This will teach you more about maths than school did (ft. Matt Parker)

0:00 If we ever met aliens or beings from a different civilization, what mass would they have also found? And what would we have found but they didn't? We chop one of the sheep in half. You have half the sheep. I have half the sheep. Now, what do you got? >> Yeah. So, I've got five plus. >> Oh, yeah. Cuz you have to invent. >> And are there numbers that couldn't be represented by chopping up a sheep? We're sending a lunar rover out onto the moon surface. And there's a little bit of space in the memory if you want to write some code to run on the lunar rover. >> You're going to write boobies. [Music] Hello Matt. Welcome to Things People Do. How are you? >> I'm good. It's a pleasure to be here. >> What on earth do you mean by maths and standup? Do you mean like you just do maths standing up or

0:47 >> Yeah. >> You do it sat down as well or is it cuz you actually like comedy and you're a comedian now? What? Help me. >> Yeah, it's best I mean best described as a ven diagram because I used to be a math teacher. >> Yeah. Category one used to be a math teacher teaching math to young people and do bits of recreational level mathematics. I'm not like a industrial mathematician. I'm like a casual hobbyist in the but on the other side I love doing comedy writing and standup and performing and initially like you said they were very separate. I was teaching maths and doing standup. >> The the hours don't overlap during the working day. So you can do both. It's exhausting but for a while I did both at the same time. However, since then, um the the diagram has merged. So now the maths communication work I do is heavily

1:34 standup inspired. And when I'm doing comedy standup, I'm still doing maths content as such. >> Maths content. Joe, um you don't do standup. You like to sit down most of the time. >> I do sit down. >> What about maths? Because I've got a feeling today's episode is going to be slightly unusual because often the dynamic is that one of us will know slightly more about the topic than the other. >> Is it? Um, today I'm so bad at maths. >> Yeah, good. >> I'm really like, >> you're not alone. >> Really? I'm not mad at >> Oh, no. He is in this room. He's alone. >> Oh, right. Okay. >> You're very much alone. >> Go on then. >> Underestimate me at your peril, Thomas. >> Maybe I will. >> Anyway, enough of the bollocks. I need to go back to the top of your answer when you said ven diagram. >> Yeah. >> [ __ ] that then. >> Oh, great. So, so ven diagram, you will

2:21 see this occasionally. is where you have a giant circle for each category >> and then if something's in both categories, you overlap the circles and you put things in the middle. >> Oh, I like that. Yeah, >> it's kind of fun. And you can build them up. You can have like uh three or four different circles, but they get incredibly elaborate. And so vend diagrams, which a lot of people remember from having to do at school or you'll see them like in advertising. People love using these and like they're kind of pointless diagrams. They're still open questions, things we don't know about ven diagrams and people are discovering new ways because it's so complicated. If you want to draw 13 circles or you know you don't have to be circles, they can be any kind of shaped regions such that there's one spot for

3:06 any combination of those 13 is phenomenally complicated. Now this is well beyond what would be useful as a diagram but mathematicians just love to find out new things. So people are still finding new arrangements for regions in ven diagrams which I I find amazing. >> That is wild. But is it finding new arrangements or just making it up? Do you know what I mean? Are they just making this up to >> You've hit on a big argument in maths. Are we inventing this stuff or are we discovering this stuff? >> And my rule of thumb is if we ever met aliens or beings from a different civilization, what maths would they have also found? and what would we have found that they didn't and they have no interest in because if aliens show up we can be like hey prime numbers and they'd be like prime numbers love them because that's

3:52 such a fundamental part of maths and that's why I think we discover I would on the we discover side but other people would on the nah it's just us playing ridiculous games it's like us solving sudokus or something like we're just generating pointless things I think we're discovering things that already existed in the universe but in a non-tangible way So, a sudoku is maths. >> Yes. >> But is that maths just because it's numbers? Could you do sudoku with pictures? >> You could do it with letters. You could do it with emojis. >> And that's still maths. >> Still maths. It winds me up. People think Sudoku is maths because it's digits. And I get that's >> got the look of math. >> So, what we're saying is maths isn't digits. >> Maths is not digits. >> The [ __ ] hell, right? Right. Just brace yourself. >> What are numbers then?

4:39 >> Wow. >> No, but who invented numbers? What the [ __ ] is that question? >> It's a good question. >> Okay. What are numbers and who invented numbers? >> I've got another question. It's more of a statement than a question. >> Go for it. >> When I went to Delhi to cover the Comwalth Games in 2010, >> show off. >> I got it's important the story. I got a tour of the local uh museum and there was a big thing which basically stated that India invented the zero and I was like invented the zero but the z a zero is nothing. How can someone invent nothing? And then it went on this um exhibit to claim that the invention of zero Matt was one of the most important things that humans had ever invented. >> None. >> None. Nothing. A zero. >> None. Yeah. >> Is a zero both nothing and something Matt. >> Oh yeah, I'd agree. Definitely. It's

5:25 really useful. And that question of what what is a number? Who discovered it is still a big question. We're still finding new types of numbers. I can say very vaguely. But there was a time before when we didn't have zero. You couldn't write down like 10 because you need a zero to write 10. One zero. So before that you'd use symbols all the way up to nine and instead of now using one and a zero you're like I need another symbol for 10. >> So if you wanted to write 100 numbers you needed a 100 different >> hundreds of different symbols or you got to do a tally or something elaborate. And when zero arrived in Europe because it was invented discovered in India made its way I believe through Italy first. And it was the accountants it was the bookkeepers who were all like this is amazing. [ __ ] hell. This I didn't think I would lose the plot this early

6:13 in the record, but we haven't even [ __ ] gotten to like algebra. We've literally asked what are numbers. >> And I I'll be honest with you, Matt. I I don't want to be disrespectful, but I don't think you've actually answered. >> No, I >> What What is a number? >> That's a good question because back in, you know, prehistory, we would use numbers to count things. So a number like five would be linked to there are five rocks. >> Yeah, I've got five sheep. >> Oh my god, there are five sheep over there. >> Yeah. >> And then the abstraction of oh the notion of there are five rocks there, there are five sheep there. Then that was like a generalization. Humans had to realize the notion of five could exist separate from just counting individual objects. So now we would say the idea of

6:59 let's say five is it's a combination of all the sets of things where there are five of them. So it's just like this notion of five things. But then we're like well what's between the whole numbers? What's between four and five? And then we go oh wait there's more numbers in here. If we look there's four and a half. Who put that there? >> You can't have four and a half sheep. >> You can't have four and a half sheep. No be alive. >> No cuz then you just go I got four I got four plus one. I got four sheep. One dead one. >> All right. We've got um 10 sheep. Okay. You take five. Um I take Is that how bad my math is? I can't 10. >> We chop one of the sheep in half. You have half the sheep. I have half a sheep. >> Yeah. So I've got five plus >> half. >> Half. Oh yeah. Cuz you had to invent >> Yeah. >> half a number. >> And then if you chop that your half a

7:44 sheep in half. Now what do you got? >> Qu. >> And are there numbers that couldn't be represented by chopping up a sheep? It turns out there are there are more numbers. Uh we call them trans sheep numbers because they they're beyond what you can do. No, we don't. >> So hoping desperately hoping. >> So glad I'm not the gullible one in this episode. >> But actually the very first use of numbers like this practically that we have evidence of other than we get tallies. We can find fragments of bone where humans have put notches in them. So they're obviously counting things way back into prehistory. It was the uh ancient Samrians the first people where we have like physical evidence they were counting and they had number systems and it seems it was basically to keep track of communal grain warehouses for brewing

8:31 beer. So that's like the original source of mathematics as humans as we know it was from stockkeeping. So you because you to have civilization to work or maybe vice versa you need to be able to brew beer on a decent scale. And so that's where maths, >> as far as we're aware, came out of. >> So maths came from a bunch of piss heads >> or vice versa. >> You clearly love maths. Like your your face lights up talking about this subject, even with the ridiculous questions you've already been offered. Um, but where did that start? You've mentioned you're a teacher, but were you a kid? And were you one of those kids that actually, as opposed to the majority of kids I knew growing up, we were, "Oh, [ __ ] hell, maths."

9:16 >> Maths. Yeah. >> What the [ __ ] this for? What? Just cuz I need to count whether someone's given me the right change from the shop, which you don't have to do now cuz no one seems to take cash. But did you have a different mindset as a child? >> Yeah. What's interesting about mathematics is it's easy to convince yourself you're not good at it and it's easy to not enjoy it at school. And the moment you think, "Oh, I'm not good at maths or I struggle with it or you don't enjoy it," which is fair enough. If you get behind, it just gets worse because now you understand even less next time and it spirals. So, particularly when you're coming out of primary school into secondary school is the sweet spot for students just convincing themselves they hate it, they're useless at it. I had the advantage of my dad was an accountant, my mom worked as a

10:02 librarian. So as a kid, they were like giving me math problems to do and convincing me this was fun before I went to school. So I showed up already convinced, hey, math is great. And it meant cuz everyone finds math difficult. That's the distinguishing thing. It's not like people who love math find it easy. They like the fact it's difficult and a challenge and rewarding. >> Yeah. So don't think, oh, I'm not good at math because I find it difficult. That's literally everyone apart from maybe like five genius savants who just showed up and somehow live and breathe maths. Everyone else, it's such a challenge to learn maths. But if you've got the can do attitude of it's okay to get things wrong. I want to give it a go. I want to learn it. And it's not necessarily just

10:49 for counting my change or things that are useful, although that is handy. That just that momentum makes all the difference learning and and enjoying math. >> Did you have a calculator at school, Joe? >> Yeah. >> Did you use it A more for doing sums or B for writing shell oil or boobies? >> Shell oil. >> I don't know that one. >> Yeah. >> No, boobies was always a go-to, but I always I'd always forget how to do it. So, I'd ask a mate. >> But I actually >> 51 three. >> Look at this. That's ingrained even >> 008. See her boobs. See her boob. >> You got turn the calculator upside down. That's the end. >> Okay. Yeah. I I really enjoyed my calculator because it had things like Well, aside from numbers and the digits, it had AC. What's AC?

11:36 >> The classic get rid. >> What does that mean? >> People refer to it as all clear. So, you're clearing everything. >> Okay. All clear. It had C. >> Yeah, regular clear. >> This not all. >> These are the deepest questions I've come up with. I mean the classic you just mash both of them a couple times and it goes to make sure >> I actually used to enjoy cuz I had the one you know the classic grazer and you uh it was solar powered >> that was go >> yeah like I enjoyed that but I remember co sin and tan >> and I remember them cuz every time I looked at my calculator I went what the [ __ ] is the point of those and not once in all of my education did I press those buttons Not even see what they did.

12:22 >> No. I was like, that's just nonsense. I'm not helping. But now that I'm a 34 year old grown adult and I've got an expert in maths right in front of me. Matt, please can you help me? What is cos, sin, and tan? >> Yeah, cos, sine, and tan. >> Oh, I've said it wrong. Well, they're always abbreviated to three letters, but for some reason, we keep sign pronounced as sign. They're the trigonomeic functions. They're another way of measuring the size of an angle. So, I um do a bit of cycling and occasionally you'll see a sign coming up like a physical sign, not a sign, and it says like uh uh gradients 21%. >> Yeah. >> They're telling you the angle of the road, but they're giving it to you as a percentage, which is actually the tangent. That's the tan of the angle of

13:07 the road coming up. >> Tan for tangent. >> Yeah. Breakthrough for me. >> Oh, yeah. Cuz you love cycling as well, don't you? >> Yeah. >> This is huge. Yeah. >> Oh, what a day. I just love the fact road signs use the tan of the angle and everyone's like, "Yep, they're just fine with that cuz it's just a percentage or a number on a sign." >> This is one which baffles me when I'm cycling. >> If you see a sign that says 20%. >> But that's not the same as one in five, even though 20 is a fifth of 100. >> Well, it depends over what distance it is. Like, have they averaged it or is there just like one spot on that road that's going to be a wall >> 20%? Yeah. on those signs, would there ever be 100% and would it just be vertical? >> It would actually be a 45 degree road

13:54 because it means for every mile you go forward, you've gone up a mile. It's 100%. Whatever you go across, you go up. This is one of those episodes, Joe, where our minds have blown every single >> This is This is You've like within the first five, 10 minutes of this chat, you're starting to make maths 100 times 100% more fun. >> You've hit a wall >> then Mr. Brown did. I'm sorry. Mr. Brown really got it. And I felt bad cuz I'm sure he loved maths as much as you did, Matt, but he had a class that was unruly >> and flicked ink cartridges on the on his back on his blue pen on his blue shirt. Obviously was writing sums and I feel bad. And I'd like to say if you're still with us, Mr. Brown, and for some reason

14:40 you're listening to this podcast about maths with Matt Parker, then I'm sorry for flicking ink cartridges on your back. It's off my chest now. Thank you. Um, so were you a like a gradeA math student then? You'd already had the you'd had you you get maths, further maths, did you? So you must have had prem your parents giving you >> Yeah, I I got the rolling start of premaths then. I really enjoyed it at school. So it meant I got good grades because it was kind of fun to do >> and I didn't mind the fact you have to really plug away at it. I hit the wall once I got to university because there's always a point in everyone's math career where you can be like if you like math, you're quote unquote good at maths, you're like, "Ah, this is great." And

15:25 you kind of get used to being the person who's good at maths and at some point you hit a wall like a a room of people and you're like, "Oh, they're all they're all better at math than me." And that for me, I got to university, I'm like, "Ah, here here's the people who are good at maths." And that's a real daunting experience. But functionally it doesn't make a big difference cuz it's always hard work. You're always chipping away at it and there's always the issue is that you never get to the end of maths. Everyone they get to a point where the next bit of maths is super difficult and beyond them. So we all just stop somewhere different before we hit the math that we're not yet able to do. I found Joe at university that the math students were the ones whose brains were so obviously much bigger than mine

16:12 that >> physically >> just it was intimidating. I remember Joe there was a table tennis team and I quite liked a bit of table tennis and I got there and there were kids who were just smashing the ball past you for some reason they all did maths. >> Is is there any relevance to sport and maths >> correlation between >> maybe they were doing table trajectories? >> Yes. >> I mean pool I'd understand cuz that's all angles. I've tried to apply my maths ability to sport and it's been unsuccessful every time. >> What examples can you give us? >> I definitely tried pool. So, I played a professional pool player. It is in the States in Brooklyn. We had a team. We had two pool players and two mathematicians. And I'm like, you set up, we're not going to do a full game, set up one of your like training drills. And they put the balls. You got to hit off here, head off there, and sink this one. And we're like, piece of cake.

16:58 We're drawing diagrams. We're working out the exact angle. Uh, and then we're way off cuz they're like, "Oh, yeah, you didn't factor in like the humidity in the room changes." But it turns out the the maths concepts we had are what they're doing, but they just know how to factor in the messiness of the real world. >> This has got me thinking, AJ, about all the different things you do in sport, which are fundamentally maths. So, let's say we had Stuart Broad, didn't we, on the pod recently. If you are Joss Butler keeping wicket to Stuart Broad and the batter edges it then you are fundamentally diving and you have to calculate the rate the ball is traveling. It's moving on up and down as well. It might be moving side to side. You have to intercept it with your hand

17:43 at exactly the right point which now I'm thinking about it Matt sounds like the most like landing on the moon style maths. And people would just do it h just taking the catch. Yeah, it's interesting. The maths our brains can do intuitively and the math that it can't. And because we've evolved to throw and catch things, our brains are just they can see the beginning of the movement of an object and our brains like, "Oh, it's going to we don't even like we're not aware of it doing anything. We just know it's going to be over there." And I find that absolutely phenomenal. And then the other side is the mass we're not good at doing. That's when you get results like um when stats took over baseball. Well, stats have always been a baseball. But when people realized, oh, we can use mathematics to locate players who will

18:29 have a bigger impact on the team. >> The money ball system, then we stats. >> Yeah. >> So, I went into Liverpool Football Club cuz they've got a big sports analytics team as you can imagine, and they're basically tracking every football player in the world across every league they can get data for. They're tracking everyone because their big impact in terms of maths and analytics impacting their team is scouting and recruitment cuz if they can spot an upand cominging incredible player and they may watch a player through several different teams they're bouncing around. But if they know the right point to get that player that'll have a big impact on their team in terms of the value of what it cost to get the player versus the impact on it. And there's no way because obviously back in the day people would smoke a cigar and say ah that kid they got

19:16 potential. whereas now they got a big spreadsheet and they're like, "This person in this country's got potential and they're worth pursuing." >> Yeah. I mean, you've brought up Liverpool, but um and seeing as you brought up football, it's it would be remiss of me not to back up the mighty seagulls and Tony Bloom um and their recruitment policy and this sort of mythical algorithm that he has from his I think it was I want to say gambling. He was had a background in sports betting. >> Sports betting. And then they've created this algorithm that they somehow nail finding these gems how you've just described >> and they bring them in. They buy them for like half a mill or a mill. They spend a year or two there and nine times

20:01 out of 10, >> I just used maths there, didn't I? >> Or 90ths out of 100. >> Yeah. >> Does that work? Yeah, it's the same thing, mate. 90% of the time uh they're a gem and they sell them on for like triple or quadruple the money. Um I just I just didn't feel comfortable you mentioning Liverpool and me not coming back at you with the mighty seagull. >> The only reason I would go Liverpool is I was I've been trying to get the government to change the street signs for a football stadium for a very long time. >> Why? >> Because the picture of a football on the UK street signs is incorrect. >> Right. >> Yeah. Football. So the light colored hexagons, I got no issues with that. That's great. The dark colored panels should be pentagons with five sides. And

20:48 they've depicted them here as hexagons with six sides, which you might think is not a big difference. Five sides, six sides. Who's complaining? >> Yeah. >> The reason it winds me up is mathematically it's impossible to make a football out of only hexagons. >> So that is mathematically impossible. >> Oh, hang on. I'm challenge you on this. If this is like legit and you're going to the government, how is it mathematically impossible when that clearly looks like a football? The circle is circle >> and it fits all the stuff in. Doesn't matter what sides, how many sides those shapes have? >> You're actually correct. So, this is a 2D flat picture of a ball. And hexagons work great in 2D. That's why they've used them for the sign. >> Okay. >> Cuz you can fit them together nice and

21:33 neatly in 3D. If you actually cut them out of that sign and tried to stitch them together into a ball and do the other side, it would never line up. You'd never be able to close that ball and finish stitching it together. >> Okay, >> which >> and that really winds up. >> Really, really winds me up. I had a parliamentary petition. >> We got we got over 20,000 signatures. It's a big issue, you know. We got to >> uh and the government wrote to me and said uh cuz they have to give a response. I got enough signatures. They had to respond. respond and said no. >> Oh, >> which is not >> how many signatures do you need? >> Well, more than 20,000 it turns out. >> Right. Okay. Right. This is calling out to all the things people do. Listeners, let's uh join the petition with Matt Parker to change. What would you change it to?

22:19 >> I don't mind. I'm As long as it's accurate. >> Okay. What if asking for accuracy pentagons? >> All brown. Oh, then if it's all brown, you can't see it. >> Yeah. >> If it's all white, are you happy with that? >> It doesn't look like a football, >> right? So, you want all of these signs changed to like a 3D >> officially >> sphere? >> Officially, only future signs. >> Well, listen, that's as they put them in. >> I think you've been very generous here. You're meeting them. >> I'm trying to meet them in the middle. I understand the expense of changing the old signs may not be warranted for my mild mathematical concern. >> But going forward, why can't we? Other countries have correct looking footballs. >> Let's make the world better. >> We're the laughingtock. >> Yeah, fair. Um, so I got someone to design an actual

23:05 custom football for me, which isn't all hexagons, but if you look at it from one specific angle, it looks like this. >> And so I took it into Liverpool so they could have a look at it. And they said there is no way the Premier League would ever go near that ball. >> Oh, they wouldn't play with it. >> No, because as it rotates, it changes how it looks. Like it's absolute nightmare. >> Spice it up a little bit. >> Spice it up. That's what I said. Each team can can opt to play with that ball for five minutes of any given 90 minutes. >> Baller League. The new Sky Sports YouTubers Baller League. >> Right. They might be up for it. >> They'll be up for that. We got to start somewhere. We got to get out of the bottom. >> The Lions Tour is here. That's right, Ben. The British and Irish Lions Tour is underway and it's a super team constructed of the best players from England, Scotland, Wales, and Ireland.

23:52 And our podcast for the love of Rugby will be covering all the action as they tour Australia. We'll be joined by players in the squad, >> bring you on the whistle insight, >> and the best lion stories from tours gone by. >> Just search for the love of rugby and we'll be your podcast for a cracking summer of rugby >> with him, Ben Youngs, >> and him, Dan Cole. >> See you there. Right, let's rewind. Let's go back to Matt, the maths teacher. >> Mhm. >> And let's pretend that I'm thick. Okay. There wasn't many objections from either of you with pretending that I'm thick. Fine, >> Joe. You're not thick. >> Thank you, Tom. >> Yeah. >> Still get that same look. >> This is my neutral resting face. >> Okay. Algebra. >> Yep.

24:38 >> As layman as possible. >> Yep. >> Could you explain to me Joe the child, the thick child >> who's struggling with the challenge of maths? >> Algebra. Correct me if I'm wrong. A equ= 1, B = 3. So if the sum reads A + B equals C, >> which is four. Yep. Yeah. >> Have I nailed algebra? >> I mean, you've done my job for me. Um, basically the beauty of algebra is if you had a situation like that where one something is one, let's say you're building a building and the door the wid like the the base of the door is 1 m high, but then you got to put this 3 m thing on top of it. And so you know the

25:23 total is going to be four. You might instead of writing down, oh, this part of the building is going to be one and three total four, you might say, well, it's going to be A whatever this bed is plus B, whatever that bed is, and that's going to give us C over here. Because then that factors into a different part of the planning um process. And the beauty of algebra, instead of just using numbers for one specific value, if you put it in terms of letters that represent numbers, you can then see what happens if you vary what each thing means while keeping that relationship whole. So if you want to design a very complicated building or system, it's handy to know, well these two numbers have to add to whatever that number over there is. But if we vary them across the plan, that relationship has to stay there. So algebra is about going from specific numbers and sums to

26:09 relationships and the way numbers interact, which gives you a lot more flexibility. >> Okay. Why is maths at school boring? Well, it's partly because it's easy to teach math badly because it takes a bit of motivation and creativity, which is why I love teaching it. You really you're you got to be on your game to convince teenagers to pay attention and learn maths because they got a lot going on in their lives. And as you say, they'd rather be doing something they find easier or more fun. >> So, you've got to really put a lot of effort in. It's also a bit boring because like sport, you got to learn the fundamentals and skills before you can be any good in a game. And so maths, a lot of it is is like, why do I have to do this worksheet of 10 problems? And like, well, you're you're practicing one skill. And what's a shame is at school, it's easy to overfocus on honing the

26:56 skills without ever playing a game because why learn all these math techniques if you ever get to do anything interesting with them? And we tend to stop short of doing that. So, I think and then this comes down to, you know, how much time teachers have and flexibility and all this stuff, but if students had more time to apply and use their math skills, it'll be a lot more fun to learn to do the boring bits like the practice to get the hang of it. >> That uh tells me, Joe, we need to do some games. Yeah, we need to gify this math chat. Okay, >> the first bit of game we're going to have has been lined up, I believe, by producer Vicky, who is claiming that she has lined up a things people do ven diagram, which when I click my fingers is going to appear on the screen behind me,

27:43 >> right? Be honest, Vicki, I was hoping for better than that. >> Right. Is it Matt? Is this legit uh a ven diagram? >> So yeah. So in the Tom circle are things Tom does or enjoys or is focused on. And then likewise in the Joe's circle you got everything that you're uh you do or or enjoy or focus on. >> We're really that simple, are we? >> Yeah. >> Cheers, Vick. >> And I don't want to do any further psychological analysis of the ven diagram, but that's >> I mean it is a ven diagram. That's what we >> It's 100% a ven diagram. Yeah, >> I know. But that has actually made me like I've enjoyed that. That was that was fun. >> Isn't that pleasing? >> And that's maths. >> That's maths, >> isn't it? I mean, I'm still not sure how the [ __ ] it is math.

28:29 >> Now that you're both enjoying this diagram, you could put this diagram in the middle of that diagram >> as a hangception level. Does that mean Does that then mean >> we could then put a picture of that ven diagram? >> Yeah. You really enjoyed how funny it was putting the diagram in the diagram. You put the whole thing again. >> So it's like when you put two mirrors next to each other and then it just f >> Yeah. >> Is that maths? >> That's 100%. >> Is it? >> Putting two mirrors and it [ __ ] off to infinity is math. >> Being able to understand how that works is maths. Absolutely. >> Are you able to try and help me understand? >> Oh, I love that stuff so much. There's a thing called the draster effect which is where you put a thing inside a thing. >> Sorry. you put okay that's the worst sentence that I could have used to

29:15 describe that but there was a hot chocolate brand I think in the Netherlands called DSA and on the packet is someone holding a plate with a packet >> of the hot chocolate that they're on so they're also on the packet >> which I just find that stuff hilarious >> and so mathematically you can analyze how all that works and so some friends of mine did some did some research into this and some programming so I for one show had a um one of these 360 cameras live on stage, but I could then take the feed from it and put it onto a screen on stage to feed it back in again so we could have this recursive effect happening live because we did all the coding to kind of make it work as we were on there. I I find that stuff super interesting and it touches on there's a

30:01 whole area of fractals and these sorts of recursive self similar structures and I think where people get confused about the why is that maths is numbers are such a prominent part of maths that everyone's like well that's maths it's the numbers maths is actually just the study of patterns you know and trying to solve problems in terms of what's the logic behind behind that? What is the pattern that we're seeing glimpses of here? And numbers are just a really good manifestation of that. That's just a really nice example of a whole lot of patterns and they ended up being really useful. So numbers are incredibly handy just in society. shapes come a close second because

30:46 geometry >> isoclesles triangles >> isles triangles all that >> or equatorial triangles >> or right angle triangles >> right angle triangle equilateral triangle >> a a rhomboid >> a romboid there are you one more side but we're okay with that >> and a polygon >> there you go >> and an octagon septagon megatron terron >> have you been working out on your romboids they're looking quite What's the rumboid? Is that my neck? >> You got trap. You got traps. Trapezoids. >> A trapezius triangle. Is that a triangle? >> Trapezium is its own thing. >> What's that thing? What's that thing where you've got two sides that never [ __ ] meet if they carried on? >> Yeah. Parallel lines. >> Where a parallelogram is if you then just cut it off and turn into a shape.

31:31 >> And what's the one where you have a shape that start not touching and then they touch? Uh, I mean the easiest version is the triangle, >> but you get these whole set of like pyramids or cones that all do the same thing in 3D. >> Like a cylindrical uh >> tube. >> Tube. >> Cylinder. You had that. >> Cylinder. That's it. A sphere. >> But naming I mean naming these shapes is fun. >> I'm just trying to recall all these stuff that I've learned that and then go well I would mock it going Yeah. Yeah. Oh, what the why am I learning? But actually, it's important to know that, oh, cuz someone's going to ask, "Oh, what's that over there?" And you go, "Oh, that's a camera. It's of a cylindrical

32:18 shape." Well, the camera So, a friend of mine who does VFX will talk about the camera frustm, which is if you take a pyramid and cut the top off, the top bit's just a smaller pyramid. >> Yeah. >> The bottom bit is now what we call a frustm. And that's the shape that us as the image and the sensor and the camera make as in terms like the mass of how we go from being here and then being an image on on the sensor. >> [ __ ] >> So these ridiculous shapes are then you the weirdest places they'll pop up. >> Yeah. >> And be useful. >> But maths is not those examples of patterns. Maths is just the idea of looking into fun patterns. >> I think we should do some more games here, Joe. Um, when you are when you are helping the kids with their maths

33:03 homework, >> uh, chips and peas, >> tell me more. >> Well, I actually struggled to begin with >> with uh the math the kids maths homework because they come home using techniques that I didn't know that I wasn't taught. So, when they actually end up teaching me and I'm like, "What do you mean chips and peas?" And they're like, "Well, a chip is 10." >> Okay. >> And P's are single. >> Oh, okay. Yeah. I was like, "That just seems really lazy. Why don't you just write 20 P's or draw that to draw them?" >> Is that ratio of peas to chips the sort of ratio you would like to see on your plate? >> I'm not very good at helping the kids with math. >> In that case, Matt, do you think if Joe gives the age of his children, you could

33:51 try him with a a maths question appropriate to that age of child and Joe can see if he can answer it? Yeah. Yeah. >> Oh, [ __ ] >> So, Jasper is now 10. >> He's 11 going into 12 secondary school. >> Okay. Jasper is 11. A question for Jasper and thus >> he's coming up into high school years. Yeah. You're the wonderful thing about going from primary to secondary is you start to generalize stuff and find patterns. >> So, there I mean this wouldn't be something you could do here and now. >> Yeah. What I love for students at that age is when you look at the nine times table, >> look at the answers. Exactly. If you add the digits of any answer in the nine times table. >> [ __ ] off, Matt. [ __ ] off, Matt.

34:38 >> I did this the other night. >> Here we go. >> My daughter was there doing her times tables and she was like I was like, "What are you doing?" She got to do the nine times tables. And I was like, "Right, I know this one. I remember this one." I said, "What's uh 9* 9?" And she's like, "It's 81. What's 6* 9?" 54. Is it 54? Yeah. Yeah. Thank you. So, I was doing that with her and then I was like, up until you get to 10 >> Yep. >> times 9. No, 11. Yeah. Up until you get to 10 time 9. This is exactly how the conversation went, Matt. Like, this is perfect. >> So, this is how [ __ ] it was. I went, all the answers, >> this is a dream conversation, >> add up to nine. >> Yeah. And she goes, "What do you mean?" I was like, "Well, what's

35:23 >> I love how you're explaining this to Matt. >> What's six and three added to >> nine?" I went, "Exactly. So, you know that that's the answer." She's answer to what that hasn't. All I know is that you're adding up these numbers that add up to nine, but it's not giving me a signal of what 4* 9 is. And I went, >> "Yeah, you're right, Maggie. You're right. Do you I'll just do the answers for you." That's the exact step you'd want to see from doing times table is spotting the patterns. I was terrible at times tables when I was at school >> because it was just memorizing things. >> What about >> 12 * 9? What's that? >> 12 * 9 is going to be >> 108. >> That feels about right. Yeah. 108. Yeah. Yeah. >> Oh, it starts again. >> N again. >> I can do that. Add all those numbers. 1

36:09 + 0 + 8, what'd you get? Nine. >> Voila. But if you get your calculator and multiply any number by 9 and then add the digits. If it's not nine, add the digits. If that's not nine, add the digits. And eventually it'll be nine. Just for bigger numbers, it takes more iterations to get there. >> That's so I can't wait to go home tonight. Even if she hasn't got maths homework, I'm saying we do. Is nine your favorite times table? >> No, probably 10. >> Yeah, 10's a classic. 10's a banger. >> Yeah, 11's nice, though, isn't it? Cuz once you realize 11, >> it's only up to a point like 11 * 11, >> but 11 feels like it should be more complicated because 9 is a horror. >> Two is quite nice. >> Two is lovely. >> Four, six, eight. Uh, >> isn't eight's tricky? Seven, >> we all agree. Seven's the worst.

36:54 >> Yeah, seven's really tricky. The only one of seven I really know is 7* 7. And that's your bank. And that's always 49. It's always 49. 8* 7, not a clue. >> No idea. >> Four * 7, >> it's 28. >> Yeah. How did you work that out? How did you get to 28? >> I went seven add seven is 14. >> Yeah. >> And then 14 add 14 is 28. >> That's a long way round of >> That's what I do. I But I have skipped the first step. I'm like uh I know double seven is 14. So I just double that in my head. So that's I get So I do the same process but start one rung upgrade. >> And why in the [ __ ] is there a minus set of numbers? That doesn't make sense. How do you have less numbers than actual numbers? >> I'm with you on that one. You've already got nothing. So how less than nothing. No, you can't go beyond nothing.

37:40 >> What's less than nothing? >> Yeah, you're right. The same deal is like when zero showed up, everyone's like, well, maybe there are more numbers >> in the same direction. >> But that's really I would say >> I would argue hard that when they said there's more numbers, they've just taken the numbers they've already got and just put the negative sign in front of it. Yeah. No, fair enough. When you say you'd argue that hard, is that something that people would >> dispute? I go, it's [ __ ] lazy. O you want you want different rather than a minus. >> Yeah, it should be like >> actually Yeah, >> it should be like >> what would you call it? What would you call a minus one? >> A better symbol or just >> a better symbol to really differentiate. I don't think the >> what's it negative sign? >> Yeah, >> I don't think that >> little dash thing not working >> is enough. What's handy about it is we

38:27 kind of use the obvious ones first because now to signify different types of numbers, we got to put like a hat on them or underline them or put an apostrophe next to them. >> So that there's now all these different ways you decorate numbers to indicate subtle changes. >> I've got some really tough questions that I want to put to you actually Matt about this. Um I'll start off with uh why if you times a minus number by a minus number do you get a positive number? Yeah. >> I mean, the lazy answer is because if it's like worms, if you take away a hole because if you're removing something that was already removed, what do you you're filling it back in again. So, >> so that's whoa. >> So, if I let and sorry for interrupting

39:14 Matt, but this is classic way these things are explained to people like me and maybe Joe who have struggled with maths in the past. >> So, there's a cake in front of Joe. Yeah. >> Okay. And I'm not giving Joe three pieces of that cake. >> Why aren't you giving me three pieces? >> That doesn't matter. So I've taken three of these pieces from Joe. So Joe doesn't have three pieces. I've then taken three more pieces from Joe. >> So I've got no pieces. >> But using that minus times minus, haven't you suddenly got? >> No. If you took away the missing like if if someone served >> So I've taken the three pieces and then I've taken them back. >> Yeah. >> If you took away the missing pieces. So, someone gave you a cake and there's a piece missing. You're like, "Hey, there's a piece missing." So, the [ __ ] my piece? >> I I'll get rid of that empty piece for you. >> To take away a lack of a piece, you got

39:59 to add a whole piece. >> This is good news, Joe, because you've gone from having no piece of of cake to six. The entire cake. >> And c can I have that? >> You can have your cake. >> You're not going to take any any more away. >> I wouldn't mind one slice. And it would probably be polite to offer our guests a slice. It would still leave you with four slices. >> I just love after all the zero slander. You got very upset at the notion of zero cake. Like you understood zero in that moment. >> Okay. So you answered that one really well. Thank you. Uh square root of four. >> Yeah. >> What is it? >> Uh -2. So >> what the [ __ ] is a square root? >> Square roots are interesting because it makes sense if you're using numbers practically to square them. So if you

40:46 wanted to work out, so in the studio here, there's a lot of squares on the wall. If you wanted to work out how many it takes to cover the wall, you'd count how many across, how many up, multiply them together. Or if it was a square, it be the same number twice. So multiplying a number by itself to get an area happens a lot. But what if you started with the area and wanted to go back to how long the side must be where to undo a square where you multiply something by itself, the square root is just the reverse of that. So if you >> So the root cause >> the root cause of the square a square. >> Yep. And so if you said the area of this square table is four, what's the square root of four? The actual answer is two because 2 * 2 would give you four. The reason I said -2 is I think it's very

41:34 funny that there are other less useful answers to the same question because as we just said a negative times a negative is a positive. So technically -2 * -2 still gives you four even though it's not the helpful answer you actually want. >> Do you think negative numbers get a bad rap? >> I I do. I think it might be the naming. >> Yeah. >> Why don't we can we come up with optimistic numbers or something? >> Yeah. Yeah. Can numbers reverse numbers. >> I like reverse numbers. >> Okay. Has there ever been anything in maths that like an equation or something a pattern that you've you've discovered or >> Yeah. or or learned that's actually changed your outlook in life. Do you know like relating to that? >> Yeah. Um there is a thing called the

42:21 optimal stopping problem. >> Okay. >> And this is the idea that let's say you're um you you say you're meeting you're dating people and you want to find a life partner. >> The first person you date you have no idea what it's like to be in a relationship, what to expect from a relationship. But the question is, do you want to end up committing to the very first person or do you think you don't understand what's out there yet? Or let's say you're, you know, um, buying a house. The first house you view, you're like, well, this seems pretty good, but I have no idea what the general market's like. Optimal stopping problem is how many experiences or viewing or data should you get to understand what's out there and then decide, I'm going to get the next best one that I come across because I think I understand it. Because if you wait too

43:06 long, you're going to miss up loads of maybe the first one was the best one. You're going to miss a bunch of opportunities. It turns out, mathematically speaking, if you take the square root of the number possible number of things you're prepared to experience or view, that's the optimal point to stop investigating and start choosing. We need to go into this more, Joe. Yeah. >> Okay. Let's use that example you've given us there, Matt, of hunting for a house. >> Yes. So when you say the maximum number you're prepared to see, this is sort of the number you can cope with mentally of houses you can remember or practically you can get round to. >> It's practically you're like look if I see a 100 houses it's going to take too long. It's too I can't do more than that. >> Okay Joe, when you bought your current house, how many houses did you look at?

43:52 For the purpose of this exercise, we'll include ones you looked at online as well as in person. In person we looked at four. >> Yeah. >> Online that's hard to It was just [ __ ] on right move. So it's constant. So I don't know. Let's say in in person four in total 54. >> Yeah. But that's a different the number you're prepared to scroll past total is a bigger number than number. >> Okay. We'll go with the inerson version then. Yeah. Okay. Just four then. So that that means if the four is a square root of like 16 or so. So that's saying maybe if you had 20 houses in you that's about the >> so I should so what we should have done was go and look at 16 to 20 houses

44:38 before deciding because that's the optimal stop. Norm the optimal stop thing if it's you think you could view up to a 100 houses before you buy is to just see 10 without making any decisions and then pick the next best one you come across uh understanding what you've seen >> the best of the 10 you'd seen >> no you want to kind of burn 10 to get a sense of what's out there now what I think is interesting is on one hand humans we always stop too soon in experiments humans tend to stop too quickly or we end up never stopping. We become obsessed with the hunt >> and there's something else out there. But also, it's not like a hard and fast rule. I think it's just an for me, the reason it was my zen moment was by taking me and my emotions out of these

45:25 situations. Just knowing, oh, this is not necessarily true of any one specific example, but on average across all examples, this is the optimal point. And so just having that as you know a a rule of maths to it just helped me to make sure I was thinking through these sorts of situations better. It's interesting a bit of math like that just changed slightly the way I conceptually go about living my life. >> Uh Matt, tell us about the adventures that you have on YouTube because you do some pretty remarkable things. >> No, wild. It's wild. >> I love YouTube. It's so much fun. I did recently get stung by a bullet ant in the Amazon. I got an email from some researchers because a lot of scientists

46:11 watch my channel and I got an email saying, "Hey, we do research um primates and ecology in the Amazon rainforest. Do you want to come out and we'll show you some of our research?" And I'm like, "Absolutely." They're like, "Oh, one of the things is um insect sting pain." Like, if you want, this is not normally offered. You can't just show up and say, "I'd like the bullet ant experience, please." >> How how big is this bullet ant? Uh about I'd say two or three like 3 centimeters maybe like an inch sort of size of a bullet. >> Yeah. >> Oh, I've gambled that whole episode is just >> discovering new things and thank you Tom and it would have been nice if you maybe dressed it up in a less patronizing way. >> No, that's where the name doesn't come from. Uh so >> [ __ ] you Matt there. So, so the but

46:57 thing is the the YouTuber side of me is like that's great content getting stung by a woman and mathematically it's interesting because how do you assign an objective number to pain and so that intrigued me. >> So you just say how what do you mean how do you assign an objective number to pain? You just go what's the score out of 10? >> Yeah, but how do you know that the pain you're experiencing? >> Well, 10 is the 10 is the worst pain you've ever had. One is no pain. Well, that would depend on your previous pain experience where your 10's going to be. >> Yeah. Let's say the worst thing that's ever happened to you is you cut your finger. Have you then had a testicle torsion? Have you had a testicle torsion? >> What is that? >> Um, Big Al had one and he said it was the most painful thing that it's possible for. >> Oh, your nut. You twist your nut. >> It's a nut twist. >> Oh, yeah. No, I haven't. No.

47:42 >> So, that 10 would be bigger than the 10 you'd previously experienced. >> Well, that's subjective. >> Exactly. >> Yeah. >> That's what I'm That's what I mean. >> Yeah. No, it is. It's objective. But if people are researching the evolution of venom, >> cuz you can measure scientifically how uh toxic it is in terms of being fatal. Yeah. >> But pain is such a whole different more complex game. >> It's difficult to study and investigate how venoms evolved if you haven't got a way to measure the pain impact of these venoms. So I got a bit over excited. I said, "Hey, before I get stung by the bullet ant, could I first of all be stung by like a calibration wasp? Yeah. And >> what do they look like? >> We all agree that's like a single unit of insect pain. Okay. And so they found me some some wasps. There's a couple.

48:30 Yeah. Calibration wasps. Then we had a slightly more painful ant. >> And then we had a terrifying wasp and then the bullet ant. And the bullet ant >> hurts but then just stays there for like eight hours. >> What? No change. >> What? Um it's a very hard question to answer. Maybe I was going to say what level of pain because it's the level of pain of a bullet ant but >> like what's a household level of pain that the bullet >> you know what it's the most painful insect on earth >> but compared to other things you can do it's not like it's not like you know ball torsion or whatever we were discussing a second it was that combination of >> bruise and rash at the same time that's what it felt localized yeah so I got stung on my um left forearm and just

49:16 from elbow to hand. It was weirdly spread out like it it just felt like I had a cycle crash and it had that real intense pain, but but it didn't subside the way you'd expect pain to go off over time cuz it's, you know, venom causing it. Um, so I had a lot of fun and it was a ridiculous mass thing to do. And at the moment, the next YouTube project is calculating pie on the moon, >> right? Um, two questions. >> Yes. What the [ __ ] is pi? >> Yeah. Okay. Yeah. >> And what do you mean on the moon? Like you're going to go on the moon to work what pi out what pi is or the moon? >> No. The second one I can answer easier. Some engineers got in touch and said we're sending a lunar rover out onto the moon surface and there's a little bit of

50:02 space in the memory if you want to write some code to run on the lunar rover. And I was like yes please. >> Are you going to write boobies? Just grow up. Just grow up. >> Boobies in the moon. >> Just use that optimal stopping point. >> Yeah. And apply it to your life sometimes. Thank you. >> I mean, I'm not here to market this, but we are crowdfunding it. And people are submitting their names or bits of text to go up on the rover to be part of the calculation. >> We've got to do it. >> There's probably a boobies in there somewhere. >> We've got to do it. Surely. Surely we can put boobies things people do. Boobies. >> Yeah. >> In that code. >> Could we? >> I'll give you I'll give you one one free

50:48 ride. >> Really? >> Yeah. Yeah. Yeah. >> Put you on the rover. Send you up there. >> We're going to the moon. >> Well, we're not. We're not. >> Fly me to the moon. >> Okay. Now I can't stop. I can't resist this. >> Let me play among the stars. >> Riding boobies on a calculator. Murf >> bound for Mars. >> No, >> it's the moon. >> [ __ ] [ __ ] >> stories, >> right? What's this called then? What's this project called? >> Moonpie. >> Moonpie.com. [Laughter] >> Wow, that's such a early 2000. >> Yes. >> Well, I got I got pi.space as the website, which I'm unduly proud of.

51:35 >> Okay. and pi to come back to your first question. >> Yeah, >> a lot of people will come across pi at school because it's the ratio of the distance around a circle and I'm pointing at the mug here versus across the circle. But the reason I love pi so much is it that's only one of so many different places it shows up. It's like the mascot for maths where you be doing some unrelated maths and pi will kind of drop out of the answer which I find absolutely incredible. >> So pi existed before we knew about pi. >> Absolutely. I was it was it was invented by Pythagoras, wasn't it? And we've somehow shortened it to PI instead of PY, which baffles me, >> Matt. Um, when I was at school, I really enjoyed economics and I would have loved to have done economics at university,

52:22 but my maths wasn't good enough, >> so I couldn't. >> Um, so I downgraded, and I think that's the right word, to geography. Then I got there, and I found that geography still required math. Math. Yeah. >> So, I was given a book called Statistics Without Tears to get me through it. And it turned out not to be true. Tears with my statistics. I'm still searching for the book, Matt, that would help me in my quest to not think that I'm rubbish at maths, but to enjoy it. >> I have a belief, a firm belief, Matt, that you would have written a book like that. >> Yeah. Oh, what? Fantastic segue. Yeah. No, I wanted because everyone talks about Pythagoras and trigonometry and what are those buttons for on the calculator. So, I wanted to set the record straight on trigonometry. So, I wrote a book called Love Triangle, which I'm very proud of. >> Very good. >> Thank you. >> Really well. >> It um came out the same week. So, the

53:09 paperback's just come out. The hardback came out the same week as the House of Beckham um Beckham Expose, which was meant to be the number one bestseller. Unbelievably, my book about trigonometry sold more copies. >> Huge. Can we Why am I the only one applauding? >> I'm mentally applauding. and not. >> Yeah. Yeah. >> You lazy sod. >> That must have been a massive blow for Posh and Bets. >> And their book had actual love triangles in it. >> I believe allegedly so. >> Allegedly. >> Yeah. >> Um Yeah. But I I was uh very pleased I could finally try to set the record straight on how wonderful. I mean, obviously I'm convinced, but I want more people. >> So, it's not just like a GCSE tech No, no, no. It's >> where you can solve stuff. Is there any anything in there that you can solve? Like a little I think of Myrtle. Have

53:56 you heard of Myrtle? It's basically >> like Wordle, but >> No, it's it's like a murder mystery book that you can solve stuff. Basically seduku with um >> pictures. >> No, it's not P. Yeah. With who done it? >> Not the point. The point is is there anything you can like solve? >> Yeah. I try to make it like a gateway book where the book you can just read it. You're like, ah, math stories about maths, how we've used maths. But I really want people to just be like, oh, that's interesting. things like multiples of nine, the digits add to nine. Like, oh, maybe I'll look into that. So, that's my A lot of people just read it and put it away, but I want a few people just to go, you know what? Maybe I will look into a bit of mathematics. >> On a a very high note, I would like everyone's favorite number. >> Oh, >> favorite number and a Y. >> Okay. Who Who wants to kick us off? I

54:42 think Matt Park. >> Can I It would be pi. Love pie so much. >> What? What do you mean? That's [ __ ] loads of numbers. I thought pi was infinity. >> That's true. So before I said there are numbers you can't represent by cutting up sheep. Pi is one of those numbers. It falls between the sheep. >> You've gone full circle. >> Yeah. >> You've gone Oh my god. >> Everyone likes a book end. >> Wow. >> So I've tried to So when you're cutting up sheep, you're basically getting fractions of a sheep. >> When you're cutting up sheep, this little cannot be clipped just on its own. when you can't you know just >> you talk about how much you love uh slicing sheep up. >> Sure. >> So you always end up with a fraction of a sheep. >> Pi as you say has infinitely many digits. It's 3.14159 and that carries

55:29 on. It never stops but it is still between three and four. It's between 3.1 and 3.2. Like we know where it is but it doesn't match any fraction. There's no fraction you can write down. Like 22 over 7's close and there are even closer ones. There is no fraction that equals pi. We call it a irrational number. It can never be pinned down to a fraction of a sheep. >> I think I'd be pi. You can't be pi. He's chosen pie. >> I got pie. You can't just copy Mount Parker. >> All right. Seven. You didn't say any conviction. >> It is seven. >> People love seven. >> Why do you like seven? >> Because it's my birthday. Oh, >> but the irony is I hate my birthday,

56:16 >> but whenever I go on the roulette machine, >> seven, >> I'll put a pound on red seven. >> I'm going to go uh for 144. >> Can I try and guess why you've gone for 144? >> Is that the amount of [ __ ] songs the Beatles put out there? >> How many chips and peas is 144? >> That's 14 chips and four P's. >> Yes, correct. Sorry. >> But it it could be other things as well though, couldn't it? Because if you really like peas, by your calculations, you max out at 9 P's. Could you remove some of your your chips? Remove two chips and substitute in for 20 peas just to make your plate a more nutritious one. >> Why is your number 144? >> Because when we do times tables, it's

57:01 the end. It's the maximum. >> No one learns the 13 times table, do they? >> So it feels like the end. You get to 144, you're done. You completed the times table. >> I do 20 times 20 400. >> Pick yourself up. >> Why are you showing off about that in front of Matt? >> I'm just saying look look how quickly I did that. 25 time 25. >> All right, Matt. Matt, I can't wait to go to the moon with you. You have been one of my favorite guests ever. >> That's very kind of you. >> I now want to add you. Well, well done >> to the growing list of guests that have left a positive impact on the show.

57:49 Brackets A uh + B closed brackets equals C. And C in this example is great guest. It's been an honor to add to the sum total of the show. >> What? He did it. >> He did it better. He did it way better. Okay. Well, before you go, if you had to solve the Ryman hypothesis or win the lottery, >> Yeah. >> which would you choose and why? >> I would go the Reman hypothesis. It's also would come with a big cash prize, but there's so much of maths because no one's solved it yet, but a lot of people have assumed it's true and done more math based on that assumption.

58:35 >> It's like we're >> What is it? >> We're miss it's a >> You don't know what it is. >> No, I do. I just want to, you know, that will summarize it for us. >> Now, it's a question about the way that primes behave. We think they line up in a particular nice pattern and all the ones we've checked do, but we don't know for certain if that will carry on for every single prime number. >> And my follow-up question to that would be, what do prime numbers and prime colors have in common? >> Ah, you can split a more complicated situation into smaller parts that build it up. I think this the second question was easier than the first. Cheers, Matt. >> My pleasure. [Music]