When you travel somewhere in a country, you have different kind of feelings when you meet somebody, when you see something which is beautiful, when you see a monument, or It's different kind of feelings. We have the same today. We travel in the same country, the world of ideas with our six guides. We spoke about mathematics, we spoke about astronomy. Let's talk about a third topic, completely different. Not completely but, rather different: paradox. What's a paradox? And the role of paradox, you will see in lecture five and six when we talk about creativity. The role of paradox. We need to understand better where paradoxes are located in the country of ideas. So like for the two other videos we need some more people, and probably the three people I need today for this video are Xeno, Epiminate, and Einstein. I'll explain why. But before going into details Let's go back for a minute to Aristote. And again and again, we come back to the same giant. Aristotle was famous for his two physics, definitely. But he was also famous for, and we will see that soon, for another incredible invention, logic. Logic. A beautiful tool for the mind, again comes from Aristotle. And it's strange, because the two dimensions of Aristotle, physics on one side and logic on the other side. Will be not attacked, but at least challenged by two different paradoxes. Zeno. Zeno. Let's tell a story of Zeno. The story of Ashil and the doctors, maybe you heard about these stories but that's where it should be told. Ashil was a runner. A runner, a good runner. The fastest in the city. And the tortoise, boom, was of course not a runner. But, he want to organize a race, between him, Achilles and the tortoise. But to make the race, more interesting, he said, gave, the tortoise, a head start. So let's with my, use my hands you have Achille here and the tortoise here. And they run this way. So, the race begins. Achille is running, but he won't catch up the tortoise because when he pass where the total used to be the tortoise is here. Even if she goes very slowly she's no more where she used to be. So there is another gap. Same for the next step. Achille runs when he's here, where the total used to be, the total is there, and what was the claim of Zeno? He said, Achille will never catch up to tortoise. Because, and you have understood, if he moves this way, the tortoise is no more, etc. etc. It was a paradox. And at the time of Aristotle, nobody could explain. To explain this, you need like, a big, big history of ideas. Leibniz, Newton they invented what? The calculus I mentioned before, but they invented the way to go to extremely small items. The limit, the derivative, the integral duce, twos type of calculus were invited by Newton and Leibniz and the products of Zeno disappear. You don't solve a paradox. It's something that should vanish when you have a new paradigm in your mind, and that's what happened with Newton and Leibniz. And of course Einstein Years after, a century after, two centuries after like he took a heritage of Leibniz and push it further again with this relativity theory etcetera. That's the story of the paradox of Zeno, but there is another one. Epimenides, Epimendes was also a paradox but completely different. He said, I lie. Think about if I say I lie, It means I don't lie. But if I don't lie, I lie. Very strange loop and that comes from Epimende. And this paradox wasn't so for two thousand years. And the new logic, the new logic and I think can be explained this way. If I have a sentence like that. This sentence have seven words. This is not true. This is not true. And at the time of Aristotle, there was the principle of non-contradiction. Very important. According to this principle. If two sentence are in full contradiction. One is true and the second is not true. For example if I tell, I am in France. And then I tell, I am not in France. The two are in full contradiction. According to this principle, one is true, one is not true. Looks simple, looks easy, looks obvious. But look at this one. This sentence has seven words is not true. So let's write the contrary. This sentence does not have seven words. And it surprise, this is not true as well. Can you imagine the shock, the shock after 2,000 years, one of the main principles of Aristotle suddenly blew up, and that's got, this the beginning of the new logic. Where Bertrand Russell played a huge role with some others and we'll see that in a minute.