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Laplace: no more to be desired than the perfection of analysis (1796)

August 14, 2019

SOURCE: Pierre-Simon Laplace. Exposition du Système du Monde, Paris, 1796.
Translation of passage found in J. Lequeux. Le Verrier: Magnificent and Detestable Astronomer. Springer, 2013.

SETTING: Newtonian mechanics ruled the day and there were no experimental anomalies and confidence in its infallibility of a natural law was growing.


In the midst of the infinite variety of phenomena that evolve continually in the heavens and on the earth, we have arrived at unraveling the small number of general laws that matter follows in its movements. Everything in nature obeys them; everything follows from them with the same necessity as the return of the seasons; the curve followed by the light atom that the wind carries away by chance is regulated in the same definite manner as the orbits of the planets…. Geometers … have at last reduced all of mechanics to general formulas that leave nothing to be desired but the perfection of analysis.


If you think we have all the fundamental laws of nature down and the rest is just a matter of perfecting analysis, you are not alone. Laplace was sure of that too … in 1796, as we saw in the above extract.

In contrast to this Laplacian outlook of naive and supreme confidence in the theory were views of people like Leibniz who 80 years earlier, in correspondences with Clarke [3], outlined his philosophical objections of Newtonian mechanics. In Leibniz’s view, Newtonian theory assumed absolute spatial coordinates, whereas there can only be relational dynamics. The Leibnizian outlook, and criticism of Newtonian theory, was well grounded. It took about two hundred years for others to fully appreciate Leibniz’s objections.

Newton himself had philosophical issues with his own theory too, in particular the implicitly assumed action-at-a-distance nature of Newtonian mechanics. In his letter to Bentley in 1692 he said,

“It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance through a Vacuum, without the Mediation of anything else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.” [4]

And yet, we still had statements, like the one above from Laplace over a hundred years later, maintaining that Newtonian mechanics is nature’s theory of mechanics, and you just have to get used to the fact that we are done. There is nothing else to do except perfect analysis. You can imagine the gallery of innocents saying, “Look, Newtonian mechanics is RIGHT. There is no experiment that shows it to be wrong, after more than a hundred years of observations. All your objections are just useless and sterile philosophical objections. You can drop more stuff from towers; you can smash more things together; you can watch more orbits; and you can say violations of the theory are ‘just around the corner’, but you’re just wasting your time and our money.”

We know that the first real experimental crack in the Newtonian standard model of mechanics came in 1859 [2], although it took much longer to be fully accepted as a problematic find within science. Newtonian mechanics held on. As we know, Einstein, who ultimately upended Newtonian mechanics, was devoted to investigating “philosophical soft spots” in the theory. He was not motivated by experimental anomalies, such as Le Verrier’s anomalous perihelion precession of Mercury, which had more mundane interpretations, such as an unseen new planet, that did not threaten the underlying theory.

The Laplacian outlook that has confidence in the completeness of current basic science knowledge has never been a good bet in history, and I am not aware of any compelling argument that we live in a very special time where such confidence is suddenly warranted.

Besides the Laplacian Outlook and the Leibniz/Einstein Outlook, there is also a third kind of outlook. I will call it the Hamlet Outlook, calling to mind Hamlet’s admonition to Horatio:

“There are more things in heaven and earth, Horatio,
Than are dreamt of in our philosophy.” [5]

Hamlet, the ever dithering, ever ineffectual being, has no outlook except cowering in the face of fate and the mysteries of what might happen next. If Hamlet were a theoretical physicist today he would mope around, staring only at experimental web pages, maybe chasing a few anomalies here and there, drinking himself into a stupor when they turn out to be statistical fluctuations, yapping that we can never know anything except the pings and bings of experimental apparatuses (which, don’t get me wrong, are extremely important), and having very weak opinions about what could be revealed by experiment in the future, which of course he takes no role in shaping or planning. Those with the Hamlet outlook are worse than those with the Laplacian outlook since they do little and create no new ideas. At least Laplacians do something, often doing impressive calculations within the standard theory of the day, even if they have the wrong overall outlook, and might accidentally contribute to progress.

Nevertheless, the Laplacian outlook will always lose, you can count on it. It might take ten years, it might take thirty years, or it might take more than two centuries, as was the case for Newtonian mechanics, but it will lose. And taking on the Hamlet outlook means you will never contribute, but you might have some fun fighting others with swords. Now, wouldn’t you rather be a Leibniz or an Einstein, even if it takes everybody else a decade or even a century to catch up, and even if you might fall short in the end?


[1] Pierre-Simon Laplace. Exposition du Système du Monde, Paris, 1796.
[2] Translation of passage found in J. Lequeux. Le Verrier: Magnificent and Detestable Astronomer. Springer, 2013.
[3] Clarke, Samuel. A Collection of Papers, which passed between the late Learned Mr. Leibniz, and Dr. Clarke, In the Years 1715 and 1716. James Knapton Press, London, 1717.
[4] Cohen, I.B. Isaac Newton’s Papers & Letters on Natural Philosophy, 2nd ed. Harvard University Press, Cambridge, 1958.
[5] Shakespeare, William. Hamlet. First Folio, 1623.

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