“As we try to understand science’s startling decline over the last half century, so shortly after reaching its pinnacle in the first half of the twentieth century, we might look to Rousseau’s influence for insight.”

When Neil Armstrong and Buzz Aldrin stepped onto the lunar surface in 1969, it marked the end of perhaps the most productive period of scientific research and application, beginning with the publication of Albert Einstein’s special theory of relativity in 1905. Universities were teeming with mathematically gifted students studying science, mathematics, and engineering, and preparing for exciting futures in the unlimited vistas of science. What went wrong?

A Strange Business

Science is a strange business. Classically, scientists worked with models involving terms such as “particle,” “wave,” and “force,” whose origins lay in pre-scientific perceptual experience. The frames of experience, such as Euclidean three-dimensional space and linear time, and the underlying hypotheses concerning regularity, such as causality, had their origins in the ordinary understanding of nature. But this ordinary understanding was put aside when Isaac Newton stated, “Whatever is not deduced from the phenomena . . . [has] no place in experimental philosophy.” While Newton’s breakthrough was immediately put into practice, only with the advent of quantum mechanics and general relativity in the twentieth century did it become fully apparent that the mathematical apparatus, not ordinary understanding, was of prime concern.

Erwin Schrödinger summarized the matter well when he contemplated the possibility of a model arising from ordinary human experience characterizing nature at the quantum level: “A completely satisfactory model of this type is not only practically inaccessible, but not even thinkable. Or, to be precise, we can, of course, think it, but however we think it, it is wrong; not perhaps quite as meaningless as a ‘triangular circle,’ but much more so than a ‘winged lion.’”

Turning to biology, the human cell—a system with tens of thousands of interconnected genes and proteins—is not imaginable from ordinary human experience, because no perceptual experience of such complexity exists. Nevertheless, we can productively build mathematical models corresponding to cellular behavior. Science as modeling behavior was the fundamental insight of Galileo and Newton. The latter constructed mathematical laws describing gravitational behavior without knowing the physical nature of gravity. In the words of historian Morris Kline, “Our mental constructions have outrun our intuitive and sense perceptions.”

The key to making all of this work is a protocol for tying these mental constructions to nature. In a previous article in Public Discourse, I listed four requirements for a scientific theory:

1. It takes the form of a model formulated in a mathematical system.
2. Precise relationships are specified between terms in the theory and measurements of corresponding events.
3. There are validating experimental data—that is, a set of future quantitative predictions derived from the theory and the corresponding measurements.
4. A rigorous statistical analysis supports acceptance of the theory based on concordance between the predictions and the measurements.

These criteria constitute a protocol for integrating reason and observation. Could such a protocol be popularized? More importantly, can we expect willing submission to such strict demands?

Rousseau’s Rejection of Science

Published in 1687, Isaac Newton’s Philosophiæ Naturalis Principia Mathematica swept the educated world. Yet only sixty-seven years later, Jean-Jacques Rousseau, in his Discourse on the Origins of Inequality among Mankind, rejected the connection to phenomena. In his Introductory Remarks he wrote, “Let us begin therefore, by laying aside facts, for they do not affect the question.” His anthropology of primitive man was not affected by facts; it was not tied to nature via observation. Absent data, he said he would read the book of nature: “You shall hear your history such as I think I have read it, not in books composed by those like you, for they are liars, but in the book of nature which never lies.” Rousseau’s arguments were not subject to observations because he declared these to be irrelevant.

Rousseau went on to assure his readers of his certainty. True, his argument was based on conjectures, but, he stated, “the consequences I mean to deduce from mine will not be merely conjectural, since, on the principles I have just established, it is impossible to form any other system, that would not supply me with the same results, and from which I might not draw the same conclusions.” Any conjectural system would yield his conclusions, so long as the system satisfied him, that is, produced the same conclusions.

Having eliminated observation, in his immensely influential work The Social Contract (1762), Rousseau went on to reject logic when he stated the fundamental problem to be solved by the social contract: “The problem is to find a form of association which will defend and protect with the whole common force the person and goods of each associate, and in which each, while uniting himself with all, may still obey himself alone, and remain as free as before.” Consider the “logic.” Statement X: A person will always be as free as before, meaning in the state of nature, where he is free to do anything he desires. Statement not-X: He will not always have such freedom, in particular, when the state says that he cannot do something he desires. Rousseau proposes to show X and not-X, thereby denying the law of contradiction.

As we try to understand science’s startling decline over the last half century, so shortly after reaching its pinnacle in the first half of the twentieth century, we might look to Rousseau’s influence for insight. According to Will and Ariel Durant, “He had not appealed to the learned and lofty with logic and argument; he had spoken to the people at large with feeling and passion in language that they could understand.” Very few people possess the ability and temperament to engage in the rigors of science and accept the discipline of logic, especially regarding issues they hold personally dear. It is much easier to embark on a fantasy as Rousseau does in his Discourse on Inequality, unfettered by facts, perhaps assisted by massive computer simulations that output childish visualizations or by running huge amounts of data through data-mining algorithms—in both cases producing results whose relation to nature will never be validated.

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