Broca's Brain - Carl Sagan [57]
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