Fear of Physics Read Free

this rod is proportional to its cross-sectional area (that is, a thicker rod will be stronger than a thinner rod made of the same material). A rod that is twice as thick has a cross-sectional area that is 4 times as large. So the weight of a supercow’s head is 8 times as great as that of a normal cow, but its neck is only 4 times stronger. Relative to a normal cow, the neck is only half as effective in holding up the head. If we were to keep increasing the dimensions of our supercow, the bones in its neck would rapidly become unable to support its head. This explains why dinosaurs’ heads had to be
so small in proportion to their gigantic bodies, and why the animals with the largest heads (in proportion to their bodies), such as dolphins and whales, live in the water: Objects act as if they are lighter in the water, so less strength is needed to hold up the weight of the head.
    Now we can understand why the physicist in the story did not recommend producing bigger cows as a way to alleviate the milk production problem! More important, even using his naive abstraction, we were able to deduce some general principles about scaling in nature. Since all the scaling principles are largely independent of shape, we can use the simplest shapes possible to understand them.
    There’s a lot more we could do with even this simple example, and I’ll come back to it. First I want to return to Galileo. Foremost among his accomplishments was the precedent he created 400 years ago for abstracting out irrelevancies when he literally created modern science by describing motion.
    One of the most obvious traits about the world, which makes a general description of motion apparently impossible, is that everything moves differently. A feather wafts gently down when loosened from a flying bird, but pigeon droppings fall like a rock unerringly on your windshield. Bowling balls rolled haphazardly by a three-year-old serendipitously make their way all the way down the alley, while a lawn mower won’t move an inch on its own. Galileo recognized that this most obvious quality of the world is also its most irrelevant, at least as far as understanding motion is concerned. Marshall McLuhan may have said that the medium is the message, but Galileo had discovered much earlier that the medium only gets in the way. Philosophers before him had argued that a medium is essential to the very existence of
motion, but Galileo stated cogently that the essence of motion could be understood only by removing the confusion introduced by the particular circumstances in which moving objects find themselves: “Have you not observed that two bodies which fall in water, one with a speed a hundred times as great as that of the other, will fall in air with speeds so nearly equal that one will not surpass the other by as much as one hundredth part? Thus, for example, an egg made of marble will descend in water one hundred times more rapidly than a hen’s egg, while in air falling from a height of twenty cubits the one will fall short of the other by less than four finger-breadths.”
    Based on this argument, he claimed, rightly, that if we ignore the effect of the medium, all objects will fall exactly the same way. Moreover, he prepared for the onslaught of criticism from those who were not prepared for his abstraction by defining the very essence of irrelevant: “I trust you will not follow the example of many others who divert the discussion from its main intent and fasten upon some statement of mine which lacks a hair’s-breadth of the truth and, under this hair, hide the fault of another which is as big as a ship’s cable.” 1
    This is exactly what he argued Aristotle had done by focusing not on the similarities in the motion of objects but on the differences that are attributable to the effect of a medium. In this sense, an “ideal” world in which there was no medium to get in the way was only a “hair’s-breadth” away from the real one.
    Once this profound