WEBVTT - Fantastic Numbers, with Antonio Padilla 0:00:03.040 --> 0:00:05.360 Welcome to stot to Blow Your Mind, production of My 0:00:05.480 --> 0:00:15.440 Heart Radio. Hey, welcome to Stuff to Blow Your Mind. 0:00:15.760 --> 0:00:18.840 My name is Robert Lamb. My co host Joe is 0:00:18.880 --> 0:00:22.600 away from work today, so I am conducting an interview 0:00:22.680 --> 0:00:28.080 here with Professor Antonio Padella, author of the new book 0:00:28.480 --> 0:00:33.040 Fantastic Numbers and Where to Find Them, a fascinating read 0:00:33.159 --> 0:00:38.239 about big numbers, fantastic numbers, black holes, and more. This 0:00:38.280 --> 0:00:40.360 is a really fun chat. I think you're all going 0:00:40.440 --> 0:00:43.640 to enjoy it, So go ahead and jump right in 0:00:43.720 --> 0:00:49.360 with me right now. Hi, Tony, Welcome to the show. Hi, 0:00:49.560 --> 0:00:53.680 Hi up, how you doing? Oh? Pretty good? Pretty good? Um? 0:00:53.720 --> 0:00:57.360 Really excited to talk about the new book Fantastic Numbers 0:00:57.360 --> 0:00:59.400 and Where to Find Them? A wonderful read, and it's 0:00:59.400 --> 0:01:02.440 a book that get into some pretty wonderful mind rending 0:01:02.800 --> 0:01:07.320 cosmological territory as well. Note I'll discuss here, but first 0:01:07.319 --> 0:01:10.119 I wanted to start with just a really basic sort 0:01:10.120 --> 0:01:13.600 of grounding question. I guess we encounter numbers every day, 0:01:13.680 --> 0:01:15.920 and you discuss some numbers that most of us don't 0:01:16.000 --> 0:01:18.840 encounter really every day. If we could back up a 0:01:18.880 --> 0:01:21.880 whole lot, I guess, and just ponder the basics here, 0:01:22.000 --> 0:01:25.160 what exactly is a number? Well, I mean, this is 0:01:25.240 --> 0:01:27.160 this is an idea I sort of, you know, delve 0:01:27.200 --> 0:01:29.000 into him in my book, because of course, when you 0:01:29.280 --> 0:01:31.920 go really back in into history, back to sort of 0:01:31.959 --> 0:01:35.080 the ancient Sunarians or something like that, you know, obviously 0:01:35.560 --> 0:01:37.880 they really began to use numbers to talk about And 0:01:37.920 --> 0:01:41.000 while I've got five jars of oil, I've got five 0:01:41.040 --> 0:01:44.199 loaves of bread. But then it sort of begs the question, 0:01:44.280 --> 0:01:46.640 is that five the same five is the five that 0:01:46.680 --> 0:01:49.040 describes the jars of oil, the same five that describes 0:01:49.920 --> 0:01:52.640 the loaves of bread. And then you really sort of 0:01:52.920 --> 0:01:55.520 when you sort of make that disconnected too, and you 0:01:55.560 --> 0:01:57.560 start to build the idea of like what I call 0:01:57.760 --> 0:02:00.600 an emancipated number, but it's independent and of the thing 0:02:01.160 --> 0:02:03.920 that it's describing, then you're really sort of making quite 0:02:04.000 --> 0:02:06.080 quite an intellectual leap. So that, for me is what 0:02:06.360 --> 0:02:08.880 is what a number is. It's kind of emancipated from 0:02:08.919 --> 0:02:12.320 from the thing that it's describing. Whether such a thing 0:02:12.400 --> 0:02:15.960 really exists in a philosophical sense, is a whole new 0:02:15.960 --> 0:02:18.680 debate that you can have. But yeah, that for me 0:02:18.800 --> 0:02:21.519 is is the key mathematical leap that I think was 0:02:21.600 --> 0:02:25.280 made you know, a long time ago, and and yeah, 0:02:25.320 --> 0:02:27.440 it's really important now getting back into that sort of 0:02:27.440 --> 0:02:30.840 philosophical territory. This is one that I know that you 0:02:30.840 --> 0:02:33.840 you tackle a lot. Uh, it's pretty standard sort of 0:02:33.840 --> 0:02:37.640 philosophical math question. But is mathematics more of a human 0:02:37.680 --> 0:02:41.239 discovery or more of a human invention? Yeah, I mean 0:02:41.600 --> 0:02:44.080 I don't think there's a straightforward answer answer to this. 0:02:44.160 --> 0:02:46.440 Of course. This this sort of you know, boils down 0:02:46.480 --> 0:02:49.560 to like a sort of alluded to whether numbers exist, 0:02:49.639 --> 0:02:52.240 whether whether maths exist, and it's kind of I mean, 0:02:52.240 --> 0:02:54.080 I'm not a philosopher, but but but I know that 0:02:54.080 --> 0:02:56.440 philosophers talk about this, and sort of this kind of 0:02:56.480 --> 0:02:58.320 three different angles that you can take on it. So 0:02:58.440 --> 0:03:01.640 so on the one hand, you've got the platonists who 0:03:01.720 --> 0:03:05.480 will say that numbers and mathematics is true and it exists, 0:03:05.520 --> 0:03:08.480 but it exists outside of space time. Is as like 0:03:08.520 --> 0:03:12.040 an abstract concept. It's not something that can affect the 0:03:12.160 --> 0:03:15.320 things in space time. It can't affect the material objects 0:03:15.320 --> 0:03:18.840 that we have arounders. You also have the nominalists, who 0:03:19.160 --> 0:03:23.760 says basically that numbers and maths only exist to sort 0:03:23.800 --> 0:03:26.360 of understand stuff. So so in some sense, we talked 0:03:26.360 --> 0:03:28.239 about the five, you know, five jars of oil, the 0:03:28.320 --> 0:03:30.960 five five loaves of bread. That's the only reason that 0:03:31.040 --> 0:03:34.080 the number five exists to describe the jars of oil, 0:03:34.160 --> 0:03:38.120 to describe the loaves of bread. And then, of course 0:03:38.640 --> 0:03:40.920 you've got the third sort of you know school, which 0:03:41.000 --> 0:03:42.960 is perhaps in some sense the most extreme, which just 0:03:42.960 --> 0:03:45.320 says the numbers that exist at all, that they're just 0:03:45.360 --> 0:03:48.640 a useful tool, that that that we used to describe 0:03:49.600 --> 0:03:52.760 the universe arounders. And I guess the analogy people use 0:03:52.840 --> 0:03:55.240 here is it's like saying, well, you could be an atheist, 0:03:55.240 --> 0:03:57.040 but you can still believe with some of the sort 0:03:57.040 --> 0:04:00.000 of moral messages that you read in the Bible or 0:04:00.040 --> 0:04:02.600 the Koran. It doesn't mean that, you know, you can't 0:04:02.600 --> 0:04:04.200 be inspired by them, but you just don't have to 0:04:04.440 --> 0:04:07.840 believe in every element of it. And I guess as 0:04:07.840 --> 0:04:10.960 a physicist, for me, it's kind of hard to sort 0:04:10.960 --> 0:04:13.280 of go with that fictionist idea and yet see a 0:04:13.400 --> 0:04:18.279 universe that is so amazingly described by mathematics. Now, is 0:04:18.320 --> 0:04:21.680 that something that's embedded in the universe or not. I 0:04:21.680 --> 0:04:24.120 guess it's really difficult to know. We've certainly not seen 0:04:24.120 --> 0:04:26.440 any evidence that it is. And yet now your book 0:04:26.440 --> 0:04:32.320 deals with, as the title indicates, fantastic numbers. Uh, what 0:04:32.320 --> 0:04:35.760 what defines for you a fantastic number? And are there 0:04:36.040 --> 0:04:39.719 categories of categorizations of numbers other than that that we 0:04:39.760 --> 0:04:42.000 need to have in our heads before we can get 0:04:42.000 --> 0:04:44.720 to the idea of what it's truly fantastic. Yes, it's 0:04:44.720 --> 0:04:47.800 so for me and my own relationship with numbers kind 0:04:47.839 --> 0:04:51.279 of and it comes from, on the one hand, you 0:04:51.320 --> 0:04:54.000 have a number, whatever that number might be, and if me, 0:04:54.080 --> 0:04:56.680 I always want to bring that sort of personality alive, 0:04:56.760 --> 0:04:59.120 the sort of real spirit of the number, sort of 0:04:59.160 --> 0:05:02.200 to the four. And so it's always been physics for 0:05:02.240 --> 0:05:04.440 me that that does that. So when you know you 0:05:04.480 --> 0:05:07.800 can have these wonderful mathematical concepts ideas like Graham's number 0:05:07.839 --> 0:05:10.599 three three, these truly bizarre and wonderful numbers to have 0:05:10.640 --> 0:05:13.600 a wonderful place in mathematics, but then you really bring 0:05:13.640 --> 0:05:15.760 them to life when you try to sort of squeeze 0:05:15.800 --> 0:05:17.719 them into our physical world. So that for me is 0:05:17.760 --> 0:05:20.359 what what makes a number fantastic. It's almost like, what 0:05:20.440 --> 0:05:23.159 makes a number fantastic is the fantastic physics that it 0:05:23.240 --> 0:05:26.400 can lead you towards and lead you to imagine and 0:05:26.480 --> 0:05:29.160 whatever that might be. You also talk about I believe 0:05:29.400 --> 0:05:32.440 specifically you're talking about Graham's number pretty early on in 0:05:32.440 --> 0:05:34.120 the book, and you point out that if you if 0:05:34.120 --> 0:05:36.440 you try and actually picture it in your head, your 0:05:36.440 --> 0:05:39.240 head collapses into a black hole. And this this made 0:05:39.240 --> 0:05:43.240 me wonder, like, what what are the largest numbers roughly 0:05:43.279 --> 0:05:46.080 speaking then an average person can fit into their head 0:05:46.080 --> 0:05:48.520 by one definition or another, Like, at what point does 0:05:48.560 --> 0:05:52.600 it just become this this other enterprise entirely? Yes, So 0:05:52.880 --> 0:05:55.599 it's a good question. So, I mean, it kind of 0:05:55.600 --> 0:05:58.320 depends on how how you sort of define the question. 0:05:58.520 --> 0:06:00.279 In some sense, we're just thinking about your rs. How 0:06:00.320 --> 0:06:02.479 many neurons have you have you got in your in 0:06:02.520 --> 0:06:05.680 your brain as about a hundred billion neurons, and so 0:06:05.960 --> 0:06:09.000 you might say that you can use them if you 0:06:09.040 --> 0:06:11.680 managed to clear your mind of every other thought to 0:06:11.800 --> 0:06:16.520 imagine a hundred billion digit number. Okay, that might not 0:06:16.560 --> 0:06:19.159 be particularly practical, it might be quite challenging for most 0:06:19.160 --> 0:06:21.640 of us. But but in principle you might say that 0:06:21.880 --> 0:06:24.760 that that that would be the limit. And of course, 0:06:24.760 --> 0:06:26.680 if you then go beyond that and start to say, well, 0:06:26.760 --> 0:06:29.800 what if I could somehow get my head to find 0:06:29.800 --> 0:06:34.680 a way to actually store information store concepts more efficiently 0:06:34.760 --> 0:06:37.720 than just the usual idea of neurons firing on and off. 0:06:37.760 --> 0:06:42.039 Let's suppose that it could do that somehow. Then then 0:06:42.080 --> 0:06:44.800 the numbers get get much bigger, and you start to 0:06:45.080 --> 0:06:48.880 the things that limited are literally preventing your head collapsing 0:06:48.880 --> 0:06:50.880 to form a black hole. Because black holes what they 0:06:50.920 --> 0:06:54.599 do is that they're they're the best thing at storing information. 0:06:54.640 --> 0:06:56.200 So if you want to get something the size of 0:06:56.240 --> 0:06:58.160 a head of a human head, and you want to say, 0:06:58.200 --> 0:07:00.719 what's the best thing the size of human head that 0:07:00.800 --> 0:07:03.560 can store information, it's a black hole the size for 0:07:03.720 --> 0:07:06.039 human head that that's the nothing can do it better, 0:07:06.480 --> 0:07:10.040 and so so so that that places a new limit, 0:07:10.080 --> 0:07:11.560 and you can ask, well, again, what what is that 0:07:11.600 --> 0:07:13.840 limit would be? But he's certainly way below grains. No, 0:07:13.920 --> 0:07:16.360 but you're not gonna get anywhere near the magnificence of 0:07:16.400 --> 0:07:20.720 Graham's number. And you could probably get a digit that's 0:07:21.240 --> 0:07:24.240 that's about tens of the seventy and number that's about 0:07:24.240 --> 0:07:27.280 ten to the seventy digits long, and so less than 0:07:27.280 --> 0:07:30.800 a Google digits long. Having said that, you could imagine 0:07:30.840 --> 0:07:34.280 a number like a google plex. A google plex has 0:07:34.880 --> 0:07:38.080 a Google digits. Now I've just said that you can't 0:07:38.120 --> 0:07:41.480 imagine a Google Digit's not possible, but a google plex 0:07:41.560 --> 0:07:43.240 you could, because what you know about a google plex 0:07:43.320 --> 0:07:45.560 is that it's a one followed by a Google zero. 0:07:45.680 --> 0:07:49.040 So you know that all the numbers that come later 0:07:49.160 --> 0:07:52.840 on as zeros, and so there's not much information in that. 0:07:52.960 --> 0:07:55.720 So it doesn't cost as much as many bits. You 0:07:55.720 --> 0:07:57.559 don't have to put as many bits in your head 0:07:58.440 --> 0:08:02.360 to imagine that. So what we're really talking about now 0:08:02.360 --> 0:08:06.440 are really a random assortment of digits. Are completely random 0:08:06.440 --> 0:08:09.119 assortment digits the kind that would appear in Graham's number. 0:08:09.440 --> 0:08:12.440 And I don't think you can get passed around tens 0:08:12.440 --> 0:08:14.840 of the seventy, which is a one with seventies zero. 0:08:14.920 --> 0:08:18.600 You couldn't get past that many digits completely randomly sort 0:08:18.600 --> 0:08:20.680 of allocated. At that point, your head is going to 0:08:20.720 --> 0:08:23.080 collapse into a black hole. Now, now backing up to 0:08:23.080 --> 0:08:25.400 the Google and the google plex. Can't can you? Can 0:08:25.440 --> 0:08:28.280 you walk as briefly through the difference between a Google 0:08:28.280 --> 0:08:31.920 and google plex, and and and maybe realms beyond that? 0:08:32.280 --> 0:08:34.600 This is this is about the only area of fantastic 0:08:34.679 --> 0:08:38.400 numbers that i'd I'd really heard anything about prior to 0:08:38.520 --> 0:08:42.240 reading your book. Yes, So, so Google is is um 0:08:42.880 --> 0:08:45.160 it's a number which is which is a one followed 0:08:45.160 --> 0:08:48.200 by a hundred zero. So I think everybody would agree 0:08:48.240 --> 0:08:51.120 that sounds like quite a big number. And it goes 0:08:51.160 --> 0:08:56.199 back to to a physicist called Edward Kasner who is Columbia, 0:08:56.559 --> 0:08:59.120 and he was writing a popular science book and he 0:08:59.200 --> 0:09:01.840 was trying to sort of know convey He really wanted 0:09:01.880 --> 0:09:03.920 to show how big infinity he was, and so he 0:09:03.960 --> 0:09:05.880 wanted to quote with numbers that we all think are 0:09:05.920 --> 0:09:08.800 really big, like a one followed by a hundred zeros. 0:09:09.400 --> 0:09:13.960 And he said, well, okay, that's really small compared to infinity, right, 0:09:14.000 --> 0:09:16.680 even though something really big is actually really small compared 0:09:16.679 --> 0:09:19.320 to infinity. So he came up with this one with 0:09:19.320 --> 0:09:22.400 a hundred zeros. He wanted a name for this number, 0:09:23.120 --> 0:09:26.319 so at the time he asked his nephew who was 0:09:26.360 --> 0:09:28.640 nine years old at the time. He was called Milton Serata. 0:09:28.880 --> 0:09:30.480 He said, can you come up with a name for this? 0:09:30.559 --> 0:09:33.000 And and Milton said, well, a Google, which is an 0:09:33.000 --> 0:09:35.679 absolute stroke of genius, right, It's such a great name. 0:09:36.800 --> 0:09:39.880 And and then so they wanted to then develop things further, 0:09:40.000 --> 0:09:43.400 so then they wanted an even bigger number, again building 0:09:43.400 --> 0:09:48.199 on this idea that it's nothing compared to infinity and 0:09:48.040 --> 0:09:50.240 and so so he said, well, okay, I'm gonna quote 0:09:50.240 --> 0:09:52.040 with the idea of a Google plex. It's going to 0:09:52.120 --> 0:09:56.560 be an even bigger number. Well how big? So Kasna 0:09:56.640 --> 0:09:59.320 then goes to to Milton. He says, well, how big 0:09:59.320 --> 0:10:01.960 should it be? And Milton's like, well, it should be 0:10:01.960 --> 0:10:05.720 a one, not followed by a hundred zeros, but zeros 0:10:05.760 --> 0:10:09.679 until you get tired. But Kasner is like, you know, 0:10:09.960 --> 0:10:12.520 a sort of you know, steamed academic at Columbia and 0:10:12.559 --> 0:10:15.439 all that. That's just not precise enough for him. So 0:10:16.760 --> 0:10:18.560 he went with it which are much more sort of 0:10:18.720 --> 0:10:21.920 well defined idea, which is a google plex should be 0:10:21.920 --> 0:10:25.760 a one followed by a Google zeros. So a Google 0:10:25.800 --> 0:10:28.240 is already massive. That's a one followed by a hundred zeros. 0:10:28.360 --> 0:10:32.439 A google plex is a one followed by a Google zero. 0:10:32.480 --> 0:10:34.719 So it's a whole new level of big compared to 0:10:34.840 --> 0:10:36.800 what we normally used to. And then it just it 0:10:36.880 --> 0:10:39.600 keeps building on that. Right, there's there's even like what 0:10:39.679 --> 0:10:42.800 a google plexian is that the next level. So so yeah, 0:10:42.840 --> 0:10:44.760 I mean this is this is a really nice, nice idea. 0:10:44.800 --> 0:10:47.319 You can really now start to to really build very 0:10:47.360 --> 0:10:51.280 big numbers, very very quickly using this this mathematical technique 0:10:51.920 --> 0:10:55.280 called recursion. So for example, you can develop the idea 0:10:55.280 --> 0:10:58.959 of a Google duplex. What a Google duplex, Well, it's 0:10:58.960 --> 0:11:02.640 a one followed by a Google plex zeros. And then 0:11:02.679 --> 0:11:05.200 you can go to a Google triplex. Well, you can 0:11:05.240 --> 0:11:06.800 probably guess what it's gonna be. It's gonna be a 0:11:06.800 --> 0:11:10.079 one followed by a Google duplex zeros. And then a 0:11:10.160 --> 0:11:15.840 Google quadruplex is a one followed by a Google triplex zeros. 0:11:15.920 --> 0:11:19.680 And you can see each time you're growing the number 0:11:20.520 --> 0:11:24.000 just by so much, by such an unimaginably large amounts, 0:11:24.000 --> 0:11:26.480 And that's what. You're not just adding zero every time, 0:11:26.520 --> 0:11:29.480 You're kind of really ballooning the number of zeros on 0:11:29.480 --> 0:11:33.240 the end of this number in Gargangian proportions. And that's 0:11:33.280 --> 0:11:37.160 what and it's this power of mathematical riccasion that allows 0:11:37.160 --> 0:11:46.520 you to do that. Now you also talk about fantastic 0:11:46.600 --> 0:11:51.920 numbers that are I guess you would say smaller than 0:11:52.000 --> 0:11:54.120 the main example that comes to mind. You refer to 0:11:54.160 --> 0:11:57.079 this several times in the book is a number associated 0:11:57.120 --> 0:12:00.719 with Olympic sprinter Hussain Bolt. Would you tell us a 0:12:00.720 --> 0:12:04.120 little bit about this number? Yeah, yeah, so so well, 0:12:04.120 --> 0:12:06.840 actually this is one of my big numbers. Actually, even 0:12:06.840 --> 0:12:11.000 though it doesn't seem that it's it's actually it's one 0:12:11.040 --> 0:12:12.920 of my big numbers. So I can read out the number. 0:12:13.080 --> 0:12:17.840 What it is one point, I think it's fifteen zero 0:12:18.160 --> 0:12:21.560 eight five eight, So it's just a number just slightly 0:12:22.240 --> 0:12:26.000 north of one. So it's it doesn't seem like a 0:12:26.000 --> 0:12:27.840 big number. But but in my book, I say it 0:12:27.880 --> 0:12:30.680 is a big number. And the reason is it's it 0:12:30.720 --> 0:12:34.360 measures the amount by which Usain Bolt managed to slow 0:12:34.480 --> 0:12:37.920 down time. And when he was he was running in 0:12:37.960 --> 0:12:40.920 the World Championships and I think Berlin Um and he 0:12:40.960 --> 0:12:43.360 set this the world record. And this is due to 0:12:43.400 --> 0:12:48.000 the effects of relativity, so that when when somebody actually 0:12:48.040 --> 0:12:52.120 moves quickly, they actually slow time actually slows down for them. 0:12:52.120 --> 0:12:55.080 And actually this is the amount by which Usain Bolt 0:12:55.120 --> 0:12:57.120 was actually able to slow down time due to the 0:12:57.160 --> 0:13:01.600 effects of Einstein's theory. And it's compared to the people 0:13:01.600 --> 0:13:05.000 in the stadium, for example, this is this was the 0:13:05.280 --> 0:13:08.280 difference that that he experienced. So it's one of the 0:13:08.320 --> 0:13:10.800 one of the weird consequences of it is that you 0:13:10.840 --> 0:13:13.760 can actually it's not that you say, but actually, even 0:13:13.760 --> 0:13:16.079 though he slowed down time, it's not that he that 0:13:16.200 --> 0:13:18.480 he actually ran the race any quicker. He still runs 0:13:18.480 --> 0:13:21.800 the race at roughly ten ms per second. It's actually 0:13:21.800 --> 0:13:25.240 an even more strange consequence. He actually the track also 0:13:25.360 --> 0:13:28.480 shrinks for him a little bit, so so he actually 0:13:28.559 --> 0:13:30.920 runs it in less time, but in the same speed. Therefore, 0:13:30.960 --> 0:13:34.920 the track shrinks because the relative to him, the tracks moving, 0:13:34.960 --> 0:13:37.440 And this is another effect of relativity, one of the 0:13:37.480 --> 0:13:41.360 remarkable things. And and yes, you could perhaps argue that 0:13:41.400 --> 0:13:43.720 he didn't actually finish the race because the tracks rank 0:13:43.800 --> 0:13:47.400 so he didn't run quite a hundred Wow. I was 0:13:47.400 --> 0:13:49.800 really blown away with this, because you know, you often 0:13:49.840 --> 0:13:53.880 hear the standard analogies concerning airplanes and pyramids and so 0:13:54.040 --> 0:13:56.600 forth when it comes to time dilation and so forth. 0:13:56.640 --> 0:13:59.840 But but I hadn't. I hadn't heard this particular example 0:14:00.040 --> 0:14:02.000 for this is great. Yeah, I mean, it's true. It's true. 0:14:02.040 --> 0:14:04.440 If like taxi drivers, if you imagine a taxi driver 0:14:04.559 --> 0:14:07.000 that's driving around I don't know any city in New 0:14:07.080 --> 0:14:10.160 York wherever, you know, sort of forty fifty years of 0:14:10.200 --> 0:14:12.520 their life because of that extra extra speed that they're 0:14:12.520 --> 0:14:15.360 picking up. That's going to accumulate over time. And actually 0:14:15.400 --> 0:14:17.760 they can probably leap forward in time by probably I 0:14:17.760 --> 0:14:20.160 think about a micro second over the course of their career. 0:14:20.200 --> 0:14:22.880 It's not a lot, but it's still fairly amazing when 0:14:22.880 --> 0:14:25.400 you think about it. So they've got the knowledge, and 0:14:25.440 --> 0:14:27.840 then they have that as well, right, Oh yeah, of course, 0:14:27.920 --> 0:14:30.520 yeah exactly, not just the knowledge, Yeah, they actually got it. 0:14:30.520 --> 0:14:33.120 They actually get a little bit younger. So your book 0:14:33.160 --> 0:14:36.360 makes makes use of written numbers, um. And and then 0:14:36.400 --> 0:14:39.040 of course you have this wonderful YouTube series number file, 0:14:39.480 --> 0:14:42.040 and in that you benefit not only from some fantastic 0:14:42.080 --> 0:14:44.880 descriptions and pop culture tie ends as you do in 0:14:44.920 --> 0:14:47.680 the book, but you also have a lot of helpful illustrations. 0:14:48.240 --> 0:14:51.840 Uh So I was I was curious since you are 0:14:51.880 --> 0:14:55.840 a regular communicator of of this this topic. Um is 0:14:55.840 --> 0:14:58.920 it is? It? Is? It? Is? It more challenging or 0:14:58.960 --> 0:15:01.840 in some cases almost too challenging to describe some of 0:15:01.840 --> 0:15:05.120 these numbers without the visual aids or the actual numerals 0:15:05.200 --> 0:15:08.520 to like visually present somebody with. Yeah, I think you 0:15:09.040 --> 0:15:11.520 so this is where the physics comes in in some respects. Right. 0:15:11.680 --> 0:15:12.960 So on the one hand, if you really want to 0:15:13.000 --> 0:15:15.560 describe the number, like I said, a number like Grams number, 0:15:16.520 --> 0:15:19.560 you do need those visual aids because it's not a 0:15:19.680 --> 0:15:22.720 number that you're going to sort of stumble across in 0:15:22.760 --> 0:15:25.280 any kind of normal environments. Right, It's not a number 0:15:25.320 --> 0:15:27.440 you're going to see on on a price tag, at 0:15:27.480 --> 0:15:30.160 least you'd hope not. And you know, so these are 0:15:30.280 --> 0:15:33.360 you need new notation, new sort of symbolism to to 0:15:33.400 --> 0:15:35.480 sort of actually even describe the number. So you've got 0:15:35.480 --> 0:15:37.760 to introduce that. There's just no getting away from it. 0:15:38.320 --> 0:15:41.880 But I guess what you can do is described the 0:15:41.880 --> 0:15:45.400 physics associated with it, and and that you can certainly do, 0:15:46.400 --> 0:15:49.280 you know, just just just with words. And you know, 0:15:49.360 --> 0:15:51.520 in the case of a number like Grahams number, you 0:15:51.560 --> 0:15:53.960 can talk about how you just can't picture in your 0:15:53.960 --> 0:15:55.880 head because your head will will collapse to for a 0:15:55.960 --> 0:15:58.440 black hole. And that's already going to make people think, wow, 0:15:58.920 --> 0:16:01.240 that number. There's something big of something big and crazy 0:16:01.280 --> 0:16:04.040 about that number. Or a google plex, you know, when 0:16:04.040 --> 0:16:06.920 you can talk about a universe that's that's a google 0:16:07.000 --> 0:16:09.600 plex meters across. And then you can ask, well, if 0:16:09.640 --> 0:16:12.520 the universe is that big, if the universe is literally 0:16:12.600 --> 0:16:16.760 that large, then it's likely that you would find multiple 0:16:16.840 --> 0:16:20.720 copies of yourself, like literally exact apple Gangers elsewhere in 0:16:20.760 --> 0:16:23.720 this ginormous universe. Yeah, I wasn't. I was. I wasn't 0:16:23.720 --> 0:16:27.120 prepared for dopple gangers to enter into the scenario. So 0:16:27.200 --> 0:16:29.240 there was there was another great part about the book 0:16:29.240 --> 0:16:32.680 for me um and another thing that that comes up 0:16:32.680 --> 0:16:35.600 in the book that I was very intrigued by. I 0:16:35.640 --> 0:16:37.760 was wondering if you might talk about is the the 0:16:37.800 --> 0:16:40.400 idea of the of the holographic truth? Yes, so the 0:16:40.440 --> 0:16:43.200 holographic truth is I mean, it's an idea. It's probably 0:16:43.200 --> 0:16:46.120 the most important idea I would say that's emerged from 0:16:46.280 --> 0:16:50.280 theoretical physics in in the last thirty years. And it's 0:16:50.320 --> 0:16:52.560 it's actually mind blowing when you really think about what 0:16:52.680 --> 0:16:56.120 it pertains to. It's it's it's this following statement that 0:16:57.120 --> 0:17:00.400 essentially one of the dimensions of space that we experience 0:17:00.440 --> 0:17:02.800 around it. So we normally talk about say three dimensions 0:17:02.800 --> 0:17:06.400 of space, Well one of them could well be an illusion. 0:17:06.880 --> 0:17:10.560 It might not exist, and it's really remarkable. So what 0:17:10.600 --> 0:17:13.200 we're saying is that there are two ways in which 0:17:13.240 --> 0:17:16.440 you can describe the physics that we see around as 0:17:16.520 --> 0:17:19.959 On the one hand, we can imagine three dimensional world 0:17:20.480 --> 0:17:23.320 with a gravitational force and the force of gravity doing 0:17:23.359 --> 0:17:25.320 its thing, with planets around the Sun and so on 0:17:25.359 --> 0:17:28.280 and so forth. On the other hand, there's a completely 0:17:28.320 --> 0:17:34.200 equivalent description of the same phenomena which just uses two 0:17:34.240 --> 0:17:38.360 dimensions and no gravity. So think of it a bit like, 0:17:38.440 --> 0:17:41.560 you know, on the one hand, somebody's you know, in English, 0:17:41.600 --> 0:17:43.840 we say if we see a place of meat balls, 0:17:43.840 --> 0:17:46.320 we call them meat balls, but a Spaniard might call 0:17:46.359 --> 0:17:49.000 them album the gas. They're both describing the same things, 0:17:49.000 --> 0:17:51.040 they're just using a different language. And that's kind of 0:17:51.040 --> 0:17:54.040 what what the holographic truth says. It says that you 0:17:54.080 --> 0:17:57.560 can have a theory like a three dimensional world with gravity, 0:17:57.920 --> 0:18:00.800 and you can use that to describe all the physical 0:18:00.800 --> 0:18:05.320 phenomena you see, or use this different language which has 0:18:05.359 --> 0:18:09.600 no gravity and only requires two dimensions of space. So 0:18:09.920 --> 0:18:12.120 is it true of our world? We don't know. It's 0:18:12.119 --> 0:18:15.240 a conjecture. It's a conjecture that has sort of evidence 0:18:15.280 --> 0:18:18.119 coming from from the physics of black holes. There are 0:18:18.119 --> 0:18:22.560 actually concrete examples that we know of of sort of 0:18:22.640 --> 0:18:25.879 toy universe is so not our universe, but but but 0:18:26.119 --> 0:18:29.120 space times that may be that the higher dimensional there 0:18:29.119 --> 0:18:31.480 may be warped in weird and wonderful ways. And you 0:18:31.480 --> 0:18:35.120 can think about gravity in these in these simple toy universes, 0:18:35.760 --> 0:18:39.000 and you can show that there's an equivalent description in 0:18:39.119 --> 0:18:42.560 one dimension less like a holographic description, and it's called 0:18:42.560 --> 0:18:45.119 a hologram because that's essentially what what holograms do? Right? 0:18:45.240 --> 0:18:46.960 If you think of a hologram, what have you got? 0:18:46.960 --> 0:18:49.919 You've got an image on a that's stored on a 0:18:49.960 --> 0:18:53.000 holographic plate. You know, it's just some light and dark 0:18:53.040 --> 0:18:55.760 bands on a holographic plate, a two dimensional plate. It's 0:18:55.800 --> 0:18:59.520 stores a bunch of information that way, But that's just 0:18:59.600 --> 0:19:01.960 one way of looking at the information. You can decode 0:19:02.000 --> 0:19:05.480 it in a different way by shining monochromatic light through 0:19:05.520 --> 0:19:08.440 it and creating a three damage. You're not creating any 0:19:08.480 --> 0:19:12.080 new information. It's the same information, just stored either in 0:19:12.080 --> 0:19:14.520 two dimensions or three. And it's that seems to be 0:19:14.560 --> 0:19:18.320 that that seems to be a fundamental property of gravitation, 0:19:18.400 --> 0:19:21.880 of gravitational worlds that you can think of them as 0:19:22.160 --> 0:19:24.880 as like as I said, a three D world with gravity, 0:19:25.000 --> 0:19:28.480 or you just forget about gravity and consider a world 0:19:28.480 --> 0:19:31.160 with one dimension or less and you can describe exactly 0:19:31.160 --> 0:19:35.760 the same physical phenomena. Now here's another question that that 0:19:35.760 --> 0:19:39.320 that came came up reading the book that that I 0:19:39.359 --> 0:19:41.880 don't know if of all our listeners are necessarily would 0:19:41.880 --> 0:19:43.360 have thought of this question. I think some of them 0:19:43.440 --> 0:19:48.280 would have. And that comes to infinity um infinity, Like 0:19:48.320 --> 0:19:50.680 sometimes it's easy to think of like, okay, infinity is 0:19:50.720 --> 0:19:52.920 the it's it's if we think of it as a number. 0:19:52.920 --> 0:19:55.399 We think it's the eight on its side representing infinity. 0:19:55.640 --> 0:19:58.040 Is infinity a number? And if it's not a number, 0:19:58.359 --> 0:20:00.800 like what do we think of it at? How do 0:20:00.840 --> 0:20:03.520 we classif high infinity? So I love this question because 0:20:03.520 --> 0:20:05.320 the answer is that it's both not a number and 0:20:05.400 --> 0:20:09.040 lots of numbers. This is the wonderful thing about infinity. 0:20:09.160 --> 0:20:11.679 So it depends how you want to think about infinity. 0:20:12.200 --> 0:20:14.840 And I think most of us when we intuitively think 0:20:14.840 --> 0:20:17.200 about infinity, we kind of think of like I don't 0:20:17.200 --> 0:20:20.280 know the infinite distance, you know, or infinite time, And 0:20:20.400 --> 0:20:22.080 what we're really thinking there is we're thinking of it 0:20:22.160 --> 0:20:24.399 is like a limit is something that's just just beyond 0:20:24.680 --> 0:20:26.760 our finite realm. That that that's you know, if you 0:20:26.840 --> 0:20:30.560 keep on counting forever, you know, it's kind of the 0:20:30.600 --> 0:20:32.560 at the end of that, you're sort of almost beyond 0:20:32.640 --> 0:20:36.640 the end of that. Now, that's in some sense thinking 0:20:36.680 --> 0:20:40.720 of infinity as not a number, as a limit of saying, 0:20:41.040 --> 0:20:45.879 you know, the whole numbers. But what Cancelor Judge cancel that, 0:20:46.000 --> 0:20:49.040 you know, the great German mathematician from the late Victorian times, 0:20:49.280 --> 0:20:52.400