Broca's Brain: The Romance of Science

PROBLEM II. REPEATED COLLISIONS AMONGTHE EARTH, VENUS AND MARS

“THAT A COMET may strike our planet is not very probable, but the idea is not absurd” (page 40.) This is precisely correct: it remains only to calculate the probabilities, which Velikovsky has unfortunately left undone.

Fortunately, the relevant physics is extremely simple and can be performed to order of magnitude even without any consideration of gravitation. Objects on highly eccentric orbits, traveling from the vicinity of Jupiter to the vicinity of the Earth, are traveling at such high speeds that their mutual gravitational attraction to the object with which they are about to have a grazing collision plays a negligible role in determining the trajectory. The calculation is performed in Appendix 1, where we see that a single “comet” with aphelion (far point from the Sun) near the orbit of Jupiter and perihelion (near point to the Sun) inside the orbit of Venus should take at least 30 million years before it impacts the Earth. We also find in Appendix 1 that if the object is a member of the currently observed family of objects on such trajectories, the lifetime against collision exceeds the age of the solar system.

But let us take the number 30 million years to give the maximum quantitative bias in favor of Velikovsky. Therefore, the odds against a collision with the Earth in any given year is 3 ? 10⁷ to 1; the odds against it in any given millennium are 30,000 to 1. But Velikovsky has (see, e.g., page 388) not one but five or six near-collisions among Venus, Mars and the Earth-all of which seem to be statistically independent events; that is, by his own account, there does not seem to be a regular set of grazing collisions determined by the relative orbital periods of the three planets. (If there were, we would have to ask the probability that so remarkable a play in the game of planetary billiards could arise within Velikovsky’s time constraints.) If the probabilities are independent, then the joint probability of five such encounters in the same millennium is on the short side of (3 ? 10⁷/10⁸)^?5 = (3 ? 10⁴)^?5 = 4.1 ? 10^?23, or almost 100 billion trillion to 1 odds. For six encounters in the same millennium the odds rise to (3 ? 10⁷/10³)^?6 = (3 ? 10⁴)^?6 = 7.3 ? 10^?28, or about a trillion quadrillion to 1 odds. Actually, these are lower limits-both for the reason given above and because close encounters with Jupiter are likely to eject the impacting object out of the solar system altogether, rather as Jupiter ejected the Pioneer 10 spacecraft. These odds are a proper calibration of the validity of Velikovsky’s hypothesis, even if there were no other difficulties with it. Hypotheses with such small odds in their favor are usually said to be untenable. With the other problems mentioned both above and below, the probability that the full thesis of Worlds in Collision is correct becomes negligible.

PROBLEM III. THE EARTH’S ROTATION

MUCH OF THE indignation directed toward Worlds in Collision seems to have arisen from Velikovsky’s interpretation of the story of Joshua and related legends as implying that the Earth’s rotation was once braked to a halt. The image that the most outraged protesters seem to have had in mind is that in the movie version of H. G. Wells’s story “The Man Who Could Work Miracles”: The Earth is miraculously stopped from rotating but, through an oversight, no provision is made for objects that are not nailed down, which then continue moving at their usual rate and therefore fly off the Earth at a speed of 1,000 miles per hour. But it is easy to see (Appendix 2) that a gradual deceleration of the Earth’s rotation at 10^?2g or so could occur in a period of much less than a day. Then no one would fly off, and even stalactites and other delicate geomorphological forms could survive. Likewise, we see in Appendix 2 that the energy required to brake the Earth is not enough to melt it, although it would result in a noticeable increase in temperature: the oceans would have been raised to the boiling point of water, an event that seems to have been overlooked by Velikovsky’s ancient sources.

These are, however, not the most serious objections to Velikovsky’s exegesis of Joshua. Perhaps the most serious is at the other end: How does the Earth get started up again, rotating at approximately the same rate of spin? The Earth cannot do it by itself, because of the law of the conservation of angular momentum. Velikovsky does not even seem to be aware that this is a problem.

Nor is there any hint that braking the Earth to a “halt” by cometary collision is any less likely than any other resulting spin. In fact, the chance of precisely canceling the Earth’s rotational angular momentum in a cometary encounter is tiny; and the probability that subsequent encounters, were they to occur, would start the Earth spinning again even approximately once every twenty-four hours is tiny squared.

Velikovsky is vague about the mechanism that is supposed to have braked the Earth’s rotation. Perhaps it is tidal gravitational; perhaps it is magnetic. Both of these fields produce forces that decline very rapidly with distance. While gravity declines as the inverse square of the distance, tides decline as the inverse cube, and the tidal couple as the inverse sixth power. The magnetic dipole field declines as the inverse cube and any equivalent magnetic tides fall off even more steeply than gravitational tides. Therefore, the braking effect is almost entirely at the distance of closest approach. The characteristic time of this closest approach is clearly about 2R/v, where R is the radius of the Earth and v the relative velocity of the comet and the Earth. With v about 25 km/sec, the characteristic time works out to be under ten minutes. This is the full time available for the total effect of the comet on the rotation of the Earth. The corresponding acceleration is less than 0.1 g, so armies still do not fly off into space. But the characteristic time for acoustic propagation within the Earth-the minimum time for an exterior influence to make itself felt on the Earth as a whole-is eighty-five minutes. Thus, no cometary influence even in grazing collision could make the Sun stand still upon Gibeon.

Velikovsky’s account of the history of the Earth’s rotation is difficult to follow. On page 236 we have an account of the motion of the Sun in the sky which by accident conforms to the appearance and apparent motion of the Sun as seen from the surface of Mercury, but not from the surface of the Earth; and on page 385 we seem to have an aperture to a wholesale retreat by Velikovsky-for here he suggests that what happened was not any change in the angular velocity of rotation of the Earth, but rather a motion in the course of few hours of the angular momentum vector of the Earth from pointing approximately at right angles to the ecliptic plane as it does today to pointing in the direction of the Sun, like the planet Uranus. Quite apart from extremely grave problems in the physics of this suggestion, it is inconsistent with Velikovsky’s own argument, because earlier he has laid great weight on the fact that Eurasian and Near Eastern cultures reported prolonged day, while North American cultures reported prolonged night. In this variant there would be no explanation of the reports from Mexico. I think I see in this instance Velikovsky hedging on or forgetting his own strongest arguments from ancient writings. On page 386 we have a qualitative argument, not reproduced, claiming that the Earth could have been braked to a halt by a strong magnetic field. The field strength required is not mentioned but would clearly (cf. calculations in Appendix 4) have to be enormous. There is no sign in rock magnetization of terrestrial rocks ever having been subjected to such strong field strengths and, what is equally important, we have quite firm evidence from both Soviet and American spacecraft that the magnetic-field strength of Venus is negligibly small-far less than the Earth’s own surface field of 0.5 gauss, which would itself have been inadequate for Velikovsky’s purpose.

PROBLEM IV. TERRESTRIAL GEOLOGY AND LUNAR CRATERS

REASONABLY enough, Velikovsky believes that a near-collision of another planet with the Earth might have had dramatic consequences here-by gravitational tidal, electrical or magnetic influences (Velikovsky is not very clear on this). He believes (pages 96 and 97) “that in the days of the Exodus, when the world was shaken and rocked… all volcanoes vomited lava and all continents quaked.” (My emphasis.)

There seems little doubt that earthquakes would have accompanied such a near-collision. Apollo lunar seismometers have found that moonquakes are most common during lunar perigee, when the Earth is closest to the Moon, and there are at least some hints of earthquakes at the same time. But the claim that there were extensive lava flows and volcanism involving “all volcanoes” is quite another story. Volcanic lavas are easily dated, and what Velikovsky should produce is a histogram of the number of lava flows on Earth as a function of time. Such a histogram will, I believe, show that not all volcanoes were active between 1500 and 600 B.C., and that there is