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Cell["1.1 An example of thinking about physics.", "Section",
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The ancient Greek philosophers had the mistaken idea that gravitation was a \
natural tendency for objects to be attracted to an almost mystical place in \
the world. This special place was said to be the center of the Earth. The \
heavier an object was the more strongly attracted it would be to that center. \
In other words, their weight determined their proper place and they all \
settled into that place. This was their idea of gravity. Today scientists \
laugh at that idea, but what tells us that this idea is wrong? What is the \
right idea?
\tThe fact that the ancient Greek idea of gravity was wrong took a long time \
to be realized\[LongDash]over a thousand years went by, with brilloiant \
people studying it every day. It was Galileo that put the proverbial \
\[OpenCurlyDoubleQuote]nail in the coffin\[CloseCurlyDoubleQuote] of the \
Greek idea of gravity. His argument went something like this; \
note\[LongDash]I will enumerate the arguments so they are easier to follow \
(this will be a standard procedure for proofs and derivations):\
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We will assume that an object that is heavy falls faster than a lighter \
object as they are each trying to get to their proper place in the world. \
This explained why it was possible to pick up small objects, but not \
buildings or mountains\[LongDash]the latter being in their proper places. \
This is the idea promoted by Aristotle.\
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"What happens when we strap a lighter object to a heavy one? There are two \
possibilities; either the combined object acts like a single object, or it \
does not. This idea is an example of the ",
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". Something either is or it is not, there is no middle where they are both \
true. These possibilities led to the next two arguments."
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If the combination forms a single object, that single object is heavier than \
either of the two components. By the assumption in step 1 the single heavier \
object must fall faster than the heavier of the two component objects alone. \
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If the combination does not form a composite object, then, by the assumption \
made in step 1, the lighter object will fall slower than the heavier. Since \
they are connected by the strap, the lighter object will slow the rate of \
fall of the heavier object, so the combination will not fall as fast as the \
heavier object. (indeed, if the strap is even lighter, then it will also make \
things fall slower).\
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"These arguments lead to the prediction that the same combination of objects \
fall both faster and slower than the heavier of the two component objects. A \
situation where a given assertion leads to two or more opposing outcomes is \
called a ",
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". No assertion that leads to a contradiction can be true. This method of \
proof is ",
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StyleBox["reductio ad absurdum",
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". Let us say that you are trying to prove an assertion. The first step in a \
proof by contradiction is to assume your assertion to be false. You then show \
that this falsehood leads to a contradiction. Since no assertion leading to a \
contradiction can be true, the falsehood is then itself false. This proves \
your original assertion cannot be false. By the law of the excluded middle, \
it must then be true. This completes a proof by contradiction."
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"In this case we have proved that Aristotle's assertion that objects fall at \
a rate according to their weight is false; this is the same as proving that \
objects fall in a way that is independent of their weight. In fact, this \
principle is ",
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Having made the prediction that objects fall independently of their weights, \
experiments were performed that confirmed this result.\
\>", "Item1Numbered",
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This is a fantastic example of the process of physics! We have an established \
idea, predicted that this idea produced results that were contradictory, thus \
formulated a new hypothesis and confirmed it by both logical reasoning and \
physical experiment. We can attempt to answer our question for the chapter: \
Physics can be defined as the process of establishing an idea about \
fundamental natural processes, predicting the consequences of that idea, and \
either confirming or refuting it. But how do we come up with an idea about \
nature?\
\>", "Text",
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