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KRONOS Vol III, No. 2
SAGAN'S APPENDICES: A Quick Appendictomy
C. J. Ransom
At the 1974 AAAS meeting, Carl Sagan claimed that the odds against the events occurring in the Solar System, as described by Velikovsky, were 1023 to 1. This figure was widely quoted in the scientific and popular literature as "proof' that the events did not happen; it was also taken on faith since no statistical verification was ever provided.
The mathematical support for 1023 to 1 was supposed to be found in an appendix to the text that Sagan gave to the press. The appendix was not supplied with the rest of the paper, however, much to Sagan's benefit. In fact, it was well over a year after the AAAS conference was no longer newsworthy before the appendix saw much circulation. Even then, Sagan failed to substantiate his widely quoted probability figure of 1013 to 1; and the origin of that particular number remains a mystery (Cf. C. J. Ransom, The Age of Velikovsky, pp. 228-230).
Students who are informed about various subjects but do not happen to know the answer to a given test question often use a standard smokescreen technique. Instead of leaving the space blank, the student answers a question slightly related in appearance to the question asked, but the answer in reality has nothing to do with the correct solution. Sagan's so-called probability calculation resembles this technique. He seems to draw a number out of a hat and then claims that number as the probability that the events occurred.
Sagan becomes his most disingenuous when he incorrectly states that "Velikovsky believes in several statistically independent collisions in a few hundred years". About this assumption, Professor Robert W. Bass, a Rhodes Scholar and expert in celestial mechanics, had this to say: At the AAAS Symposium on Velikovsky, Sagan "claimed that the odds against multiple planetary near-collisions were 1023 to 1. When I asked him afterwards how he could have computed this without employing "ergodic theory", Sagan told me that the proof would appear as an Appendix to a forthcoming paper by him based on his AAAS presentation. He mentioned that he had followed a published method, used by such scientists as Öpik and Urey, to obtain apparently reasonable statistics about meteoritic collisions with the Moon, Mars, and Venus; but in such calculations it is assumed (as an approximation) that the collisions were statistically independent events. Because the planetary motions inherently tend under their mutual gravitational attractions toward some sort of quasi periodicity, in which future near-misses can be causally related to past near-misses, this assumption is absolutely identical to the assumption that Newton's Law of Gravity may be ignored! (That is, the planets are regarded as non-interacting random billiard balls, an approximation used in the kinetic theory of gases.) For the reason indicated (planetary masses are comparable while the analogy with meteoritic collision seems of questionable applicability), I am skeptical of Professor Sagan's figure of 1023 to 1. (See R. W. Bass, "Can Worlds Collide?" KRONOS I:3, November, 1975, p. 60–emphasis in text).
Sagan's calculation for a planetary collision was also based on the erroneous premise that the surfaces of Venus and Earth actually "scraped". It is obvious from Worlds in Collision (p. 372) that this is not what Velikovsky suggested. To support his incorrect grazing collision assumption, Sagan referred to what he claimed was a statement on page 87 of Worlds in Collision–"The waters were piled up to the height of sixteen hundred miles, and they could be seen by all the nations of the earth". The statement is not there. It is on page 72. But it does not matter what page Sagan had in mind. It is quite clear that Velikovsky never intended to convey the idea of a grazing collision. The statement in question was not taken literally by Velikovsky and is followed by an immediate qualifier "The figure in this sentence intends to say that the heap of water was tremendous." Nothing more, nothing less. Furthermore, a Venus approach to the Earth within one or two Earth-radii would exceed the Roche limit of both bodies, something which the historical records appear to rule out.
To cloud the issue further, Sagan estimates the probability that one of the Apollo objects (either dead comets or asteroids) would be the size of Venus. This is totally irrelevant to the argument at hand; it is as useful as measuring all the Hondas in the world and then calculating the probability of finding one the size of a Mack truck.
In a six-part NASA news release series of 1976, Sagan described the Viking mission and some of what scientists expected from the Viking probes. While discussing the possibility of life on Mars, Sagan said that he had heard many odds quoted including "a million to one against". Following this, Sagan said, "When I hear such high odds, I always lay my dollar down".
Regarding the planetary scenario postulated by Velikovsky, Sagan claims to have calculated the odds against it as being 1023 to 1. Although this figure was shown to be spurious, the odds stated are such that Sagan, by his own reasoning, would certainly have to bet that Velikovsky was right.
Finally, we may appropriately conclude this section with a statement by Chris Sherrerd: "The basic issue is not whether we can prove the plausibility or non-plausibility of Dr. Velikovsky's hypothesis, but rather how much do the ancient historical records and oral traditions have to say to the physical sciences? The answer is–a great deal, to him who is willing to set aside his bondage to the religious dogmas of scientistic humanism long enough to listen, and to seriously subject to honest scientific investigations what he hears."
Sagan's second appendix approaches accuracy only when he admits that one of the often quoted "scientific proofs" used against Velikovsky's ideas throughout the fifties and sixties was actually false. It was argued by astronomer Cecilia Payne-Gaposchkin and others that if the Earth stopped rotating, everything not tied down would exit the Earth at 900 miles per hour. Sagan, as did hundreds of open-minded investigators before him, realized that this was not true.
When one is in the business of setting up straw men, if one fails, another must be introduced. So Sagan provided another calculation supposedly demonstrating that, if the Earth stopped, the average temperature increase would be anywhere from 100°K to 240°K. However, this is based on the erroneous assumption that all of the Earth's energy would be directly converted into fairly evenly distributed heat. Similar false reasoning about airplanes would lead to the conclusion that passengers should notice a large temperature rise upon landing.
It should also be mentioned that Sagan perpetuated the mistaken notion that Velikovsky insists that the Earth actually stopped rotating during the time of Joshua (Cf. Worlds in Collision, "The Most Incredible Story," p. 44; "Epilogue," pp. 385-387). This type of mistake is often made by Sagan and others when dealing with Velikovsky's ideas; and such errors are then used to support the claim that Velikovsky's work should not be investigated.
Appendix Three deals with the "present temperature of Venus if heated by a close passage to the Sun". This appendix is entirely erroneous. It is based upon Sagan's misrepresentation of page 77 of Worlds in Collision and his obvious misunderstanding of page 371. Moreover, it concludes with a useless calculation relating to a completely inaccurate thermal model of Venus.
Sagan incorrectly implies that, according to Velikovsky's theory, Venus was heated only by a close approach to the Sun. Sagan assumed that Venus was at a certain temperature (6000°K) 3500 years ago, that it received no additional heat from the Sun, and radiated perfectly since that time. The temperature he then calculated for Venus today (79°K) was naturally much lower than the actual present temperature of the planet. This enabled Sagan to claim that Venus could not have been 6000°K 3500 years ago. But, by the same logic, Venus must have been hotter than 6000°K 3500 years ago, even if Velikovsky had never presented his theory.
By omitting any reference to the material presented on page 371 of Worlds in Collision, Sagan is able to conclude Appendix Three by invoking his own pet theory–"The Venus Greenhouse Effect". Indeed, it would appear that this was the sole reason for Appendix Three's existence. However, the untenable position of the Venus greenhouse theory has been duly discussed elsewhere in this issue ("The Venus 'Greenhouse Theory'–Debunked"; see also Velikovsky Reconsidered, N. Y., 1976, pp. xxii-xxviii; Yale Scientific Magazine, April, 1967, pp. 9-10 and references 19 and 20 of p. 10).
Interestingly enough, in his book The Cosmic Connection (1973), Sagan passed the following comment about the Venus greenhouse theory. "I had earlier proposed a specific theory, in terms of the greenhouse effect, to explain how the surface of Venus could be at such high temperatures. But my conclusions against cold-surface models in 1968 did not depend upon the validity of the greenhouse explanation: It was just that a hot surface explained the data and a cold surface did not" (p. 84–emphasis added).
In this appendix and in other instances, Sagan stresses that Velikovsky did not make a certain calculation, as if this negated the concept, demonstrated that the idea was not worth considering, or that this was unprecedented in the scientific community. However, Laplace, one of the world's finest mathematicians, presented the nebular theory for the origin of the Solar System and gave no mathematical support for his cosmological hypothesis. This theory is still widely acclaimed. Like Laplace, Velikovsky did not present his reconstruction of the recent activity of the Solar System in mathematical terms. Unlike Laplace, Velikovsky's model was based, to a considerable extent, on ancient observational data.
The title of Appendix Four–"Magnetic Field Strengths Necessary to Circularize an Eccentric Cometary Orbit"–makes it clear that this appendix has little, if anything, to do with the total thesis of Worlds in Collision. Although Velikovsky clearly and correctly suggested in 1950 that electromagnetic fields played a greater role in the Solar System than most scientists then thought, his model for orbital changes was fully compatible with those forces responsible for the behavior of comet Oterma III. "Before 1938 Oterma III had an orbit entirely between the orbits of Jupiter and Saturn. During a near approach to Jupiter in that year it changed its orbit so that it was entirely between Mars and Jupiter" (R. W. Bass, "Did Worlds Collide?" Pensée VIII, Summer, 1974, p. 15).
Furthermore, according to Bass, "if one removed Venus from its present orbit and gave it the initial conditions of the comet Oterma III, the initial orbit of Venus would lie entirely between the orbits of Saturn and Jupiter, while in less than two decades, Venus would work itself inward into an orbit lying entirely between the orbits of Mars and Jupiter! . . . Thus we can be quite sure that the solar system is not stable in the sense of Laplace and Littlewood" (R. W. Bass, "Can Worlds Collide?" KRONOS 1:3, p. 68; Bass, Pensée, Ibid.; R. W. Bass, "'Proofs' of the Stability of the Solar System," KRONOS II:2, November, 1976, p. 28; see also R. A. Lyttleton, The Comets and Their Origin, Cambridge, 1953, p. 13, Fig. 3).
For additional commentary on the circularization problem, the reader is referred to pages 82 and 99 in the articles by Greenberg and Juergens, respectively, elsewhere in this issue.
Sagan concluded Appendix Four with irrelevant remarks about rock magnetization. More relevant comments about magnetic field reversals and the remanent magnetic field evidence in rocks can be found in Earth in Upheaval, "Magnetic Poles Reversed" and a forthcoming paper by Ralph Juergens–"Geogullibility and Geomagnetic Reversals".
Overall, Sagan's appendices exhibit the same critical sloppiness as the text which they pretend to support. They have very little to do with Velikovsky's historical model of the recent events in the Solar System and are as error-filled as the rest of the paper. Anyone with a physics background, and especially anyone with this background who is familiar with Velikovsky's ideas, should read these appendices since they demonstrate the depths to which one can go when one considers himself so great an authority that he does not need to think about what he writes.
C. J. Ransom