venus. Guessing, one could
reasonably say: none, one, two, three, four, or five. The chance of
hitting on the right Figure was one in six, or the chance of any one
side of a die’s coming up in a throw. The smallness of the guessed
satellites would necessarily follow from their not having been
discovered in the age of Newton. Their proximity to the parent planet
and their short periods of revolution were but one guess, not two, by
anybody who knew of the work of Newton and Kepler.
The nearness of the
satellites to the primary could have been assumed on the basis of what
was known about the satellites of Jupiter and Saturn, lo, one of the
Galilean (or Medicean) satellites of Jupiter, revolves around the
giant planet in 1 day 18.5 hours (the satellite closest to Jupiter was
discovered in 1892 by Barnard and is known as the “fifth
satellite” in order of discovery; it revolves around Jupiter, a planet
ten thousand times the size of Mars, in 1 1.9 hours). The three
satellites of Saturn discovered by Cassini before the days
of Swift - Tethys, Dione and Rhea - revolve respectively in 1 day
21.3 hours, 2 days 17 hours, and 4 days 12.4 hours. (Mimas and Enceladus,
discovered by Herschelin 1789, revolve in 22. 6 hours and 1 day
8.9 hours.) The far removed satellites of Jupiter were not yet
discovered in the days of Newton and Swift.
It remains to compare the figures of Swift with those of Hall:
there was no true agreement between what the former wrote in his novel
and what the latter found through his telescope. For Deimos, Swift’s
figure, expressed in miles from the surface of Mars, is 18,900 miles;
actually it is 12,500 miles; Swift gave its revolution time as 21.5
hours—actually it is 30.3 hours. For Phobos, Swift’s figures are 10,500
miles from the surface and 10 hours revolution period, whereas the true
Figures are 3,700 miles and 7.65 hours. Remarkable remains the fact that
for the inner satellite Swift assumed a period of revolution,
though not what it is, but shorter than the Martian period of rotation,
which is true.
However, Swift did
not know the rotational period of Mars and therefore he was not
aware of the uniqueness of his figure. If he were to calculate as an
astronomer should, he would either have decreased the distance
separating the inner satellite from Mars - a distance for which he gave
thrice its true value - or increased its revolution period to comply
with the Keplerian laws by assuming the specific weight of Mars as
comparable with that of Earth. But Swift had no ambitions toward
scientific inquiry in his satirical novel.
References
1.
The reference is found in the collected works of Kepler (Astronomica
opera omnia, ed. C. Frisch, vol. VI, p. 557) published in 1866.