Sometimes even the greats get it wrong

A really clever idea!

There is no doubt that Aristotle was one of the greatest thinkers there as every been. In the history of human intelligence he is definitely up there amongst the greats and in a way that is the problem.

This problem is not Aristotle's fault, after all he was well dead and buried for the majority of the time his legacy was causing problems. It is part of the human condition I suppose. To go up against a great man is to some how imply that you are equal or greater than the man and is ideas. This is wrong, but is often the way.

The upshot of this is that it can become more difficult to dispute the ideas of a great man after his death than during his life. As time goes on the ideas mature and solidify in the mind of those left behind, even if the idea is complete nonsense. One of these is Aristotle's idea on weight and its behaviour.

Aristotle believed that the falling speed of an object was proportional to its weight. The heavier the object the higher is "falling speed". This it turns out is complete rubbish. But it took almost 2000 years before it was proven to be well wide of the mark. Why did it take so long? two reasons I think. One is that it was actually difficult, without the use of an accurate clock, to come up with any experiment that could prove things one way or another. The other reason is that I think many people accepted Aristotle's thinking and did not both to question it.

Eventually both of these reasons were addressed and solved by Galileo. He solved it with the rather elegant experiment, he also raised doubt with an equally elegant thought experiment. It goes like this...

you have 2 stones, let's call them A and B. One, A, is twice the size and weight of the other, B.

Now according to Aristotle, the larger, A, of the two will fall fastest. Ok. But if we now tie the two together, with a long piece of string, what happens?

According to Aristotle, A will fall faster than B and at some point will be far enough ahead of B that the string will go taught.  B, the slower of the two will then actually slow down A, so the combination of A + B will be slower than A alone. Or would the two weights attached by the taught string suddenly realise the have a combined weight of A+B and start to fall even faster?

This is the paradox that confronts us if we choose to believe Aristotle.

The reality is that neither of the outcomes given above actually happens. Provided air resistance can be ignored, which it pretty much can for heavy weights, such as marble balls. All objects, irrespective of their individual weights fall at the same speed. (This experiment was performed on the moon using a feather and a hammer. There is no atmosphere on the moon to produce air resistance. The result was that the hammer and the feather fell at the same rate and touched the ground at the same time.)

What I think is really clever is the way the that Galileo proved this. He did a number of different experiments including dropping object from a large tower, what he found was that irrespective of the weight, they all fall at the same rate. He also discovered that this rate was not constant but changed, being dependent on the height of the fall.

He also did some clever work to determine the rate of the acceleration. He did not have a clock accurate enough to perform detailed measurements. So what he needed to do was slow things down, so that he could get away using a less accurate clock. He achieved this by rolling balls down slopes of different inclines. This is a far clever idea than it may first appear and is not at all as obvious as it seems in hindsight. Galileo discovered that

v = at + u (1)

v - velocity when you reach bottom of slope (or tower)
t - time it takes to reach the bottom
u - the initial velocity
a - acceleration

now equation (1) looks very similar to y = mx + c (equation of a straight line), so we would expect Galileo's equation to generate a straight line, which is what it does. What Galileo had discovered was a value for "a", which turns out to be acceleration due to gravity, these days taken to be about 10 m/s².

This is probably the first known calculation of the parameter.

What is interesting is that "a" is not a constant. It gets higher the further North or South of the equator we go. It also gets less the higher we get. So acceleration due to gravity at the top of Everest (28^oN) is lower than acceleration due to gravity at see level at 28^oN. This would have been unknown to Galileo though because the degree of accuracy to determine these differences was probably smaller than he could detect with experiments.


So it just goes to show that even the greats get it wrong sometimes. Newton, Einstein, they have all backed the odd donkey in their day. The point is that it does not matter that they have come up with some really shockers. The fact that they came up with anything at all is the important thing.

More important maybe that although they have had some truly brilliant insights it does not mean that they are infallible. Even their most amazing ideas must be held up for scrutiny. People should not feel intimidated when they do question the greats be them alive or dead.