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Speaker 6: Hey Daniel, what are your favorite numbers in physics?

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Speaker 3: Oh? There are so many good ones. I mean, I

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Speaker 3: love planks constant, which tells us about like when things

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Speaker 3: become quantum. I love the speed of light that tells

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Speaker 3: us all about relativity. Too many to choose from. There

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Speaker 3: are a number of favorites there.

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Speaker 6: But have you ever wondered why numbers are so important

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Speaker 6: in the universe.

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Speaker 3: I mean, numbers are like the currency of physics. We're

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Speaker 3: predicting things happening at times and places, and those are

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Speaker 3: just numbers.

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Speaker 6: Wow. So does that mean you get paid in numbers?

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Speaker 3: I get a number of dollars every year.

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Speaker 6: I guess we all get paid in numbers if there's

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Speaker 6: just numbers in our bank accounts. If you're so lucky,

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Speaker 6: the whole universe is just numbers. I think you said

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Speaker 6: that a number of times. I'm the number one fan

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Speaker 6: of numbers. I think I know a number of those

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Speaker 6: in physics and math. Too many to number. Hi, I'm

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Speaker 6: poorhe McK cartoonists and the author of Oliver's Great Big Universe.

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Speaker 3: Hi, I'm Daniel. I'm a particle physicist, and I've been

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Speaker 3: a professor at UC Irvine for a large number of years.

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Speaker 6: Oh, too many to count? Or do you go into

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Speaker 6: some sort of like weird subspace when you do physics.

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Speaker 3: No, I think I'm going to enter a puba phase eventually,

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Speaker 3: and then emerge as an emeritus professor.

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Speaker 6: That's a butterfly. That's a beautiful tenured emeritus butterfly.

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Speaker 3: As a white haired moth.

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Speaker 6: I think instead of wings, do you just have a

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Speaker 6: bunch of research papers taped together.

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Speaker 3: I'm going to fly too close to the universe on

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Speaker 3: wings of research papers.

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Speaker 6: Right, But you know, butterflies don't have mouths, right, so

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Speaker 6: you won't be able to talk.

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Speaker 3: Yeah, but they have those long noses, and so I'm

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Speaker 3: already set.

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Speaker 6: There you go. You can sniff out science from there.

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Speaker 3: I can snort up all the information in the universe.

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Speaker 6: Boy, that sounds a little illegal.

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Speaker 3: Are you going to arrest a butterfly? Is that what

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Speaker 3: has come to?

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Speaker 6: Maybe a cocaine sniffling butterfly. Maybe maybe it'll be our

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Speaker 6: informant for you know, figuring out how the universe works.

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Speaker 3: Maybe altering your mental state is important for understanding the universe.

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Speaker 6: I hear that's called the butterfly effect.

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Speaker 3: I think that's something else.

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Speaker 6: Meant something else? Did I get that wrong?

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Speaker 3: I think it's called microducing.

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Speaker 6: Yeah, I think this is called micro punning, which it

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Speaker 6: doesn't work as well. But anyways, welcome to our podcast,

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Speaker 6: Daniel and Jorge Explain the Universe, a production of iHeartRadio.

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Speaker 3: In which we give you a drip, drip, drip, little

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Speaker 3: doses of the incredible wonder we discovered about the universe,

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Speaker 3: everything that's out there that makes sense, and everything out

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Speaker 3: there that still puzzles us as we try to fit

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Speaker 3: the entire universe into a pattern that makes sense to

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Speaker 3: our little human minds.

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Speaker 6: That's right, We try to get you high on the

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Speaker 6: little dopamine had of wonder and amazement at how our

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Speaker 6: universe works and ways in which it still puzzles scientists

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Speaker 6: even today.

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Speaker 3: And one thing that still puzzles scientists and philosophers is

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Speaker 3: at any of it makes sense that these mathematical models

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Speaker 3: we build on our head can actually describe and even

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Speaker 3: predict what's going to happen out there in the universe.

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Speaker 3: That somehow mathematics seems to be not just the currency

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Speaker 3: of our physics, but the currency of the universe itself.

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Speaker 6: Wait, wait, are you saying math is more important than physics?

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Speaker 3: I mean, is English more important than Shakespeare? You can't

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Speaker 3: really compare the two things, you know.

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Speaker 6: Wait, in this analogy, Shakespeare's math in English is physics.

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Speaker 3: No, Shakespeare's physics and English is math. Physics is speaking

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Speaker 3: in the language of mathematics. We are writing poetry in

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Speaker 3: the language of math.

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Speaker 6: I see I see? So is physics a comedy or

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Speaker 6: a tragedy.

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Speaker 3: It's a tragic comedy, for sure.

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Speaker 6: It's a tragic comedy.

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Speaker 3: We're all waiting for the final twist. Nobody knows how

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Speaker 3: it ends.

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Speaker 6: That's right, it never ends well for Shakespeare.

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Speaker 3: But we laugh along the way.

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Speaker 6: And you also have to wear tights when you do physics.

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Speaker 7: Mmmm.

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Speaker 3: And as always, the jester is the wisest one.

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Speaker 6: Oh, I see, that's the engineer and the team.

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Speaker 3: Did you just call engineers jokers? I mean, I'm just

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Speaker 3: going to step slowly away from that.

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Speaker 6: No, I know. We have a great sense of humor,

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Speaker 6: is what I'm saying. We're the smaltest person in the room.

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Speaker 3: Often laugh at and unwisely ignored.

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Speaker 6: But yeah, it seems like there are a lot of

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Speaker 6: numbers in physics. There's an infinite number of numbers in math,

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Speaker 6: let's face it. But in physics it seems like there

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Speaker 6: are special numbers out there that have kind of a

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Speaker 6: special status because they're sort of significant in how the

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Speaker 6: universe works.

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Speaker 3: Yeah, there are certain constants which seem to be important

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Speaker 3: that tell us something about the universe. The speed of light,

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Speaker 3: planks constant, the gravitational constant. There are even numbers that

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Speaker 3: don't have units, you know, like the number of particles

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Speaker 3: we've discovered or ratios of masses that we think reveal

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Speaker 3: something deep about the universe. But even more than that,

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Speaker 3: there are systems of numbers. There are patterns of numbers

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Speaker 3: that reflect pwer turns we see in the universe, mathematical

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Speaker 3: constructs and all sorts of fancy mathematics that really are

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Speaker 3: crucial to understanding how the universe operates.

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Speaker 6: And this is kind of especially true at the microscopic level, right,

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Speaker 6: That's where a lot of these numbers and a lot

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Speaker 6: of this math comes from, and it comes from our

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Speaker 6: attempted understanding how things work at the particle level.

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Speaker 3: Math an interesting point. I would say that math describes

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Speaker 3: the universe at every level. You know, we have mathematics

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Speaker 3: for fluid dynamics and for planetary evolution and for the

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Speaker 3: expansion of the whole universe. It's mathematics up and down.

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Speaker 6: Okay, so it's at every level. But it seems like

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Speaker 6: in the standard model there are especially some interesting numbers.

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Speaker 3: Yes, absolutely, the theories of particle physics are very mathematical,

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Speaker 3: and not just in the sense that they're predicting numbers

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Speaker 3: and places and times. But the patterns we see in

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Speaker 3: the standard model use complex mathematical theories like group theory

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Speaker 3: and field theory and all sorts of like heavy hitting

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Speaker 3: mathematical apparatuses.

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Speaker 6: Right, which sort of eraises the question of whether the

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Speaker 6: universe itself is math thematical. Like maybe if you dig

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Speaker 6: down deep enough into the stuff we're all made out

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Speaker 6: of at the end, maybe we're just mathematical equations or formulas.

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Speaker 3: Yeah, And it makes you wonder, like what does that mean?

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Speaker 3: And our numbers real the way like stuff is real?

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Speaker 3: You know, like where is the number two? If two

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Speaker 3: is a physical thing, does it exist somewhere in the universe.

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Speaker 3: There's a whole fascinating branch of philosophy. But like how

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Speaker 3: we learn things about numbers because you can't like do

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Speaker 3: experiments with the number two and the number seven. It's

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Speaker 3: all sort of mental games.

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Speaker 6: Right, right, Like maybe the universe is not really physical.

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Speaker 6: Maybe it's just sort of like conceptual theoretical.

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Speaker 3: Yeah, but then you wonder, like what breeds fire into

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Speaker 3: all those concepts it makes us experience it. The other

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Speaker 3: side of that argument is that numbers are not universal,

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Speaker 3: they're not physical, they're not natural they're just sort of

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Speaker 3: the way that our human mind works. That you can

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Speaker 3: use numbers as a way to describe the universe, but

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Speaker 3: it doesn't mean they're part of the universe, the way

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Speaker 3: you can like describe the color orange a bunch of words,

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Speaker 3: but none of those words are orange or fully capture

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Speaker 3: the oranginess of an orange.

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Speaker 6: Mm and is one really the loneliest number? Is another

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Speaker 6: big physics question.

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Speaker 3: Right, Yes, yes, a very deep physics question. But we

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Speaker 3: have to see a lot of value in math. There's

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Speaker 3: lots of times when mathematicians have developed some cool little

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Speaker 3: technique just for fun because they see cool patterns that

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Speaker 3: they like playing with them, and then later on physicists

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Speaker 3: will come along and be like, hey, that looks useful,

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Speaker 3: and just like pluck it out of their hands and

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Speaker 3: go insert it into our physics equations and get great insights.

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Speaker 3: There's a lot of hints there that the laws we

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Speaker 3: used to describe the universe are deeply mathematical.

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Speaker 6: Yeah, it seems like there are a lot of new

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Speaker 6: ideas coming up all the time about how to explain

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Speaker 6: the patterns that we see in the universe, maybe with

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Speaker 6: new kinds of math, and so to be on the podcast,

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Speaker 6: we'll be asking the question, what are atonians? Did I

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Speaker 6: say that right?

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Speaker 3: Or is it as I think it's oct onions, Like,

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Speaker 3: give me eight onions for that recipe please.

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Speaker 6: Isn't it like a blooming onion? Isn't that a dish

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Speaker 6: in a fried dish in one of these famous restaurants?

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Speaker 6: Is this like a fried onion that looks like an octopus?

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Speaker 3: Are you shilling for Outback Steakhouse? Now?

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Speaker 6: Oh? Is it out Back?

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Speaker 3: I don't know, never been.

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Speaker 6: Maybe Applebee's is interested.

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Speaker 3: I think it's maybe octonians or octanians, depending on where

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Speaker 3: you are in the world.

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Speaker 6: So this is an interesting word. It sort of sounds

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Speaker 6: like octo, which is eight. Then you're ending it with onions,

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Speaker 6: which is a vegetable or a tuber. But it's also

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Speaker 6: sort of how some particle names ends, right.

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Speaker 3: Mm hmm yeah ions exactly?

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Speaker 6: Oh yeah, right right, yeah ions? So is it octinions? Then?

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Speaker 3: I think we should have eight different pronunciations of this word.

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Speaker 6: Now a trace you go, and then we'll spend eighty

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Speaker 6: eight minutes talking about it here on the podcast.

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Speaker 3: As part of our Cult of eight. There you go,

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Speaker 3: send eight dollars to join.

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Speaker 6: There you go, We'll have eight dollars in our pockets.

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Speaker 6: In our eight pockets because I wear cargo pants exactly.

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Speaker 3: Maybe these are the spiders of the universe.

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Speaker 6: It's all an intricate web of eight Well, anyways, as usually,

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Speaker 6: we were wondering how many people out there had thought

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Speaker 6: about or even heard of the word octonions and what

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Speaker 6: they think it might mean.

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Speaker 3: Thanks very much to everybody who participates in this audience

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Speaker 3: contribution segment of the podcast. We'd love if you joined

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Speaker 3: the crew. Please write to me two questions at Danielandjorge

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Speaker 3: dot com.

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Speaker 6: So think about it for a second. What do you

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Speaker 6: think are octonions? And are they sold at Applebee's or

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Speaker 6: out back to steakhouse?

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Speaker 3: And would they make you cry if you chomp them?

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Speaker 6: Here's what people had to say.

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Speaker 3: What are onions? So octors? The prefix for eight onions

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Speaker 3: being something layers, probably so eight layers stars.

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Speaker 7: I don't know, Honestly, I have no idea, but if

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Speaker 7: I were to have to guess, I would construct the word.

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Speaker 8: So.

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Speaker 7: I think the prefix oct means it has to do

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Speaker 7: with eight and so maybe it has to do with glue,

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Speaker 7: ons or any type of similar particle or force. Carrier

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Speaker 7: that is dependent on matrices for transformation.

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Speaker 6: All right, well pretty much the same. What I've been

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Speaker 6: guessing something to do with onions and eight and or particles.

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Speaker 3: Yeah, reasonable guesses, absolutely.

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Speaker 6: Is it like what happens when you smash together eight onions?

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Speaker 6: You get an ooked onion.

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Speaker 3: We're working on the onion collider right now. We just

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Speaker 3: need a little bit more funding. Eight dollars more and

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Speaker 3: we'll be there.

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Speaker 6: You need a little bit more garlic that you're going

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Speaker 6: to say, a bit more seasoning. You need eighty eight

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Speaker 6: billion dollars.

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Speaker 3: I won't say no to eighty eight billion dollars, that's

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Speaker 3: for sure.

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Speaker 6: Yeah, there you go. And then what happens at the

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Speaker 6: end when you collide the onions? Would you have to

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Speaker 6: et them?

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Speaker 3: I disappeared to my private island with all the cash.

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Speaker 6: I think they can give you eight years in prison

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Speaker 6: for that, Daniel, only if they catch me, only they

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Speaker 6: smell off the crime.

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Speaker 3: I'll have an army of cocaine infused butterflies to protect me.

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Speaker 6: Oh my gosh, you are a super villain there. I mean,

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Speaker 6: I've heard of sharks with lasers, but m the drug

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Speaker 6: butterflies is a new level of villainy.

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Speaker 3: And they will never see me coming.

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Speaker 6: All right, Well, stick into it, Daniel. What is in octonian?

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Speaker 6: And what do you think is the right way to

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Speaker 6: pronounce it?

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Speaker 3: I pronounce it octonians, but it does make it sound

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Speaker 3: like creatures from the planet Octo or something.

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Speaker 6: M I see you're going for the more tony pronunciation Octonians.

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Speaker 3: Octonians exactly.

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Speaker 8: So.

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Speaker 3: Octonians are a kind of number, and they're sort of

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Speaker 3: in the category of complex numbers, but they're an extension

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Speaker 3: of complex numbers the way complex numbers have like two

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Speaker 3: components to them, the real and the imaginary part, which

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Speaker 3: are an extension of real numbers. They just have one component.

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Speaker 3: Octonians have eight components, one real and seven imaginary components.

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Speaker 6: Well, okay, wait, hold on, I think maybe some of

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Speaker 6: us might not be super familiar with our high school math.

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Speaker 6: What is an imaginary number in the first place.

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Speaker 3: Imaginary numbers were invented in the sixteen hundreds, and they're

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Speaker 3: called imaginary because you don't see them in reality. They're

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Speaker 3: very useful in math. And there's basically one imaginary number,

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Speaker 3: which is I, which is the square root of minus one.

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Speaker 3: There's no real number, which if you multiply it by

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Speaker 3: itself gives you minus one. So they invented a number.

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Speaker 3: They just call it I, and they say, if you

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Speaker 3: multiply I by itself, you get minus one. So it's

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Speaker 3: a new kind of number. It's different from any of

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Speaker 3: the numbers on the normal number line.

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Speaker 6: Right, because like we had the number negative one, and

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Speaker 6: we have the function to take a square root of something,

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Speaker 6: But when you mix the two, it's like you get

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Speaker 6: something that's almost impossible, or that it's not on the

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Speaker 6: regular number line that we all use in our everyday lives.

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Speaker 3: Exactly, because any number on the regular number line we

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Speaker 3: call the real numbers, if you square it, you get

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Speaker 3: a positive number. Three squared is nine. Negative three squared

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Speaker 3: is also nine because the two negatives give you a positive.

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Speaker 3: So there's no number on the real number line which

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Speaker 3: if you square it will give you a negative answer.

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Speaker 3: So there's no number that's an answer to the question

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Speaker 3: what is the square root of negative one? So they

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Speaker 3: had to invent a new kind of number. Sort of

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Speaker 3: imagine the real number line is like the X axis.

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Speaker 3: They invented a new axis like the y axis, which

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Speaker 3: is like the imaginary direction. So instead of having a

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Speaker 3: number line, and they have a number plane where every

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Speaker 3: number is two components, a real component and this imagineric component.

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Speaker 6: Right, because you came up with I, or mathematicians came

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Speaker 6: up with I, and then you can have a whole

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Speaker 6: number line based on I. You can have like two

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Speaker 6: I and three I or four point seven I or

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Speaker 6: eight I.

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Speaker 3: Or negative two I. Right. The imaginary number line goes

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Speaker 3: both ways, h right, right?

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Speaker 6: And can you also have I?

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Speaker 3: You can have not it and like I'm not doing the.

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Speaker 6: Dishes, Yes, that's what I mean, Like zero I would

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Speaker 6: you call it not I?

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Speaker 3: Oh? You can have zero? Yeah, the zero in the

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Speaker 3: number line is just zero comma zero, right, zero real

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Speaker 3: numbers and zero imaginary.

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Speaker 8: Right.

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Speaker 6: So in physics, when you talk about an imaginary number,

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Speaker 6: you talk about like a number that has both a

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Speaker 6: real component and an imaginary component, so you write it

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Speaker 6: as two numbers like seven plus eight I exactly.

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Speaker 3: That's what we call a complex number, something with a

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Speaker 3: real and an imaginary component, sort of like a coordinate

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Speaker 3: on the two dimensional complex plane. If you imagine real

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Speaker 3: numbers or x and imaginary numbers are y right.

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Speaker 6: And I think like all of most of quantum particle

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Speaker 6: physics is based on imaginary numbers, right, Like it's a

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Speaker 6: convenient you know, mathematical space to do all of the mas.

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Speaker 3: In Yeah, exactly. So there's a few important things to

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Speaker 3: know about complex numbers. Number one, they turned out to

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Speaker 3: be really useful Back in the sixteen hundreds when they

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Speaker 3: were invented, before we had quantum mechanics, they were already useful.

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Speaker 3: Italian mathematicians came up with them as a way to

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Speaker 3: like solve problems, and they found that they could get

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Speaker 3: to the solutions of tricky math problems much more rapidly

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Speaker 3: if they used these imaginary numbers, even though they didn't

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Speaker 3: believe in them. They didn't believe that they represented anything

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Speaker 3: in the universe. But now all of our quantum mechanics

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Speaker 3: relies on these complex numbers. Like the wave function that

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Speaker 3: we talk about all the time in quantum mechanics, that's

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Speaker 3: actually a complex valued object. That's why you can't observe

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Speaker 3: it directly. You can only observe it when it's squared.

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Speaker 3: That gives you the probability. The wave function itself is

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Speaker 3: a complex number, has a real component and an imaginary component.

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Speaker 3: We couldn't do quantum mechanics without complex numbers, they represent

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Speaker 3: something real about the universe.

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Speaker 6: No wait, wait, what are you saying. Are you saying

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Speaker 6: like somehow the universe or particles are themselves imaginary or

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Speaker 6: that they sort of operate in a two dimensional space.

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Speaker 3: We don't know if the wave function is real, if

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Speaker 3: it actually exists in the universe. What we do know

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Speaker 3: is that the mathematics needed to describe what particles do

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00:19:05,480 --> 00:19:08,760
Speaker 3: in which direction they go has to have complex numbers

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00:19:08,840 --> 00:19:11,399
Speaker 3: in it. Like that, math just does not work without

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Speaker 3: complex numbers. So in our models, in our calculations, the

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Speaker 3: wave function that describes all these particles have complex values

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Speaker 3: in them. Now, when you predict the outcome of an experiment,

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Speaker 3: it always just gives you actual numbers or real numbers

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Speaker 3: that you can measure the particle will be at this

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Speaker 3: location at that time. But the intermediate states, the calculations

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Speaker 3: we do between the observations require complex numbers. Does that

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Speaker 3: mean that the universe is complex, that there are imaginary

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Speaker 3: components to it? We don't know. Deep question for philosophy.

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Speaker 6: Well, the universe is definitely complicated, whether it's complex or

399
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Speaker 6: real or imaginary. Maybe it is the topic for another podcast,

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Speaker 6: but here today we're talking about maybe a different kind

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Speaker 6: of imaginary number, one that is maybe eight times more

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00:19:55,040 --> 00:19:58,359
Speaker 6: imaginary than an imaginary number. So that's dig into that

403
00:19:58,400 --> 00:20:00,720
Speaker 6: and see whether or not it can help explain more

404
00:20:00,760 --> 00:20:02,639
Speaker 6: of the universe that we see around this and what

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Speaker 6: would that mean. But first, let's take a quick break.

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Speaker 6: All right, we're talking about Oktonians or our Kanyans, which

466
00:23:21,040 --> 00:23:25,359
Speaker 6: are maybe extra imaginary numbers that might describe how the

467
00:23:25,480 --> 00:23:28,639
Speaker 6: universe works at the particle level. We're digging into that

468
00:23:28,760 --> 00:23:32,120
Speaker 6: here today now, Daniel, you're saying that imaginary numbers play

469
00:23:32,160 --> 00:23:35,320
Speaker 6: a big part in describing how things work at the

470
00:23:35,760 --> 00:23:36,480
Speaker 6: quantum level.

471
00:23:36,520 --> 00:23:40,240
Speaker 3: Exactly, we need complex numbers in order to do quantum mechanics.

472
00:23:40,560 --> 00:23:43,920
Speaker 3: Like if they hadn't been invented already early this century

473
00:23:43,960 --> 00:23:46,720
Speaker 3: when we were developing quantum mechanics, we might have invented

474
00:23:46,720 --> 00:23:49,320
Speaker 3: them then. As it is, they already existed in the

475
00:23:49,359 --> 00:23:51,600
Speaker 3: sort of mathematical toolbox, and so we could just pluck

476
00:23:51,640 --> 00:23:54,080
Speaker 3: them out and say, oh, this is helpful, let's use it.

477
00:23:54,280 --> 00:23:56,960
Speaker 6: Well, was that a big surprise, Like, wait a minute,

478
00:23:57,000 --> 00:23:58,520
Speaker 6: what does that mean about the universe that you need

479
00:23:58,560 --> 00:24:00,000
Speaker 6: imaginary numbers.

480
00:23:59,680 --> 00:24:03,760
Speaker 3: To dis Yeah, it has deep consequences for mathematical philosophy.

481
00:24:04,240 --> 00:24:06,600
Speaker 3: You know, you can wonder if the wave function is real,

482
00:24:06,720 --> 00:24:09,560
Speaker 3: does that mean that imaginary numbers are real in some

483
00:24:09,640 --> 00:24:12,640
Speaker 3: philosophical sense, even if we don't call them real numbers

484
00:24:12,680 --> 00:24:15,200
Speaker 3: in a mathematical sense. We don't know what that means.

485
00:24:15,520 --> 00:24:19,439
Speaker 3: But imaginary numbers are also important in mathematics itself. It

486
00:24:19,480 --> 00:24:23,000
Speaker 3: tells us something about how numbers work even before they

487
00:24:23,000 --> 00:24:24,600
Speaker 3: were applied to quantum mechanics.

488
00:24:25,200 --> 00:24:28,080
Speaker 6: Interesting, so there may be something point to something funda

489
00:24:28,080 --> 00:24:29,679
Speaker 6: mental about the nature of the universe.

490
00:24:29,920 --> 00:24:33,159
Speaker 3: Yeah, perhaps, because complex numbers are not just like something

491
00:24:33,200 --> 00:24:35,840
Speaker 3: mathematicians invented. You can't just say, well, I'm going to

492
00:24:35,880 --> 00:24:37,600
Speaker 3: take two numbers and stick them together, and now I've

493
00:24:37,600 --> 00:24:39,439
Speaker 3: got a new kind of number. When you do that,

494
00:24:39,440 --> 00:24:41,480
Speaker 3: you also have to decide, like, what are the rules

495
00:24:41,520 --> 00:24:43,320
Speaker 3: of those numbers, how do you add them, how do

496
00:24:43,320 --> 00:24:45,760
Speaker 3: you subtract them, what happens when you multiply the two numbers,

497
00:24:45,800 --> 00:24:47,239
Speaker 3: et cetera. So you have to come up with what

498
00:24:47,280 --> 00:24:50,639
Speaker 3: mathematicians call a division algebra, which is basically just like

499
00:24:50,680 --> 00:24:53,320
Speaker 3: all the rules of how the math works for these numbers.

500
00:24:53,800 --> 00:24:56,560
Speaker 3: And it's not always easy to come up with that system.

501
00:24:56,720 --> 00:24:58,800
Speaker 3: For example, you can do it for complex numbers, but

502
00:24:58,880 --> 00:25:01,439
Speaker 3: you can't do it for t triplets of numbers. So

503
00:25:01,480 --> 00:25:04,320
Speaker 3: it works for single numbers, it works for pairs of numbers,

504
00:25:04,520 --> 00:25:06,760
Speaker 3: it doesn't work for triplets of numbers.

505
00:25:07,160 --> 00:25:08,920
Speaker 6: Okay, wait, hold on, and I think you're talking about

506
00:25:09,000 --> 00:25:12,679
Speaker 6: now increasing the imaginariness of a number. So like a

507
00:25:12,720 --> 00:25:15,919
Speaker 6: regular imaginary number has a real component and then an

508
00:25:15,960 --> 00:25:20,119
Speaker 6: imaginary component which you get by multiplying another number by

509
00:25:20,160 --> 00:25:23,119
Speaker 6: the number I. So like an imaginary number is seven

510
00:25:23,200 --> 00:25:26,959
Speaker 6: plus eight I. Now you're talking about like adding a

511
00:25:27,000 --> 00:25:27,800
Speaker 6: third component.

512
00:25:28,080 --> 00:25:31,600
Speaker 3: Yeah, call it J. Right, J is like another square

513
00:25:31,680 --> 00:25:34,840
Speaker 3: root of negative one, a different a unique square root

514
00:25:34,920 --> 00:25:37,600
Speaker 3: of negative one. Now thing says you can't have more? Right,

515
00:25:37,680 --> 00:25:41,480
Speaker 3: maybe there's multiple square roots of negative one. And after

516
00:25:41,520 --> 00:25:44,600
Speaker 3: people discover complex numbers, mathematicians are like, oh, that's cool.

517
00:25:44,920 --> 00:25:47,639
Speaker 3: Can you do the same thing with three numbers? If

518
00:25:47,680 --> 00:25:50,280
Speaker 3: you put three numbers together like a real number, and

519
00:25:50,320 --> 00:25:52,560
Speaker 3: then some number of I and some number of J,

520
00:25:53,359 --> 00:25:57,040
Speaker 3: can you also then make like consistent mathematics, so you

521
00:25:57,040 --> 00:26:00,600
Speaker 3: know how to multiply, divide, subtract, et cetera. Hundreds of

522
00:26:00,680 --> 00:26:01,159
Speaker 3: years on that.

523
00:26:01,280 --> 00:26:03,840
Speaker 6: Let me think about that for a second. So now

524
00:26:03,840 --> 00:26:06,560
Speaker 6: we have a number plus a number. I pleasent a

525
00:26:06,640 --> 00:26:09,440
Speaker 6: J number and you're saying Jay's another square root of

526
00:26:09,560 --> 00:26:11,720
Speaker 6: a negative one. So if I'm multiplied J times J,

527
00:26:11,960 --> 00:26:14,480
Speaker 6: I get negative one. What if I'm apply iye times J.

528
00:26:14,680 --> 00:26:16,159
Speaker 3: So this is exactly what you have to do. You

529
00:26:16,160 --> 00:26:18,640
Speaker 3: have to come up with the rules of this triplet

530
00:26:18,680 --> 00:26:21,400
Speaker 3: system to figure out what happens when you multiply different

531
00:26:21,480 --> 00:26:24,399
Speaker 3: numbers together, what happens when you divide them. And it

532
00:26:24,440 --> 00:26:29,040
Speaker 3: turns out there's no consistent way to define multiplication and

533
00:26:29,160 --> 00:26:31,720
Speaker 3: division so that it all makes sense and keeps the

534
00:26:31,720 --> 00:26:35,560
Speaker 3: mathematicians happy. If you have I and J in addition

535
00:26:35,600 --> 00:26:38,480
Speaker 3: to the real numbers, like, you cannot build a mathematical

536
00:26:38,520 --> 00:26:41,439
Speaker 3: system based on numbers with three components. You can do

537
00:26:41,480 --> 00:26:43,720
Speaker 3: it with one, that's just the normal numbers. You can

538
00:26:43,720 --> 00:26:46,040
Speaker 3: do it with two, that's just the complex numbers. You

539
00:26:46,080 --> 00:26:47,200
Speaker 3: can't do it with three.

540
00:26:47,920 --> 00:26:51,160
Speaker 6: But I feel like when you said before, like having

541
00:26:51,200 --> 00:26:53,880
Speaker 6: two numbers or like a reel and an imaginary it's

542
00:26:53,880 --> 00:26:55,480
Speaker 6: sort of like an X and a Y. Isn't this

543
00:26:55,640 --> 00:26:56,879
Speaker 6: just like having X, Y and Z.

544
00:26:57,160 --> 00:26:58,639
Speaker 3: Yeah, you might imagine you should be able to do

545
00:26:58,680 --> 00:27:00,879
Speaker 3: with any set of numbers exactly the way you can

546
00:27:00,920 --> 00:27:03,439
Speaker 3: define spaces in any dimensions. You can have a one

547
00:27:03,480 --> 00:27:06,240
Speaker 3: dimensional space, of two dimensional space, so three dimensional space,

548
00:27:06,320 --> 00:27:10,440
Speaker 3: a nineteen dimensional space, an infinite dimensional space. Geometry has

549
00:27:10,480 --> 00:27:14,520
Speaker 3: no restrictions, right, But the rules of mathematics, for some

550
00:27:14,600 --> 00:27:17,879
Speaker 3: reason constrain the number of numbers we can pack in

551
00:27:17,920 --> 00:27:21,560
Speaker 3: together and still have everything makes sense. Mathematicians worry about

552
00:27:21,600 --> 00:27:24,240
Speaker 3: like does every number have an inverse? If I take

553
00:27:24,280 --> 00:27:26,560
Speaker 3: a number, is there always some other number I can

554
00:27:26,640 --> 00:27:30,119
Speaker 3: multiply it by to get one? Are there unique zeros

555
00:27:30,240 --> 00:27:33,000
Speaker 3: or not? And it turns out that mathematics based on

556
00:27:33,000 --> 00:27:36,199
Speaker 3: triplets just doesn't work. There's no way to put it together.

557
00:27:36,560 --> 00:27:40,800
Speaker 3: This is famous Irish mathematician named William Rowan Hamilton who

558
00:27:40,840 --> 00:27:43,680
Speaker 3: spent like decades on this, and he said once every morning,

559
00:27:43,680 --> 00:27:46,080
Speaker 3: coming down to breakfast, my kids ask me, well, Papa,

560
00:27:46,119 --> 00:27:48,639
Speaker 3: can you multiply triplets? And he always said, nope, I

561
00:27:48,720 --> 00:27:52,240
Speaker 3: can only add and subtract them. So we spent decades

562
00:27:52,280 --> 00:27:54,879
Speaker 3: like try to figure out how to multiply and divide

563
00:27:54,960 --> 00:27:57,119
Speaker 3: triplets of numbers and never succeeded.

564
00:27:57,440 --> 00:28:01,600
Speaker 6: WHOA, but XYZ space works in three D space all

565
00:28:01,640 --> 00:28:03,560
Speaker 6: around this? Or are you saying our three D space

566
00:28:03,600 --> 00:28:08,040
Speaker 6: doesn't work mathematically, or just triplet imaginary numbers don't work mathematically.

567
00:28:08,080 --> 00:28:11,719
Speaker 3: Triplet imaginary numbers don't work mathematically. Like you might think, well,

568
00:28:11,720 --> 00:28:14,960
Speaker 3: why can't you just put three numbers together and then say,

569
00:28:15,040 --> 00:28:18,800
Speaker 3: you know, multiplying two triplets means multiplying the components, right.

570
00:28:18,920 --> 00:28:20,720
Speaker 3: I don't think we want to get too mathematical on

571
00:28:20,760 --> 00:28:24,320
Speaker 3: the podcast today, But this creates problems of having numbers

572
00:28:24,320 --> 00:28:27,680
Speaker 3: that don't have inverses, like one comma one coma zero

573
00:28:28,080 --> 00:28:30,560
Speaker 3: doesn't have an inverse, but it's non zero.

574
00:28:30,840 --> 00:28:32,440
Speaker 6: Okay, I think I see what you're saying. I think

575
00:28:32,440 --> 00:28:34,960
Speaker 6: you're saying it's possible to just have like coordinates in

576
00:28:35,000 --> 00:28:37,080
Speaker 6: three D space, like x, Y and z. But if

577
00:28:37,080 --> 00:28:40,360
Speaker 6: you want to call it like X plus y, I

578
00:28:40,440 --> 00:28:42,920
Speaker 6: plus z J, that doesn't work. Like if you want

579
00:28:42,920 --> 00:28:44,920
Speaker 6: to put them all together as one number with an

580
00:28:44,960 --> 00:28:48,240
Speaker 6: addition sign between the different coordinates, that doesn't work.

581
00:28:48,360 --> 00:28:50,680
Speaker 3: It doesn't work if you also require that you can

582
00:28:50,720 --> 00:28:53,120
Speaker 3: do things with these numbers, like can you take any

583
00:28:53,120 --> 00:28:55,360
Speaker 3: of these two numbers and multiply them together and still

584
00:28:55,400 --> 00:28:57,640
Speaker 3: get a number. If you add them together, do you

585
00:28:57,640 --> 00:28:59,360
Speaker 3: still get a number? We rely on that for the

586
00:28:59,360 --> 00:29:01,200
Speaker 3: normal numbers right, any number you give me, I can

587
00:29:01,200 --> 00:29:03,840
Speaker 3: always find another number to multiply it by to get one.

588
00:29:04,240 --> 00:29:06,360
Speaker 3: Or if you give me two numbers I multiply together,

589
00:29:06,440 --> 00:29:08,760
Speaker 3: I always get a number that's not a zero if

590
00:29:08,800 --> 00:29:10,720
Speaker 3: both of the numbers you gave me were not zero.

591
00:29:11,280 --> 00:29:13,760
Speaker 3: You can't build rules like that, which you need to

592
00:29:13,840 --> 00:29:16,240
Speaker 3: do any interesting math or any interesting physics. You can't

593
00:29:16,280 --> 00:29:18,440
Speaker 3: build rules like that for triplets. You can do it

594
00:29:18,480 --> 00:29:21,200
Speaker 3: for singles and for pairs, but not for triplets.

595
00:29:21,360 --> 00:29:24,320
Speaker 6: Okay, so it doesn't work for three triple imaginary numbers,

596
00:29:24,360 --> 00:29:28,000
Speaker 6: but maybe for four imaginary numbers it does work exactly.

597
00:29:28,080 --> 00:29:31,520
Speaker 3: And the same Irish mathematician William Hamilton he discovered that

598
00:29:31,560 --> 00:29:34,480
Speaker 3: if you put four numbers together, like four d space

599
00:29:35,000 --> 00:29:39,120
Speaker 3: one reel in three imaginary numbers, you call these quaternions.

600
00:29:39,480 --> 00:29:42,800
Speaker 3: This actually works. That the mathematics hangs together. You can

601
00:29:42,880 --> 00:29:45,959
Speaker 3: build multiplication and division. You can do all the mathematics

602
00:29:46,000 --> 00:29:48,600
Speaker 3: you need on quadruples of numbers, even though you can't

603
00:29:48,600 --> 00:29:49,560
Speaker 3: do it on triplets.

604
00:29:50,160 --> 00:29:52,520
Speaker 6: Okay, so now that means that my number is not

605
00:29:52,640 --> 00:29:55,080
Speaker 6: just like eight, and it's not just like a plus

606
00:29:55,520 --> 00:29:58,760
Speaker 6: four I. It's like eight plus four I plus seven

607
00:29:58,960 --> 00:30:02,120
Speaker 6: J plus five K exactly.

608
00:30:02,600 --> 00:30:06,040
Speaker 3: And in that system, I squared is negative one, J

609
00:30:06,280 --> 00:30:10,479
Speaker 3: squared is negative one. K squared is negative one. And

610
00:30:10,560 --> 00:30:13,480
Speaker 3: if you multiply I times J times k, you also

611
00:30:13,520 --> 00:30:16,920
Speaker 3: get negative one. And that's the key. J and K

612
00:30:17,040 --> 00:30:19,680
Speaker 3: are other square roots of negative one, and that one

613
00:30:19,720 --> 00:30:23,040
Speaker 3: equation makes it all hang together. And when Hamilton had

614
00:30:23,040 --> 00:30:26,200
Speaker 3: this insight, he was like walking across this bridge in Dublin.

615
00:30:26,400 --> 00:30:29,080
Speaker 3: It came to him in a flash, and he actually

616
00:30:29,160 --> 00:30:33,360
Speaker 3: chiseled the formula onto the bridge like mathematical graffiti in

617
00:30:33,400 --> 00:30:34,840
Speaker 3: the moment because he didn't want to forget it.

618
00:30:34,880 --> 00:30:36,080
Speaker 6: And you can still see it today.

619
00:30:37,120 --> 00:30:39,200
Speaker 3: It's actually worn down, but they put a plaque on

620
00:30:39,240 --> 00:30:40,800
Speaker 3: that spot to commemorate it.

621
00:30:41,400 --> 00:30:45,320
Speaker 6: And more important, was this kid impressed or because the

622
00:30:45,400 --> 00:30:47,560
Speaker 6: kids seemed really interested in what was going on with

623
00:30:47,600 --> 00:30:49,200
Speaker 6: the math and his father.

624
00:30:49,320 --> 00:30:51,040
Speaker 3: Yeah, I think he was just rooting for his dad,

625
00:30:51,160 --> 00:30:55,680
Speaker 3: you know, struggling with this crazy multiplication.

626
00:30:56,120 --> 00:30:58,520
Speaker 6: And how much can a kid know about imaginary numbers.

627
00:31:00,240 --> 00:31:03,720
Speaker 3: It's fascinating that the mathematics of it tells us what's allowed.

628
00:31:03,960 --> 00:31:06,240
Speaker 3: You can build a one D number, two D number,

629
00:31:06,280 --> 00:31:08,760
Speaker 3: a four D number, but not a three D number.

630
00:31:08,840 --> 00:31:09,720
Speaker 3: It's really interesting.

631
00:31:10,400 --> 00:31:12,560
Speaker 6: Can you go five and six and seven?

632
00:31:12,880 --> 00:31:16,440
Speaker 3: You can't. About one hundred years later, mathematicians proved that

633
00:31:16,480 --> 00:31:18,720
Speaker 3: the only sets of numbers you can do are one

634
00:31:18,960 --> 00:31:25,120
Speaker 3: real numbers, two complex numbers, four quaternions, and eight octonians.

635
00:31:25,520 --> 00:31:29,080
Speaker 6: Ooh, and what can you keep going like sixteen thirty two?

636
00:31:29,480 --> 00:31:31,200
Speaker 3: Nope, those are the only ones.

637
00:31:31,480 --> 00:31:32,000
Speaker 6: What do you mean?

638
00:31:32,240 --> 00:31:35,520
Speaker 3: Everything else runs into mathematical problems. You can't have consistent

639
00:31:35,600 --> 00:31:39,560
Speaker 3: multiplication and division without running into ugly problems with the zeros.

640
00:31:39,560 --> 00:31:42,600
Speaker 3: It only works for one, two, four, and eight.

641
00:31:42,800 --> 00:31:43,200
Speaker 6: That's it.

642
00:31:43,600 --> 00:31:46,120
Speaker 3: That's it, nothing more, nothing more in the universe. They

643
00:31:46,160 --> 00:31:48,400
Speaker 3: prove this, and I try to find a way to

644
00:31:48,440 --> 00:31:51,160
Speaker 3: like explain this in intuitive sense, but the proof is very,

645
00:31:51,280 --> 00:31:55,280
Speaker 3: very complicated. But everybody's totally convinced that one, two, four,

646
00:31:55,280 --> 00:31:58,560
Speaker 3: and eight are the only dimensions allowed for numbers that

647
00:31:58,600 --> 00:32:00,800
Speaker 3: have consistent multiplication and division.

648
00:32:01,000 --> 00:32:04,480
Speaker 6: You mean for like complex numbers, Yeah, complex numbers with

649
00:32:04,520 --> 00:32:07,160
Speaker 6: like extra imaginary dimensions exactly.

650
00:32:07,480 --> 00:32:09,960
Speaker 3: You could have one extra imaginary dimension, which gives you

651
00:32:10,200 --> 00:32:13,120
Speaker 3: our familiar complex numbers are of two D. You can

652
00:32:13,160 --> 00:32:17,320
Speaker 3: have three imaginary dimensions, which gives you four D numbers quaternions,

653
00:32:17,600 --> 00:32:21,520
Speaker 3: or you can have seven imaginary dimensions plus one reel

654
00:32:21,680 --> 00:32:25,280
Speaker 3: gives you eight dimensions for octonians.

655
00:32:24,760 --> 00:32:27,840
Speaker 6: And still be consistent with our rules of math that

656
00:32:27,880 --> 00:32:31,160
Speaker 6: we know about in our universe. Could those be different

657
00:32:31,200 --> 00:32:32,120
Speaker 6: in another universe.

658
00:32:32,360 --> 00:32:34,600
Speaker 3: You can come up with whatever rules of math you want,

659
00:32:34,840 --> 00:32:36,400
Speaker 3: but if you want to do physics with it, you

660
00:32:36,400 --> 00:32:38,280
Speaker 3: need to know how to multiply the numbers, how to

661
00:32:38,280 --> 00:32:40,560
Speaker 3: divide them. You need some confidence that you're not going

662
00:32:40,640 --> 00:32:43,080
Speaker 3: to run into zeros all the time. So these are

663
00:32:43,080 --> 00:32:46,880
Speaker 3: like pretty basic requirements for mathematical system that's going to

664
00:32:47,000 --> 00:32:49,760
Speaker 3: underlie physics. You can invent math however you like and

665
00:32:49,800 --> 00:32:52,200
Speaker 3: have it be useless or useful or whatever, but if

666
00:32:52,200 --> 00:32:54,160
Speaker 3: you wanted to do physics, you have to follow these

667
00:32:54,200 --> 00:32:55,040
Speaker 3: basic rules.

668
00:32:55,200 --> 00:32:57,280
Speaker 6: Okay, Now, I think the idea is that, you know,

669
00:32:57,280 --> 00:32:59,080
Speaker 6: we had real numbers for a long time, and they

670
00:32:59,120 --> 00:33:02,520
Speaker 6: weren't great for regular physics, and then we found quantum

671
00:33:02,560 --> 00:33:06,160
Speaker 6: mechanics and particles, and we've figured out that one dimensional

672
00:33:06,520 --> 00:33:10,360
Speaker 6: imaginary numbers work really well to describe the math and

673
00:33:10,400 --> 00:33:14,840
Speaker 6: those theories where you have one extra imaginary dimension. But

674
00:33:14,920 --> 00:33:17,440
Speaker 6: you're saying, mathematician is also found out that you can

675
00:33:17,800 --> 00:33:23,640
Speaker 6: have three extra imaginary numbers. Or dimensions in a quaternion,

676
00:33:23,760 --> 00:33:27,680
Speaker 6: or seven extra imaginary dimensions in a Olktonian. And now

677
00:33:28,000 --> 00:33:30,880
Speaker 6: I think maybe what you're saying is that scientists are wondering,

678
00:33:31,080 --> 00:33:35,040
Speaker 6: do these extra super numbers also maybe describe something about

679
00:33:35,080 --> 00:33:36,280
Speaker 6: the universe exactly?

680
00:33:36,400 --> 00:33:39,360
Speaker 3: Because obviously one D numbers are very relevant to physics,

681
00:33:39,720 --> 00:33:42,800
Speaker 3: two D numbers are very relevant to quantum mechanics. These

682
00:33:42,840 --> 00:33:46,240
Speaker 3: four D numbers we probably haven't heard of quaternions, but

683
00:33:46,320 --> 00:33:49,280
Speaker 3: these days we actually just call them four dimensional vectors,

684
00:33:49,600 --> 00:33:54,360
Speaker 3: and they're crucial for relativity, like special relativity combined space

685
00:33:54,480 --> 00:33:57,720
Speaker 3: and time into a four dimensional structure where three of

686
00:33:57,760 --> 00:33:59,680
Speaker 3: them are similar to each other and one of them

687
00:33:59,720 --> 00:34:01,840
Speaker 3: is right. Doesn't that sound familiar.

688
00:34:01,920 --> 00:34:03,080
Speaker 6: It sounds like space time.

689
00:34:03,280 --> 00:34:06,960
Speaker 3: It sounds like space time exactly. And quaternions have exactly

690
00:34:07,000 --> 00:34:11,000
Speaker 3: that structure, three imaginary numbers and one real. So the

691
00:34:11,040 --> 00:34:13,920
Speaker 3: real numbers like time, and the three imaginary numbers are

692
00:34:13,920 --> 00:34:17,480
Speaker 3: like three dimensions of space. And so these quaternions the

693
00:34:17,640 --> 00:34:20,840
Speaker 3: rules of space time vectors. We call them four vectors.

694
00:34:20,920 --> 00:34:23,680
Speaker 3: We call them four vectors now instead of quaternions. Are

695
00:34:23,800 --> 00:34:27,000
Speaker 3: absolutely crucial to relativity.

696
00:34:26,520 --> 00:34:29,799
Speaker 6: Meaning you need you can only do relativity math if

697
00:34:29,800 --> 00:34:33,040
Speaker 6: you're using quaternions or it's just helpful to use them.

698
00:34:33,160 --> 00:34:36,319
Speaker 3: No, they're fundamental to special relativity, absolutely, like you can't.

699
00:34:36,320 --> 00:34:38,919
Speaker 6: You can't prove relativity without going into quaternions.

700
00:34:39,040 --> 00:34:41,480
Speaker 3: Exactly if we didn't already have quaternions, we would have

701
00:34:41,560 --> 00:34:44,759
Speaker 3: needed to invent them or discover them, depending on your

702
00:34:44,800 --> 00:34:47,960
Speaker 3: philosophical take. When we build relativity the same way, we

703
00:34:48,160 --> 00:34:51,839
Speaker 3: absolutely need complex numbers to describe quantum mechanics. So all

704
00:34:51,840 --> 00:34:54,680
Speaker 3: the self consistent ways we know how to build complex

705
00:34:54,800 --> 00:34:58,640
Speaker 3: numbers so far are very very useful for physics. And

706
00:34:58,920 --> 00:35:01,320
Speaker 3: it turns out there's a emitted number of these sets.

707
00:35:01,360 --> 00:35:04,399
Speaker 3: You can't just like make up any number. So if one, two,

708
00:35:04,440 --> 00:35:07,479
Speaker 3: and four are super valuable for physics, then maybe eight

709
00:35:07,640 --> 00:35:08,480
Speaker 3: is also.

710
00:35:08,840 --> 00:35:12,480
Speaker 6: Mmmmm, now you need four for relativity? Does it also

711
00:35:12,520 --> 00:35:14,200
Speaker 6: work if you call them fornians.

712
00:35:15,520 --> 00:35:19,400
Speaker 3: For they're a little crunchier, but they still.

713
00:35:19,200 --> 00:35:24,480
Speaker 6: Were all right, I'm just kidding. So you're saying, now

714
00:35:24,520 --> 00:35:27,319
Speaker 6: the question is like the numbers with seven extra imaginary

715
00:35:27,320 --> 00:35:31,200
Speaker 6: dimensions also, maybe could they be used for something in physics?

716
00:35:31,360 --> 00:35:34,480
Speaker 3: That's exactly the question, and it's worth thinking about because

717
00:35:34,480 --> 00:35:37,520
Speaker 3: we've made progress so many times when we've developed some

718
00:35:37,640 --> 00:35:42,239
Speaker 3: mathematical tool group theory, field theory complex numbers, and then

719
00:35:42,320 --> 00:35:45,600
Speaker 3: later found it applicable to physics. So let's like get

720
00:35:45,640 --> 00:35:48,239
Speaker 3: ahead of the game. Let's say, oh, here's a kind

721
00:35:48,239 --> 00:35:51,400
Speaker 3: of mathematical tool which has been useful complex numbers of

722
00:35:51,440 --> 00:35:54,279
Speaker 3: dimensions one, two, and four. If there's only one more

723
00:35:54,360 --> 00:35:57,680
Speaker 3: kind of complex number out there, let's see if maybe

724
00:35:57,680 --> 00:36:00,719
Speaker 3: it tells us something about physics. Maybe it's the mathematical

725
00:36:00,719 --> 00:36:03,399
Speaker 3: structure to understand some other patterns that are out there

726
00:36:03,400 --> 00:36:04,879
Speaker 3: that we didn't have explanations for.

727
00:36:05,560 --> 00:36:07,440
Speaker 6: But does it seem kind of random to you? Like

728
00:36:07,600 --> 00:36:10,800
Speaker 6: you need one xtra imaginary dimension to explain quantum physics

729
00:36:10,800 --> 00:36:14,319
Speaker 6: that's at the microscopic level, but then you need three

730
00:36:14,360 --> 00:36:18,759
Speaker 6: extra imaginary dimensions to describe relativity, which is usually at

731
00:36:18,760 --> 00:36:21,920
Speaker 6: a macro level. Isn't it kind of random? Like you

732
00:36:21,960 --> 00:36:24,040
Speaker 6: need four here? Eight there too? Here?

733
00:36:24,280 --> 00:36:27,160
Speaker 3: Nobody understands it, right, then nobody has an intuitive understanding

734
00:36:27,200 --> 00:36:30,080
Speaker 3: for why one, two, four, and eight, Like there is

735
00:36:30,160 --> 00:36:32,520
Speaker 3: this proof that shows that these are definitely the only

736
00:36:32,560 --> 00:36:35,880
Speaker 3: ones you can do. Nobody really knows philosophically what it means,

737
00:36:35,960 --> 00:36:39,400
Speaker 3: but it's very suggestive. Right If two D numbers are

738
00:36:39,400 --> 00:36:43,000
Speaker 3: needed for quantum mechanics, four D numbers are needed for relativity. Well,

739
00:36:43,040 --> 00:36:46,719
Speaker 3: we've spent the last hundred years looking for quantum mechanical relativity.

740
00:36:47,040 --> 00:36:50,680
Speaker 3: Maybe octonians are the key to that, right, two times

741
00:36:50,680 --> 00:36:54,160
Speaker 3: four equals eight. After all, maybe the mathematical structure we

742
00:36:54,239 --> 00:36:58,160
Speaker 3: need to understand quantum gravity is based on octonians.

743
00:36:58,280 --> 00:37:02,400
Speaker 6: But why good otonias as even try to apply quaternions

744
00:37:02,520 --> 00:37:04,520
Speaker 6: to like quantum gravity?

745
00:37:04,560 --> 00:37:07,840
Speaker 3: Well, absolutely nobody has a consistent theory of quantum gravity

746
00:37:07,880 --> 00:37:10,359
Speaker 3: that works. And every time we try to write down

747
00:37:10,360 --> 00:37:13,919
Speaker 3: the theory of quantum gravity, it breaks mathematically, it does

748
00:37:13,960 --> 00:37:16,160
Speaker 3: not work. So it might just be that we're using

749
00:37:16,160 --> 00:37:18,040
Speaker 3: the wrong kind of number.

750
00:37:18,520 --> 00:37:20,719
Speaker 6: Oh, I see, Like maybe the key to it all

751
00:37:20,880 --> 00:37:24,680
Speaker 6: is just to go to Applebee's and order sometonians.

752
00:37:27,040 --> 00:37:30,759
Speaker 3: Absolutely, it might be, well, I mean that is.

753
00:37:30,760 --> 00:37:33,719
Speaker 6: A joke, Like I think that's what you're saying. It's like,

754
00:37:33,719 --> 00:37:36,399
Speaker 6: why why don't we order an Actonian and see if

755
00:37:36,280 --> 00:37:40,320
Speaker 6: it satisfies or it helps us combine these theories of physics.

756
00:37:40,400 --> 00:37:43,080
Speaker 3: Yeah, absolutely, because remember that there's lots of ways to

757
00:37:43,120 --> 00:37:45,600
Speaker 3: make progress in physics when you don't understand the patterns

758
00:37:45,600 --> 00:37:48,040
Speaker 3: you're looking at. One way is to see more of

759
00:37:48,080 --> 00:37:50,480
Speaker 3: the pattern. You're like, well, what are all these particles?

760
00:37:50,480 --> 00:37:53,200
Speaker 3: Why do we have these particles not other particles. One

761
00:37:53,239 --> 00:37:56,759
Speaker 3: strategy is discover more particles. That's what I'm doing, building colliders,

762
00:37:56,800 --> 00:37:59,400
Speaker 3: smashing stuff together, looking to see more of the pattern,

763
00:37:59,640 --> 00:38:01,800
Speaker 3: hoping that if you see more of it, you'll figure

764
00:38:01,840 --> 00:38:04,560
Speaker 3: out what's going on. Another approach is not to discover

765
00:38:04,640 --> 00:38:08,920
Speaker 3: anything new, but find new mathematical structures that naturally describe

766
00:38:08,920 --> 00:38:12,000
Speaker 3: the patterns you're seeing. For example, that's how we thought

767
00:38:12,040 --> 00:38:14,719
Speaker 3: up the Higgs boson, And it wasn't just discovered, it

768
00:38:14,800 --> 00:38:17,160
Speaker 3: was thought up by looking at the patterns that exist

769
00:38:17,239 --> 00:38:20,000
Speaker 3: already in the particles that we had, coming up with

770
00:38:20,080 --> 00:38:23,600
Speaker 3: a new mathematical structure to describe that group theory and

771
00:38:23,600 --> 00:38:26,960
Speaker 3: the unification of electromagnetism and the weak force, and realizing

772
00:38:27,000 --> 00:38:29,840
Speaker 3: that that needed a Higgs boson. And so there's a

773
00:38:29,840 --> 00:38:32,000
Speaker 3: lot of progress to be made in just coming up

774
00:38:32,040 --> 00:38:34,360
Speaker 3: with a new mathematical way to look at the patterns

775
00:38:34,360 --> 00:38:36,440
Speaker 3: we already seem interesting.

776
00:38:36,520 --> 00:38:38,719
Speaker 6: Like that's a way to do science, like try to

777
00:38:38,719 --> 00:38:40,799
Speaker 6: look for patterns and then come up with ideas that

778
00:38:40,880 --> 00:38:43,880
Speaker 6: might make sense of those patterns. And then go back

779
00:38:43,920 --> 00:38:46,320
Speaker 6: to the experiments to see if those theories are.

780
00:38:46,200 --> 00:38:49,319
Speaker 3: True exactly, because mathematics has its own rules, right, you

781
00:38:49,360 --> 00:38:52,800
Speaker 3: can't just invent whatever mathematics you want. Mathematics is telling

782
00:38:52,880 --> 00:38:55,000
Speaker 3: us very clearly, Hey guys, there's only four kind of

783
00:38:55,040 --> 00:38:56,600
Speaker 3: numbers you can use, by the way, if you want

784
00:38:56,640 --> 00:39:00,200
Speaker 3: to describe physics. And that seems like a pretty big clue. Well,

785
00:39:00,200 --> 00:39:02,239
Speaker 3: if we only have four tools, let's make sure to

786
00:39:02,400 --> 00:39:05,000
Speaker 3: use all of them, right, especially if the first three

787
00:39:05,080 --> 00:39:08,279
Speaker 3: were so absolutely useful. So even if we haven't yet

788
00:39:08,280 --> 00:39:11,359
Speaker 3: figured out what they apply to, it's worth thinking about

789
00:39:11,400 --> 00:39:12,759
Speaker 3: what they might be applied to.

790
00:39:12,960 --> 00:39:15,200
Speaker 6: Mmm. Interesting, Okay, So I think what you're saying is

791
00:39:15,200 --> 00:39:17,640
Speaker 6: that maybe, like if we take the universe and we

792
00:39:17,800 --> 00:39:21,279
Speaker 6: peel back its layers one by one and try to

793
00:39:21,280 --> 00:39:23,040
Speaker 6: get to the core of it, maybe at the center

794
00:39:23,040 --> 00:39:26,440
Speaker 6: of it is an actonium exactly.

795
00:39:26,480 --> 00:39:28,960
Speaker 3: An octonian could be the center of the onion, eight

796
00:39:29,040 --> 00:39:29,520
Speaker 3: layers down.

797
00:39:30,400 --> 00:39:32,640
Speaker 6: Yeah, there you go, I see where you're walking me to. Yes,

798
00:39:34,640 --> 00:39:37,560
Speaker 6: all right, Well let's get into what these ideas are about.

799
00:39:37,560 --> 00:39:40,879
Speaker 6: How Atonians might describe what's inside of the universe, what's

800
00:39:40,880 --> 00:39:43,040
Speaker 6: at the core of it, How does it all work.

801
00:39:43,200 --> 00:39:45,879
Speaker 6: How does it make sense mathematically? Will these theories work?

802
00:39:46,000 --> 00:39:48,560
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Speaker 6: All right, we're talking about otonians and are they the

856
00:42:33,840 --> 00:42:37,480
Speaker 6: imaginary numbers that scientists have been dreaming about to explain

857
00:42:37,719 --> 00:42:41,160
Speaker 6: everything in the universe. So, Daniel, you were saying that

858
00:42:41,239 --> 00:42:45,320
Speaker 6: the numbers is one imaginary number really helped describe quantum mechanics,

859
00:42:45,760 --> 00:42:50,280
Speaker 6: numbers with three imaginary numbers really help describe special relativity

860
00:42:50,280 --> 00:42:53,360
Speaker 6: and relativity, and because it lets you do math with

861
00:42:53,480 --> 00:42:56,360
Speaker 6: space time, three dimensions of space and one of time.

862
00:42:56,800 --> 00:42:59,880
Speaker 6: Now you're saying that maybe if you want to combine

863
00:43:00,280 --> 00:43:05,719
Speaker 6: theories quantum mechanics and special relativity, maybe you need an

864
00:43:05,800 --> 00:43:08,680
Speaker 6: extra imaginary number, which might be the uctonian.

865
00:43:08,840 --> 00:43:12,080
Speaker 3: Yeah, it might be exactly. And we try to figure

866
00:43:12,080 --> 00:43:15,360
Speaker 3: out where this might be relevant to the universe. And

867
00:43:15,480 --> 00:43:17,560
Speaker 3: one thing we can do to figure that out is

868
00:43:17,640 --> 00:43:20,600
Speaker 3: to look at the properties of octonians, like what do

869
00:43:20,640 --> 00:43:24,760
Speaker 3: ooktonians do the quaternions and complex numbers and real numbers

870
00:43:25,080 --> 00:43:29,240
Speaker 3: don't do. How are they different? And that's one fruitful

871
00:43:29,280 --> 00:43:31,560
Speaker 3: way to understand where they might be relevant.

872
00:43:31,719 --> 00:43:33,840
Speaker 6: What do you mean, like what can they do that's special?

873
00:43:34,040 --> 00:43:36,719
Speaker 3: So it's more about what they can't do. Every time

874
00:43:36,760 --> 00:43:40,480
Speaker 3: you add more complex numbers, you sort of lose some ability.

875
00:43:40,680 --> 00:43:43,239
Speaker 3: Like within real numbers, you can order them, right, you

876
00:43:43,239 --> 00:43:45,160
Speaker 3: can say this number is bigger than that number, is

877
00:43:45,200 --> 00:43:47,600
Speaker 3: bigger than that number. They have a very well defined order.

878
00:43:47,640 --> 00:43:50,440
Speaker 3: But once you go to complex numbers, you can't necessarily

879
00:43:50,480 --> 00:43:53,600
Speaker 3: say that, like which number is bigger one or i?

880
00:43:53,640 --> 00:43:55,600
Speaker 3: They have like the same magnitude, but you can no

881
00:43:55,680 --> 00:43:59,040
Speaker 3: longer rank them necessarily. So as you add complex dimensions,

882
00:43:59,239 --> 00:44:02,040
Speaker 3: you actually lose use some capabilities.

883
00:44:01,480 --> 00:44:04,239
Speaker 6: Things say crazier kind of right, like it's it's kind

884
00:44:04,239 --> 00:44:06,680
Speaker 6: of hard to order things in a plane or in

885
00:44:06,719 --> 00:44:08,320
Speaker 6: an xy plane exactly.

886
00:44:08,560 --> 00:44:11,880
Speaker 3: And then when you go to quaternions basically space time vectors,

887
00:44:12,120 --> 00:44:15,680
Speaker 3: what you lose is commutation. The fact that like A

888
00:44:15,880 --> 00:44:18,680
Speaker 3: times B is usually equal to B times a, but

889
00:44:18,719 --> 00:44:22,480
Speaker 3: that's not true for four dimensional vectors, because multiplying numbers

890
00:44:22,480 --> 00:44:25,200
Speaker 3: in four dimensions is like rotation. It's like taking a

891
00:44:25,280 --> 00:44:29,480
Speaker 3: vector and turning it, and in four dimensional space, rotations

892
00:44:29,560 --> 00:44:33,000
Speaker 3: don't commute. It like matters what order you do rotations in.

893
00:44:33,520 --> 00:44:35,759
Speaker 3: If you first turn left and then you turn up,

894
00:44:35,800 --> 00:44:37,680
Speaker 3: you get it to a different place than if you

895
00:44:37,719 --> 00:44:38,720
Speaker 3: do it in the other direction.

896
00:44:38,840 --> 00:44:40,800
Speaker 6: For example, Wait, wait, I thought that you said that

897
00:44:40,880 --> 00:44:44,919
Speaker 6: quaternions and elktunians work because they follow all the math rules.

898
00:44:44,920 --> 00:44:46,960
Speaker 6: You're saying now that maybe they sort of work, but

899
00:44:47,080 --> 00:44:49,680
Speaker 6: you kind of have to give up some math rules exactly.

900
00:44:49,719 --> 00:44:52,480
Speaker 3: These math rules that we require don't include that they commute.

901
00:44:52,520 --> 00:44:54,600
Speaker 3: They only include that you can multiply and divide an

902
00:44:54,600 --> 00:44:57,800
Speaker 3: add and subtract. Commutation is not a requirement. It turns

903
00:44:57,840 --> 00:45:00,600
Speaker 3: out that as the numbers get more complex, you lose

904
00:45:00,600 --> 00:45:03,080
Speaker 3: some of the properties we're familiar with of real numbers.

905
00:45:03,600 --> 00:45:07,480
Speaker 3: So complex numbers you lose the ability to order them quaternions,

906
00:45:07,600 --> 00:45:09,800
Speaker 3: you lose the ability to multiply them in any order

907
00:45:09,840 --> 00:45:12,000
Speaker 3: you want. A times B is not the same as

908
00:45:12,040 --> 00:45:14,200
Speaker 3: B times A. So that's really interesting. It tells us

909
00:45:14,200 --> 00:45:16,880
Speaker 3: something about the structure of space time, right that this

910
00:45:16,960 --> 00:45:22,000
Speaker 3: is really about space now Octonians. Even weirder Octonians, which

911
00:45:22,000 --> 00:45:25,439
Speaker 3: you lose is the associative property. The associated property tells

912
00:45:25,520 --> 00:45:28,239
Speaker 3: us basically, you can distribute numbers within a parenthesis, like

913
00:45:28,520 --> 00:45:31,040
Speaker 3: do you do the multiplication within the parentheses first, or

914
00:45:31,080 --> 00:45:33,040
Speaker 3: do you distribute the number through the parentheses? Sort of

915
00:45:33,040 --> 00:45:36,000
Speaker 3: hard to think about the associated property of math intuitively.

916
00:45:36,200 --> 00:45:37,960
Speaker 3: In a physical sense, it would be sort of like,

917
00:45:38,120 --> 00:45:40,080
Speaker 3: you know, you're used to putting your socks on and

918
00:45:40,120 --> 00:45:42,240
Speaker 3: then your shoes. What if you first put your socks

919
00:45:42,280 --> 00:45:45,120
Speaker 3: in your shoes and then put your feet into the socks,

920
00:45:45,280 --> 00:45:47,080
Speaker 3: you'd end up in the same place. Right, it doesn't

921
00:45:47,080 --> 00:45:49,600
Speaker 3: really matter if you put the socks on first or

922
00:45:49,640 --> 00:45:52,759
Speaker 3: put the socks in the shoes, But for Octonians it

923
00:45:52,840 --> 00:45:56,919
Speaker 3: does matter. The associated property doesn't hold for Octonians.

924
00:45:57,320 --> 00:46:00,840
Speaker 6: M I see, you lose another math rule, and you

925
00:46:00,880 --> 00:46:03,000
Speaker 6: also lose the ability to order them, and you also

926
00:46:03,040 --> 00:46:05,359
Speaker 6: lose the ability to like commute them.

927
00:46:05,360 --> 00:46:08,800
Speaker 3: You said exactly, So that's a clue, right. It tells

928
00:46:08,880 --> 00:46:12,040
Speaker 3: us that maybe the fundamental nature of the universe doesn't

929
00:46:12,080 --> 00:46:16,719
Speaker 3: respect this associated property. Maybe parentheses actually do matter to

930
00:46:17,000 --> 00:46:20,640
Speaker 3: whatever mathematics really rules the universe. That's just like a clue,

931
00:46:20,680 --> 00:46:23,000
Speaker 3: and then we go off hunting in the physical world

932
00:46:23,120 --> 00:46:27,040
Speaker 3: for maybe something that's like that. Is there some theory

933
00:46:27,080 --> 00:46:29,799
Speaker 3: of physics that we can build that doesn't have this

934
00:46:29,880 --> 00:46:34,440
Speaker 3: requirement of associativity of our numbers, Maybe that's the right direction.

935
00:46:34,640 --> 00:46:37,080
Speaker 3: It's a very very vague clue, but that's the kind

936
00:46:37,120 --> 00:46:38,960
Speaker 3: of clue we can get from looking at the structure

937
00:46:39,000 --> 00:46:41,400
Speaker 3: of the mathematics of Octonians.

938
00:46:41,680 --> 00:46:43,680
Speaker 6: Oh, I see, because the pattern is that every time

939
00:46:43,680 --> 00:46:48,280
Speaker 6: you have one of these imaginary number sets, their limitations

940
00:46:48,360 --> 00:46:52,160
Speaker 6: somehow correspond to a rule or a feature of the universe.

941
00:46:52,600 --> 00:46:55,160
Speaker 6: Like when you had one extra dimension and you can't

942
00:46:55,200 --> 00:46:59,400
Speaker 6: order those numbers, that corresponds to something special about quantum particles,

943
00:46:59,719 --> 00:47:03,760
Speaker 6: or when you have a quaternion and you can't commute

944
00:47:03,760 --> 00:47:06,600
Speaker 6: them that means something special about how you can rotate

945
00:47:06,680 --> 00:47:07,800
Speaker 6: or not things in space.

946
00:47:07,880 --> 00:47:11,239
Speaker 3: Mm hmm exactly. So what does this mean about the

947
00:47:11,320 --> 00:47:15,080
Speaker 3: universe that Actonians don't respect the associative property. It's very strange,

948
00:47:15,080 --> 00:47:18,160
Speaker 3: it's very unphysical. We have like no intuition for it.

949
00:47:18,400 --> 00:47:20,120
Speaker 3: What it tells us is that a theory of the

950
00:47:20,200 --> 00:47:23,800
Speaker 3: universe built on Octonians is going to be very counterintuitive.

951
00:47:23,880 --> 00:47:25,560
Speaker 6: Wait, doesn't it just mean you can't put on your

952
00:47:25,560 --> 00:47:26,879
Speaker 6: socks and your shoes at the same time.

953
00:47:28,320 --> 00:47:30,440
Speaker 3: It means it makes a difference whether you put your

954
00:47:30,440 --> 00:47:32,400
Speaker 3: socks in your shoes and then put them both on,

955
00:47:32,600 --> 00:47:34,520
Speaker 3: or put your socks on and then your shoes.

956
00:47:34,880 --> 00:47:39,600
Speaker 6: Yeah, it would make a difference, for sure, I would work.

957
00:47:40,920 --> 00:47:42,640
Speaker 3: I mean, I think some people put their underwear and

958
00:47:42,680 --> 00:47:44,200
Speaker 3: their pants on at the same time, don't they. I

959
00:47:44,239 --> 00:47:44,600
Speaker 3: don't know.

960
00:47:44,680 --> 00:47:47,319
Speaker 6: Oh, well, well, why didn't you start with that analogy.

961
00:47:47,520 --> 00:47:49,280
Speaker 3: I didn't want to talk about underwear? I guess.

962
00:47:51,800 --> 00:47:54,920
Speaker 6: So you're saying that, uh, Quaternions, you can't do that.

963
00:47:54,960 --> 00:47:56,680
Speaker 6: You can't put your underwear inside of your pants and

964
00:47:56,680 --> 00:47:58,200
Speaker 6: then put them on both at the same time.

965
00:47:58,600 --> 00:48:02,440
Speaker 3: You can for you can Forquians, you can't for Octonians.

966
00:48:01,960 --> 00:48:04,799
Speaker 6: That's right. I'm sorry you can't for Octonians. You're asking like,

967
00:48:04,960 --> 00:48:08,239
Speaker 6: is there a rule in the universe that somehow corresponds

968
00:48:08,320 --> 00:48:10,520
Speaker 6: to that limitation with your pants?

969
00:48:11,480 --> 00:48:14,560
Speaker 3: Exactly? The underlying rule of the universe is somehow related

970
00:48:14,600 --> 00:48:16,080
Speaker 3: to underpants. We don't know.

971
00:48:17,120 --> 00:48:19,120
Speaker 6: Yeah, there you go, or d end up looking like

972
00:48:19,160 --> 00:48:21,920
Speaker 6: Superman with the other world outside of your pants.

973
00:48:22,400 --> 00:48:25,200
Speaker 3: Exactly. Maybe he's the original Octonian.

974
00:48:24,960 --> 00:48:30,520
Speaker 6: That's right. Maybe maybe any Kryptonians to just really describe

975
00:48:30,520 --> 00:48:31,440
Speaker 6: the universe.

976
00:48:31,200 --> 00:48:33,480
Speaker 3: We don't know. But in the meantime, physicists are on

977
00:48:33,520 --> 00:48:36,719
Speaker 3: the hunt for eights. We're looking for things out there

978
00:48:36,719 --> 00:48:39,879
Speaker 3: in nature patterns which include the number eight. And there

979
00:48:39,880 --> 00:48:43,520
Speaker 3: are some pantalizing hints, you know. For example, string theory

980
00:48:43,600 --> 00:48:47,640
Speaker 3: we know likes to exist in ten spatial dimensions because

981
00:48:47,840 --> 00:48:50,880
Speaker 3: the mathematics of how those things compactify works best in

982
00:48:50,960 --> 00:48:53,680
Speaker 3: ten dimensions. So some people have said, ooh, well, that's

983
00:48:53,719 --> 00:48:57,320
Speaker 3: sort of like eight spatial dimensions and one time dimension

984
00:48:57,520 --> 00:49:00,520
Speaker 3: plus one dimension for like along the string, and so

985
00:49:00,560 --> 00:49:02,120
Speaker 3: there's kind of an eight there.

986
00:49:02,239 --> 00:49:05,040
Speaker 6: But ten, you said, didn't work. Why are they fixated

987
00:49:05,080 --> 00:49:07,319
Speaker 6: with ten? If ten doesn't hold mathematically?

988
00:49:07,480 --> 00:49:10,240
Speaker 3: Because string theory works in ten dimensions, there's a different

989
00:49:10,239 --> 00:49:13,080
Speaker 3: set of rules there. Mathematically, string theory works in ten,

990
00:49:13,400 --> 00:49:16,359
Speaker 3: Octonians work in eight. Can we somehow marry the two?

991
00:49:16,800 --> 00:49:18,239
Speaker 3: Well maybe if we take those ten.

992
00:49:18,160 --> 00:49:19,800
Speaker 6: Dimensions the difference and make it nine.

993
00:49:20,640 --> 00:49:23,680
Speaker 3: There's no compromising in math. It's not a negotiation with

994
00:49:23,760 --> 00:49:24,360
Speaker 3: the universe.

995
00:49:24,640 --> 00:49:30,200
Speaker 6: You can't split the difference. Well, I can't make quantum gravity. Worry.

996
00:49:30,200 --> 00:49:31,680
Speaker 6: How about uh, we'll split the difference.

997
00:49:31,760 --> 00:49:33,560
Speaker 3: I'll give you points on the back end, all right,

998
00:49:33,600 --> 00:49:34,120
Speaker 3: how about that?

999
00:49:34,120 --> 00:49:36,600
Speaker 6: That's right. Yes, we'll only make both of them half work.

1000
00:49:37,719 --> 00:49:39,600
Speaker 3: No, people are like, well, can we take eight of

1001
00:49:39,640 --> 00:49:42,480
Speaker 3: those ten string dimensions and say those are described by

1002
00:49:42,480 --> 00:49:45,279
Speaker 3: Octonians and then another one in them is time and

1003
00:49:45,280 --> 00:49:47,760
Speaker 3: another one is a string dimension. It's a real stretch.

1004
00:49:48,120 --> 00:49:51,600
Speaker 3: But people are looking for eightishness somewhere out there in

1005
00:49:51,600 --> 00:49:55,120
Speaker 3: the patterns and wondering if it can be described by Octonians.

1006
00:49:55,239 --> 00:49:58,560
Speaker 6: Can't you just decrease the number of dimensions in string

1007
00:49:58,640 --> 00:49:59,839
Speaker 6: theory or it wouldn't work.

1008
00:50:00,040 --> 00:50:02,320
Speaker 3: Well, now it doesn't work. It only works in ten dimensions.

1009
00:50:02,360 --> 00:50:04,520
Speaker 3: There's another version of it that works in twenty six,

1010
00:50:04,840 --> 00:50:07,800
Speaker 3: but string theory doesn't work in eight dimensions. Another direction

1011
00:50:07,840 --> 00:50:09,719
Speaker 3: people are going in is to try to describe the

1012
00:50:09,760 --> 00:50:12,600
Speaker 3: strong force. The strong force is something we really don't

1013
00:50:12,680 --> 00:50:16,640
Speaker 3: understand very well. But it has eight gluons. Right, there's

1014
00:50:16,680 --> 00:50:20,040
Speaker 3: the number eight, So maybe Octonians would be a better

1015
00:50:20,080 --> 00:50:22,560
Speaker 3: way to describe the strong force. Maybe the whole reason

1016
00:50:22,880 --> 00:50:26,640
Speaker 3: we have trouble doing calculations in quantum chromodynamics is because

1017
00:50:26,640 --> 00:50:28,040
Speaker 3: we're used in the wrong kind of math, and it

1018
00:50:28,080 --> 00:50:30,480
Speaker 3: would all just like click beautifully into place if we

1019
00:50:30,560 --> 00:50:31,919
Speaker 3: replaced it with octonians.

1020
00:50:32,160 --> 00:50:34,600
Speaker 6: Wait, what do I mean there are only eight gluons?

1021
00:50:34,760 --> 00:50:37,520
Speaker 6: You're just looking for things in nature that you know

1022
00:50:37,560 --> 00:50:39,480
Speaker 6: about so far that somehow count it eight.

1023
00:50:39,680 --> 00:50:42,600
Speaker 3: Yeah, exactly, And there are eight kinds of gluons because

1024
00:50:42,640 --> 00:50:45,640
Speaker 3: remember that there are three different colors in the strong

1025
00:50:45,680 --> 00:50:49,880
Speaker 3: force red, green, and blue, and each gluon carries two colors,

1026
00:50:50,280 --> 00:50:52,120
Speaker 3: and so the way the mathematics works is that it's

1027
00:50:52,160 --> 00:50:55,160
Speaker 3: three squared minus one. You get eight different kinds of

1028
00:50:55,239 --> 00:50:58,000
Speaker 3: gluons that you can have. So, yeah, we're just looking

1029
00:50:58,000 --> 00:51:00,480
Speaker 3: for things in nature that have eight in them. Like,

1030
00:51:00,560 --> 00:51:03,680
Speaker 3: what about the universe is eightish? Can we describe it

1031
00:51:03,719 --> 00:51:08,360
Speaker 3: with octonians? So far nobody's made it work Octonians mathematically beautiful,

1032
00:51:08,440 --> 00:51:11,640
Speaker 3: mathematically consistent, so far, totally physically useless.

1033
00:51:11,920 --> 00:51:14,239
Speaker 6: Huh, Like, what did you decide to try to make

1034
00:51:14,280 --> 00:51:17,560
Speaker 6: quantum gravity work with octonians? Where does that put us?

1035
00:51:17,640 --> 00:51:20,839
Speaker 6: Aren't there like eight dimensions or things like that in

1036
00:51:20,880 --> 00:51:23,440
Speaker 6: between the two of them, like the wave function plus

1037
00:51:23,640 --> 00:51:24,759
Speaker 6: the space.

1038
00:51:24,480 --> 00:51:28,680
Speaker 3: Time throwing some oranges and a couple of socks. Yeah, exactly.

1039
00:51:29,040 --> 00:51:30,960
Speaker 3: I know people are working on that, right, there's a

1040
00:51:30,960 --> 00:51:33,399
Speaker 3: lot of people studying the nature of octonians and trying

1041
00:51:33,400 --> 00:51:36,440
Speaker 3: to use them to build a physical theory, but nobody's

1042
00:51:36,440 --> 00:51:38,719
Speaker 3: succeeded so far. Just sort of like a direction some

1043
00:51:38,760 --> 00:51:42,200
Speaker 3: people are sniffing in as we try to build mathematically

1044
00:51:42,239 --> 00:51:44,120
Speaker 3: consistent theories of quantum gravity.

1045
00:51:44,360 --> 00:51:45,919
Speaker 6: Wow, you're just looking for the number eight.

1046
00:51:46,120 --> 00:51:48,719
Speaker 3: Yes, exactly. We're desperate for clues because this is the

1047
00:51:48,719 --> 00:51:51,840
Speaker 3: biggest unsolved problem in physics. How to marry quantum mechanics

1048
00:51:51,840 --> 00:51:54,440
Speaker 3: and relativity. We haven't figured out in one hundred years.

1049
00:51:54,760 --> 00:51:57,359
Speaker 3: So we're like digging deep in the mathematical toolbox to like, well,

1050
00:51:57,360 --> 00:51:58,960
Speaker 3: what else we got in here? Let's see what else

1051
00:51:58,960 --> 00:51:59,600
Speaker 3: could be useful.

1052
00:52:00,640 --> 00:52:02,760
Speaker 6: Well, I can't seem to get up before eight am?

1053
00:52:02,920 --> 00:52:05,520
Speaker 6: Could that be a rule of the universe? I could

1054
00:52:05,560 --> 00:52:06,000
Speaker 6: blame that.

1055
00:52:06,000 --> 00:52:08,399
Speaker 3: On Well, we could flip the blame. You could say,

1056
00:52:08,440 --> 00:52:10,919
Speaker 3: nobody solved this problem because you won't get up before

1057
00:52:10,960 --> 00:52:11,440
Speaker 3: eight am.

1058
00:52:12,239 --> 00:52:14,799
Speaker 6: Well, that would still make sense. That would still that's

1059
00:52:14,800 --> 00:52:16,440
Speaker 6: still an explanation for the universe.

1060
00:52:17,160 --> 00:52:19,280
Speaker 3: Or maybe it would take an announcement of quantum gravity

1061
00:52:19,320 --> 00:52:21,200
Speaker 3: to get you out of it before eight am.

1062
00:52:21,840 --> 00:52:24,839
Speaker 6: Unlikely, unlikely in this universe. I don't think that would

1063
00:52:24,880 --> 00:52:29,680
Speaker 6: mathematically hold. Yeah, I think I think there's YouTube for that.

1064
00:52:30,280 --> 00:52:33,040
Speaker 6: I'll just catch it on YouTube later. All right, Well,

1065
00:52:33,040 --> 00:52:36,000
Speaker 6: but it's sort of an interesting idea or direction in

1066
00:52:36,040 --> 00:52:38,520
Speaker 6: which to look for new theories about the universe. Like

1067
00:52:38,960 --> 00:52:41,719
Speaker 6: maybe you put your octagoggles on and look for things

1068
00:52:41,719 --> 00:52:46,200
Speaker 6: that work or that seem to manifest themselves in sets

1069
00:52:46,239 --> 00:52:49,759
Speaker 6: of eight. Maybe that could be a way to get

1070
00:52:49,800 --> 00:52:51,760
Speaker 6: to the theory of everything exactly.

1071
00:52:51,800 --> 00:52:55,480
Speaker 3: If mathematics really does reflect something deep about the universe,

1072
00:52:55,800 --> 00:52:59,560
Speaker 3: then mathematicians building tools can actually construct sort of like

1073
00:52:59,600 --> 00:53:02,120
Speaker 3: proto bits of future physics theories that we could just

1074
00:53:02,160 --> 00:53:04,799
Speaker 3: like click into place. We've done it before with group

1075
00:53:04,840 --> 00:53:08,200
Speaker 3: theory and field theory and differential geometry, so we hope

1076
00:53:08,200 --> 00:53:09,239
Speaker 3: it happens again.

1077
00:53:09,200 --> 00:53:11,200
Speaker 6: Right, And that's kind of what's happening with strength there.

1078
00:53:11,360 --> 00:53:13,440
Speaker 6: Although that one seems to be following the rule.

1079
00:53:13,239 --> 00:53:15,600
Speaker 3: Of ten, yeah, or the rule of twenty six.

1080
00:53:15,640 --> 00:53:19,279
Speaker 6: So it sounds like maybe physicis you need to sit

1081
00:53:19,320 --> 00:53:21,719
Speaker 6: down and peel more onions.

1082
00:53:22,280 --> 00:53:23,320
Speaker 3: And stop crying.

1083
00:53:23,960 --> 00:53:27,960
Speaker 6: That's right, stop pretend pretend to tears come from cutting

1084
00:53:28,000 --> 00:53:31,000
Speaker 6: these onions and not from being a physicist, and maybe

1085
00:53:31,000 --> 00:53:34,240
Speaker 6: that will inspire some new theory. That may it'll crack open,

1086
00:53:34,600 --> 00:53:37,160
Speaker 6: they'll peel away the truth of the universe.

1087
00:53:37,280 --> 00:53:38,839
Speaker 3: Or maybe we should just take a break in good

1088
00:53:38,880 --> 00:53:40,800
Speaker 3: Applebee's and have a bloomin onion.

1089
00:53:41,480 --> 00:53:44,120
Speaker 6: Yeah, there you go. There are different ways. As long

1090
00:53:44,160 --> 00:53:47,920
Speaker 6: as it's after eight am, I'll join you, all right. Well,

1091
00:53:47,960 --> 00:53:51,600
Speaker 6: and interesting dive into mathematics and how it matches up

1092
00:53:51,640 --> 00:53:54,480
Speaker 6: with physics and how it's helping us maybe understand how

1093
00:53:54,520 --> 00:53:56,680
Speaker 6: it all works, or at least how it has helped

1094
00:53:56,719 --> 00:53:58,520
Speaker 6: us and maybe could help us in the future.

1095
00:53:58,719 --> 00:54:01,799
Speaker 3: And future mathematicians and physicists might look back and say, oh,

1096
00:54:01,920 --> 00:54:04,280
Speaker 3: it was so obvious how it all clicked into place.

1097
00:54:04,400 --> 00:54:06,800
Speaker 3: But here we are at the forefront of human ignorance,

1098
00:54:07,160 --> 00:54:08,600
Speaker 3: just not seeing it come together.

1099
00:54:09,000 --> 00:54:11,200
Speaker 6: All right, Well, we hope you enjoyed that. Thanks for

1100
00:54:11,280 --> 00:54:13,319
Speaker 6: joining us. See you next time.

1101
00:54:17,719 --> 00:54:20,600
Speaker 3: For more science and curiosity. Come find us on social

1102
00:54:20,640 --> 00:54:25,600
Speaker 3: media where we answer questions and post videos. We're on Twitter, Discord, Instant,

1103
00:54:25,640 --> 00:54:29,120
Speaker 3: and now TikTok. Thanks for listening and remember that Daniel

1104
00:54:29,120 --> 00:54:32,600
Speaker 3: and Jorge Explain the Universe is a production of iHeartRadio.

1105
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Speaker 3: For more podcasts from iHeartRadio Visit the iHeartRadio app, Apple Podcasts,

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Speaker 3: or wherever you listen to your favorite shows.

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1128
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Speaker 12: So what do we do with it?

1129
00:55:58,719 --> 00:55:58,919
Speaker 3: Right?

1130
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Speaker 12: How do we utilize the opportunities that we have that

1131
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Speaker 12: they don't right? And a lot of that is educating ourselves,

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Speaker 12: educating ourselves on how to not make the same mistakes

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Speaker 12: they did.

1134
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