You’re much more likely to hear “common sense” invoked as a concept at a cocktail party than at a scientific discussion. In fact, common sense should be invoked more often in scientific discussions, where it is sometimes deficient and scorned. Scientists may string out a detailed argument that reaches an implausible conclusion contradicting common sense. But many other scientists nevertheless accept the implausible conclusion, because they get caught up in the details of the argument.

I was first exposed to this fallacy when my high school teacher of plane geometry, Mr. Bridgess, gave us students a test consisting of a 49-step proof on which we had to comment. The proof purported to demonstrate that all triangles are isosceles, i.e. have two equal sides. Of course that conclusion is wrong: most triangles have unequal sides, and only a tiny fraction has two equal sides. Yet there it was, a 49-step proof, couched in grammatically correct language of geometry, each step apparently impeccable, and leading inexorably to the patently false conclusion that all triangles are isosceles. How could that be?

None of us geometry students detected the reason. It turned out that, somewhere around step 37, the proof asked us to drop a perpendicular bisector from the triangle’s apex to its base, then to do further operations. The proof tacitly assumed that that perpendicular bisector did intersect the triangle’s base, as is true for isosceles and nearly-isosceles triangles. But for triangles whose sides are very unequal in length, the perpendicular bisector doesn’t intersect the base, and all of the proof’s steps from step 38 onwards were fictitious. Conclusion: don’t get bogged down in following the details of a proof, if it leads to an implausible conclusion.

Distinguished scientists who should know better still fall into equivalents of Mr. Bridgess’s trap. I’ll tell you two examples. My first example involves the famous Michelson-Morley experiment, one of the key experiments of modern physics. Beginning in 1881, the American physicists A.A. Michelson and E.W. Morley measured that the speed of light in space did not depend on light’s direction with respect to the Earth’s direction of motion. This discovery became explained only two decades later by Albert Einstein’s theory of relativity, for which the Michelson-Morley experiment offered crucial support.

Another two decades later, though, another physicist carried out a complicated re-analysis of Michelson’s and Morley’s experiment. He concluded that their conclusion had been wrong. If so, that would have shaken the validity of Einstein’s formulation of relativity. Of course Einstein was asked his assessment of the re-analysis. His answer, in effect, was: “I don’t have to waste my time studying the details of that complex re-analysis to figure out what’s wrong with it. Its conclusion is obviously wrong.” That is, Einstein was relying on his common sense. Eventually, other physicists did waste their time on studying the re-analysis, and did discover where it had made a mistake.

That example of Mr. Bridgess’s fallacy comes from the field of physics over 80 years ago. My other example comes from the field of archaeology today. Throughout most of human pre-history, human evolution was confined to the Old World, and the Americas were uninhabited. Humans did eventually penetrate from Siberia over the Bering Strait land bridge into Alaska during the last Ice Age. But, for thousands of years thereafter, they were still prevented from spreading further south by the ice sheet that stretched uninterruptedly across Canada, from the Pacific Ocean to the Atlantic Ocean.

The first well-attested settlement of the Americas south of the Canada/U.S. border occurred around 13,000 years ago, as the ice sheets were melting. That settlement is attested by the sudden appearance of stone tools of the radiocarbon-dated Clovis culture, named after the town of Clovis, New Mexico, where the tools and their significance were first recognized. Clovis tools have now been found over all of the lower 48 U.S. states, south into Mexico. That sudden appearance of a culture abundantly filling up the entire landscape is what one expects and observes whenever humans first colonize fertile empty lands.

But any claim by an archaeologist to have discovered “the first X” is taken as a challenge by other archaeologists to discover an earlier X. In this case, archaeologists feel challenged to discover pre-Clovis sites, i.e. sites with different stone tools and dating to before 13,000 years ago. Every year nowadays, new claims of pre-Clovis sites in the U.S. and South America are advanced, and subjected to detailed scrutiny. Eventually, it turns out that most of those claims are invalidated by the equivalent of technical errors at step 37: e.g., the radiocarbon sample was contaminated with older carbon, or the radiocarbon-dated material really wasn’t associated with the stone tools. But, even after complicated analyses and objections and rebuttals, a few pre-Clovis claims have not yet been invalidated. At present, the most widely discussed such claims are for Chile’s Monte Verde site, Pennsylvania’s Meadowcroft site, and one site each in Texas and in Oregon. As a result, the majority of American archaeologists currently believe in the validity of pre-Clovis settlement.

To me, it seems instead that pre-Clovis believers have fallen into the archaeological equivalent of Mr. Bridgess’s fallacy. It’s absurd to suppose that the first human settlers south of the Canada/U.S. border could have been airlifted by non-stop flights to Chile, Pennsylvania, Oregon, and Texas, leaving no unequivocal signs of their presence at intermediate sites. If there really had been pre-Clovis settlement, we would already know it and would no longer be arguing about it. That’s because there would now be hundreds of undisputed pre-Clovis sites distributed everywhere from the Canada/U.S. border south to Chile.

As Mr. Bridgess told us plane geometry students, “Use common sense, and don’t be seduced by the details. Eventually, someone will discover the errors in those details.” That advice is as true in modern science as it is in plane geometry.