Posts Tagged ‘proofs’

I think I was around 12 when I read about the famous thought experiment by Galileo that disproved the old notion of Aristotle that heavier bodies fall faster than lighter ones.

Suppose we have two stones, the first being lighter than the second. Release the two stones from a height to fall to Earth. Stone 2, being heavier than stone 1, falls more rapidly. If they are joined together, argues Galileo, then the combined object should fall at a speed somewhere between that of the light stone and that of the heavy stone since the light stone by falling more slowly will retard the speed of the heavier. But if we think of the two stones tied together as a single object, then Aristotle says it falls more rapidly than the heavy stone. How do the stones know if they are one object or two?

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I remember being stunned by the simplicity and elegance of the argument. No tower of Pisa needed, no pendulum, no inclined plane, nothing! Just a clever way of arranging thoughts.

In any case, I was telling my dad about this argument a couple of weeks ago. He asked me why then do pieces of paper fall to ground more slowly than rocks. It took me a few minutes to come up with a satisfactory answer.

Two questions then for you dear readers.

1. Where exactly does Galileo’s reasoning break down in the presence of air resistance?

2. What are your favorite examples of arguments in theoretical CS or math which are too clever for their own good?