 Mae'n ffordd o'r cyffredin. Mae'n ffordd o'r cyffredin. Felly, rydyn ni'n ddiddordeb yn ymgyrch. Mae'r nu'n Alex Bellos. Rydyn ni'n ddiddordeb yn ymweld, ond rydyn ni'n ddigreithio ar y maeth a ffilosfwy, a rydyn ni'n ddiddordeb yn ymgyrchol, ac rydyn ni'n gartion ymgyrchu gyda'r cyffredin yn South America ar 5 ymgyrch, a rydyn ni'n ddiddordeb yn ymgyrch gyda'r llwyaf Brasunol. Felly, wrth gwrs bwysig ymddian nhw'n dda'r talk, mae'n dweud o'r matemathau, sy'n ystod y byddwch am ystod o'r brosidion hynny. Yn 4 yma, Alexus Adventure's Numbland hefyd edrych, a'r ystod yma rwy'r ysgrifennu o amser. A wrth gwrs, ynddo'r ysgrifennu, Alexus ryw'r ysgrifennu yna'r llwytag i'r mae oedd yn rhyfedd feddoriaeth a ychydig yn y bwysig i'r ffordd fydd. Mae'r llwys hon o'r llwyddiad, wedi bod yn deimón i'r beddech chi yw'r llwyddiad favour. Mae'r llwyddiad i'r meddwl, yna'r llwyddiad. Roedd ychydig yn ymweliad yn y teimlo hwnnw. Felly, rwy'n dweud, rwy'n gwybod ymlaen, ond rwy'n gwybod ymlaen y gwybod. Ond rwy'n gwybod ymlaen, yma, bydd ymlaen y gwybod ymlaen, oherwydd, y gwybod ymlaen, yma, ar yr ymlaen yn y math ymlaenau a'r gwybod. A'r ysgrifent yw'r gw holdau yma yma yn y blynyddoedd gweithio'r bydd. Ond rwy'n gwybod o'r gwybod, mae'n gwybod, yw'r ddwych yn gwybod arall os oeddeithasau'r gwybod, felly if you do any ideas of things that you might want to write on my blog, because it's the Gasion, it can get really loads and loads of views from all over the world, do get in touch with me, so either on social media or I will be selling, well I won't be selling, the shop will be selling both of these books, unfortunately not the Brazilian football book a numberland and looking glass and right after this talk I will be in the shop signing books if you were to want to buy one or if you wanted to ask me any questions, I'm not a professional mathematician, so I don't stay at home writing theorems all day. I am a populariser. What I try and do is I use the skills of journalism that I learnt through almost a 20-year career in newspapers, in the Guardian. I was basically written for everyone on Fleet Street to tell stories through maths. This idea that, especially now, you can get any bit of information that you like just by googling it. Often you only really take things in or you only want to learn when there's a kind of story behind it. Where do you start when you write about maths? It's probably the most abstract and arcane subject to write about, as I would say is one of the most difficult things to try and make exciting. One of the ways that you tell stories is by telling stories about oneself, about myself. When Alex's Adventure in Numbland came out four years ago, I would give talks to universities, PhD students, businesses, schools, literary festivals, science festivals, basically everybody. I noticed that at the end of each talk someone would always put their hand up and say, I'd say, yes sir, what would you like to ask me? And they'd say, what's your favourite number? I can remember just internally just wanting to collapse and die, just thinking, what a stupid question. Who on earth has a favourite number? I thought they were trying to ridicule what I was trying to do. Until I was asked this so many times that once exasperated I said, well what's your favourite number? And rather than a kind of, it was 12. You mean you've got a favourite number? Oh yeah, and the person next to them said, oh yeah no mine's seven. And then I said, well how many people here have got favourite numbers and over half the audience put their hands up? And then, because I don't have a favourite number, I just thought, well this is interesting. So using the tools that are available to me, i.e. the internet, I thought it would be really interesting to see if there's any way that I could scientifically, or as scientifically as possible, analyse or quantify, classify in any way these emotional responses that we have to numbers. And so what I did, I set up a survey, a quick simple survey, favouritenumber.net, and on favouritenumber.net it just said, what's your favourite number and why? I didn't want to suggest it between one and ten or only write digits, fractions are not allowed. It's also a favourite number space and why. And then I realised I was starting to have ideas above my station. So I was going to find the world's favourite number and so I also bought this site just to make sure that it wasn't biased towards Britain and Australia, South Africa. And you're dying to know what the results were and said the results were this. Hopefully you can, it's light here but on the TV I think it's going to be seeing better. Basically, and this, when it came out it was actually in most of the newspapers and Metro called it the most confusing top ten list ever in, which it is. Now if you go back to favouritenumber.net now it has all the results as there's an Excel file of all the results. It's got loads of other sort of facts and figures about it. So this is normally the bit in my talk that I spend quite a lot of time talking about emotional responses but you guys are not interested in that. You want to get to the hard math which is what we're coming to. So I'm going to, if you're interested in that, just go to favouritenumber.net. So let's get back to what I want to say about this. So what is interesting about favourite numbers essentially, and a couple of days after it came out, it was a question on have I got news for you. And they went through, they had the kind of pop pickers music and they did the top ten countdown. And everyone thought it was hilarious that four is fourth and five is fifth. That this was some sort of brilliantly funny. Actually that's the least interesting or the least unusual. Because what you find when you try and look at the spread of favourite numbers, firstly you notice that you really can see there really are trends. It's that essentially we like low numbers and the bigger number they get we like them less. And so things should essentially have their numerical value as their position and where they are in terms of favourite number. But certain qualities of numbers push them up the list and certain push them down. And essentially what pushes you up, which makes you punch above your weight, is being odd and especially prime. But with the low numbers there are only two non-prime odd numbers between 1 and 20, which are minus 15. So essentially odd and prime are the same thing. Basically being odd and prime pushes you up and being even, but especially round numbers pushes you down. So people tend to as favourites prefer odd numbers than even numbers. And actually you could have said I could have told you that. You didn't need to do a survey. You know 40,000 people entered my survey from all over the world. And if you think what are the numbers that are the most magical, the most mystical numbers, the numbers that we attribute most non-mathematical meaning since the dawn of civilisation, it's odd numbers. Well in the western civilisation it's odd numbers. And Shakespeare noticed this 100 years ago. Felfstaff and Mary Wives of Windsor, they say there is divinity in odd numbers, either in nativity, chance or death. And what are the most mystical numbers of them all? Well seven obviously. Three because of the Holy Trinity. Thirteen unlucky thirteen. You won't find an even number that is as mystical as any of those odd numbers. And why is that? There are lots of reasons, but I made an animation to talk about a reason why I think seven was, actually did we do sound? We didn't check the sound, so hopefully this is going to work. It's not going to be either too quiet or break your eardrums. We've been obsessed by the number seven for as long as we know. Go back to the earliest writing that there is on Babylonian clay tablets, and they're just full of sevens. And you have seven dwarfs, seven sins, seven seas, seven sisters. The list just goes on and on. So why is seven so special? One argument is that there are seven planets in the sky visible to the naked eye. To me that's just a coincidence. There's a much more compelling reason. Seven is the only number among those we can count in our hands, that's those from one to ten, that cannot be divided or multiplied within the group. So one, two, three, four, and five you can double them. Six, eight, and ten you can half them, and nine you can divide by three. Seven is the only one that remains. It's unique. It's a loner, the outsider, and humans interpret this arithmetical property in cultural ways. By associating seven with a group of things, you kind of make them special too. The point here is that we're always sensitive to arithmetical patterns, and this influences our behaviour, even if we're not conscious of it, and irrespective of our ability at maths. Okay, there's another way that we're always sensitive to numerical patterns. And the number seven, and this is something which is, you know, a test which has been done in many psychology departments of university for decades, which is think of a number to the top of your head between one and ten, and what are you thinking of? That's not fair, because most people who haven't been primed and know say seven, because seven feels... What's going on in someone's brain? Think of a random number, an arbitrary number, just put something at the top of your head. So don't think about it between one and ten. What you're actually doing, you wouldn't choose one, is this getting feedback? Is that a problem? Okay, okay, right. So you wouldn't choose one, because one just sounds, it's just not random enough, you wouldn't choose ten. You wouldn't choose five, because five is exactly half in the middle, that's just, you wouldn't. And you actually wouldn't do two, and then the repressive elimination, you wouldn't do four, six, eight. So what you're actually doing is you're doing seven, which is the one which is arithmetically, numerically most difficult to get, is the one that also feels the most random and arbitrary. So we're subconsciously basically doing maths. And this sort of difficulty of thinking about sevens is, to me, the only possible reason why seven in all cultures, in all times, has always been the most spiritual number, or the number at which people give the most spiritual, mystical meanings to it. And some people might say, ah, that's just mumbo-jumbo, that's numerology. Actually, I think you can look at, and it is really interesting why certain numbers resonate for certain things, you know, with the religion or mysticism or kind of existence, more than others. And I think this is, essentially as a maths populariser, you're saying, look, maths is everywhere where we need to realise that we're reacting and bouncing off numbers all the time. And there are quite interesting, more interesting sort of psychology experiments that show that we do, for example, think longer about odd numbers than we think about even numbers. You think, well, that's kind of crazy, what do you mean? The experiment is this. On a screen, you see two digits together. Either they're both odd, they're both even, or one is even and one is odd. All you need to do is if they're both the same, that's why they're both even or both odd, you just press a button. And so sometimes, you know, three, four, you wouldn't press the button, one's even, one's odd. Two, eight, you'd press the button, they're both even. It turns out that humans are much better at pressing the button when they're both even rather than when they're both odd. Basically, you're 10% slower when they're both odd. And also, you make a lot more mistakes. In other words, we find even numbers much easier to process and odd numbers, because they're harder to process, they stick in our brains longer and they also... ..there's something more ethical in dealing with odd numbers. Now, thereby end the section where my book was How Life Reflects Numbers and Numbers Reflect Life. That was kind of how Life Reflects Numbers a little bit. So I've got a whole chapter on that in the book on our, you know, emotional psychological responses to numbers that are maybe quite surprising and not really well known. But this builds up to what are... It's all arithmetic, these very simple arithmetic that we are aware of. And most especially, the numbers that stick out are the prime numbers. So I want to just now start talking about the prime numbers and actually get into something slightly more mathematics. So the prime numbers are, I don't need to tell you, they are the numbers greater than two that are only, or two or greater, that are only divisible by themselves and one. So they're 2, 3, 5, 7, 11, 13, 17. And this is one of... It's kind of... It's pretty much like the first interesting thing you find out about numbers actually. Because what's interesting about the prime numbers is that it's very hard to predict what number is going to be prime. In fact, you can't do it. You've just got to go along and divide everything underneath it if nothing divides it, it's prime. And they appear in a kind of hazzard way. There's no way of predicting whether a number is going to be prime or not. And that is something sort of so basic that has really interested the first people who would call themselves mathematicians, and still now is a huge area of research. Now, Eris Dostines, who was a famous Greek, Eris Dostines is one of the kind of... No one really knows very much. Pythagoras, like, super famous. Archimedes, super famous. Everyone knows the household names. Eris Dostines, you've got to feel sorry for him because he was brilliant. He invented loads of really interesting things. He was a polymath. He was the founder of geography, for example. But his nickname was Beta. So he was always known as the guy who was second best because he had the bad luck of being around at the same time as Archimedes just off the scale. Anyway, one of the most famous things that Eris Dostines did is the sieve of Eris Dostines, which is a way of how do you find prime numbers below a certain number? This is probably the most basic algorithm, you know, computer science essentially, the science of algorithms. This is probably the most basic algorithm, the first algorithm in mathematics. You can say the first algorithm in science. And all you want to do is find what the prime numbers below a certain number, there it's 100. What you do is that you start off at the bottom, you get to a number if it's free, it's prime, and then you eliminate all the multiples of it. So let's start, but one's not prime. We go to two, two is free, so it's prime, and then we delete because it's sieving out the numbers. And we delete all the multiples of two. Yep, we got that, there's a question? Right, then we go to three. Three's free, so three's prime, and then we delete all the multiples of three. So that's just basically that line. And it's really nice, not me you never do it, but if you do it in, you get these nice patterns when you do six rows or six columns. Then four has been taken when you got rid of the twos. Get to five as prime, so let's get rid of all the fives, five, six has been taken because it was crossed with the twos but also doing cross with the threes. Get to seven, that's prime, get rid of the sevens and the next one is 11. And what the sieve says is that if we're going to all numbers below n, say, you only need to go to the square root of m. Square root of 100 is 10, so once you've got to 10, you know that it's all covered. Very simple proof. Three lines in the back of my book if you're interested, but it will be on sale. It's a little bit better. From this, it's a nice pattern, but you can tell a few things. One is that all prime numbers have to be one less or one more than a multiple of six. Or two less or two more than a multiple of three because they have to be on the first line or the fifth line. And also basically what you see is that if you were to carry on, there's no preordain predictable pattern. They seem to obey they're obviously not random because they're always the same, but there's a kind of random element to where they are actually distributed, which is what's fascinating. Now, since prime numbers have been the possibly one of the most researched bits of mathematics for 2,000 years, you think, well, what are the new things to find out about that? But in 1963 54-year-olds Polish-American mathematician Stanislaw Ulam was in a lecture and he got really, in America, got really bored. He just started to doodle and he had made a grid like you sometimes do and he wrote all the numbers in a spiralling out. And then he just started to cross off the primes. And what he'd found, which had never been noticed before, was that when you do this, it turns out that most of the primes all are on the same diagonals, or linked up with diagonals. And so this is between 1 and 100, which is the same knowledge, but in a 10x10 grid starting with the middle, going out. And it's random, but it's not totally random. There's fragments of order there. And if we bump it up to the first 65,000 digits, this is with primes of the dots. Again, there's elements of order there. So when we say yes, the primes are completely randomly distributed. It's not entirely true. There's this sort of balance between order and chaos, which is kind of where the interesting stuff goes on. Something's like totally ordered, a bit boring. Something is totally chaotic. It's just like what you're going to say about it. But it's these sort of the kind of music coming through the noise, which is really what is interesting. So Stan Ulab was one of the great sort of 20th century mathematicians, where he's sort of an interesting guy, and his best mate, Stan Ulab, I should say, was born in Poland, and he was part of this group of amazing mathematicians who in the 1920s and 30s were all in Levov, which was in Poland, which is now in Ukraine. And because of the Second World War, most of them got out. And Ulab got out thanks to this guy called John von Neumann, who saw a picture of them there, and they were kind of best friends. So Ulab's here on the right, John von Neumann on the left, John von Neumann who is Hungarian, also got out before the war. In the middle, it kind of looks a bit like there's some kind of pretty rent boy they've picked up. He's actually Richard Feynman, America's greatest physicist. And this is taken because they were all, you could say that these three guys in the western world were possibly the three scientists who I mean, I say this within earshot of Bletchley, the three scientists who changed the modern world more than anyone else because you've got a Manhattan Project in Los Alamos, which is where this was taken, it's just down the road actually. They invented nuclear weapons which really shaped the 20th century when he won the Second World War, for example. And von Neumann of all the amazing things that he did, probably the greatest mathematician in terms of the breadth of what he did on the 20th century, as well as pretty much inventing computers with a little help from Alan Turing. He huge basically, there probably isn't a branch of math that he didn't, and theoretical physics that he didn't make a really serious contribution to. But most importantly, he's sort of remembered for the kind of structure of the beginning of computing and helping at Los Alamos really sort of develop some of the first computers that there were. Now, as quite a lot of these Emma Gray, Eastern Europeans were, they were quite sort of politically active and politically thoughtful, and actually von Neumann was incredibly right-wing and wanted to sort of nuke Russia. So, not very progressive. He's also struggling with these ideas of, you know, he was kind of, saw the future clearer within anyone else at the time of the 1940s, 1950s. He was essentially inventing, you know, computing as we know it today. And he started to just think about robots and robots maybe taking over the world, you know, the 1950s Hollywood movies of kind of robots taking over, et cetera, et cetera. He wanted, well, what would it take for a machine to replicate for a machine to make a copy of itself? And this is actually a logical sort of mathematical question, because well, that's the way he saw it. And if you think about it, just so you have a machine and it has you want to get this machine, so a kind of computer, which is a computer, to replicate, how does it replicate? You need to give it some instructions that say, replicate. So if you just say you give it the instructions, let's call it the blueprint. This is the blueprint of what it needs to do. Just so this machine can read the blueprint and then it can make a new machine. Okay? So does the new machine contain a blueprint? Because if it does, there would have to be instructions to make a blueprint within the blueprint. But then the blueprint itself would have to have instructions about how to make it and you get this infinite regress. So he realised that if you want to have a machine that replicates by this process of reading the instructions on how to replicate itself, you cannot do it without adding another element which would be something that just copies the blueprint. So what happens when you want to you have a machine, read the instructions, the instructions will replicate just the machine and then you need a blueprint copier which copies the blueprint and hands the blueprint to the new machine and then the entire things you have replicated the machine and blueprint and you have a machine and blueprint. What's interesting is that this was very inspiring for all the biologists working at the time because several years later when people worked out how DNA works, it's pretty much exactly as von Neumann had worked out mathematically how it has to work. So DNA is essentially the blueprint, it's the instructions for how to build cells but in DNA there is no instructions on how to build DNA because DNA is a double helix and it splits and then regrows because each end is the same on the two ends of the double helix. So DNA has this element of being instructions but also being a copying machine that copies itself. It's another great idea of how you understand how the math has to be like that because the math says it has to be like that and then when you actually discover what it is it's exactly, I told you so. So von Neumann wanted to build a machine that replicated cells so something which could read that had a machine, it had instructions, it had a copier and he tried to work at how to actually build one and then realize that he was getting too bogged down in the mechanics because he was not interested in the mechanics of how he actually built this machine and speaking to Ulam he said well why don't you completely simplify it and they invented this new mathematical idea which is what I want to talk about now for the rest of the talk called the cellular automaton. So the cellular automaton was an idea invented by von Neumann with Ulam's help which is a grid of cells and each cell can have a certain number of states and what it does just depends on the states of neighbouring cells and he built a pattern full of cellular automata which theoretically could self reproduce although they didn't have computers that were big enough because it was 200,000 live cells that would have taken thousands of generations to do that but theoretically it was kind of proved so this was the 1950s this idea the sort of simplification of this model called cellular automata you think I haven't explained it particularly well that's because what they're doing was much more complicated than what I want to talk about which is in the late 60s a British mathematician at Cambridge John Conway kind of reinvented this idea of the cellular automata what is one of the most famous pieces of recreational maths and was actually in a sense responsible for the first computer craze which is called the game of life which he sort of took and simplified from where Von Neumann and Ulam started off and I'm going to just go through what the game of life is simply at first because it's actually very simple but using it we can get really complicated in a really beautiful way so this is a grid a two-dimensional grid it's got cells in each square is a cell a cell can either be alive or dead it's a live cell the black one is a live cell everything around it is dead it has eight neighbours so all the ones around it's eight neighbours and there are I could write this on one line but I've split it up into five lines which basically explains the rules or the genetic laws of the game of life and now it's not a game with winners or losers as we'll get to it's essentially a world which is this grid and all you want to do is you want to put some live cells and then just see how they grow so it's kind of a model of evolution so this gets this idea of how numbers reflect life how we can use numbers and maths to kind of model life so let's get there if you have a live cell and it has zero one live neighbours it will die by loneliness if the live cell has two or three live neighbours it will survive and if it has four or more live neighbours it will die by overcrowding okay so the cells can either be alive or dead there's just two states so if von Lehmann had 27 states it's really complicated if two states live or dead if there's a dead cell if it has exactly three live neighbours it will become alive all other cases it remains dead so this is the entirety all the rules of the game of life what we do is that you have a pattern with a number of live cells you apply all the genetic laws the genetic laws on each of the cells in the universe at the same time and then you get the next generation so I hope we're just going to go through it now very simply and if you haven't understood it put up your hand because you should all be able to understand if you don't know what it is already so this is say the north generation at the beginning we have one pattern like that let's look at this one here this one here it's only surrounded by one so this is going to die he's going to die this one here it's surrounded by one life cell it's going to die from loneliness this one here it's surrounded by two live cells so it's going to survive and this one here it's dead but it's surrounded by three live cells this one is going to be born so that would be the next generation of that, that becomes that we're clear, we're good yes because there are only two live cells each one is only surrounded by a single live cell that will die okay this is a new three very very simple pattern three live cells this will become that and it will then die and Conway shows laws that we're going to encourage the most unpredictable patterns also he didn't want things all to die or everything to keep on growing and it became it's impossible really to work out what's going to happen without doing it and this was in the late 60s so he didn't have computers he didn't have computers he had a go board and then a go board you have go boards next to it it's really really complicated but he still managed to find some quite interesting stuff so what happens to this one here three live cells becomes that forever so it's what's called a stable form it gets to the block and it stays at the block this one here it's called the blinker this one here so look carefully we're just applying those simple rules at the beginning what's going to happen each click is a new generation traffic lights which is four blinkers so first it was like this new world and they were kind of like naturalists texonomists going seeing these new creatures and giving them names and then when they started with all the three cell patterns, four cell patterns went to five cell patterns they saw this happen which sort of blew their minds and was the first sign that really is going to be very versatile this game so this five cell pattern if you look what happened to this five cell pattern it was that so after four generations exactly the same pattern but one down and one along so if you keep on doing it it keeps on going and it's called a glider because it looks when you do it fast that it's gliding along now John Conway told this to Martin Gardner in 1970, Scientific American and Scientific American did an article and Martin Gardner is kind of the king of all popular science writers and had the famous column for like most 30 years in Scientific American and the column that was his most famous column that got more interested that caused more response than anything else was his first column on the game of life and Conway said, is there a pattern that keeps on the number of live cells keeps on growing and I'll give $50 to anyone who could find it and one of the readers called Bill Gosper at MIT who was a student but starting to use the simple computers that they had there and actually this is where the word hack comes from let me say you're a hacker the original hackers were people at MIT who had been at the MIT model railway club and the hackers just a kind of creative customization of the model railway the hackers got into the game of life and that's why some hackers the glider is like an emblem for hackers still even now but it became essentially the first kind of computer craze because the laws are so simple but you get such amazingly complex I hope I've got enough time to show you complex behaviour that it was one of the first things that computers could do and were absolute wow so I'm going to show you now the first pattern which gets bigger the number of life cells increases without bound and it's called the glider gun and it's 36 life cells and basically it's kind of breathing and it just creates gliders it shoots gliders out and it's got interesting so it means that you kind of have a way of shooting gliders so and then another similar pattern was discovered should we get that this is the eater the eater eats everything that use fire at it so we're going to have things coming at it just eats it and it will just eat it so what you had is that game of life stopped being about discovering new things and actually about kind of engineering we had 5 minutes left we're almost at the end rather than just like invent patterns it was constructing massive things where you had fired gliders because you could clean up the gliders with eaters and what I want to show you is one of my favourite patterns and if we can come and talk to me about game of life afterwards but I'm going to get to golly which is the the best software for playing with game of life okay this is a pattern it's not very clear there but if you're looking there hopefully it's a lot clearer this is a kind of classic game of life engineering pattern and I'm just going to play it without telling you what it is so what we've got at the moment and let's go in it's essentially a kind of giant game of bagatell with gliders getting everywhere and lots and lots of collisions okay so I'm going to escape get back to under generation one and then tell you what it is this is the Civiveris Dostines that we were talking about before this is a pattern which civs prime numbers so let's show you how what's going on here we've got spaceships coming out spaceship is basically anything which which glides number two, number three four is not prime so it's not there so the position of these spaceships if it's prime it's there if it's not prime it gets there's a kind of Polish corridor here of glider fire which basically that is that comes at every three time units so it gets everything divisible by three this one everything divisible by five everything divisible by seven everything divisible by nine and what happens here is that the thing over here is producing one every odd number there's no point in doing even numbers because apart from two which you get for free even number is a prime number so here let's go from the beginning and I'll show it again because when we can actually sometimes it is when it's linked up let's go enter generation one beautiful screen okay so here two three four is not there five that seven is going to come through this is nine nine divisible by three so bang it doesn't go through this one's 11 it's going to go through that's 13 that's 15 15 is divisible by three and five what's up to five coming through smash gets it so actually this is just a fantastic reinterpretation of the sort of aerostosthenes and this we can carry on forever and the bigger it gets it will keep on putting out just even just prime numbers now that on the final thought you can say well we already had the sort of aerostosthenes what the use is this well of course there's no use apart from it's mathematically quite interesting but what can you actually do with the game of life as we've seen it's so simple every cell is only listening to the eight cells next to it and these five very very simple rules well actually you can build a pattern in the game of life to do absolutely anything that any computer would do so absolutely absolutely anything how does that work very quickly my final slide so I might be going over by like a minute or two PowerPoint here we go slide show so we saw those gliders straight streams what is a computer a computer is essentially a bunch of wires and a logic gates and a memory register we can emulate all of those things in the game of life by using wires are going to be lines of gliders so you've got a stream of gliders there when there's no glider it's a zero when there's a glider it's a one which is just like the kind of a pulse or an absence of pulse which is basically how you make all computers also computers and in my book I talk about exactly how you can build up all the logic gates and the memory register so it's kind of amazing to think that you could create everything that's in my MacBook Pro could just be one absolutely massive pattern that you just press play and then you just wait and as I talk about my book also it's a big kind of sort of philosophical idea that maybe that life itself is some kind of cellular automata so that we are all a generation you have billions and trillions of generations on of some kind of initial formation and that that is sort of discreet rather than continuous a heart as this is so I'm running out of time I hope I gave you an idea with the sort of emotions and favourite numbers of how life reflects numbers which is what I'm interested in is how we position ourselves so we have these numbers all over the place how we respond to them but also how numbers themselves and maths can be used to sort of model aspects about life in kind of interesting and provocative ways not only life kind of philosophy like why we're here what are we I would say that yeah my two books I will be in the books tent or in the shop just by buying the food thing in a few minutes if you want to ask many questions or buy a book and do get in touch with me on social media if you've got anything interesting you want to ask on my garden blog anything about maths do get in touch thank you very much