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Now, it turns out, though, that there are several problems with this model. The main problem is that it s wrong. It s just not true. (Laughter) And I m going to talk about three reasons why it s wrong. So the first reason is a logical reason. It s the problem of the fallacy of affirming the consequent. So that s another fancy, academic way of saying that false theories can make true predictions. So just because the prediction comes true doesn t actually logically prove that the theory is correct. And I have a good example of that too, again from the history of science. This is a picture of the Ptolemaic universe with the Earth at the center of the universe and the sun and the planets going around it. The Ptolemaic model was believed by many very smart people for many centuries. Well, why? Well the answer is because it made lots of predictions that came true. The Ptolemaic system enabled astronomers to make accurate predictions of the motions of the planet, in fact more accurate predictions at first than the Copernican theory which we now would say is true. So that s one problem with the textbook model. A second problem is a practical problem, and it s the problem of auxiliary hypotheses. Auxiliary hypotheses are assumptions that scientists are making that they may or may not even be aware that they re making. So an important example of this comes from the Copernican model, which ultimately replaced the Ptolemaic system. So when Nicolaus Copernicus said, actually the Earth is not the center of the universe, the sun is the center of the solar system, the Earth moves around the sun. Scientists said, well okay, Nicolaus, if that s true we ought to be able to detect the motion of the Earth around the sun. And so this slide here illustrates a concept known as stellar parallax. And astronomers said, if the Earth is moving and we look at a prominent star, let s say, Sirius — well I know I m in Manhattan so you guys can t see the stars, but imagine you re out in the country, imagine you chose that rural life — and we look at a star in December, we see that star against the backdrop of distant stars. If we now make the same observation six months later when the Earth has moved to this position in June, we look at that same star and we see it against a different backdrop. That difference, that angular difference, is the stellar parallax. So this is a prediction that the Copernican model makes. Astronomers looked for the stellar parallax and they found nothing, nothing at all. And many people argued that this proved that the Copernican model was false.

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