Strange Paradoxes in Maths │ The History of Mathematics with Luc de Brabandère
Can you cross a square?
Is someone lying, or not?
Discover the strange paradoxes revealed by maths.
We could say paradoxes are the “black holes” or the ”blind spots” of both mathematics and logic. Discover some of the most fascinating paradoxes with philosopher Luc de Brabandère.
He guides us through the history of mathematics, from Egyptians measuring with the Sun to modern algorithms for self-driving cars.
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Can you cross a square? Is someone lying or not? Discover the strange paradoxes revealed by maths.
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Sometimes, when you are a logician or a mathematician, you face strange problems. Problems you really don't know how to solve, and those problems are called paradoxes.
Let's start with logic. If I tell you I am a liar, and if this is true, I am not a liar. If this is not true, then I am a liar. You cannot escape the loop. This is called a paradox. In mathematics, you also have paradoxes. A famous one was Zeno. He told his friends it's impossible to cross a square. It's impossible to go from A to B. Yes, he said, because if you want to go from A to B, you first have to go halfway. And then, halfway. And then, halfway. You never can reach the other end of the square, because you can go as far as you want, there is still a little distance, you have to start with halfway. That was Zeno's paradox. And paradoxes in logic were "solved" by Bertrand Russell and the new kind of logic. Paradoxes in mathematics, at least this one, were solved by, at the same time, Leibniz and Newton with the invention of calculus, and you will see in the next video how they did it.
Let's have another example of a beautiful paradox in mathematics. Let's take a right-angled triangle again, A, B, C. I will prove to you that AC = AB + BC. You say “No, it's not possible”. Yes, and I will prove it to you. Let's start with AC. I propose to build this like stairs, like this, and you replace the straight line by your stairs. If you look at the sum of the horizontal pieces, it's exactly the distance here (BC). If you look at the sum of the vertical pieces, it's exactly the distance here (AB). Now, if you go to very, very thin stairs, with a very limited number of steps, you'll finally have AC = AB + BC. It's another paradox and it's important because mathematicians make progress when they embrace paradoxes.
Next time we will explain how that scourge of school children, calculus, was invented.
