If brain twisters like this tie your neurons in knots, you are not alone. In a nation that can’t even make the clocks on its VCRs stop blinking, it’s no wonder that such abstract logic escapes all but a select few. Those who fret about such failings blame the sorry state of science education, but a sure-to-be-controversial new book finds a more fundamental–and disturbing–cause. In “Uncommon Sense: The Heretical Nature of Science” (240 pages. Oxford. $23), published this month, physicist Alan Cromer argues that the formal thinking needed for math and science, far from being the natural development that psychologists since Piaget have claimed, represents an abnormal mode of thought. “Science and objective thinking are unnatural activities,” Cromer asserts. “The mind wasn’t designed to study physics.”
That became clear in the introductory-science courses that Cromer has taught at Northeastern University for 32 years. To get across the notion of volume and proportionality, for instance, he asks how many one-inch cubes it takes to fill a cube two inches on a side. “Many of my college students don’t get it, even when the blocks are on a table in front of them,” be says. Nor, given the right answer (eight), can they figure out how many of the little blocks fill a three-inchon-a-side cube (27). That requires what Piaget called “formal operational” thought, a stage of development that the Swiss psychologist said everyone masters at age 14 or so. Forget it, says Cromer. The mind is not hard wired for abstract, logical thought. “We no longer believe that our students come to us with the laws of physics buried in their heads,” he laments. Few students, or adults for that matter, master two other aspects of formal thought-noncontradiction and impossibility. Without them you cannot solve the long-lost-sister puzzle.
What is basic to the mind, argues Cromer, is the conceit that we have direct, intuitive knowledge of how the world works. If you shoot a projectile straight across an empty field, and simultaneously drop a projectile from the same height, which hits the ground first? No matter how often early scientists ran the experiment, everyone from Aristotle to Galileo insisted the dropped object would land first. Like Cromer’s students, they preferred to believe their intuition rather than their eves.
If science is an unnatural human activity, then, contrary to the prevailing scholarship, it must not be an inevitable development of civilization. In a quick tour of classical cultures, Cromer persuasively argues just that. While India and China, for instance, developed sophisticated technologies (gunpowder, paper) and practical math, they were not scientific. None developed the tradition of pure reason and deductive thinking that produced Euclid’s geometry and the discovery of irrational numbers (those, like the square root of two, that cannot be expressed as the ratio of two whole numbers like i or f). Science developed, instead, at only one time and in only one place: classical Greece. Give Cromer credit for championing the extremely on-fashionable “dead European male” view of history.
What did Greece have that other civilizations didn’t? Other cultures believed that individuals are directly connected to the natural world. That notion remains strong today, as evidenced by the widespread belief in astrology. Abandoning this connection is crucial to science, which requires an appreciation that there is an external reality separate from oneself. Greece, with its tradition of reasoned debate in the assembly, glorified objectivity. Also, the gods of the Homerian epics are subject to natural law and recognize impossibilities: if a god is asked for a favor, he responds, “if I can and if it is not impossible.” Such cultural nudges could have been enough to induce minds, at least some of them, to think scientifically.
Cromer’s conclusions have obvious implications for teaching science. If few students master formal, logical thinking, then science classes cannot assume such thinking. They must inculcate it. They must fill in the mental structures needed to understand science. Cromer doesn’t prescribe exactly how, but he makes a convincing case for a curriculum that respects the highly unnatural thinking that science requires.
As for Amy, Barbara and Carol. Assume Carol lied about there being two or three liars. Then none or one of the women lied. Carol, then, is the only liar. That means Amy and Barbara told the truth. But that is impossible–the man had only one lost sister. The assumption–that Carol lied–must be wrong, since it leads to a contradiction. Carol must be telling the truth–there are at least two liars, Amy and Barbara. Neither of them, then, can be the sister. Carol is.
