Can you measure randomness? │ The History of Mathematics with Luc de Brabandère
Does anything happen by chance?
Not according to probability theory.
Even the randomness of rolling of a six at dice can be calculated.
Philosopher Luc de Branbandère guides us through the history of mathematics, from Egyptians measuring with the Sun to modern algorithms for self-driving cars.
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Rolling dice is not a question of luck, as probability theory shows. Subscribe now to the new series, ‘The History of Maths’ on the YouTube channel ‘What makes it tick?’
According to Aristotle, once more, random doesn't exist. Nothing happens by chance. Everything is written, and you go, you reach a purpose, no chance, no random. This lasted for 2,000 years.
Blaise Pascal, a philosopher as well as a mathematician, challenged this claim of Aristotle's. No, no, random does exist. And he opened a new field called probability. He called this the geometry of chance, and this was one of the most difficult fields in mathematics, how you measure random.
Let's start just today with a very simple exercise. If you have a dice and you roll the dice, how much chance do you have of getting a 6? 1/6. This stage is not too difficult, but now if you throw the die 6 times are you sure you’ll get a 6? Of course not.
How much chance do you have of getting a 6 with 6 throws? This is difficult. Let's start with 2 throws. If you throw the dice twice, how much chance do you have of getting a 6? First, 1/6 at the first throw, plus 1/6 on the second one. Each time you didn't get the 6 the first time means 5/6 so you have 11 chances in 36. That's only after 2 shots. Now imagine 6, it becomes quite difficult to calculate.
There is a smart solution, if you do this. Change the question, reformulate the question. The question was how many chances you have to get a 6 with 6 throws. It’s much easier to calculate the opposite, how many chances you have of not getting a 6 in 6 throws. That's much easier because it's the first throw 5 chances in 6 of not getting a 6. You can do that 6 times?
Finally, the probability of not getting a 6 in 6 shots is (5/6 )^6 and is roughly something like 1/3.
Creativity and probability go well together.
Join us next time as we explore one of the oldest enigmas in maths, the constant Pi.
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