Murray Gell-Mann’s ‘totalitarian principle’ is the modern version of Plato’s plenitude

Idea that whatever can exist does exist can guide scientific pursuits

Plato and Murray Gell Mann

Plato’s principle of plenitude is reborn in the modern belief, credited to Murray Gell-Mann (right), that whatever can exist must exist.

Left: © Marie-Lan Nguyen/Wikimedia Commons (CC-BY 2.5); Right: Joi/Wikimedia Commons (CC-BY 2.5)

Science, like baseball, has a lot of unwritten rules.

Every baseball player knows that you don’t flip your bat after hitting a home run, you never steal a base when you have a big lead, and you cover your mouth with your glove when having a conference on the mound. None of those regulations are codified in the official rules — it’s just how pros play the game.

In science, the official rulebook consists of the laws of nature — equations or otherwise precisely stated descriptions of nature’s behavior that enable scientists to make accurate predictions about how things happen in the world. Science’s unwritten rules aren’t so strict. They are merely guidelines, suggestions for how best to play the game but without the totalitarian force of true natural law.

One such less-than-totalitarian principle is known as the … totalitarian principle. It is commonly expressed as “whatever is not forbidden is compulsory.” In other words, whatever the laws of nature allow must, in fact, exist or happen.

That sounds a little bit like the opposite of totalitarianism, which would seem to require doing only what is compulsory, with everything else forbidden. And that’s just one of the confusions posed by the totalitarian principle discussed in a new paper by the historian Helge Kragh.

Kragh notes that the origin of the totalitarian principle in physics is usually attributed to Murray Gell-Mann, the Nobel laureate who died in May at the age of 89. But many sources, Kragh notes, claim that Gell-Mann borrowed the phrasing from T.H. White, author of the King Arthur story The Sword in the Stone.

True enough, White used the phrase “everything not forbidden is compulsory” in The Sword in the Stone; it was on signs above tunnel entrances in an ant colony. But that ant colony appeared only in the 1958 edition of The Once and Future King, in which The Sword in the Stone was incorporated. Nothing like the totalitarian principle phrasing was found in previous versions, Kragh reports.

Yet Gell-Mann first described the idea in 1956, two years earlier. In a paper concerned with new particles and the strong nuclear force, Gell-Mann asserted that for some particles “any process which is not forbidden by a conservation law actually does take place.” He called it an assumption that “is related to the state of affairs that is said to prevail in a perfect totalitarian state. Anything that is not compulsory is forbidden.”

Kragh doesn’t think Gell-Mann articulated the principle very clearly. For one thing, he was talking only about the strong force. And though he described his idea as related to totalitarianism, he had inverted the phrasing. So Kragh suggests that Gell-Mann doesn’t really deserve credit for originating the idea. Nevertheless, subsequent physicists often attributed the principle to Gell-Mann and sometimes labeled it as totalitarian. A 1969 paper, for instance, mentioned “an unwritten precept in modern physics, often facetiously referred to as Gell-Mann’s totalitarian principle, which states that in physics ‘anything which is not prohibited is compulsory.’”

In any case, the underlying idea definitely did not originate with Gell-Mann. It rather descends from the philosophy of Plato, who believed that all possible ideal “forms” should actually exist in physical reality. In the 1930s, philosopher-historian Arthur Lovejoy referred to that idea as the “principle of plenitude” and discussed how it had been applied by other philosophers throughout history. But while the plenitude principle’s influence was widely recognized in biology, its use by physicists seems relatively recent. Kragh suggests that the totalitarian principle is in essence the successor of the plenitude principle “specially adapted to modern physics.”

One example of plenitude reasoning in physics (without naming it that) came from Paul Dirac, the physicist who in 1931 predicted the existence of half magnets. (He called them magnetic monopoles — magnets with only a single pole, not both a north and a south.) Dirac’s quantum equations seemed to allow particles with a single magnetic pole to exist, and so, he decided, they probably did.

Subsequent searches have failed to find monopoles. But another hypothetical particle permitted by the laws of physics, the neutrino, did eventually turn up after nuclear reactors produced the particles copiously enough to enable their detection.

When Gell-Mann first mentioned the totalitarian principle, he recognized that depending on it posed a danger: Maybe there are laws you don’t know about. Thus the totalitarian principle offers physicists a two-sided blade. One, it suggests that if you discern that something is not forbidden, it’s a good idea to design an experiment to look for it. Two, if you look for it but don’t find it, then maybe that’s a sign that there’s some previously unknown law of nature that prevents it, and you should begin theoretical inquiries to look for the missing law. Kragh cites the discovery of baryon conservation in the 1950s as a consequence of failure to detect the decay of certain particles called baryons.

Similarly, failure to find magnetic monopoles led to investigations that produced the theory of cosmic inflation, the best current explanation of the early history of the universe. (Inflation indicates that monopoles very well could exist but that the rapid expansion of space in the early universe diluted their concentration so much that we would be unlikely to encounter one in our neighborhood today.)

In spite of such fruitful results from applying the totalitarian principle, it remains a mere guideline for scientific pursuits, not a guarantee of success. For one thing, it might not imply that anything that can exist does exist now — perhaps some possible things will come into existence only in the future. And saying that anything that’s possible must exist is inherently ambiguous because of the fuzzy meaning of the word possible. You never really know for sure what’s possible and what isn’t.

“What is considered physically or genuinely possible,” Kragh writes, “depends on the best scientific knowledge at any given time.”

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Tom Siegfried is a contributing correspondent. He was editor in chief of Science News from 2007 to 2012 and managing editor from 2014 to 2017.

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