Is π Random? Exploring the Elusive Normal Numbers

Is pi random? Pi is fixed and predetermined, but its digits look just like random digits! We'll define normal numbers by exploring why pi's digits look random. Then we'll see what it would mean if pi is a normal number.

00:00 Introduction
00:18 Why do pi's digits look random?
01:02 Normal numbers
03:17 Is pi normal?
04:47 What if pi is normal?

[minecraft]

0:17 if pi is normal, that means both of these digit sequenses are digits from pi

[unvergebeneid]

2:27 thank you for confirming that being rational and being normal is mutually exclusive.

[YouTube_username_not_found]

The normal numbers set reminds me of the Cantor set, which is uncountably infinite yet has measure 0. If we examine its other properties we notice It has a hausdorff dimension less than 1 .. which brings us to the next question:
What is the Hausdorff dimension of the normal numbers set?

[edwardnedharvey]

You said if we randomly pick a number between 0 and 1, there is a 100% chance that we will not pick any rational number. Which is amazing, considering there are infinitely many. I guess that's a consequence of uncountably vs countably infinite. I guess if there's an infinite sequence of blue objects, and somebody inserts a red object at a random position within the sequence, there is also a 0% chance that anybody looking through the sequence for finite time could ever find the red one. Pretty amazing. Thanks!

[Lucky]

4:08 WHICH measure are we talking about?

[SuryaBudimansyah]

Since you talked about pi, suggestion: please talk about other popular irrational/transcendental constants like e, Sqrt(2), golden ratio, etc

[atrus]

Awesome video! Is there a name for numbers that are normal in all bases?

[dlevi]

I find it surprising that the Copeland–Erdős constant is normal - except for 2 and 5, all primes end in 1, 3, 7 or 9, so the first few hundred digits look far from normal. Yet it is.

[Erotemic]

The fact that the probability of picking a rational number from the reals between 0 and 1 is 0 is so unintuitive to me. I understand how it follows from measure theory, but it also feels like a contradiction regarding our theory of uncountably infinite sets is just staring us in the face. You would think that if x is in set S, and you select s from S uniformly at random, then P(x = s) > 0, but that's not true when S is uncountably infinite (I think it's also not true if S is just countably infinite? In other words, is the probability of randomly selecting 0 from the set of natural numbers also zero? It seems like that is the case.).

[nickronca]

My beliefs: Pi is normal and we will never be able to prove it.

[compositeboson]

edit: pi is not normal, like not at all buttt its also normal because that would be cool

[compositeboson]

why the discriminant *of the quadratic polynomial* = b^2-4ac
edit: corrected the sentence