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Laplace

Among those few who had more keenly critical minds than Voltaire and the other so-called philosophes, the metaphysics of Newton created an opposite reaction. By questioning it, his contemporaries, Berkeley (1685-1753) and Hume, established scientific empiricism and laid the foundations for our contemporary scientific method. Just as the leading philosophers ot England (soon followed by Hegel, 1770-1831) pierced Newton’s metaphysical fog, so the leading scientists of France refused to climb the bandwagon of secular Newtonianism and kept in mind the distinction between what Newton had proved and what he had not proved. Historians usually ascribe the reserve of the Academic des Sciences towards Newton to an obscurantist clinging to Cartesian tradition; but these strictures of the French scientists gave the impetus to the studies of Laplace, the greatest genius in mathematical astronomy since Newton. With the emergence of Laplace, gravitational celestial mechanics was more firmly established and the role of providence in sustaining the immutable order was abrogated.

Laplace (1749-1827) was cited throughout the nineteenth century and also has been quotedby opponents of Velikovsky as having provided the mathematical proof that the solar system, and hence nature, is built like a mechanical clock. But this is only one side of his total view. In his Exposition du système du monde he uses two pages to argue that mankind should learn to accept without obsessive fear the likelihood that a comet may strike the Earth.1 In his other major work, Theorie analytique des probabilités, he insists that the motions of the Earth are not unalterable, being subject to several unpredictable forces, among which is the impact of meteorites.2 He realized that the resistance to accepting the alterability of the sky springs also from the fear that thereby moral law may be destroyed. For this reason he continues the discussion of this topic by delving into psychology and arguing along lines similar to that of Hume’s ethics, that a feeling of sympathy among men can exist without traditional metaphysics.3 It is worth noting that his treatment of psychology touches upon the importance of childhood memories and upon the role of unconscious thinking.4

Laplace observed that from his mathematical formulas it was possible to draw the conclusion that “nature has arranged everything in the sky to insure the permanence of the planetary system, with the same purpose that it seems to have adopted on Earth for the preservation of individuals and the perpetuation of species,”5 but he added that such a conclusion was wrong, even though “we are naturally inclined to believe that the order by which things seem to renew themselves on Earth has existed at all times and will exist forever.”6 In reality, the stability of the present order “is disturbed by various causes that can be ascertained by careful analysis but which are impossible to frame within a calculation.”7 He summed up his views in the words: Le ciel même, malgré l’ordre de ses mouvements n’est pas inalterable.8 He warned specifically that in his mathematical formulas about the solar system he had not taken comets into account, staling, just as specifically, that the motion of the Earth might be affected by meteorites, and one should therefore study the historical evidence, even though this evidence covers only a few millennia.

Laplace stressed that the human race is beset by a great fear that a comet may upset the Earth, a fear that manifested itself dramatically after Lexell’s comet in 1770 had passed at only 2,400,000 km from the Earth. Shorly thereafter Lalande published a list of the comets that had passed closest to the Earth.9 Men should be free from this fear, Laplace argued, for the probability of one striking the Earth within the span of a human lifetime is slim, even though the probability of such an impact occurring in the course of centuries is very great (très grande).10 He proceeded to describe the possible effects of a collision with a comet, painting a picture that is in close agreement with that outlined by Velikovsky. Much in the geology of the Earth and in human history could be explained by assuming that such an impact had taken place. However, if it is true. it must also ha assumed that the colliding cornei: naa a mass similar to that of the Earth.11 Velikovsky conjectures that this comet was Venus, which has the required mass.

Laplace summed up his hypothesis in these words:

 
 

The axis and the movement of rotation would be changed. The seas would abandon their ancient positions, in order to precipitate themselves toward the new equator; a great portion of the human race and the animals would be drowned in the universal deluge, or destroyed by the violent shock imparted to the terrestrial globe; entire species would be annihilated; all monuments of human industry overthrown; such are the disasters which the shock of a comet would produce, if its mass were comparable to that of the earth.

We see then, in effect, why the ocean has receded from the high mountains, upon which it has left incontestable marks of its sojourn. We see how the animals and plants of the south have been able to exist in the climate of the north, where their remains and imprints have been discovered; finally, it explains the newness of the human civilization, certain monuments of which do not go further back than five thousand years. The human race, reduced to a small number of individuals, and to the most deplorable state, solely occupied for a length of time with the care of its own preservation, must have lost entirely the remembrance of the sciences and the arts; and when progress of civilization made these wants felt anew, it was necesary to begin again, as if man had been newly placed upon the earth.

Scientific literature never mentions the Laplace statements listed above. He won immediate fame for having provided the mathematical proof of the stability of the solar system that was missing in Newton, despite the fact that he had emphatically warned against such an interpretation of his conclusions.

The interpretation of Laplace’s theories was influenced by a minor point he made. He felt the need to refute Newton’s argument that the fact that all the planets and their satellites rotate counterclockwise is proof of divine providence.12 After calculating the statistical near-impossibility that such rotation may be a chance arrangement, he concluded that it must be the result of a common mechanical phenomenon.13 Hence, he proposed the nebular hypothesis which had already occurred independently to the theologian Emanuel Swedenborg (1688-1722), to the philosopher Kant and to the astronomer Heinrich Lambert (1728-77). But Laplace did not yet know of the satellites that revolve clockwise, or of Venus’ clockwise rotation. The uniform direction of the rotation and revolution of the planets and their satellites, far from being a key point of his view, was considered by him to be a stumbling block to his probabilistic view of the universe.

The following quotation indicates to what distortions Laplace’s theories were subjected by the interpreters:

 
 

We are naturally led to ponder on the great truth of the stability and permanence of the solar system as demonstrated by the discoveries of Lagrange and Laplace... The arrangements, therefore, upon which the stability of the solar system depends, must have been the result of design, the contrivance of that omniscience which foresaw all that was future, and of that infinite skill which knew how to provide for the permanence of His work. How the comets, whose motions are not regulated by such laws, and which move in so many different directions, may in the future interfere with the order of the system, can only be conjectured. They have not interfered with it in the past, owing no doubt to the smallness of their density; and we cannot doubt that the same wisdom which has established so great a harmony in the movement of the planetary system, that the inequalities which necessarily arise from their mutual action arrive at a maximum, and then disappear, will also have made provision for future stability of the system.14

Since Laplace was concerned with eliminating providential order, he proved (within the limits of the formal rigour that was considered sufficient by mathematicians of his age) that the mutual gravitational influence of the planets cannot disrupt the system.15 But this is an empirical, not a metaphysical, conclusion which is valid only if other factors are excluded, that is, if it is assumed that the solar system is isolated in the universe, that the Sun does not suffer alteration, and that no other matter and no other forces beside gravitation and inertia are present in the space where the Sun and the planets move.

Interpreting Laplace as supporting the theological assumptions of Newton has destroyed the scientific achievements of the Renaissance. We are back at scholasticism, and Aristotle is again il maestro di color che sanno on an issue that Galileo considered central to the new thought. In the First Day in the Dialogue on the Great World Systems, wtlich is concerned with the refutation of the concept of the immutability of the heavens, the great astronomer formulated his creed in these uneauivocal terms:

I cannot without great wonder, nay more, disbelief, hear it being attributed to natural bodies as a great honour and perfection that they are impassible, immutable, inalterable, etc.: as, conversely, I hear it esteemed a great imperfection to be alterable, generable, mutable, etc. It is my opinion that the Earth is very noble and admirable by reason of the many and different alterations, mutations, generations, etc., which incessantly occur in it... I say the same concerning the Moon, Jupiter, and all the other globes of the Universe... These men who so extol incorruptibility, inalterability, etc., speak thus, I believe, out of the great desire they have to live long and for fear of death.16
Galileo is in precise agreement with Dewey’s argument and with Velikovsky’s psychological assumption.

Laplace was interpreted to meet the psychological need to believe in the eternal stability of the solar system. The following quotation from An Analytical View of Sir Isaac Newton’s Principia by H. P. Brougham and E. J. Routh are a good example of a general tendency:

The other changes which take place in the orbits and motions of the heavenly bodies, were found by these great geometricians [Laplace and Legendre] to follow a law of periodicity which assures the eternal stability of the system.
These changes in the heavenly paths and motions oscillate, as it were, round a middle point, from which they never depart on either hand, beyond a certain distance; so that at the end of thousands of years the whole system in each separate case (each body having its own secular period) returns to the exact position in which it was when these vast successions of ages began to roll.17

The religious tone of the presentation is obvious. Laplace is construed to be saying that heavenly bodies can have only two types of movements: cyclical movements and uniform rectilinear movements; that is, movements that are equivalent with a state of rest. It is a full return, with some added sophistication, to the Aristotelian doctrine that the heavenly bodies can have only circular motions, motions reconcilable with immobility.


References

  1. Oeuvres complètes (Paris, 1884), VI, 234.
  2. VII, p. cxx.
  3. VII, p. cxxiv.
  4. VII, p. cxxx.
  5. VI, p. 478.
  6. VII, p. cxx.
  7. VII, p. 121.
  8. Ibid.
  9. VI, 235.
  10. VI, 234.
  11. Ibid. (The following translation is by Kenneth Heuer, The End of the World (New York, 1953).
  12. VI, 479.
  13. A Philosophical Essay on Probabilities, transl. by F. W. Truscott and F. L. Emory (New York, 1951), Part II, Ch. IX, 97.
  14. David Brewster, Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton (Edinburgh, 1855), Vol. 1, 359-60.
  15. Several reviewers stated or intimated that the Newtonian theory is absolutely confirmed by the ephemerides. But, as every student of astronomy is taught, the Newtonian theory, in spite of the contributions of Laplace, is only nearly confirmed. The discrepancy between the predictions and the events may be explained by the inadequacy of our mathematical equipment in matters of three-body or n-body problems, or by the inadequcy of the theory, or by the possibility (which is extremely rarely mentioned in the texts of celestial mechanics) that a third factor may be at work besides gravitation and inertia.
  16. Dialogue on the Great World Systems, Ed. by Giorgio de Santillana (Chicago, 1953), 68-69.
  17. (London, 1885), 122, 124.

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