The Birth of Modern Science
In Two New Sciences, Galileo (1638) presents his theories in the form of a dialog among three people: Simplicio, who represents the views of Aristotle; Salviati, who represents Galileo; and Sagredo, who represents the intelligent layman. At one point, after discussing whether Aristotle had ever tested by experiment whether a heavier stone would fall to the ground faster than a lighter stone, Simplicio and Salviati continue:
Salviati [Galileo]: If then we take two bodies whose natural speeds are different, it is clear that on uniting the two, the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter. Do you not agree with me in this opinion? Simplicio [Aristotle]: You are unquestionably right.
Salviati [Galileo]: But if this is true, and if a large stone moves with a speed of, say, eight, while a smaller moves with a speed of four, then when they are united, the system will move with a speed less than eight; but the two stones when tied together make a stone larger than that which before moved with a speed of eight. Hence, the heavier body moves with less speed than the lighter one; an effect which is contrary to your supposition. Thus, you see now, from your assumption that the heavier body moves more rapidly than the lighter one, I infer that the heavier body moves more slowly.
Simplicio [Aristotle]: I am all at sea... This is, indeed, quite beyond my comprehension...
Galileo had actually proved theoretically in 1604 that falling bodies are accelerated toward the ground at a constant rate. An object falling to the ground experiences what came to be known as uniformly accelerated motion. In fact, Galileo actually defined uniform acceleration in terms of the behavior of falling bodies. However, with the clocks and instruments available to him at the time, he could not directly test whether his theoretical predictions were correct. The legend that he dropped weights from the Leaning Tower of Pisa is very likely false.
Galileo realized that there was an indirect way of testing his theory. If an object is falling to the ground at a slower rate, as when a ball rolls down a smooth inclined plane, it can be timed with good accuracy. Galileo actually constructed such a plane and left detailed notes on his experiment (Figure 3.2). In Two New Sciences, it is Salviati who describes in great detail how the hundreds of experiments were performed. By changing the angle of inclination and determining the acceleration of the ball as it rolled down, Galileo was able to infer that in the limiting case, when the
FIGURE 3.2 Picture painted in 1841 by G. Bezzuoli. Galileo (the tall man in the center, pointing with his right hand at the open book) demonstrates one of his experiments with the ball rolling down an inclined plane. Changing the angle of inclination of the plane allowed Galileo to infer that when the angle was 90° (vertical plane), the acceleration of the ball was also constant. He could not perform this last experiment because he lacked a timing device accurate enough to time the rapidly falling ball. (From the 1841 painting by G. Bezzuoli. Used with permission of Alinari/Art Resource, New York.)
angle was 90°, the acceleration, having been constant for all the other angles, had to be constant too. And 90° was, of course, free fall.
Thus, we see how Galileo not only was able to argue against the Aristotelian approach with his mathematical rationalism, but in the process, he established the modern scientific method from observation to hypothesis. From the mathematical analysis of the hypothesis, predictions are drawn, and these can in turn be tested by experimental observation. Galileo was aware of his having founded the experimental method. In Two New Sciences, he writes:
Salviati: ... we may say the door is now open, for the first time, to a new method fraught with numerous and wonderful results which in future years will command the attention of other minds.
Galileo (1638; reprint 1914, p. 243)
PIONEERS OF PHYSICS: GALILEO’S DIALOG WITH ARISTOTLE
Simplicio: Your discussion is really admirable; yet I do not find it easy to believe that a bird- shot falls as swiftly as a cannon ball.
Salviati: Why not say a grain of sand as rapidly as a grindstone? But Simplicio, 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 hairbreadth of truth and, under this hair, hide the fault of another, which is as big as a ship’s cable. Aristotle says that “an iron ball of one hundred pounds falling from a height of one hundred cubits reaches the ground before a one-pound ball has fallen a single cubit.” I say that they arrive at the same time. You find, on making the experiment, that the larger outstrips the smaller by two fingerbreadths; now you would not hide behind these two fingers the 99 cubits of Aristotle, nor would you mention my small error and at the same time pass over in silence his very large one.
Dialog Concerning Two New Sciences, 1638, translated by Henry Crew and Alfonso de Salvio (Macmillan, New York, 1914; reprinted by Dover, New York. With permission), pp. 64-65.