1 00:00:08,520 --> 00:00:11,600 Speaker 1: Hey, Daniel, what are your favorite numbers in physics? 2 00:00:11,920 --> 00:00:14,600 Speaker 2: Oh? There are so many good ones. I mean I 3 00:00:14,640 --> 00:00:17,960 Speaker 2: love planks constant, which tells us about like when things 4 00:00:17,960 --> 00:00:20,919 Speaker 2: become quantum. I love the speed of light that tells 5 00:00:21,000 --> 00:00:24,640 Speaker 2: us all about relativity. Too many to choose from. There 6 00:00:24,680 --> 00:00:25,919 Speaker 2: are a number of favorites there. 7 00:00:26,880 --> 00:00:29,960 Speaker 1: But have you ever wondered why numbers are so important 8 00:00:30,000 --> 00:00:30,680 Speaker 1: in the universe? 9 00:00:30,800 --> 00:00:34,000 Speaker 2: I mean, numbers are like the currency of physics. We're 10 00:00:34,000 --> 00:00:37,360 Speaker 2: predicting things happening at times and places, and those are 11 00:00:37,479 --> 00:00:38,080 Speaker 2: just numbers. 12 00:00:38,280 --> 00:00:40,519 Speaker 1: Wow. So does that mean you get paid in numbers? 13 00:00:42,200 --> 00:00:43,880 Speaker 2: I get a number of dollars every year. 14 00:00:44,440 --> 00:00:46,519 Speaker 1: I guess we all get paid in numbers if there's 15 00:00:46,560 --> 00:00:49,320 Speaker 1: just numbers in our bank account. If you're so lucky, 16 00:00:50,080 --> 00:00:52,960 Speaker 1: the whole universe is just numbers. I think you said 17 00:00:52,960 --> 00:00:56,600 Speaker 1: that a number of times. I'm the number one fan 18 00:00:56,760 --> 00:00:58,840 Speaker 1: of numbers. I think I know a number of those 19 00:00:59,320 --> 00:01:17,600 Speaker 1: in physics and math. Too many to number. Hi. I'm 20 00:01:17,640 --> 00:01:21,000 Speaker 1: Jorge Mack, cartoonists and the author of Oliver's Great Big Universe. 21 00:01:21,400 --> 00:01:24,040 Speaker 2: Hi, I'm Daniel. I'm a particle physicist, and I've been 22 00:01:24,040 --> 00:01:27,319 Speaker 2: a professor at UC Irvine for a large number of years. 23 00:01:27,760 --> 00:01:30,240 Speaker 1: Oh, too many to count? Or do you go into 24 00:01:30,240 --> 00:01:33,200 Speaker 1: some sort of like weird subspace when you do physics. 25 00:01:34,200 --> 00:01:36,080 Speaker 2: No, I think I'm going to enter a puba phase 26 00:01:36,120 --> 00:01:38,760 Speaker 2: eventually and then emerge as an emeritus professor. 27 00:01:39,680 --> 00:01:44,040 Speaker 1: That's a butterfly. That's a beautiful tenured emeritus. 28 00:01:43,520 --> 00:01:45,320 Speaker 2: Butterfly, as a white haired moth. 29 00:01:45,440 --> 00:01:49,040 Speaker 1: I think instead of wings, do you just have a 30 00:01:49,080 --> 00:01:51,200 Speaker 1: bunch of research papers taped together. 31 00:01:53,200 --> 00:01:55,200 Speaker 2: I'm going to fly too close to the universe on 32 00:01:55,240 --> 00:01:56,960 Speaker 2: wings of research papers. 33 00:01:56,720 --> 00:01:59,600 Speaker 1: Right, But you know, butterflies don't have mouths, right, so 34 00:01:59,640 --> 00:02:00,600 Speaker 1: you won't be to talk. 35 00:02:00,840 --> 00:02:03,000 Speaker 2: Yeah, but they have those long newses, and so I'm 36 00:02:03,000 --> 00:02:03,880 Speaker 2: already said. 37 00:02:04,560 --> 00:02:09,480 Speaker 1: There you go. You can sniff out science from there. 38 00:02:09,720 --> 00:02:10,000 Speaker 1: M hmm. 39 00:02:10,160 --> 00:02:12,640 Speaker 2: I can snort up all the information in the universe. 40 00:02:12,960 --> 00:02:15,280 Speaker 1: Oh boy, that sounds a little illegal. 41 00:02:15,440 --> 00:02:17,560 Speaker 2: Are you going to arrest a butterfly? Is that what 42 00:02:17,720 --> 00:02:18,200 Speaker 2: has come to? 43 00:02:18,880 --> 00:02:22,600 Speaker 1: Maybe a cocaine sniffing butterfly. Maybe maybe it will be 44 00:02:22,639 --> 00:02:25,520 Speaker 1: our informant for, you know, figuring out how the universe works. 45 00:02:26,680 --> 00:02:30,240 Speaker 2: Maybe altering your mental state is important for understanding the universe. 46 00:02:30,320 --> 00:02:32,480 Speaker 1: M I hear that's called the butterfly effect. 47 00:02:33,760 --> 00:02:35,440 Speaker 2: I think that's something else. 48 00:02:35,280 --> 00:02:38,760 Speaker 1: Meant something else. Did I get that wrong. 49 00:02:39,040 --> 00:02:40,360 Speaker 2: I think it's called microducing. 50 00:02:40,639 --> 00:02:43,920 Speaker 1: Yeah, I think this is called micro punning, which it 51 00:02:43,919 --> 00:02:46,120 Speaker 1: doesn't work as well. But anyways, welcome to our podcast 52 00:02:46,200 --> 00:02:50,240 Speaker 1: Daniel and Jorge Explain the Universe, a production of iHeartRadio. 53 00:02:49,680 --> 00:02:52,000 Speaker 2: In which we give you a drip, drip, drip, little 54 00:02:52,080 --> 00:02:55,440 Speaker 2: doses of the incredible wonder we discovered about the universe, 55 00:02:55,880 --> 00:02:58,480 Speaker 2: everything that's out there that makes sense, and everything out 56 00:02:58,480 --> 00:03:00,880 Speaker 2: there that still puzzles us as we try to fit 57 00:03:00,960 --> 00:03:04,320 Speaker 2: the entire universe into a pattern that makes sense to 58 00:03:04,440 --> 00:03:06,000 Speaker 2: our little human minds. 59 00:03:06,400 --> 00:03:08,200 Speaker 1: That's right, We try to get you high on the 60 00:03:08,240 --> 00:03:11,560 Speaker 1: little dopamin head of wonder and amazement at how our 61 00:03:11,639 --> 00:03:14,840 Speaker 1: universe works and the surprising ways in which it still 62 00:03:15,000 --> 00:03:16,639 Speaker 1: puzzles scientists even today. 63 00:03:16,800 --> 00:03:20,120 Speaker 2: And one thing that still puzzles scientists and philosophers is 64 00:03:20,160 --> 00:03:23,760 Speaker 2: at any of it makes sense that these mathematical models 65 00:03:23,760 --> 00:03:26,440 Speaker 2: we build on our head can actually describe and even 66 00:03:26,480 --> 00:03:29,840 Speaker 2: predict what's going to happen out there in the universe. 67 00:03:30,400 --> 00:03:33,720 Speaker 2: That somehow mathematics seems to be not just the currency 68 00:03:33,760 --> 00:03:36,760 Speaker 2: of our physics, but the currency of the universe itself. 69 00:03:36,920 --> 00:03:39,720 Speaker 1: Wait, wait, are you saying math is more important than physics. 70 00:03:41,760 --> 00:03:44,360 Speaker 2: I mean, is English more important than Shakespeare. You can't 71 00:03:44,400 --> 00:03:45,760 Speaker 2: really compare the two things, you know. 72 00:03:47,280 --> 00:03:51,160 Speaker 1: Wait with this analogy, Shakespeare's math in English is physics. 73 00:03:51,280 --> 00:03:54,640 Speaker 2: No, Shakespeare's physics and English is math. Physics is speaking 74 00:03:54,640 --> 00:03:57,640 Speaker 2: in the language of mathematics. We are writing poetry in 75 00:03:57,680 --> 00:03:58,600 Speaker 2: the language of math. 76 00:03:58,840 --> 00:04:02,040 Speaker 1: I see. I see. So physics a comedy or a tragedy. 77 00:04:02,840 --> 00:04:04,320 Speaker 2: It's a tragic comedy, for sure. 78 00:04:04,400 --> 00:04:05,720 Speaker 1: It's a tragic comedy. 79 00:04:06,720 --> 00:04:09,120 Speaker 2: We're all waiting for the final twist. Nobody knows how 80 00:04:09,120 --> 00:04:09,480 Speaker 2: it ends. 81 00:04:09,520 --> 00:04:12,279 Speaker 1: That's right, it never ends well for Shakespeare. 82 00:04:12,920 --> 00:04:14,320 Speaker 2: But I hope we laugh along the way. 83 00:04:14,520 --> 00:04:17,000 Speaker 1: And you also have to wear tights when you do physics. 84 00:04:17,040 --> 00:04:17,400 Speaker 3: Mmmm. 85 00:04:17,680 --> 00:04:20,360 Speaker 2: And as always, the jester is the wisest one. 86 00:04:21,240 --> 00:04:24,680 Speaker 1: I see. That's the engineer and the team. 87 00:04:24,800 --> 00:04:27,400 Speaker 2: Did you just call engineers jokers? I mean, I'm just 88 00:04:27,400 --> 00:04:28,720 Speaker 2: gonna step slowly away from that. 89 00:04:29,160 --> 00:04:30,680 Speaker 1: No. I know. We have a great sense of humor, 90 00:04:30,800 --> 00:04:35,280 Speaker 1: is what I'm saying. We're the smaltest person in the room. 91 00:04:35,000 --> 00:04:36,880 Speaker 2: Often laughed at and unwisely ignored. 92 00:04:37,040 --> 00:04:38,600 Speaker 1: But yeah, it seems like there are a lot of 93 00:04:38,680 --> 00:04:41,560 Speaker 1: numbers in physics. There's an infinite number of numbers in math, 94 00:04:41,640 --> 00:04:43,400 Speaker 1: let's face it. But in physics it seems like there 95 00:04:43,400 --> 00:04:45,599 Speaker 1: are special numbers out there that have kind of a 96 00:04:45,680 --> 00:04:48,599 Speaker 1: special status because they're sort of significant in how the 97 00:04:48,680 --> 00:04:49,360 Speaker 1: universe works. 98 00:04:49,440 --> 00:04:52,280 Speaker 2: Yeah, there are certain constants which seem to be important 99 00:04:52,360 --> 00:04:55,320 Speaker 2: to tell us something about the universe, the speed of light, 100 00:04:55,760 --> 00:04:59,440 Speaker 2: planks constant, the gravitational constant. There are even numbers that 101 00:04:59,480 --> 00:05:02,279 Speaker 2: don't have units, you know, like the number of particles 102 00:05:02,320 --> 00:05:05,200 Speaker 2: we've discovered or ratios of masses that we think reveal 103 00:05:05,320 --> 00:05:08,040 Speaker 2: something deep about the universe. But even more than that, 104 00:05:08,080 --> 00:05:12,200 Speaker 2: there are systems of numbers. There are patterns of numbers 105 00:05:12,440 --> 00:05:17,080 Speaker 2: that reflect patterns we see in the universe, mathematical constructs 106 00:05:17,120 --> 00:05:20,400 Speaker 2: and all sorts of fancy mathematics that really are crucial 107 00:05:20,440 --> 00:05:22,880 Speaker 2: to understanding how the universe operates. 108 00:05:23,120 --> 00:05:26,039 Speaker 1: And this is kind of especially true at the microscopic level, right, 109 00:05:26,040 --> 00:05:27,600 Speaker 1: That's where a lot of these numbers and a lot 110 00:05:27,600 --> 00:05:29,440 Speaker 1: of this math comes from, and it comes from our 111 00:05:30,560 --> 00:05:33,280 Speaker 1: understanding how things work at the particle level. 112 00:05:33,520 --> 00:05:36,279 Speaker 2: Math an interesting point. I would say that math describes 113 00:05:36,320 --> 00:05:38,680 Speaker 2: the universe at every level. You know, we have mathematics 114 00:05:38,720 --> 00:05:41,839 Speaker 2: for fluid dynamics and for planetary evolution and for the 115 00:05:41,880 --> 00:05:45,919 Speaker 2: expansion of the whole universe. It's mathematics up and down. 116 00:05:46,000 --> 00:05:48,240 Speaker 1: Okay, so it's at every level, but it seems like 117 00:05:48,360 --> 00:05:51,040 Speaker 1: in the Standard model there are especially some interesting numbers. 118 00:05:51,200 --> 00:05:55,520 Speaker 2: Yes, absolutely, the theories of particle physics are very mathematical, 119 00:05:55,680 --> 00:05:58,520 Speaker 2: and not just in the sense that they're predicting numbers 120 00:05:58,560 --> 00:06:01,960 Speaker 2: and places in time. But the patterns we see in 121 00:06:02,000 --> 00:06:06,040 Speaker 2: the Standard Model use complex mathematical theories like group theory 122 00:06:06,080 --> 00:06:08,200 Speaker 2: and field theory and all sorts of like heavy hitting 123 00:06:08,279 --> 00:06:10,320 Speaker 2: mathematical apparatuses. 124 00:06:09,960 --> 00:06:11,919 Speaker 1: Right, which sort of eraises a question of whether the 125 00:06:12,000 --> 00:06:15,479 Speaker 1: universe itself is mathematical. Like maybe if you dig down 126 00:06:15,520 --> 00:06:17,760 Speaker 1: deep enough into the stuff we're all made out of 127 00:06:17,800 --> 00:06:21,720 Speaker 1: at the end, maybe we're just mathematical equations or formulas. 128 00:06:21,839 --> 00:06:23,880 Speaker 2: Yeah, and it makes you wonder, like what does that mean? 129 00:06:24,000 --> 00:06:27,440 Speaker 2: And our numbers real the way like stuff is real? 130 00:06:28,000 --> 00:06:30,360 Speaker 2: You know, like where is the number two? If two 131 00:06:30,440 --> 00:06:33,839 Speaker 2: is a physical thing, does it exist somewhere in the universe. 132 00:06:34,120 --> 00:06:37,280 Speaker 2: There's a whole fascinating branch of philosophy. But like how 133 00:06:37,320 --> 00:06:39,880 Speaker 2: we learn things about numbers because you can't like do 134 00:06:40,000 --> 00:06:42,920 Speaker 2: experiments with the number two and the number seven. It's 135 00:06:42,960 --> 00:06:44,839 Speaker 2: all sort of mental games. 136 00:06:44,760 --> 00:06:47,440 Speaker 1: Right, right, Like maybe the universe is not really physical, 137 00:06:47,480 --> 00:06:50,039 Speaker 1: maybe it's just sort of like conceptual theoretical. 138 00:06:50,200 --> 00:06:52,719 Speaker 2: Yeah, but then you wonder, like what breeds fire into 139 00:06:52,720 --> 00:06:56,320 Speaker 2: all those concepts it makes us experience it. The other 140 00:06:56,360 --> 00:06:59,440 Speaker 2: side of that argument is that numbers are not universal, 141 00:06:59,440 --> 00:07:02,080 Speaker 2: they're not physics, they're not natural. They're just sort of 142 00:07:02,120 --> 00:07:05,040 Speaker 2: the way that our human mind works. That you can 143 00:07:05,200 --> 00:07:07,880 Speaker 2: use numbers as a way to describe the universe, but 144 00:07:07,880 --> 00:07:10,600 Speaker 2: it doesn't mean they're part of the universe. The way 145 00:07:10,600 --> 00:07:13,640 Speaker 2: you can like describe the color orange using a bunch 146 00:07:13,680 --> 00:07:16,280 Speaker 2: of words, but none of those words are orange or 147 00:07:16,280 --> 00:07:18,720 Speaker 2: fully capture the oranginess of an orange. 148 00:07:19,000 --> 00:07:23,040 Speaker 1: Mm and is one really the loneliest number? Is another 149 00:07:23,040 --> 00:07:24,280 Speaker 1: big physics question, right. 150 00:07:25,680 --> 00:07:28,760 Speaker 2: Yes, yes, a very deep physics question. But we have 151 00:07:28,840 --> 00:07:31,000 Speaker 2: to see a lot of value in math. There's lots 152 00:07:31,040 --> 00:07:34,960 Speaker 2: of times when mathematicians have developed some cool little technique 153 00:07:35,120 --> 00:07:37,320 Speaker 2: just for fun, because they see cool patterns and they 154 00:07:37,400 --> 00:07:39,840 Speaker 2: like playing with them, and then later on physicists will 155 00:07:39,840 --> 00:07:41,920 Speaker 2: come along and be like, hey, that looks useful, and 156 00:07:42,000 --> 00:07:44,240 Speaker 2: just like pluck it out of their hands and go 157 00:07:44,280 --> 00:07:47,600 Speaker 2: insert it into our physics equations and get great insights. 158 00:07:47,680 --> 00:07:49,760 Speaker 2: There's a lot of hints there that the laws we 159 00:07:49,880 --> 00:07:52,360 Speaker 2: use to describe the universe are deeply mathematical. 160 00:07:52,560 --> 00:07:54,000 Speaker 1: Yeah, it seems like there are a lot of new 161 00:07:54,000 --> 00:07:56,800 Speaker 1: ideas coming up all the time about how to explain 162 00:07:56,840 --> 00:07:58,800 Speaker 1: the patterns that we see in the universe, maybe with 163 00:07:58,920 --> 00:08:01,720 Speaker 1: new kinds of math and so to be. On the podcast, 164 00:08:01,720 --> 00:08:11,000 Speaker 1: we'll be asking the question, what are octonions? Did I 165 00:08:11,000 --> 00:08:12,880 Speaker 1: say that right? Or is it actonions? 166 00:08:13,240 --> 00:08:16,280 Speaker 2: I think it's oct onions, Like, give me eight onions 167 00:08:16,280 --> 00:08:17,239 Speaker 2: for that recipe, please. 168 00:08:17,560 --> 00:08:20,120 Speaker 1: Isn't it like a blooming onion? Isn't that a dish 169 00:08:20,120 --> 00:08:23,520 Speaker 1: in a fried dish in one of these famous restaurants? 170 00:08:24,240 --> 00:08:27,320 Speaker 1: Is this like a fried onion that looks like an octopus? 171 00:08:28,560 --> 00:08:30,480 Speaker 2: Are you shilling for Outback Steakhouse? Now? 172 00:08:30,600 --> 00:08:31,520 Speaker 1: Oh? Is it out back? 173 00:08:31,640 --> 00:08:32,480 Speaker 2: I don't know, never been. 174 00:08:32,520 --> 00:08:33,800 Speaker 1: Maybe Applebee's is interested. 175 00:08:36,320 --> 00:08:40,040 Speaker 2: I think it's maybe octonians or octanians, depending on where 176 00:08:40,080 --> 00:08:40,840 Speaker 2: you are in the world. 177 00:08:41,040 --> 00:08:43,280 Speaker 1: So this is an interesting word. It sort of sounds 178 00:08:43,320 --> 00:08:47,359 Speaker 1: like octo, which is eight. Then you're ending it with onions, 179 00:08:47,679 --> 00:08:52,440 Speaker 1: which is a vegetable or a tuber. But it's also 180 00:08:52,480 --> 00:08:55,040 Speaker 1: sort of how some particle names ends, right. 181 00:08:55,040 --> 00:08:57,439 Speaker 2: Mm hmm, yeah, ions exactly. 182 00:08:57,200 --> 00:09:00,720 Speaker 1: Oh yeah, right right yeah ions. So is it denions? 183 00:09:00,840 --> 00:09:04,920 Speaker 2: Then I think we should have eight different pronunciations of 184 00:09:04,960 --> 00:09:05,320 Speaker 2: this word. 185 00:09:05,400 --> 00:09:07,800 Speaker 1: Now a trace you go, and then we'll spend eighty 186 00:09:07,800 --> 00:09:11,600 Speaker 1: eight minutes talking about it here on the podcast as. 187 00:09:11,480 --> 00:09:14,560 Speaker 2: Part of our Cult of eight. There you go, send 188 00:09:14,600 --> 00:09:15,520 Speaker 2: eight dollars to join. 189 00:09:15,720 --> 00:09:17,920 Speaker 1: There you go. We'll have eight dollars in our pockets. 190 00:09:18,240 --> 00:09:22,000 Speaker 1: In our eight pockets because I wear cargo pants exactly. 191 00:09:22,040 --> 00:09:23,760 Speaker 2: Maybe these are the spiders of the universe. 192 00:09:23,840 --> 00:09:27,120 Speaker 1: It's all an intricate web of eight. Well, anyways, as usually, 193 00:09:27,120 --> 00:09:29,120 Speaker 1: we were wondering how many people out there had thought 194 00:09:29,120 --> 00:09:32,080 Speaker 1: about or even heard of the word octonions and what 195 00:09:32,120 --> 00:09:33,560 Speaker 1: they think it might mean. 196 00:09:33,800 --> 00:09:37,000 Speaker 2: Thanks very much to everybody who participates in this audience 197 00:09:37,080 --> 00:09:41,000 Speaker 2: contribution segment of the podcast. We'd love if you joined 198 00:09:41,040 --> 00:09:44,400 Speaker 2: the crew. Please write to me two questions at Danielandjorge 199 00:09:44,600 --> 00:09:45,320 Speaker 2: dot com. 200 00:09:45,360 --> 00:09:46,920 Speaker 1: So think about it for a second. What do you 201 00:09:46,960 --> 00:09:51,000 Speaker 1: think are octonions? And are they sold at Applebee's or 202 00:09:51,080 --> 00:09:52,079 Speaker 1: out back to steakhouse? 203 00:09:52,240 --> 00:09:54,000 Speaker 2: And would they make you cry if you chop them? 204 00:09:54,040 --> 00:09:55,319 Speaker 1: Here's what people had to say. 205 00:09:55,160 --> 00:09:59,280 Speaker 4: What are onions, so octors, the prefix for eight onions 206 00:09:59,320 --> 00:10:05,640 Speaker 4: being something players, probably so eight layers stars. 207 00:10:05,920 --> 00:10:09,520 Speaker 3: I don't know, Honestly, I have no idea, but if 208 00:10:09,520 --> 00:10:14,320 Speaker 3: I were to have to guess, I would deconstruct the word. 209 00:10:14,679 --> 00:10:19,160 Speaker 3: So I think the prefix oct means it has to 210 00:10:19,200 --> 00:10:21,440 Speaker 3: do with eight and so maybe it has to do 211 00:10:21,600 --> 00:10:27,560 Speaker 3: with glue ons or any type of similar particle or 212 00:10:27,760 --> 00:10:36,520 Speaker 3: force carrier that is dependent on matrices for transformation. 213 00:10:37,080 --> 00:10:40,040 Speaker 1: All right, well, pretty much the same as what I've 214 00:10:40,080 --> 00:10:43,160 Speaker 1: been guessing. Something to do with onions and eight and 215 00:10:43,320 --> 00:10:44,000 Speaker 1: or particles. 216 00:10:44,760 --> 00:10:47,280 Speaker 2: Yeah, reasonable guess is absolutely. 217 00:10:46,960 --> 00:10:49,800 Speaker 1: Is it like what happens when you smash together eight onions? 218 00:10:50,960 --> 00:10:51,960 Speaker 1: You get an ooked onion. 219 00:10:52,480 --> 00:10:54,560 Speaker 2: We're working on the onion collider right now. We just 220 00:10:54,559 --> 00:10:56,880 Speaker 2: need a little bit more funding, eight dollars more and 221 00:10:56,920 --> 00:10:57,440 Speaker 2: we'll be there. 222 00:10:58,280 --> 00:11:01,080 Speaker 1: You need a little bit more garlic, You're gonna say 223 00:11:01,280 --> 00:11:04,440 Speaker 1: a bit more seasoning. You need eighty eight billion dollars. 224 00:11:05,760 --> 00:11:07,880 Speaker 2: I won't say no to eighty eight billion dollars, that's 225 00:11:07,880 --> 00:11:08,240 Speaker 2: for sure. 226 00:11:08,280 --> 00:11:11,599 Speaker 1: Yeah, there you go. And then what happens at the 227 00:11:11,720 --> 00:11:13,440 Speaker 1: end when you collide the onions? Would you have to 228 00:11:14,040 --> 00:11:14,600 Speaker 1: eat them? 229 00:11:14,679 --> 00:11:18,440 Speaker 2: I disappeared to my private island with all the cash. 230 00:11:18,640 --> 00:11:20,120 Speaker 1: I think they can give you eighty years in prison 231 00:11:20,160 --> 00:11:24,040 Speaker 1: for that, Daniel, only if they catch me, only they 232 00:11:24,040 --> 00:11:25,240 Speaker 1: smell of the crime. 233 00:11:26,920 --> 00:11:30,200 Speaker 2: I'll have an army of cocaine infused butterflies to protect me. 234 00:11:30,360 --> 00:11:34,600 Speaker 1: Oh my gosh, you are a super villain there. I mean, 235 00:11:34,640 --> 00:11:38,760 Speaker 1: I've heard of sharks with lasers, but m drug butterflies 236 00:11:38,800 --> 00:11:40,560 Speaker 1: is a new level of villainy and they will never 237 00:11:40,600 --> 00:11:44,160 Speaker 1: see me coming. All right, Well, stick into it, Daniel. 238 00:11:44,200 --> 00:11:46,160 Speaker 1: What is an octonian and what do you think is 239 00:11:46,160 --> 00:11:47,360 Speaker 1: the right way to pronounce it. 240 00:11:47,559 --> 00:11:50,600 Speaker 2: I pronounced it octonians, but it does make it sound 241 00:11:50,679 --> 00:11:53,440 Speaker 2: like creatures from the planet Octo or something. 242 00:11:53,840 --> 00:11:58,120 Speaker 1: M I see you're going for the more tony pronunciation Octonians. 243 00:11:58,360 --> 00:11:59,880 Speaker 2: Octonians exactly. 244 00:12:00,720 --> 00:12:00,800 Speaker 1: So. 245 00:12:01,000 --> 00:12:04,520 Speaker 2: Octonians are a kind of number, and they're sort of 246 00:12:04,520 --> 00:12:08,600 Speaker 2: in the category of complex numbers, but they're an extension 247 00:12:08,600 --> 00:12:11,640 Speaker 2: of complex numbers the way complex numbers have like two 248 00:12:11,720 --> 00:12:14,920 Speaker 2: components to them, the real and the imaginary part, which 249 00:12:14,920 --> 00:12:17,440 Speaker 2: are an extension of real numbers. They just have one component. 250 00:12:17,720 --> 00:12:23,920 Speaker 2: Octonians have eight components, one real and seven imaginary components. 251 00:12:24,320 --> 00:12:26,280 Speaker 1: Well, okay, wait, hold on, I think maybe some of 252 00:12:26,360 --> 00:12:29,920 Speaker 1: us might not be super familiar with our high school math. 253 00:12:30,080 --> 00:12:32,240 Speaker 1: What is an imaginary number in the first place. 254 00:12:32,320 --> 00:12:34,800 Speaker 2: Imaginary numbers were invented in the sixteen hundreds, and they're 255 00:12:34,800 --> 00:12:38,280 Speaker 2: called imaginary because you don't see them in reality. They're 256 00:12:38,320 --> 00:12:42,400 Speaker 2: very useful in math. And there's basically one imaginary number, 257 00:12:42,480 --> 00:12:46,040 Speaker 2: which is I, which is the square root of minus one. 258 00:12:46,240 --> 00:12:49,240 Speaker 2: There's no real number which, if you multiplied by itself, 259 00:12:49,600 --> 00:12:52,520 Speaker 2: gives you minus one. So they invented a number. They 260 00:12:52,559 --> 00:12:55,240 Speaker 2: just call it I, and they say, if you multiply 261 00:12:55,360 --> 00:12:57,840 Speaker 2: I by itself, you get minus one. So it's a 262 00:12:57,880 --> 00:13:00,440 Speaker 2: new kind of number. It's different from any of the 263 00:13:00,520 --> 00:13:02,920 Speaker 2: numbers on the normal number line. 264 00:13:02,600 --> 00:13:05,600 Speaker 1: Right, because like we had the number negative one, and 265 00:13:05,640 --> 00:13:08,400 Speaker 1: we have the function to take a square root of something, 266 00:13:08,480 --> 00:13:10,400 Speaker 1: but when you mix the two, it's like you get 267 00:13:10,400 --> 00:13:13,680 Speaker 1: something that's almost impossible, or that it's not on the 268 00:13:13,720 --> 00:13:16,920 Speaker 1: regular number line that we all use in our everyday. 269 00:13:16,559 --> 00:13:19,920 Speaker 2: Lives exactly, because any number on the regular number line 270 00:13:19,960 --> 00:13:22,000 Speaker 2: we call the real numbers, if you square it, you 271 00:13:22,040 --> 00:13:25,520 Speaker 2: get a positive number. Three squared is nine. Negative three 272 00:13:25,559 --> 00:13:28,720 Speaker 2: squared is also nine because the two negatives give you 273 00:13:28,760 --> 00:13:31,880 Speaker 2: a positive. So there's no number on the real number line, 274 00:13:31,880 --> 00:13:34,480 Speaker 2: which if you square it will give you a negative answer. 275 00:13:34,920 --> 00:13:37,320 Speaker 2: So there's no number that's an answer to the question 276 00:13:37,679 --> 00:13:39,680 Speaker 2: what is the square root of negative one? So they 277 00:13:39,679 --> 00:13:42,400 Speaker 2: had to invent a new kind of number, sort of 278 00:13:42,480 --> 00:13:45,880 Speaker 2: imagine the real number line is like the x axis. 279 00:13:45,960 --> 00:13:48,600 Speaker 2: They invented a new axis, like the y axis, which 280 00:13:48,679 --> 00:13:51,439 Speaker 2: is like the imaginary direction. So instead of having a 281 00:13:51,559 --> 00:13:54,280 Speaker 2: number line, and they have a number plane where every 282 00:13:54,360 --> 00:13:58,200 Speaker 2: number is two components, a real component and this imaginary component. 283 00:13:58,760 --> 00:14:01,360 Speaker 1: Right, because you came up with us or mathematicians came 284 00:14:01,440 --> 00:14:03,200 Speaker 1: up with I, and then you can have a whole 285 00:14:03,280 --> 00:14:05,360 Speaker 1: number line based on I. You can have like two 286 00:14:05,400 --> 00:14:07,960 Speaker 1: I and three I or four point seven I or 287 00:14:08,000 --> 00:14:08,439 Speaker 1: eight I. 288 00:14:08,720 --> 00:14:11,880 Speaker 2: Or negative two I. Right, the imaginary number line goes 289 00:14:11,960 --> 00:14:14,240 Speaker 2: both ways, right, right? 290 00:14:14,280 --> 00:14:15,480 Speaker 1: And can you also have not I? 291 00:14:15,880 --> 00:14:17,520 Speaker 2: You can have not it and like I'm not doing the. 292 00:14:17,440 --> 00:14:21,240 Speaker 1: Dishes, Yes, that's what I mean, Like zero I, would 293 00:14:21,280 --> 00:14:22,080 Speaker 1: you call it not I? 294 00:14:23,040 --> 00:14:24,840 Speaker 2: Oh? You can have zero? Yeah, the zero in the 295 00:14:24,920 --> 00:14:28,240 Speaker 2: number line is just zero Comma zero, right, zero real 296 00:14:28,320 --> 00:14:29,800 Speaker 2: numbers and zero imaginary. 297 00:14:30,000 --> 00:14:33,480 Speaker 1: Right. So in physics, when you talk about an imaginary number, 298 00:14:34,000 --> 00:14:35,960 Speaker 1: you talk about like a number that has both a 299 00:14:36,000 --> 00:14:39,000 Speaker 1: real component and an imaginary component, so you write it 300 00:14:39,040 --> 00:14:43,360 Speaker 1: as two numbers like seven plus eight I exactly. 301 00:14:43,400 --> 00:14:46,040 Speaker 2: That's what we call a complex number, something with a 302 00:14:46,120 --> 00:14:49,560 Speaker 2: real and an imaginary component, sort of like a coordinate 303 00:14:49,640 --> 00:14:53,440 Speaker 2: on the two dimensional complex plane. If you imagine real 304 00:14:53,520 --> 00:14:56,000 Speaker 2: numbers or x and imaginary numbers are y. 305 00:14:56,400 --> 00:14:58,680 Speaker 1: Right, And I think like all of most of quantum 306 00:14:58,680 --> 00:15:01,400 Speaker 1: particle physics is based on imaginary numbers, right, Like it's 307 00:15:01,400 --> 00:15:05,320 Speaker 1: a convenient mathematical space to do all of the math in. 308 00:15:05,720 --> 00:15:07,920 Speaker 2: Yeah, exactly. So there's a few important things to know 309 00:15:07,960 --> 00:15:10,600 Speaker 2: about complex numbers. Number one, they turned out to be 310 00:15:10,680 --> 00:15:13,640 Speaker 2: really useful. Back in the sixteen hundreds when they were invented, 311 00:15:13,680 --> 00:15:17,200 Speaker 2: before we had quantum mechanics, they were already useful. Italian 312 00:15:17,200 --> 00:15:20,239 Speaker 2: mathematicians came up with them as a way to solve problems, 313 00:15:20,360 --> 00:15:22,960 Speaker 2: and they found that they could get to the solutions 314 00:15:22,960 --> 00:15:25,680 Speaker 2: of tricky math problems much more rapidly if they used 315 00:15:25,720 --> 00:15:28,400 Speaker 2: these imaginary numbers, even though they didn't believe in them, 316 00:15:28,480 --> 00:15:31,400 Speaker 2: they didn't believe that they represented anything in the universe. 317 00:15:31,880 --> 00:15:34,720 Speaker 2: But now all of our quantum mechanics relies on these 318 00:15:34,800 --> 00:15:37,720 Speaker 2: complex numbers. Like the wave function that we talk about 319 00:15:37,720 --> 00:15:41,160 Speaker 2: all the time. In quantum mechanics, that's actually a complex 320 00:15:41,360 --> 00:15:44,840 Speaker 2: valued object. That's why you can't observe it directly. You 321 00:15:44,880 --> 00:15:47,640 Speaker 2: can only observe it when it's squared. That gives you 322 00:15:47,680 --> 00:15:51,160 Speaker 2: the probability. The wave function itself is a complex number, 323 00:15:51,240 --> 00:15:54,760 Speaker 2: has a real component and an imaginary component. We couldn't 324 00:15:54,760 --> 00:15:58,400 Speaker 2: do quantum mechanics without complex numbers. They represent something real 325 00:15:58,520 --> 00:15:59,440 Speaker 2: about the universe. 326 00:16:00,120 --> 00:16:01,640 Speaker 1: Wait, wait, what are you saying. Are you saying like 327 00:16:01,720 --> 00:16:06,320 Speaker 1: somehow the universe or particles are themselves imaginary, or that 328 00:16:06,400 --> 00:16:09,400 Speaker 1: they sort of operate in a two dimensional space. 329 00:16:09,640 --> 00:16:11,400 Speaker 2: We don't know if the wave function is real, if 330 00:16:11,440 --> 00:16:14,600 Speaker 2: it actually exists in the universe. What we do know 331 00:16:14,800 --> 00:16:18,680 Speaker 2: is that the mathematics needed to describe what particles do 332 00:16:18,760 --> 00:16:22,080 Speaker 2: in which direction they go has to have complex numbers 333 00:16:22,080 --> 00:16:24,680 Speaker 2: in it. Like that. Math just does not work without 334 00:16:24,680 --> 00:16:28,680 Speaker 2: complex numbers. So in our models, in our calculations, the 335 00:16:28,720 --> 00:16:32,000 Speaker 2: wave function that describes all these particles have complex values 336 00:16:32,000 --> 00:16:34,640 Speaker 2: in them. Now, when you predict the outcome of an experiment, 337 00:16:34,680 --> 00:16:37,120 Speaker 2: it always just gives you actual numbers or real numbers 338 00:16:37,120 --> 00:16:38,920 Speaker 2: that you can measure the particle will be at this 339 00:16:39,040 --> 00:16:42,800 Speaker 2: location at that time. But the intermediate states. The calculations 340 00:16:42,800 --> 00:16:46,800 Speaker 2: we do between the observations require complex numbers. Does that 341 00:16:46,840 --> 00:16:49,480 Speaker 2: mean that the universe is complex, that there are imaginary 342 00:16:49,480 --> 00:16:53,360 Speaker 2: components to it? We don't know. Deep question for philosophy. 343 00:16:53,880 --> 00:16:57,760 Speaker 1: Well, the universe is definitely complicated, whether it's complex or 344 00:16:57,800 --> 00:17:02,160 Speaker 1: real or imaginary. Maybe it is the topic for another podcast. 345 00:17:02,160 --> 00:17:04,880 Speaker 1: But here today we're talking about maybe a different kind 346 00:17:04,880 --> 00:17:08,320 Speaker 1: of imaginary number, one that is maybe eight times more 347 00:17:08,320 --> 00:17:11,600 Speaker 1: imaginary than an imaginary number. So to dig into that 348 00:17:11,680 --> 00:17:14,000 Speaker 1: and see whether or not it can help explain more 349 00:17:14,000 --> 00:17:15,919 Speaker 1: of the universe that we see around this and what 350 00:17:15,960 --> 00:17:18,879 Speaker 1: would that mean. But first, let's take a quick break. 351 00:17:31,400 --> 00:17:35,160 Speaker 1: All right, we're talking about Oktonians or Kanyans, which are 352 00:17:35,359 --> 00:17:39,800 Speaker 1: maybe extra imaginary numbers that might describe how the universe 353 00:17:39,840 --> 00:17:43,960 Speaker 1: works at the particle level. We're digging into that here today. Now, Daniel, 354 00:17:44,000 --> 00:17:47,119 Speaker 1: you're saying that imaginary numbers play a big part in 355 00:17:47,320 --> 00:17:50,399 Speaker 1: describing how things work at the quantum level. 356 00:17:50,440 --> 00:17:54,200 Speaker 2: Exactly, we need complex numbers in order to do quantum mechanics. 357 00:17:54,520 --> 00:17:57,880 Speaker 2: Like if they hadn't been invented already early this century 358 00:17:57,920 --> 00:18:00,680 Speaker 2: when we were developing quantum mechanics, we might have invented 359 00:18:00,680 --> 00:18:03,240 Speaker 2: them then, As it is, they already existed in the 360 00:18:03,280 --> 00:18:05,520 Speaker 2: sort of mathematical toolbox, and so we could just pluck 361 00:18:05,560 --> 00:18:08,040 Speaker 2: them out and say, oh, this is helpful, let's use it. 362 00:18:08,240 --> 00:18:10,919 Speaker 1: Well, was that like a big surprise, Like, wait a minute, 363 00:18:10,920 --> 00:18:12,440 Speaker 1: what does that mean about the universe that you need 364 00:18:12,480 --> 00:18:14,280 Speaker 1: imaginary numbers to describe it? 365 00:18:14,359 --> 00:18:18,399 Speaker 2: Yeah? It has deep consequences for mathematical philosophy. You know, 366 00:18:18,440 --> 00:18:20,840 Speaker 2: you can wonder if the wave function is real, does 367 00:18:20,880 --> 00:18:24,680 Speaker 2: that mean that imaginary numbers are real in some philosophical sense, 368 00:18:24,720 --> 00:18:26,840 Speaker 2: even if we don't call them real numbers in a 369 00:18:26,920 --> 00:18:30,200 Speaker 2: mathematical sense. We don't know what that means. But imaginary 370 00:18:30,280 --> 00:18:33,879 Speaker 2: numbers are also important in mathematics itself. It tells us 371 00:18:33,880 --> 00:18:37,520 Speaker 2: something about how numbers work even before they were applied 372 00:18:37,520 --> 00:18:38,520 Speaker 2: to quantum mechanics. 373 00:18:39,160 --> 00:18:42,320 Speaker 1: Interesting, so there may be something point to something fundamental 374 00:18:42,320 --> 00:18:43,640 Speaker 1: about the nature of the universe. 375 00:18:43,840 --> 00:18:47,120 Speaker 2: Yeah. Perhaps, because complex numbers are not just like something 376 00:18:47,160 --> 00:18:49,800 Speaker 2: mathematicians invented. You can't just say, well, I'm going to 377 00:18:49,840 --> 00:18:51,560 Speaker 2: take two numbers and stick them together, and now I've 378 00:18:51,560 --> 00:18:53,359 Speaker 2: got a new kind of number. When you do that, 379 00:18:53,400 --> 00:18:55,440 Speaker 2: you also have to decide, like, what are the rules 380 00:18:55,440 --> 00:18:57,240 Speaker 2: of those numbers, how do you add them? How do 381 00:18:57,280 --> 00:18:59,840 Speaker 2: you subtract them? What happens when you multiply the two numbers. 382 00:19:00,320 --> 00:19:02,160 Speaker 2: So you have to come up with what mathematicians call 383 00:19:02,240 --> 00:19:04,879 Speaker 2: a division algebra, which is basically just like all the 384 00:19:05,000 --> 00:19:07,800 Speaker 2: rules of how the math works for these numbers. And 385 00:19:07,880 --> 00:19:10,520 Speaker 2: it's not always easy to come up with that system. 386 00:19:10,640 --> 00:19:12,760 Speaker 2: For example, you can do it for complex numbers, but 387 00:19:12,800 --> 00:19:15,520 Speaker 2: you can't do it for triplets of numbers. So it 388 00:19:15,520 --> 00:19:18,240 Speaker 2: works for single numbers, it works for pairs of numbers, 389 00:19:18,480 --> 00:19:20,680 Speaker 2: it doesn't work for triplets of numbers. 390 00:19:21,080 --> 00:19:22,880 Speaker 1: Okay, wait, hold on, and I think you're talking about 391 00:19:22,920 --> 00:19:26,600 Speaker 1: now increasing the imaginariness of a number. So like a 392 00:19:26,640 --> 00:19:29,879 Speaker 1: regular imaginary number has a real component and then an 393 00:19:29,920 --> 00:19:34,080 Speaker 1: imaginary component which you get by multiplying another number by 394 00:19:34,080 --> 00:19:37,040 Speaker 1: the number I. So like an imaginary number is seven 395 00:19:37,160 --> 00:19:40,919 Speaker 1: plus eight I. Now you're talking about like adding a 396 00:19:40,960 --> 00:19:41,760 Speaker 1: third component. 397 00:19:42,040 --> 00:19:45,520 Speaker 2: Yeah, call it J. Right, J is like another square 398 00:19:45,600 --> 00:19:48,800 Speaker 2: root of negative one, a different a unique square root 399 00:19:48,840 --> 00:19:51,560 Speaker 2: of negative one. Now thing says you can't have more, right, 400 00:19:51,600 --> 00:19:55,399 Speaker 2: Maybe there's multiple square roots of negative one. And after 401 00:19:55,440 --> 00:19:58,560 Speaker 2: people discover complex numbers, mathematicians are like, oh, that's cool. 402 00:19:58,880 --> 00:20:01,600 Speaker 2: Can you do the same thing with three numbers. If 403 00:20:01,600 --> 00:20:04,240 Speaker 2: you put three numbers together like a real number, and 404 00:20:04,280 --> 00:20:06,520 Speaker 2: then some number of I and some number of J, 405 00:20:07,280 --> 00:20:10,960 Speaker 2: can you also then make like consistent mathematics so you 406 00:20:11,000 --> 00:20:14,439 Speaker 2: know how to multiply, divide, subtract, etc. People spend hundreds 407 00:20:14,440 --> 00:20:15,120 Speaker 2: of years on that. 408 00:20:15,200 --> 00:20:17,760 Speaker 1: Let me think about that for a second. So now 409 00:20:17,760 --> 00:20:20,520 Speaker 1: we have a number plus a number I pleasent a 410 00:20:20,600 --> 00:20:23,439 Speaker 1: J number and you're saying, Jay's another square root of 411 00:20:23,480 --> 00:20:25,639 Speaker 1: a negative one. So if I'm multiplied J times J, 412 00:20:25,920 --> 00:20:28,040 Speaker 1: I get negative one. What if I'm look at IE 413 00:20:28,040 --> 00:20:28,399 Speaker 1: times J. 414 00:20:28,600 --> 00:20:30,080 Speaker 2: So this is exactly what you have to do. You 415 00:20:30,119 --> 00:20:32,600 Speaker 2: have to come up with the rules of this triplet 416 00:20:32,640 --> 00:20:35,359 Speaker 2: system to figure out what happens when you multiply different 417 00:20:35,400 --> 00:20:38,320 Speaker 2: numbers together, what happens when you divide them. And it 418 00:20:38,400 --> 00:20:43,000 Speaker 2: turns out there's no consistent way to define multiplication and 419 00:20:43,080 --> 00:20:45,639 Speaker 2: division so that it all makes sense and keeps the 420 00:20:45,680 --> 00:20:49,520 Speaker 2: mathematicians happy. If you have I and J in addition 421 00:20:49,560 --> 00:20:52,440 Speaker 2: to the real numbers, like, you cannot build a mathematical 422 00:20:52,480 --> 00:20:55,359 Speaker 2: system based on numbers with three components. You can do 423 00:20:55,400 --> 00:20:57,640 Speaker 2: it with one that's just the normal numbers. You can 424 00:20:57,680 --> 00:21:00,280 Speaker 2: do it with two that's just the complex numbers. Can't 425 00:21:00,400 --> 00:21:01,160 Speaker 2: do it with three. 426 00:21:01,880 --> 00:21:05,080 Speaker 1: But I feel like when you said before, like having 427 00:21:05,160 --> 00:21:07,840 Speaker 1: two numbers, or like an real and an imaginary. It's 428 00:21:07,840 --> 00:21:09,439 Speaker 1: sort of like an X and a Y. Isn't this 429 00:21:09,560 --> 00:21:10,800 Speaker 1: just like having X, Y and Z. 430 00:21:11,080 --> 00:21:12,560 Speaker 2: Yeah, you might imagine you should be able to do 431 00:21:12,600 --> 00:21:14,639 Speaker 2: it with any set of numbers, exactly the way you 432 00:21:14,680 --> 00:21:17,280 Speaker 2: can define spaces in any dimensions. You're gonna have a 433 00:21:17,280 --> 00:21:20,200 Speaker 2: one dimensional space or two dimensional space, so three dimensional space, 434 00:21:20,280 --> 00:21:24,400 Speaker 2: a nineteen dimensional space, an infinite dimensional space. Geometry has 435 00:21:24,400 --> 00:21:28,440 Speaker 2: no restrictions, right, But the rules of mathematics, for some 436 00:21:28,520 --> 00:21:31,800 Speaker 2: reason constrain the number of numbers we can pack in 437 00:21:31,840 --> 00:21:35,520 Speaker 2: together and still have everything makes sense. Mathematicians worry about 438 00:21:35,560 --> 00:21:38,200 Speaker 2: like does every number have an inverse? If I take 439 00:21:38,200 --> 00:21:40,520 Speaker 2: a number, is there always some other number I can 440 00:21:40,560 --> 00:21:44,000 Speaker 2: multiply it by to get one? Are there unique zeros 441 00:21:44,160 --> 00:21:46,919 Speaker 2: or not? And it turns out that mathematics based on 442 00:21:46,960 --> 00:21:50,119 Speaker 2: triplets just doesn't work. There's no way to put it together. 443 00:21:50,480 --> 00:21:54,760 Speaker 2: This is famous Irish mathematician named William Rowan Hamilton who 444 00:21:54,760 --> 00:21:57,600 Speaker 2: spent like decades on this, and he said once every morning, 445 00:21:57,640 --> 00:22:00,000 Speaker 2: coming down to breakfast, my kids ask me, well, pop up, 446 00:22:00,119 --> 00:22:02,600 Speaker 2: can you multiply triplets? And he always said nope, I 447 00:22:02,640 --> 00:22:05,280 Speaker 2: can always I can only add and subtract them. So 448 00:22:05,320 --> 00:22:07,760 Speaker 2: we spent decades like try to figure out how to 449 00:22:07,840 --> 00:22:11,080 Speaker 2: multiply and divide triplets of numbers and never succeeded. 450 00:22:11,400 --> 00:22:14,720 Speaker 1: WHOA, but X, Y Z space works in three D 451 00:22:14,800 --> 00:22:17,040 Speaker 1: space all around this? Or are you saying that three 452 00:22:17,119 --> 00:22:20,960 Speaker 1: D space doesn't work mathematically or just triplet imaginary numbers 453 00:22:20,960 --> 00:22:21,959 Speaker 1: don't work mathematically? 454 00:22:22,000 --> 00:22:25,679 Speaker 2: Triplet imaginary numbers don't work mathematically. Like you might think, well, 455 00:22:25,680 --> 00:22:28,920 Speaker 2: why can't you just put three numbers together and then say, 456 00:22:28,960 --> 00:22:32,720 Speaker 2: you know, multiplying two triplets means multiplying the components, right. 457 00:22:32,840 --> 00:22:34,639 Speaker 2: I don't think we want to get two mathematical on 458 00:22:34,680 --> 00:22:38,240 Speaker 2: the podcast today. But this creates problems of having numbers 459 00:22:38,280 --> 00:22:41,639 Speaker 2: that don't have inverses, like one comma one coma zero 460 00:22:42,000 --> 00:22:44,480 Speaker 2: doesn't have an inverse, but it's non zero. 461 00:22:44,800 --> 00:22:46,359 Speaker 1: Okay, I think I see what you're saying. I think 462 00:22:46,400 --> 00:22:48,919 Speaker 1: you're saying it's possible to just have like coordinates in 463 00:22:48,920 --> 00:22:51,040 Speaker 1: three D space, like x, Y and z, But if 464 00:22:51,040 --> 00:22:54,280 Speaker 1: you want to call it like X plus y, I 465 00:22:54,400 --> 00:22:56,840 Speaker 1: plus z J, that doesn't work like if you want 466 00:22:56,840 --> 00:22:58,879 Speaker 1: to put them all together as one number with an 467 00:22:58,920 --> 00:23:02,200 Speaker 1: addition sign between the different coordinates, that doesn't work. 468 00:23:02,280 --> 00:23:04,640 Speaker 2: It doesn't work if you also require that you can 469 00:23:04,680 --> 00:23:07,040 Speaker 2: do things with these numbers, like can you take any 470 00:23:07,080 --> 00:23:09,320 Speaker 2: of these two numbers and multiply them together and still 471 00:23:09,320 --> 00:23:11,560 Speaker 2: get a number. If you add them together, do you 472 00:23:11,600 --> 00:23:13,320 Speaker 2: still get a number? We rely on that for the 473 00:23:13,320 --> 00:23:15,119 Speaker 2: normal numbers. Right, any number you give me, I can 474 00:23:15,160 --> 00:23:17,800 Speaker 2: always find another number to multiply it by to get one. 475 00:23:18,160 --> 00:23:20,320 Speaker 2: Or if you give me two numbers I multiply together, 476 00:23:20,359 --> 00:23:22,720 Speaker 2: I always get a number that's not a zero if 477 00:23:22,720 --> 00:23:24,600 Speaker 2: both of the numbers you gave me were not zero. 478 00:23:25,240 --> 00:23:27,760 Speaker 2: You can't build rules like that, which you need to 479 00:23:27,760 --> 00:23:30,200 Speaker 2: do any interesting math or any interesting physics. You can't 480 00:23:30,200 --> 00:23:32,399 Speaker 2: build rules like that for triplets. You can do it 481 00:23:32,400 --> 00:23:35,160 Speaker 2: for singles and for pairs, but not for triplets. 482 00:23:35,320 --> 00:23:38,280 Speaker 1: Okay, so it doesn't work for three triple imaginary numbers, 483 00:23:38,320 --> 00:23:41,680 Speaker 1: but maybe for four imaginary numbers it does work. 484 00:23:41,600 --> 00:23:45,400 Speaker 2: Exactly and the same. Irish mathematician William Hamilton he discovered 485 00:23:45,400 --> 00:23:47,760 Speaker 2: that if you put four numbers together, like four D 486 00:23:48,000 --> 00:23:53,040 Speaker 2: space one reel in three imaginary numbers, you call these quaternions. 487 00:23:53,440 --> 00:23:56,800 Speaker 2: This actually works that the mathematics hangs together. You can 488 00:23:56,800 --> 00:23:59,760 Speaker 2: build multiplication and division, you can do all the mathematics 489 00:23:59,800 --> 00:24:02,240 Speaker 2: you know need on quadruples of numbers, even though you 490 00:24:02,280 --> 00:24:03,480 Speaker 2: can't do it on triplets. 491 00:24:04,080 --> 00:24:06,480 Speaker 1: Okay, So now that means that my number is not 492 00:24:06,560 --> 00:24:09,040 Speaker 1: just like eight, and it's not just like A plus 493 00:24:09,480 --> 00:24:12,719 Speaker 1: four I. It's like eight plus four I plus seven 494 00:24:12,920 --> 00:24:16,040 Speaker 1: J plus five K exactly. 495 00:24:16,520 --> 00:24:20,000 Speaker 2: And in that system, I squared is negative one, J 496 00:24:20,200 --> 00:24:24,439 Speaker 2: squared is negative one. K squared is negative one. And 497 00:24:24,480 --> 00:24:27,440 Speaker 2: if you multiply I times J times k, you also 498 00:24:27,480 --> 00:24:30,879 Speaker 2: get negative one. And that's the key J and K 499 00:24:31,040 --> 00:24:33,640 Speaker 2: or other square roots of negative one, and that one 500 00:24:33,680 --> 00:24:36,960 Speaker 2: equation makes it all hang together. And when Hamilton had 501 00:24:36,960 --> 00:24:40,120 Speaker 2: this insight, he was like walking across this bridge in Dublin. 502 00:24:40,320 --> 00:24:42,960 Speaker 2: It came to him in a flash, and he actually 503 00:24:43,080 --> 00:24:47,320 Speaker 2: chiseled the formula onto the bridge like mathematical graffiti in 504 00:24:47,359 --> 00:24:48,800 Speaker 2: the moment because he didn't want to forget it. 505 00:24:48,840 --> 00:24:50,000 Speaker 1: And you can still see it today. 506 00:24:51,080 --> 00:24:53,119 Speaker 2: It's actually worn down, but they put a plaque on 507 00:24:53,160 --> 00:24:54,760 Speaker 2: that spot to commemorate it. 508 00:24:55,359 --> 00:24:58,960 Speaker 1: And more important was this kid I pressed or because 509 00:24:59,200 --> 00:25:01,359 Speaker 1: the kids seem really interested in what was going on 510 00:25:01,400 --> 00:25:02,879 Speaker 1: with the math and his father. 511 00:25:03,240 --> 00:25:04,960 Speaker 2: Yeah, I think he was just rooting for his dad, 512 00:25:05,080 --> 00:25:09,639 Speaker 2: you know, day his struggling with this crazy multiplication. 513 00:25:10,040 --> 00:25:12,479 Speaker 1: And how much can a kid know about imaginary numbers. 514 00:25:14,160 --> 00:25:17,640 Speaker 2: It's fascinating that the mathematics of it tells us what's allowed. 515 00:25:17,920 --> 00:25:20,160 Speaker 2: You can build a one D number, two D number, 516 00:25:20,200 --> 00:25:22,720 Speaker 2: a four D number, but not a three D number. 517 00:25:22,760 --> 00:25:23,680 Speaker 2: It's really interesting. 518 00:25:24,359 --> 00:25:26,520 Speaker 1: Can you go five and six and seven? 519 00:25:26,800 --> 00:25:30,399 Speaker 2: You can't. About one hundred years later, mathematicians proved that 520 00:25:30,440 --> 00:25:32,680 Speaker 2: the only sets of numbers you can do are one 521 00:25:32,880 --> 00:25:39,080 Speaker 2: real numbers, two complex numbers, four quaternions, and eight octonians. 522 00:25:39,440 --> 00:25:43,080 Speaker 1: Ooh, and what can you keep going like sixteen thirty two? 523 00:25:43,440 --> 00:25:45,159 Speaker 2: Nope, those are the only ones. 524 00:25:45,400 --> 00:25:45,920 Speaker 1: What do you mean? 525 00:25:46,200 --> 00:25:49,440 Speaker 2: Everything else runs into mathematical problems. You can't have consistent 526 00:25:49,520 --> 00:25:53,480 Speaker 2: multiplication and division without running into ugly problems with the zeros. 527 00:25:53,520 --> 00:25:56,560 Speaker 2: It only works for one, two, four, and eight. 528 00:25:56,720 --> 00:25:59,359 Speaker 1: That's it. That's nothing more in the hing more. 529 00:25:59,280 --> 00:26:01,720 Speaker 2: In the universe. They prove this, and I try to 530 00:26:01,760 --> 00:26:03,840 Speaker 2: find a way to like explain this in intuitive sense, 531 00:26:04,000 --> 00:26:07,520 Speaker 2: but the proof is very, very complicated. But everybody's totally 532 00:26:07,560 --> 00:26:10,160 Speaker 2: convinced that one, two, four, and eight are the only 533 00:26:10,200 --> 00:26:14,760 Speaker 2: dimensions allowed for numbers that have consistent multiplication and division. 534 00:26:14,920 --> 00:26:18,359 Speaker 1: You mean for like complex numbers, Yeah, complex numbers with 535 00:26:18,480 --> 00:26:21,080 Speaker 1: like extra imaginary dimensions exactly. 536 00:26:21,400 --> 00:26:23,919 Speaker 2: You could have one extra imaginary dimension, which gives you 537 00:26:24,119 --> 00:26:27,040 Speaker 2: our familiar complex numbers are of two D. You can 538 00:26:27,119 --> 00:26:31,240 Speaker 2: have three imaginary dimensions, which gives you four D numbers quaternions. 539 00:26:31,520 --> 00:26:35,480 Speaker 2: Or you can have seven imaginary dimensions plus one reel 540 00:26:35,600 --> 00:26:39,159 Speaker 2: gives you eight dimensions for octonians. 541 00:26:38,720 --> 00:26:41,760 Speaker 1: And still be consistent with our rules of math that 542 00:26:41,840 --> 00:26:45,080 Speaker 1: we know about in our universe. Could does be different 543 00:26:45,119 --> 00:26:46,080 Speaker 1: in another universe. 544 00:26:46,320 --> 00:26:48,520 Speaker 2: You can come up with whatever rules of math you want, 545 00:26:48,800 --> 00:26:50,320 Speaker 2: but if you want to do physics with it, you 546 00:26:50,359 --> 00:26:52,199 Speaker 2: need to know how to multiply the numbers, how to 547 00:26:52,240 --> 00:26:54,520 Speaker 2: divide them. You need some confidence that you're not going 548 00:26:54,560 --> 00:26:57,000 Speaker 2: to run into zeros all the time. So these are 549 00:26:57,040 --> 00:27:00,800 Speaker 2: like pretty basic requirements for mathematical system that's going to 550 00:27:00,960 --> 00:27:03,679 Speaker 2: underlie physics. You can invent math however you like and 551 00:27:03,720 --> 00:27:06,160 Speaker 2: have it be useless or useful or whatever, but if 552 00:27:06,160 --> 00:27:08,120 Speaker 2: you wanted to do physics, you have to follow these 553 00:27:08,160 --> 00:27:08,959 Speaker 2: basic rules. 554 00:27:09,119 --> 00:27:11,199 Speaker 1: Okay, Now, I think the idea is that you know, 555 00:27:11,240 --> 00:27:13,000 Speaker 1: we had real numbers for a long time, and they 556 00:27:13,040 --> 00:27:16,439 Speaker 1: weren't great for regular physics. And then we found quantum 557 00:27:16,480 --> 00:27:20,080 Speaker 1: mechanics and particles, and we've figured out that one dimensional 558 00:27:20,440 --> 00:27:24,280 Speaker 1: imaginary numbers work really well to describe the math and 559 00:27:24,359 --> 00:27:28,800 Speaker 1: those theories where you have one extra imaginary dimension. But 560 00:27:28,840 --> 00:27:31,359 Speaker 1: you're saying, mathematician is also found out that you can 561 00:27:31,760 --> 00:27:37,600 Speaker 1: have three extra imaginary numbers or dimensions in a quaternion, 562 00:27:37,720 --> 00:27:41,600 Speaker 1: or seven extra imaginary dimensions in a Olktonian. And now 563 00:27:41,960 --> 00:27:44,800 Speaker 1: I think maybe what you're saying is that scientists are wondering, 564 00:27:45,040 --> 00:27:49,000 Speaker 1: do these extra super numbers also maybe describe something about 565 00:27:49,000 --> 00:27:49,960 Speaker 1: the universe. 566 00:27:49,800 --> 00:27:53,320 Speaker 2: Exactly, Because obviously one D numbers are very relevant to physics, 567 00:27:53,640 --> 00:27:56,760 Speaker 2: two D numbers are very relevant to quantum mechanics. These 568 00:27:56,800 --> 00:28:00,199 Speaker 2: four D numbers you probably haven't heard of quaternions, but 569 00:28:00,280 --> 00:28:03,240 Speaker 2: these days we actually just call them four dimensional vectors, 570 00:28:03,560 --> 00:28:08,280 Speaker 2: and they're crucial for relativity. Like special relativity combines space 571 00:28:08,400 --> 00:28:11,720 Speaker 2: and time into a four dimensional structure where three of 572 00:28:11,720 --> 00:28:13,680 Speaker 2: them are similar to each other and one of them 573 00:28:13,720 --> 00:28:15,840 Speaker 2: is different. Right, doesn't that sound familiar? 574 00:28:15,880 --> 00:28:17,040 Speaker 1: It sounds like space time. 575 00:28:17,200 --> 00:28:20,920 Speaker 2: It sounds like space time exactly, And quaternions have exactly 576 00:28:20,960 --> 00:28:24,919 Speaker 2: that structure, three imaginary numbers and one real. So the 577 00:28:25,000 --> 00:28:27,840 Speaker 2: real numbers like time and the three imaginary numbers are 578 00:28:27,880 --> 00:28:31,439 Speaker 2: like three dimensions of space. And so these quaternions the 579 00:28:31,560 --> 00:28:34,760 Speaker 2: rules of space time vectors. We call them four vectors. 580 00:28:34,880 --> 00:28:37,640 Speaker 2: We call them four vectors now instead of quaternions are 581 00:28:37,720 --> 00:28:40,920 Speaker 2: absolutely crucial to relativity. 582 00:28:40,480 --> 00:28:43,719 Speaker 1: Meaning you need you can only do relativity math if 583 00:28:43,760 --> 00:28:47,040 Speaker 1: you're using quaternions, or it's just helpful to use them. 584 00:28:47,120 --> 00:28:50,040 Speaker 2: No, they're fundamental to special relativity absolutely like. 585 00:28:49,960 --> 00:28:52,840 Speaker 1: You can't you can't prove relativity without going into quaternions. 586 00:28:52,960 --> 00:28:55,360 Speaker 2: Exactly if we didn't already have quaternions, we would have 587 00:28:55,520 --> 00:28:58,719 Speaker 2: needed to invent them or discover them, depending on your 588 00:28:58,720 --> 00:29:01,920 Speaker 2: philosophical take. When we build relativity the same way, we 589 00:29:02,080 --> 00:29:05,760 Speaker 2: absolutely need complex numbers to describe quantum mechanics. So all 590 00:29:05,800 --> 00:29:08,600 Speaker 2: the self consistent ways we know how to build complex 591 00:29:08,720 --> 00:29:12,600 Speaker 2: numbers so far are very very useful for physics. And 592 00:29:12,840 --> 00:29:15,280 Speaker 2: it turns out there's a limited number of these sets. 593 00:29:15,280 --> 00:29:18,280 Speaker 2: You can't just like make up any number. So if one, two, 594 00:29:18,360 --> 00:29:21,400 Speaker 2: and four are super valuable for physics, then maybe eight 595 00:29:21,600 --> 00:29:22,440 Speaker 2: is also. 596 00:29:22,800 --> 00:29:26,440 Speaker 1: Mmmmm, Now you need four for relativity. Does it also 597 00:29:26,440 --> 00:29:33,320 Speaker 1: work if you call them formianss. 598 00:29:31,560 --> 00:29:33,280 Speaker 2: They're a little crunchier, but they still were. 599 00:29:35,560 --> 00:29:38,520 Speaker 1: All right, I'm just kidding. So you're saying, now the 600 00:29:38,600 --> 00:29:41,920 Speaker 1: question is, like, do numbers with seven extra imaginary dimensions 601 00:29:42,160 --> 00:29:45,160 Speaker 1: also maybe could they be used for something in physics? 602 00:29:45,280 --> 00:29:48,400 Speaker 2: That's exactly the question, and it's worth thinking about because 603 00:29:48,400 --> 00:29:51,480 Speaker 2: we've made progress so many times when we've developed some 604 00:29:51,600 --> 00:29:56,160 Speaker 2: mathematical tool group theory, field theory, complex numbers and then 605 00:29:56,280 --> 00:29:59,520 Speaker 2: later found it applicable to physics. So let's like get 606 00:29:59,520 --> 00:30:02,160 Speaker 2: ahead of the game. Let's say, oh, here's a kind 607 00:30:02,200 --> 00:30:05,360 Speaker 2: of mathematical tool which has been useful complex numbers of 608 00:30:05,360 --> 00:30:08,240 Speaker 2: dimensions one, two, and four. If there's only one more 609 00:30:08,320 --> 00:30:11,600 Speaker 2: kind of complex number out there, let's see if maybe 610 00:30:11,640 --> 00:30:14,680 Speaker 2: it tells us something about physics. Maybe it's the mathematical 611 00:30:14,680 --> 00:30:17,320 Speaker 2: structure to understand some other patterns that are out there 612 00:30:17,320 --> 00:30:18,800 Speaker 2: that we didn't have explanations for. 613 00:30:19,520 --> 00:30:21,360 Speaker 1: But does it seem kind of random to you? Like 614 00:30:21,520 --> 00:30:24,720 Speaker 1: you need one extra imaginary dimension to explain quantum physics 615 00:30:24,720 --> 00:30:28,280 Speaker 1: that's at the microscopic level, but then you need three 616 00:30:28,280 --> 00:30:32,680 Speaker 1: extra imaginary dimensions to describe relativity, which is usually at 617 00:30:32,680 --> 00:30:35,880 Speaker 1: a macro level, isn't it kind of random? Like you 618 00:30:35,920 --> 00:30:37,960 Speaker 1: need four here eight there too? Here? 619 00:30:38,240 --> 00:30:41,120 Speaker 2: Nobody understands it, right, then nobody has an intuitive understanding 620 00:30:41,160 --> 00:30:44,040 Speaker 2: for why one, two, four, and eight? Like, there is 621 00:30:44,080 --> 00:30:46,440 Speaker 2: this proof that shows that these are definitely the only 622 00:30:46,480 --> 00:30:49,840 Speaker 2: ones you can do. Nobody really knows philosophically what it means, 623 00:30:49,920 --> 00:30:53,320 Speaker 2: but it's very suggestive. Right, If two D numbers are 624 00:30:53,360 --> 00:30:56,960 Speaker 2: needed for quantum mechanics, four D numbers are needed for relativity. Well, 625 00:30:56,960 --> 00:31:00,680 Speaker 2: we've spent the laste hundred years looking for quantum mechanical relativity. 626 00:31:01,000 --> 00:31:04,600 Speaker 2: Maybe Octonians are the key to that, right, two times 627 00:31:04,640 --> 00:31:08,120 Speaker 2: four equals eight? After all, maybe the mathematical structure we 628 00:31:08,160 --> 00:31:11,920 Speaker 2: need to understand quantum gravity is based on Octonians. 629 00:31:12,200 --> 00:31:16,480 Speaker 1: But why Goodtonians as anyone tried to apply quaternions to 630 00:31:17,360 --> 00:31:18,440 Speaker 1: like quantum gravity? 631 00:31:18,520 --> 00:31:21,760 Speaker 2: Well, absolutely nobody has a consistent theory of quantum gravity 632 00:31:21,800 --> 00:31:24,239 Speaker 2: that works. And every time we try to write down 633 00:31:24,280 --> 00:31:27,840 Speaker 2: the theory of quantum gravity, it breaks mathematically, it does 634 00:31:27,880 --> 00:31:30,080 Speaker 2: not work. So it might just be that we're using 635 00:31:30,120 --> 00:31:31,920 Speaker 2: the wrong kind of number. 636 00:31:32,480 --> 00:31:34,680 Speaker 1: Oh, I see, Like, maybe the key to it all 637 00:31:34,840 --> 00:31:38,640 Speaker 1: is just to go to Applebee's and order Sometonians. 638 00:31:40,960 --> 00:31:44,320 Speaker 2: Absolutely, it might be well, I. 639 00:31:44,200 --> 00:31:46,920 Speaker 1: Mean that is a joke, but like, I think that's 640 00:31:46,920 --> 00:31:49,160 Speaker 1: what you're saying. It's like, why why don't we order 641 00:31:49,200 --> 00:31:52,320 Speaker 1: an Actonian and see if it satisfies or it helps 642 00:31:52,400 --> 00:31:54,240 Speaker 1: us combine these theories of physics. 643 00:31:54,360 --> 00:31:57,040 Speaker 2: Yeah. Absolutely, because remember that there's lots of ways to 644 00:31:57,040 --> 00:31:59,520 Speaker 2: make progress in physics when you don't understand the patterns 645 00:31:59,520 --> 00:32:02,000 Speaker 2: you're looking at. One way is to see more of 646 00:32:02,000 --> 00:32:04,360 Speaker 2: the pattern. You're like, well, what are all these particles? 647 00:32:04,400 --> 00:32:07,120 Speaker 2: Why do we have these particles not other particles. One 648 00:32:07,200 --> 00:32:10,720 Speaker 2: strategy is discover more particles. That's what I'm doing, building colliders, 649 00:32:10,720 --> 00:32:13,360 Speaker 2: smashing stuff together and looking to see more of the pattern, 650 00:32:13,640 --> 00:32:15,760 Speaker 2: hoping that if you see more of it, you'll figure 651 00:32:15,800 --> 00:32:18,520 Speaker 2: out what's going on. Another approach is not to discover 652 00:32:18,600 --> 00:32:22,880 Speaker 2: anything new, but find new mathematical structures that naturally describe 653 00:32:22,880 --> 00:32:25,920 Speaker 2: the patterns you're seeing. For example, that's how we thought 654 00:32:26,000 --> 00:32:28,800 Speaker 2: up the Higgs boson. It wasn't just discovered. It was 655 00:32:28,880 --> 00:32:31,640 Speaker 2: thought up by looking at the patterns that exist already 656 00:32:31,640 --> 00:32:34,120 Speaker 2: in the particles that we had, coming up with a 657 00:32:34,200 --> 00:32:37,600 Speaker 2: new mathematical structure to describe that group theory and the 658 00:32:37,680 --> 00:32:41,040 Speaker 2: unification of electromagnetism and the weak force and realizing that 659 00:32:41,040 --> 00:32:43,960 Speaker 2: that needed a Higgs boson. And so there's a lot 660 00:32:43,960 --> 00:32:46,080 Speaker 2: of progress to be made in just coming up with 661 00:32:46,120 --> 00:32:49,360 Speaker 2: a new mathematical way to look at the patterns we already. 662 00:32:48,960 --> 00:32:51,880 Speaker 1: Seem interesting, Like, that's a way to do science, Like 663 00:32:52,360 --> 00:32:54,240 Speaker 1: try to look for patterns and then come up with 664 00:32:54,280 --> 00:32:57,040 Speaker 1: ideas that might make sense of those patterns, and then 665 00:32:57,200 --> 00:33:01,000 Speaker 1: go back to the experiments to see if those theories are. 666 00:33:00,440 --> 00:33:03,520 Speaker 2: Exactly Because mathematics has its own rules, right, you can't 667 00:33:03,560 --> 00:33:06,959 Speaker 2: just invent whatever mathematics you want. Mathematics is telling us 668 00:33:07,040 --> 00:33:09,320 Speaker 2: very clearly, Hey guys, there's only four kind of numbers 669 00:33:09,320 --> 00:33:10,640 Speaker 2: you can use, by the way, if you want to 670 00:33:10,640 --> 00:33:13,640 Speaker 2: describe physics. And that seems like a pretty big clue. 671 00:33:13,640 --> 00:33:15,720 Speaker 2: It's like, well, if we only have four tools, let's 672 00:33:15,720 --> 00:33:18,280 Speaker 2: make sure to use all of them, right, especially if 673 00:33:18,320 --> 00:33:21,680 Speaker 2: the first three were so absolutely useful, So even if 674 00:33:21,720 --> 00:33:24,320 Speaker 2: we haven't yet figured out what they applied to, it's 675 00:33:24,360 --> 00:33:26,720 Speaker 2: worth thinking about what they might be applied to. 676 00:33:26,880 --> 00:33:27,240 Speaker 3: Mmm. 677 00:33:27,440 --> 00:33:29,880 Speaker 1: Interesting, Okay, So I think what you're saying is that maybe, 678 00:33:29,920 --> 00:33:32,360 Speaker 1: like if we take the universe and we peel back 679 00:33:32,400 --> 00:33:35,440 Speaker 1: its layers one by one and try to get to 680 00:33:35,480 --> 00:33:37,320 Speaker 1: the core of it. Maybe at the center of it 681 00:33:37,400 --> 00:33:40,400 Speaker 1: is an Atonium exactly. 682 00:33:40,440 --> 00:33:42,880 Speaker 2: An Actonian could be the center of the onion eight 683 00:33:42,960 --> 00:33:43,520 Speaker 2: layers down. 684 00:33:44,320 --> 00:33:45,040 Speaker 1: Yeah, there you go. 685 00:33:45,160 --> 00:33:46,240 Speaker 2: I see where you're walking me to. 686 00:33:46,360 --> 00:33:50,920 Speaker 1: Yes, all right, well, let's get into what these ideas 687 00:33:51,000 --> 00:33:54,600 Speaker 1: are about. How Altonians might describe what's inside of the universe, 688 00:33:54,640 --> 00:33:57,000 Speaker 1: what's at the core of it. How does it all work, 689 00:33:57,120 --> 00:33:59,840 Speaker 1: How does it make sense mathematically? Will these theories work? 690 00:34:00,040 --> 00:34:14,000 Speaker 1: Let's stick into that. But first let's take another quick break. 691 00:34:14,840 --> 00:34:17,120 Speaker 1: All right, we're talking about Octonians, and are they the 692 00:34:17,160 --> 00:34:20,800 Speaker 1: imaginary numbers that scientists have been dreaming about to explain 693 00:34:21,040 --> 00:34:24,520 Speaker 1: everything in the universe. So, Daniel, you were saying that 694 00:34:24,560 --> 00:34:28,640 Speaker 1: the numbers is one imaginary number really helped describe quantum mechanics, 695 00:34:29,080 --> 00:34:33,600 Speaker 1: numbers with three imaginary numbers really help describe special relativity 696 00:34:33,600 --> 00:34:36,680 Speaker 1: and relativity, and because it lets you do math with 697 00:34:36,800 --> 00:34:39,680 Speaker 1: space time, three dimensions of space and one of time. 698 00:34:40,120 --> 00:34:43,280 Speaker 1: Now you're saying that maybe if you want to combine 699 00:34:43,280 --> 00:34:48,239 Speaker 1: these two theories, quantum mechanics and special relativity, maybe you 700 00:34:48,320 --> 00:34:52,560 Speaker 1: need an extra imaginary number, which might be the Octonian. 701 00:34:52,160 --> 00:34:55,400 Speaker 2: Yeah, it might be exactly, And we're trying to figure 702 00:34:55,400 --> 00:34:58,680 Speaker 2: out where this might be relevant to the universe. And 703 00:34:58,800 --> 00:35:00,920 Speaker 2: one thing we can do to figure that out is 704 00:35:00,960 --> 00:35:03,920 Speaker 2: to look at the properties of octonians, like what do 705 00:35:03,960 --> 00:35:08,080 Speaker 2: octonians do the quaternions and complex numbers and real numbers 706 00:35:08,400 --> 00:35:12,560 Speaker 2: don't do. How are they different? And that's one fruitful 707 00:35:12,600 --> 00:35:14,880 Speaker 2: way to understand where they might be relevant. 708 00:35:15,040 --> 00:35:17,160 Speaker 1: What do you mean, like, what can they do that's special? 709 00:35:17,360 --> 00:35:20,040 Speaker 2: So it's more about what they can't do. Every time 710 00:35:20,080 --> 00:35:23,799 Speaker 2: you add more complex numbers, you sort of lose some ability. 711 00:35:24,000 --> 00:35:26,520 Speaker 2: Like within real numbers, you can order them, right, you 712 00:35:26,560 --> 00:35:28,480 Speaker 2: can say this number is bigger than that number, is 713 00:35:28,520 --> 00:35:30,920 Speaker 2: bigger than that number. They have a very well defined order. 714 00:35:30,920 --> 00:35:33,759 Speaker 2: But once you go to complex numbers, you can't necessarily 715 00:35:33,800 --> 00:35:36,920 Speaker 2: say that, like which number is bigger one or I? 716 00:35:36,960 --> 00:35:38,960 Speaker 2: They have like the same magnitude, but you can no 717 00:35:39,000 --> 00:35:42,360 Speaker 2: longer rank them necessarily. So as you add complex dimensions 718 00:35:42,600 --> 00:35:44,640 Speaker 2: you actually lose some capabilities. 719 00:35:44,800 --> 00:35:47,560 Speaker 1: Things say crazier kind of right, like it's it's kind 720 00:35:47,560 --> 00:35:50,000 Speaker 1: of hard to order things in a plane or in 721 00:35:50,040 --> 00:35:51,640 Speaker 1: an X y plane exactly. 722 00:35:51,880 --> 00:35:55,200 Speaker 2: And then when you go to quaternions, basically space time vectors. 723 00:35:55,440 --> 00:35:59,000 Speaker 2: What you lose is commutation, the fact that like A 724 00:35:59,200 --> 00:36:02,000 Speaker 2: times b is usually equal to B times a. But 725 00:36:02,040 --> 00:36:05,800 Speaker 2: that's not true for four dimensional vectors, because multiplying numbers 726 00:36:05,800 --> 00:36:08,520 Speaker 2: in four dimensions is like rotation. It's like taking a 727 00:36:08,600 --> 00:36:12,799 Speaker 2: vector and turning it, and in four dimensional space, rotations 728 00:36:12,880 --> 00:36:16,319 Speaker 2: don't commute. It like matters what order you do rotations in. 729 00:36:16,840 --> 00:36:19,080 Speaker 2: If you first turn left and then you turn up, 730 00:36:19,120 --> 00:36:21,000 Speaker 2: you get it to a different place than if you 731 00:36:21,040 --> 00:36:22,040 Speaker 2: do it in the other direction. 732 00:36:22,160 --> 00:36:24,120 Speaker 1: For example, Wait, wait, I thought that you said that 733 00:36:24,200 --> 00:36:28,239 Speaker 1: quaternions and olktunians work because they follow all the math rules. 734 00:36:28,239 --> 00:36:30,279 Speaker 1: You're saying now that maybe they sort of work, but 735 00:36:30,400 --> 00:36:33,000 Speaker 1: you kind of have to give up some math rules exactly. 736 00:36:33,040 --> 00:36:35,800 Speaker 2: These math rules that we require don't include that they commute. 737 00:36:35,840 --> 00:36:37,920 Speaker 2: They only include that you can multiply and divide an 738 00:36:37,920 --> 00:36:41,120 Speaker 2: add and subtract. Commutation is not a requirement. It turns 739 00:36:41,160 --> 00:36:43,880 Speaker 2: out that as the numbers get more complex, you lose 740 00:36:43,920 --> 00:36:46,400 Speaker 2: some of the properties we're familiar with of real numbers. 741 00:36:46,880 --> 00:36:50,800 Speaker 2: So complex numbers you lose the ability to order them quaternions, 742 00:36:50,920 --> 00:36:53,080 Speaker 2: you lose the ability to multiply them in any order 743 00:36:53,160 --> 00:36:55,319 Speaker 2: you want. A times B is not the same as 744 00:36:55,360 --> 00:36:57,520 Speaker 2: B times A. So that's really interesting. It tells us 745 00:36:57,560 --> 00:37:00,400 Speaker 2: something about the structure of space time, right, this is 746 00:37:00,440 --> 00:37:05,400 Speaker 2: really about space now, Octonians. Even weirder Octonians, which you 747 00:37:05,440 --> 00:37:09,280 Speaker 2: lose is the associative property. The associated property tells us basically, 748 00:37:09,320 --> 00:37:12,000 Speaker 2: you can distribute numbers within a parenthesis, like do you 749 00:37:12,040 --> 00:37:14,520 Speaker 2: do the multiplication within the parentheses first, or do you 750 00:37:14,520 --> 00:37:16,520 Speaker 2: distribute the number through the parentheses. It's sort of hard 751 00:37:16,520 --> 00:37:19,600 Speaker 2: to think about the associated property of math intuitively. In 752 00:37:19,640 --> 00:37:21,640 Speaker 2: a physical sense, it would be sort of like, you know, 753 00:37:21,680 --> 00:37:24,200 Speaker 2: you're used to putting your socks on and then your shoes. 754 00:37:24,280 --> 00:37:26,320 Speaker 2: What if you first put your socks in your shoes 755 00:37:26,480 --> 00:37:28,920 Speaker 2: and then put your feet into the socks, you'd end 756 00:37:29,000 --> 00:37:31,040 Speaker 2: up in the same place. Right, It doesn't really matter 757 00:37:31,440 --> 00:37:33,239 Speaker 2: if you put the socks on first or put the 758 00:37:33,280 --> 00:37:36,880 Speaker 2: socks in the shoes, But for Octonians it does matter. 759 00:37:37,239 --> 00:37:40,239 Speaker 2: The associated property doesn't hold for Octonians. 760 00:37:40,640 --> 00:37:44,160 Speaker 1: M I see, you lose another math rule, and you 761 00:37:44,200 --> 00:37:46,319 Speaker 1: also lose the ability to order them, and you also 762 00:37:46,360 --> 00:37:48,680 Speaker 1: lose the ability to like commute them. 763 00:37:48,680 --> 00:37:52,120 Speaker 2: You said exactly, So that's a clue, right. It tells 764 00:37:52,200 --> 00:37:55,360 Speaker 2: us that maybe the fundamental nature of the universe doesn't 765 00:37:55,400 --> 00:38:00,120 Speaker 2: respect this associative property. Maybe parentheses actually do matter to 766 00:38:00,320 --> 00:38:03,960 Speaker 2: whatever mathematics really rules the universe. That's just like a clue, 767 00:38:04,000 --> 00:38:06,320 Speaker 2: and then we go off hunting in the physical world 768 00:38:06,440 --> 00:38:10,360 Speaker 2: for maybe something that's like that. Is there some theory 769 00:38:10,400 --> 00:38:13,040 Speaker 2: of physics that we can build that doesn't have this 770 00:38:13,200 --> 00:38:17,760 Speaker 2: requirement of associativity of our numbers. Maybe that's the right direction. 771 00:38:17,920 --> 00:38:20,400 Speaker 2: It's a very very vague clue, but that's the kind 772 00:38:20,440 --> 00:38:22,280 Speaker 2: of clue we can get from looking at the structure 773 00:38:22,320 --> 00:38:24,720 Speaker 2: of the mathematics of Octonians. 774 00:38:25,000 --> 00:38:26,920 Speaker 1: Oh, I see, because the pattern is that every time 775 00:38:27,000 --> 00:38:31,600 Speaker 1: you have one of these imaginary number sets, their limitations 776 00:38:31,680 --> 00:38:35,480 Speaker 1: somehow correspond to a rule or a feature of the universe. 777 00:38:35,920 --> 00:38:38,479 Speaker 1: Like when you had one extra dimension and you can't 778 00:38:38,520 --> 00:38:42,799 Speaker 1: order those numbers, that corresponds to something special about quantum particles, 779 00:38:43,040 --> 00:38:47,080 Speaker 1: or when you have a quaternion and you can't commute 780 00:38:47,080 --> 00:38:49,920 Speaker 1: them that means something special about how you can rotate 781 00:38:50,000 --> 00:38:52,440 Speaker 1: or not things in space m M exactly. 782 00:38:52,920 --> 00:38:55,960 Speaker 2: So what does this mean about the universe that Octonians 783 00:38:56,000 --> 00:38:59,560 Speaker 2: don't respect the associative property. It's very strange, it's very unphysical, 784 00:39:00,080 --> 00:39:02,759 Speaker 2: like no intuition for it. What it tells us is 785 00:39:02,760 --> 00:39:05,440 Speaker 2: that a theory of the universe built on Octonians is 786 00:39:05,480 --> 00:39:07,120 Speaker 2: going to be very counterintuitive. 787 00:39:07,200 --> 00:39:08,880 Speaker 1: Wait, doesn't it just mean you can't put on your 788 00:39:08,880 --> 00:39:10,200 Speaker 1: socks and your shoes at the same time. 789 00:39:11,640 --> 00:39:13,759 Speaker 2: It means it makes a difference whether you put your 790 00:39:13,760 --> 00:39:15,719 Speaker 2: socks in your shoes and then put them both on, 791 00:39:15,920 --> 00:39:17,840 Speaker 2: or put your socks on and then your shoes. 792 00:39:18,200 --> 00:39:22,160 Speaker 1: Yeah, it would make a difference, for sure. I'm sure 793 00:39:22,400 --> 00:39:22,960 Speaker 1: would work. 794 00:39:24,239 --> 00:39:25,960 Speaker 2: I mean, I think some people put their underwear in 795 00:39:26,000 --> 00:39:27,520 Speaker 2: their pants on at the same time, don't they. I 796 00:39:27,560 --> 00:39:27,920 Speaker 2: don't know. 797 00:39:28,000 --> 00:39:30,640 Speaker 1: Oh, well, well, why didn't you start with that analogy? 798 00:39:30,840 --> 00:39:32,600 Speaker 2: I didn't want to talk about underwear? I guess. 799 00:39:35,120 --> 00:39:38,239 Speaker 1: So you're saying that, uh, Quaternions, you can't do that. 800 00:39:38,280 --> 00:39:40,000 Speaker 1: You can't put your underwear inside of your pants and 801 00:39:40,000 --> 00:39:41,520 Speaker 1: then put them on both at the same time. 802 00:39:41,880 --> 00:39:45,120 Speaker 2: You can for you can for quaternions. You can't for Octonians, 803 00:39:45,280 --> 00:39:45,640 Speaker 2: That's right. 804 00:39:45,680 --> 00:39:48,360 Speaker 1: I'm sorry you can't for Octonians. You're asking, like, is 805 00:39:48,400 --> 00:39:51,719 Speaker 1: there a rule in the universe that somehow corresponds to 806 00:39:51,800 --> 00:39:55,320 Speaker 1: that limitation with your pants exactly? 807 00:39:55,560 --> 00:39:58,680 Speaker 2: The underlying rule of the universe is somehow related to underpants. 808 00:39:58,920 --> 00:39:59,440 Speaker 2: We don't know. 809 00:39:59,800 --> 00:40:02,319 Speaker 1: Hey, yeah, there you go, or d end up looking 810 00:40:02,360 --> 00:40:06,279 Speaker 1: like Superman with another word outside of your pants exactly. 811 00:40:06,360 --> 00:40:08,520 Speaker 2: Maybe he's the original Octonian. 812 00:40:08,280 --> 00:40:13,800 Speaker 1: That's right. Maybe maybe any Kryptonians to just really describe 813 00:40:13,840 --> 00:40:14,360 Speaker 1: the universe. 814 00:40:14,520 --> 00:40:16,799 Speaker 2: We don't know. But in the meantime, physicists are on 815 00:40:16,840 --> 00:40:20,040 Speaker 2: the hunt for eights. We're looking for things out there 816 00:40:20,040 --> 00:40:23,160 Speaker 2: in nature patterns which include the number eight. And there 817 00:40:23,200 --> 00:40:26,880 Speaker 2: are some pantalizing hints, you know. For example, string theory 818 00:40:26,920 --> 00:40:30,960 Speaker 2: we know likes to exist in ten spatial dimensions because 819 00:40:31,160 --> 00:40:34,200 Speaker 2: the mathematics of how those things compactify works best in 820 00:40:34,280 --> 00:40:37,000 Speaker 2: ten dimensions. So some people have said, ooh, well, that's 821 00:40:37,040 --> 00:40:40,640 Speaker 2: sort of like eight spatial dimensions and one time dimension 822 00:40:40,840 --> 00:40:43,839 Speaker 2: plus one dimension for like along the string, and so 823 00:40:43,880 --> 00:40:45,319 Speaker 2: this is kind of an eight there. 824 00:40:45,560 --> 00:40:48,360 Speaker 1: But ten, you said didn't work? Why are they fixated 825 00:40:48,400 --> 00:40:50,640 Speaker 1: with ten if ten doesn't hold mathematically? 826 00:40:50,800 --> 00:40:53,560 Speaker 2: Because string theory works in ten dimensions. There's a different 827 00:40:53,560 --> 00:40:56,399 Speaker 2: set of rules there. Mathematically, string theory works in ten. 828 00:40:56,719 --> 00:41:00,319 Speaker 2: Octonians work in eight. Can we somehow marry the two? Well, 829 00:41:00,360 --> 00:41:01,000 Speaker 2: maybe if. 830 00:41:00,840 --> 00:41:03,120 Speaker 1: We take those ten dimensions the difference and make it nine. 831 00:41:03,960 --> 00:41:07,000 Speaker 2: There's no compromising in math. It's not a negotiation with 832 00:41:07,080 --> 00:41:07,680 Speaker 2: the universe. 833 00:41:07,960 --> 00:41:13,520 Speaker 1: You can't split the difference, well, I can't make quantum gravity. Worry. 834 00:41:13,520 --> 00:41:15,000 Speaker 1: How about uh, we'll split the difference. 835 00:41:15,080 --> 00:41:16,879 Speaker 2: I'll give you points on the back end. All right? 836 00:41:16,920 --> 00:41:17,440 Speaker 2: How about that? 837 00:41:17,440 --> 00:41:19,919 Speaker 1: That's right? Yes, we'll only make both of them half work. 838 00:41:21,040 --> 00:41:22,920 Speaker 2: No, people are like, well, can we take eight of 839 00:41:22,960 --> 00:41:25,799 Speaker 2: those ten string dimensions and say those are described by 840 00:41:25,800 --> 00:41:28,600 Speaker 2: Octonians and then another one of them is time and 841 00:41:28,600 --> 00:41:31,080 Speaker 2: another one is a string dimension. It's a real stretch. 842 00:41:31,440 --> 00:41:34,920 Speaker 2: But people are looking for eightishness somewhere out there in 843 00:41:34,920 --> 00:41:38,440 Speaker 2: the patterns and wondering if it can be described by Octonians. 844 00:41:38,560 --> 00:41:41,880 Speaker 1: Can't you just decrease the number of dimensions in string 845 00:41:41,960 --> 00:41:43,520 Speaker 1: theory or it wouldn't work anymore? 846 00:41:43,560 --> 00:41:45,640 Speaker 2: No, it doesn't work. It only works in ten dimensions. 847 00:41:45,680 --> 00:41:47,839 Speaker 2: There's another version of it that works in twenty six, 848 00:41:48,160 --> 00:41:51,120 Speaker 2: but string theory doesn't work in eight dimensions. Another direction 849 00:41:51,160 --> 00:41:53,040 Speaker 2: people are going in is to try to describe the 850 00:41:53,080 --> 00:41:55,919 Speaker 2: strong force. The strong force is something we really don't 851 00:41:56,000 --> 00:42:00,719 Speaker 2: understand very well. But it has eight gluons, right, number eight, 852 00:42:01,120 --> 00:42:04,240 Speaker 2: So maybe Octonians would be a better way to describe 853 00:42:04,280 --> 00:42:06,960 Speaker 2: the strong force. Maybe the whole reason we have trouble 854 00:42:07,040 --> 00:42:10,360 Speaker 2: doing calculations in quantum chromodynamics is because we're used in 855 00:42:10,400 --> 00:42:11,880 Speaker 2: the wrong kind of math, and it would all just 856 00:42:11,920 --> 00:42:15,200 Speaker 2: like click beautifully into place if we replaced it with octonians. 857 00:42:15,480 --> 00:42:18,279 Speaker 1: Wait, what do mean there are only eight gluons? You're 858 00:42:18,320 --> 00:42:21,080 Speaker 1: just looking for things in nature that you know about 859 00:42:21,120 --> 00:42:22,799 Speaker 1: so far that somehow count it eight. 860 00:42:23,000 --> 00:42:25,919 Speaker 2: Yeah, exactly, And there are eight kinds of gluons because 861 00:42:25,960 --> 00:42:30,400 Speaker 2: remember that there are three different colors in the strong force, red, green, 862 00:42:30,480 --> 00:42:33,759 Speaker 2: and blue, and each gluon carries two colors, And so 863 00:42:33,800 --> 00:42:36,080 Speaker 2: the way the mathematics works is that it's three squared 864 00:42:36,120 --> 00:42:39,200 Speaker 2: minus one. You get eight different kinds of gluons that 865 00:42:39,280 --> 00:42:41,640 Speaker 2: you can have. So, yeah, we're just looking for things 866 00:42:42,000 --> 00:42:44,480 Speaker 2: in nature that have eight in them. Like, what about 867 00:42:44,480 --> 00:42:47,839 Speaker 2: the universe is eightish? Can we describe it with octonians? 868 00:42:48,080 --> 00:42:52,880 Speaker 2: So far nobody's made it work. Octonians mathematically beautiful, mathematically consistent, 869 00:42:53,000 --> 00:42:54,960 Speaker 2: so far totally physically useless. 870 00:42:55,239 --> 00:42:57,560 Speaker 1: Huh, Like, what did you decide to try to make 871 00:42:57,600 --> 00:43:00,880 Speaker 1: quantum gravity work with octonians? Where does that put us? 872 00:43:00,960 --> 00:43:04,160 Speaker 1: Aren't there like eight dimensions or things like that? In 873 00:43:04,200 --> 00:43:06,759 Speaker 1: between the two of them, like the wave function plus 874 00:43:06,960 --> 00:43:08,080 Speaker 1: the space. 875 00:43:07,800 --> 00:43:12,000 Speaker 2: Time throwing some oranges and a couple of socks. Yeah, exactly. 876 00:43:12,360 --> 00:43:14,239 Speaker 2: I know people are working on that, right. There a 877 00:43:14,280 --> 00:43:16,680 Speaker 2: lot of people studying the nature of optunians and trying 878 00:43:16,719 --> 00:43:19,680 Speaker 2: to use them to build a physical theory, but nobody 879 00:43:19,760 --> 00:43:22,040 Speaker 2: succeeded so far. Just sort of like a direction some 880 00:43:22,080 --> 00:43:25,520 Speaker 2: people are sniffing in as we try to build mathematically 881 00:43:25,560 --> 00:43:27,440 Speaker 2: consistent theories of quantum gravity. 882 00:43:27,680 --> 00:43:29,239 Speaker 1: Wow, you're just looking for the number eight. 883 00:43:29,440 --> 00:43:32,000 Speaker 2: Yes, exactly. We're desperate for clues because this is the 884 00:43:32,040 --> 00:43:35,160 Speaker 2: biggest unsolved problem in physics. How to marry quantum mechanics 885 00:43:35,160 --> 00:43:37,760 Speaker 2: and relativity. We haven't figured out in one hundred years. 886 00:43:38,080 --> 00:43:40,680 Speaker 2: So we're like digging deep in the mathematical toolbox to like, well, 887 00:43:40,680 --> 00:43:42,279 Speaker 2: what else we got in here? Let's see what else 888 00:43:42,280 --> 00:43:42,920 Speaker 2: could be useful. 889 00:43:43,920 --> 00:43:46,080 Speaker 1: Well, I can't seem to get up before eight am? 890 00:43:46,239 --> 00:43:48,839 Speaker 1: Could that be a rule of the universe? I could 891 00:43:48,880 --> 00:43:49,319 Speaker 1: blame that. 892 00:43:49,320 --> 00:43:51,719 Speaker 2: On Well, we could flip the blame. You could say 893 00:43:51,719 --> 00:43:54,239 Speaker 2: nobody's solved this problem because you won't get up before 894 00:43:54,280 --> 00:43:54,760 Speaker 2: eight am. 895 00:43:55,560 --> 00:43:58,359 Speaker 1: Well, that would still make sense. That Still, that's still 896 00:43:58,360 --> 00:44:00,160 Speaker 1: an explanation for the universe. 897 00:44:00,480 --> 00:44:02,600 Speaker 2: Or maybe it would take an announcement of quantum gravity 898 00:44:02,640 --> 00:44:04,880 Speaker 2: to get you out of it before eight am. 899 00:44:05,160 --> 00:44:08,080 Speaker 1: Unlikely, unlikely in this universe. I don't think that was 900 00:44:08,200 --> 00:44:13,799 Speaker 1: mathematically hold. Yeah, I think there's YouTube for that. I'll 901 00:44:13,840 --> 00:44:16,440 Speaker 1: just catch it on YouTube later, all right, Well, but 902 00:44:16,480 --> 00:44:19,600 Speaker 1: it's sort of an interesting idea or direction in which 903 00:44:19,680 --> 00:44:22,560 Speaker 1: to look for new theories about the universe. Like maybe 904 00:44:22,640 --> 00:44:25,120 Speaker 1: you put your octogoggles on and look for things that 905 00:44:25,760 --> 00:44:29,879 Speaker 1: work or that seem to manifest themselves in sets of eight. 906 00:44:30,040 --> 00:44:33,600 Speaker 1: Maybe that could be a way to get to a 907 00:44:33,680 --> 00:44:35,080 Speaker 1: theory of everything exactly. 908 00:44:35,120 --> 00:44:38,800 Speaker 2: If mathematics really does reflect something deep about the universe, 909 00:44:39,080 --> 00:44:42,880 Speaker 2: then mathematicians building tools can actually construct sort of like 910 00:44:42,960 --> 00:44:45,440 Speaker 2: proto bits of future physics theories that we could just 911 00:44:45,480 --> 00:44:48,120 Speaker 2: like click into place. We've done it before with group 912 00:44:48,160 --> 00:44:51,520 Speaker 2: theory and field theory and differential geometry, so we hope 913 00:44:51,520 --> 00:44:52,560 Speaker 2: it happens again. 914 00:44:52,520 --> 00:44:54,520 Speaker 1: Right, And that's kind of what's happening with strength there. 915 00:44:54,680 --> 00:44:56,760 Speaker 1: Although that one seems to be following the rule. 916 00:44:56,560 --> 00:44:58,840 Speaker 2: Of ten yeah, or the rule of twenty six. 917 00:44:58,960 --> 00:45:02,600 Speaker 1: So it sounds like maybe physicists you need to sit 918 00:45:02,640 --> 00:45:04,320 Speaker 1: down and peel more onions. 919 00:45:05,600 --> 00:45:06,600 Speaker 2: And stop crying. 920 00:45:07,239 --> 00:45:10,680 Speaker 1: That's a right stop pretend. Pretend that tears come from 921 00:45:10,960 --> 00:45:14,000 Speaker 1: cutting these onions and not from being a physicist. And 922 00:45:14,040 --> 00:45:16,959 Speaker 1: maybe that will inspire some new theory. That may it'll 923 00:45:17,000 --> 00:45:20,440 Speaker 1: crack open, they'll peel away the truth of the universe. 924 00:45:20,600 --> 00:45:22,160 Speaker 2: Or maybe we should just take a break in good 925 00:45:22,200 --> 00:45:24,120 Speaker 2: Applebee's and have a bloomin onion. 926 00:45:24,800 --> 00:45:27,440 Speaker 1: Yeah, there you go. There are different ways. As long 927 00:45:27,480 --> 00:45:31,239 Speaker 1: as it's after eight am, I'll join you, all right, Well, 928 00:45:31,239 --> 00:45:34,920 Speaker 1: and interesting dive into mathematics and how it matches up 929 00:45:34,960 --> 00:45:37,799 Speaker 1: with physics and how it's helping us maybe understand how 930 00:45:37,840 --> 00:45:39,959 Speaker 1: it all works, or at least how it has helped 931 00:45:40,040 --> 00:45:41,840 Speaker 1: us and maybe could help us in the future. 932 00:45:42,040 --> 00:45:45,120 Speaker 2: And future mathematicians and physicists might look back and say, oh, 933 00:45:45,239 --> 00:45:47,600 Speaker 2: it was so obvious how it all clicked into place. 934 00:45:47,719 --> 00:45:50,120 Speaker 2: But here we are at the forefront of human ignorance, 935 00:45:50,480 --> 00:45:51,920 Speaker 2: just not seeing it come together. 936 00:45:52,320 --> 00:45:54,520 Speaker 1: All right, Well, we hope you enjoyed that. Thanks for 937 00:45:54,600 --> 00:45:56,640 Speaker 1: joining us. See you next time. 938 00:46:01,040 --> 00:46:04,280 Speaker 2: For more science and curiosity. Come find us on social media, 939 00:46:04,320 --> 00:46:07,880 Speaker 2: where we answer questions and post videos. We're on Twitter, 940 00:46:08,000 --> 00:46:11,360 Speaker 2: disc Org, Insta, and now TikTok. Thanks for listening, and 941 00:46:11,400 --> 00:46:14,120 Speaker 2: remember that Daniel and Jorge Explain the Universe is a 942 00:46:14,160 --> 00:46:18,759 Speaker 2: production of iHeartRadio. For more podcasts from iHeartRadio, visit the 943 00:46:18,840 --> 00:46:22,960 Speaker 2: iHeartRadio app, Apple Podcasts, or wherever you listen to your 944 00:46:23,040 --> 00:46:23,800 Speaker 2: favorite shows.