The Importance of Experimental Error

You have probably heard Galileo’s experiment wherein he verified that acceleration due to gravity does not depend on mass by releasing two cannonballs of different mass from the tower of Pisa and observed that they hit the ground at the same time. The problem is that it never happened. At least, I hope that it never happened.

The problem arises from uncontrolled variables. Acceleration due to gravity only matches actual acceleration when all forces other than gravity sum to zero. On the surface of the earth, however, one other force has significance in most problems: friction. Thus, when Galileo released the cannonballs and they gained speed, both gravity and friction acted upon them. FG is directly proportional to mass; friction approximately with surface area (if I recall correctly, it does not vary directly with surface area; however, my purpose here is to show the inequality between the actual rates of acceleration of the cannonballs, not the exact relationship). Mass varies with volume, or with r3; surface area varies with r2. Thus, the net force on the cannonball is not directly proportional to mass when at non-zero speed, and the larger cannonball falls faster. However, as FF would have been small relative to FG for a metal cannonball, the cannonballs would probably have appeared to hit the ground at the same time.

Yet if this had been the observed result, the experiment would have either (depending on whether Galileo attributed the difference to friction or to the antiquated theories) been inconclusive or even supported the theory that heavier objects have greater acceleration due to gravity. Only because of the error in collecting data did the experiment come to the correct conclusion.

This makes me wonder: how many conclusions of experimental science are due to such slight inaccuracies which may have produced an incorrect conclusion? As one obvious example, take Newtonian physics. Newtonian physics is not actually true, ignoring as it does relativity. However, because the effects of relativity are small, most experiments seem to verify Newtonian physics. Only after relativity was first hypothesized were sufficiently precise experiments designed. Thus, it seems to me that even the physical sciences are not, at their core, inductive, conducting experiments and then looking for relationships. Great changes in scientific theory arise from purely theoretical hypotheses later experimentally verified. Why, therefore, expect inductive reasoning, insufficient even in the physical sciences, to work in the social sciences?


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