Neil deGrasse Tyson "Some infinities are bigger than others" (from Joe Rogan Experience #919)

Hello, freak bitches. Well, isn't that the definition of infinity? That somewhere, some, if there is really an infinity, there is not only a you and an I, but there's a you and an I and everybody else we've ever met, and all the exact events in the exact same order have gone down an infinite number of times, including this conversation. Okay, except. Except. There is, I don't know how many people know this, but often it's mind-blowing when you learn, that some infinities are bigger than others. Joe Rogan just leaned two feet away from the microphone. Yeah, not all infinities are the same size. But if it's infinity, then it's infinity. It's infinite. Well, okay. Don't you remember when you were a kid? They said, what's the biggest number? You know, a million. Well, there's a million and one. Okay, how about a billion? Well, there's a billion and one. There's an annoying kid, always added one to it. Okay, how about infinity? Well, infinity and one. Okay, well, it turns out infinity and one and infinity are the same number. Okay, so here's the, so for example, the number of counting numbers, so one, two, three, up to infinity. Okay? Right. The numbers you would use to count things. That's infinite. The number of irrational numbers, so the numbers that you cannot represent as a fraction. Okay? That there's more, there are more of those than there are counting numbers by far. So these are orders of infinity. Then there are more, there are more transcendental numbers than there are irrational numbers. What's a transcendental number? So that's a number that you'll never find as a solution to an algebraic equation. So pi is a transcendental number. E is a transcendental. These are magic numbers that show up in mathematics. And there's turns out there's like an even bigger infinity of those than there is of these other two classes of numbers. And they use the Hebrew letter aleph in ranking. So it's aleph one, aleph two, aleph three, aleph four. I think there are five levels of infinity. So my point is just because there's infinite universes, to me, doesn't mean there's infinite conversations that have happened. And I'd want to really explore the depths of infinities before I say and agree with you that this conversation has happened a million, you know, infinite number of times in just this way, except you have a different engineer sitting next to us or... And an infinite number of times where it's been Jamie too, right? Yeah, in principle. I mean, that's the argument that's given. But I think that there's some nested infinities in there that deserve some explanation. My feet on brain is not handling this well. Well, that's fine. As I've said, as I say in the epigraph of the book... Book is not available yet, but I have a copy. Haha. Astrophysics for people in a hurry. Astrophysics for people in a hurry. But you got to say it right. You say it's called astrophysics for people in a hurry. Oh, you got to say it quick. You got to say it because you're in a hurry. So the epigram on that is the universe is under no obligation to make sense to you. That's rational. And I've tweeted that before. That makes sense to me. And so it makes sense to you that the universe is under no obligation to make sense. So it's okay if your brain hurts when I say there's a ranking of infinities, but you shouldn't say that doesn't make sense, therefore it is not true. I definitely wouldn't say that. But what confuses me is the word infinity because I had always taken the word infinity to mean something that has no end. So how can something that has no end be larger than something else that has no end? So the way they do that mathematically, the way to demonstrate that mathematically is you map one item in the set of this infinity to corresponding items in the set of the other infinity. And so you do this. So you take the one and you map it to like the first transcendental number. Take the two to the second. You just keep doing this. And when you do that mathematically, what you find that one infinity outstrips the other infinity. Wow. And then you're left with more with more numbers. So that shows you that you have a bigger infinity.