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 contra ...He apparently never understood the flaw, as his reasoning would imply that a nearly-isosceles triange must be isosceles.
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. ...
The proof tacitly assumed that that perpendicular bisector did intersect the triangle’s base, as is true for isosceles and nearly-isosceles triangles. ...
Conclusion: don’t get bogged down in following the details of a proof, if it leads to an implausible conclusion.
Mathematics is all about understanding what is a valid proof, and what is not. Diamond did not get the point.
It figures, as his books are filled with illogical arguments that he takes to be conclusive.
Here is his second example:
This discovery became explained only two decades later by Albert Einstein’s theory of relativity, for which the Michelson-Morley experiment offered crucial support.This is a funny one, because the textbooks agree that Michelson-Morley was crucial for the development and demonstration of relativity, but Einstein himself regarded it as unimportant for his contribution. That is because Einstein's work was largely a reformulation of Lorentz's, and Einstein relied on Lorentz's analysis of Michelson-Morley.
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.
The experiment was re-done many times. If Einstein did not care much about the first experiment, why would he bother with the subsequent ones? This is a story of indifference, not common sense.
Diamond ends up arguing that the Clovis ppl were the first settlers of the Americas. I have no idea about that.