How can we know pi if we can never finish writing it?

Transcript

Okay, how can we know what these numbers are if we can't even write them down? Like, pie. Everyone knows this number, but do we actually know it? Like, there are literal competitions for trying to remember pie. People memorize thousands of digits. Insane people record YouTube videos of them trying to remember pie. And yet somehow, after all of that work, they still haven't memorized one number. They can't remember pie. Not even one percent of it. Let's say you know 100 digits. Out of the first thousand, that's 10 percent. Pretty good. But the more digits we count, the smaller your share gets. Okay, so does that mean that we don't actually know what pie is? Because it does sound confusing. I mean, the number goes on forever. How are we supposed to know that? Well, take a circle and measure all the way around it. Then divide that by the distance straight across its middle. That ratio equals pie. And it doesn't matter how big or small the circle is. And also, by the way, infinity and infinitely repeating digits are different things. Like, one divided by three gives us 0.3 forever. But it's not infinity. And we can also describe every digit immediately. It's always another three. But pie, on the other hand, never settles into a repeating pattern. And that's why it's so strange. An endless number that doesn't repeat. But if you take the circumference of any circle, and you divide it by its diameter, it will always give you this endlessly accurate number. So we know what pie is. Just we can't write it down.

Transcribed automatically from the video, so small errors are possible.