Alright, Matt, you know how you and I were talking about a bunch of different things we could talk about on the podcast and the math when you came up with you remember that one? I feel pretty clever about that one. Yeah, the math one I saw it do doing some math hacks on the internet and I never thought about before and I thought I did there probably a lot more math hacks than that. And since I'm a math hack in a different sense of the word hack, I thought it'd be fun to learn about tricks and have you put together tricks for me and then you would teach me math tricks.
Okay, well, I didn't really do that, but I kind of did something better, I think. I would like to introduce you to Dr. Kevin, Eva, math professor at Pepperdine University. Hi, how you doing?
I'm doing super and I happen to know Dr. Kevin, Eva, mathematics professor at Pepperdine University and think rather highly of him. Let me tell you how Matthew, Dr. Eager is Matt.
He's sitting here wearing a shirt in front of me that says God said and a bunch of equations and it says let there be a lot and there was light. Is that what it says? Yeah, and there was light. Yep.
And those are Maxwell's equations. Yeah, that's right. That predicts the existence of light. It's pretty cool.
It's pretty cool. So, Matt, what were you hoping for in a math episode to be totally transparent here? Kevin, you have how much time before you have to leave for the airport? Maybe half an hour ish.
Yeah. Oh, wow. Okay. Well, no dinking around out on the front end.
I was going to do all this stuff about like, hey, doesn't weird out live right by Pepperdine and doesn't need part of like some church. I heard without teachers Sunday school at church there on campus. I'm not a weird out for a long time. Does he really follow that?
Actually, how do I want church, not the campus church, but yes, same combination just down the road. Really? Yes. Oh, I didn't know that.
I knew it. I knew there was some kind of weird out thing. Yeah. Wow.
Okay. I had a buddy who went to Pepperdine. He's like, where now with my Sunday school teacher? What?
Are you serious? I would have Pepperdine if we were to be my Sunday teacher. So, I went to visit Kevin at Pepperdine and I've got to say that's one of the most beautiful campuses I've ever been to in my entire life. Is that right there?
Yeah. It's been really great. Actually, yeah, the campus is great. The communities have been better.
What do you mean? Yeah, you know, it's a kind of thing where if you're there for a long time, you kind of forget that other places aren't at school and until people come and say, wow, this is a wonderful place and you introduce them around and yeah, and then the community comes together and actually the best place to see community is when things are tough. Last year, we lost four students to a car crash. That was really tough on everybody, but it was really beautiful to see the community come together at that moment as well.
How big is this in a body? Oh, I have to look at undergrad. I would say there's about 3000. We also have some graduate programs, but it's harder to count those because it's not everybody's full time.
Depends on how you measure that. Yeah. I've only ever seen it from the road. I've driven by a couple times and it was red.
Yeah. Okay. But I thought I wasn't going to do that. So we didn't do that and that doesn't count.
Okay. So the math thing, that was your question. What did I envision? What I envisioned was this.
I imagined that you destined would ask me a question and it would be something like this. Well, Matt, when I give you the following problem, how would you attack that in your brain? And then I would think for a minute and I would describe to you my mental process and then you would try to be polite, but deep down, you'd be like, that's a very bad way to come at it because I'm not good at the math. But you would very gently be like, that's great.
But here's maybe another thing that you could do and this would make you better at math on the fly. And then I would learn. And then everybody in the third chair would be like, yeah, I totally already knew that. You can be down.
There's wouldn't aren't totally no all of that. It would make them better at math too. That's how I imagine the episode. Well, let me just full disclosure.
Let me tell you how I'm at Kevin. So he emailed me and we went back and forth a little bit and then we had lunch together and we found that we had similar interests. And then I had to take a mega math test. I'll call it is called the PhD preliminary exam.
And you remember me preparing for that exam, Matt? You remember how not cool I was to be around? Do you remember that I suffer from nail pattern baldness? Okay.
Yeah. So I wasn't. I wasn't. If you remember that and I probably just about as much remember what it was like for you warming up for that exam.
It was not good. It was not good. I remember. You were pretty pleasant at time during that.
It was pretty hard. And so I'm not going to go into. All the things of the exam, but Kevin volunteered to help me with that exam. I'm talking like over Zoom sessions.
He was teaching you how to solve partial differential equations with the Frobenius method and like the separation of variables. All these things he spent a lot of time and just volunteered. Nobody knows he did that. It was just completely.
I mean, yeah, I really appreciate it. Kevin. Thank you very much. You're welcome.
Thank you. That's fun. Yeah. So he's the man is my point, Matt.
He's the guy that's going to ask these questions because he did that to me during this exam. He was trying to explain everything to me and he did it in a way that I can understand. So I was Kevin, do you have an interesting math things that you could talk about with us? Sure.
Let's start with this one. Matt pick up. I don't like to say forage of number. Tell me what number you picked.
3511 3511. Okay. Dustin, is that a multiple of nine? Of nine?
Yeah. No. It's got 11 at the end. That feels very prime number.
What was it? 3511? 3511. Oh, let me divide it by nine.
Let's see. It's not. Yeah, it's not. It's not.
So do you know how to figure that out without pulling up calculators? Or you know, spending a bunch of time on pencil and paper? I don't. I had to punch into a calculator.
So you're saying there's a three trick? Yeah. All of the digits make up a number add up to something that is visible by three. It's visible by three.
Is that how it works? Yeah. That's right. I don't know if that would work for nine as well.
Yeah. I'm up one plus one plus five plus three. I got to 10. And I thought, what?
That doesn't seem like it worked for the three. So I bet it would work for the nine. So my guess was no. Matt, hold on.
You're not supposed to be teaching me stuff in this episode. I didn't know that you add the digits up. And if if it's a number, you're not supposed to be teaching me stuff in this episode. And if if they are multiple of three, the whole thing's divisible by three.
That works. I think so. But I'm going to defer to Dr. Kevin Iga from Pepperdine University.
Yeah, that's exactly right. That's right. So actually, yes, it works for three and it works for nine. It doesn't work for any other number, but it works for three and it works for nine.
Really? Yeah. And the way you think about this is if you want to know if something's a multiple of nine, well, I want you to imagine a clock, but instead of having 12 hours in the day, so it goes one, two, three, four, I go all the 12 and then it repeats, right? Yeah.
Instead, let's make it go up to nine. So one, two, three, four, five, seven, eight, nine and then it goes back to one. I don't like that. So the first 33% of the clock goes to three.
Is that correct? Right. And then the second two thirds of it goes to six and then the rest goes to nine. Okay.
That's right. So I'm imagining a piece of time. Yeah. Exactly.
Exactly. So now you kind of think about what's going on with a number like 3511. Well, let's start with 11 just to make things easier. So 11 is that a multiple of nine?
Well, no, but let's see if we can see it. Well, 11 is 10 plus one. Right. That's what 11 means.
And so 10 in the nine nine hour clock is the same as one, right? Yeah. So instead of 11, that is 10 plus one. I can think of it as the first 10 turning to a one.
So 10 plus one becomes one plus one. Okay. Yeah. So in fact, as far as the nine hour clock is concerned, 11 is the same as one plus one or two.
Yes. Now, let's take another two digit number. Just in this time, you pick a two digit number, 37, which is the number that everybody always picks. Yeah, 37.
So 37 is three times 10 plus seven. Right. That's what it means. Yes.
And on a nine hour clock, 10 is the same as one. Hold on. You're going fast. Is he going fast?
Do you matter? Is he just going fast to me? I'm feeling my mind warming up. Okay.
I'm making a lot of agreement sounds, but they're not maybe all totally on it. Okay. Hold on. Wait, say it again now.
So 37 is three times 10. Okay. Plus seven. Got it.
Yeah. So 10, we already established 10 in the nine nine hour clock is the same as one. Yeah. So I've got this little dial in my head that's just buzzing around.
Okay. It goes around around around. And then it goes one more. Right.
Okay. I see. So 10 is going around one on the nine hour clock. And then one more.
Okay. Got it. So instead of going three times 10, I can go three times one. Right.
Hold on. If I only care about how far it is on the nine hour clock. Okay. So instead of going three times 10, I can go three times one.
Right. Hold on. If I only care about how far it is on the nine o'clock on the nine hour clock. Right.
Okay. Yes. Now it just clicked right there. Right.
It doesn't matter how many times we go around because we're going to end up in the same place on the wheel. Right. Got it. Instead of going three times 10 plus seven, I can go three times one plus seven.
Okay. In other words, just add three plus seven. Yes. Okay.
I see it. The same thing works with 100. 100 is just 10 tens, which is just turn 10 to one. 10 times 10 becomes one one.
So it's one times one. 100 is also one. I see on the clock on the nine o'clock. Yeah.
Nine hours. Yeah. And a thousand, likewise, it's also going to be a one. Okay.
And that's just because we're base 10. Got it. Right. And so whenever I write any number in base 10, I can take each of the digits and just add them all up.
And that will be the same on the nine o'clock, nine hour clock as the number itself. Okay. So Dr. Iga, would you prefer Dr.
Eve Kevin? Either way. Kevin Kevin. Kevin.
All right. So give me a number and I would like to try to tell you if it's divisible by nine. Okay. Let's go with 57.
57. So that's 12. And 12 is not divisible by nine. Right.
The nine hour clock. That would be nine. It'd be like 10, it'd be like three o'clock on the nine o'clock. Nine hour clock.
Right. That's right. That's right. So it's not divisible by nine.
However, it is divisible by three. That's right. Whoa. Okay.
Matt, do you want to try one? I guess you already did the original one. No, I'm in trouble. Okay.
So I had the three tricks, but I didn't feel whoa. When you said that, I didn't feel that at all. I felt. Which is a very different emotion.
Right. So I knew that 57 wasn't divided by nine because of knowledge. Right. I just knew that it wasn't.
Okay. So let's try slightly bigger number than 57 then. Um, probably 300 21. Okay.
321. Well, that is definitely divisible by three. Yep. Because the sum of the digits is six, six, and divisible by three.
So that's great. But I'm not understanding the trick for translating this to nine. Just do the same thing. Just see if it's divisible by nine.
What do you mean? Like the sum of the digits? Yep. Yep.
Well, six isn't divisible by nine. There we go. So it's not divisible by nine. Seriously it.
That's really it. Yep. Why was acting like this was hard? Yeah.
This works for three divisible by three. This has to work. If it's divisible by nine. The other one that's like it is not quite the same.
It's divisible by eleven. For that you have to add every other digit and subtract every other one. Whoa. Hold on.
Okay. No, no, no, no more. Okay. 7474224.
Okay. So. That's eight. Okay.
Now plus 75 plus one. So, every other digit and you add some track. So 74,000 means add seven. Subtract four.
Yeah. Okay. Got it. And then add two.
That too. I'm going to take two away. I'm going to add four. Right.
Okay. seven now. What happened? So we ask is that I'm a little bit 11 heck, no.
No, no, no. You said it was not a little bit. So, wow, dude, this. This is Matt.
If you've ever eaten lunch with Kevin, this is how it works. You just have a couple of little like, Oh, how's it going? Yeah. I think that's neat.
Do you think I think that's great? Let's drink that. to the core of the earth in this philosophical topic. And that's what every lunch I've ever had with this line.
I love it. So you're saying you take it. So all we have to do is just drop. If we drop the seven and run the same number, 42, 24, this is going to work because it's four.
Yeah. No. Yeah. Yeah.
You're right. 4, 2, 2, 4, the multiple are 11. Wait, wait, wait, wait. Oh, no, wait, wait.
Four. So that's four minus two is two plus two is four minus four is zero. Is that right? Yeah.
And so that's a multiple of 11. Try it, and you're a calculator. All right, calculating one second. Mm.
How care, like, four, two, four divided by 11? Three 84. Matt Whitman, you just figured that out. I'm proud of you.
I don't know that I did. I don't know that I got there the same way you did. Now I'm concerned. Okay.
We need to run another number. All right. Let's get us another number. Uh, it's going to be 36,000 and five.
36,000 and five. Okay. I got this one. So three minus six is minus three plus zero minus zero plus five minus three plus five is two.
Not visible by 11. No. There we go. 36 is here.
Zero zero five divided by 11. Checking the math. No, not visible by five. Wow.
Is this how the savants do it? I've seen a bunch of savants on like videos and stuff. They'll say all this crazy stuff. And is this how they're what they're doing?
I don't know what they're doing. I guess you have to have them on the podcast to tell you. Oh, but this is a trick. The trick only works for a couple of numbers like this, but I would say you go to a magic show and they're playing with numbers and you're asking people to do stuff 80% of the time.
Something like this is involved. Okay. My guess. This is just kind of really handy kind of thing that you can do in a lot of these magic tricks to force people to choose a particular letter of alphabet or something like that.
Hey, is it okay if we jump on real quick here and tell people about the thing you've been working on? Yeah, that'd be awesome. It's my understanding that you've been doing the 10 minute Bible hour podcast for a long time. And I guess it was about a year or more ago.
You went through every book of the Bible, Genesis, Exodus, Leviticus, all the way through. And you were making videos out of those episodes. Is that right? Yeah, more or less.
Yeah, it's not exactly the same audio you're playing with it to make it make it more sense for the video stuff. But yeah, that's basically it. You don't put this on your YouTube channel or just going to go somewhere else. Have you figured that out?
For now, I'm just going to put on my YouTube channel and see what happens. I mean, it's a channel where I've talked about the Bible for a long time, so I think it ought to work. You've put like a tremendous amount of money and effort into this, right? Because you've like hired graphic design people and you're investing in this.
Dude, this is the hardest I've ever tried. Probably anything ever to be honest. Are you scared? Yes, you know I am.
I mean, you're smart. You know what different people who make things on YouTube do. And you know that my vibe has always been kind of this. Heave the bowling ball down the alley.
It's going to bang against all of the kid bumpers all the way down. But it's going to knock down some pins by the end. It'll be all right. And the sort of the slip shod goofy, sometimes intentionally bad production is sort of part of the fun and the style of it.
I still want it to feel like that, but I want it to feel like that. And I'm also trying really hard. And I roped in a couple of really skillful people to help me. And so now it's like, oh, dang, now everybody's going to know I'm trying.
And so now, yeah, a little nervous. You're nervous because you're trying. Yes, I mean, I try on all of it. But this is different.
I think the Bible came from God. And I know that that's not everybody thinks that. Right. I think that I think that yeah, I know.
I don't want to embarrass him. By making a crappy bunch of videos of his book that he made. No, I just wanted to come on here and talk about it because I know you're scared. And I know how much effort I think.
I think the first draft I saw of this was over six months ago, right? The first draft you saw was 11 months ago. Yeah. So I know you're scared and I'm not being sarcastic about that.
Like you have reason to be scared. You've invested a tremendous amount of time, talent, energy, effort. And let's just say it, man, the algorithm's not going to like it. You know, I don't think so.
You're making stuff about the Bible. The algorithm's not going to like it. You're not going to get a sensational algorithm to promote that. So I think you just have to be aware that you're going to put it out there.
The joke that you and I always make with microphones off is the video that would really perform is how many nuns does it take to stop a 50-kil bullet? It's orphans. Orphans. Oh, it was orphans.
I'm sorry. Yeah. Yeah. The more sensationalistic, the more the algorithm likes it, even if it's because of important things.
Yes. That's the punch line. That is the punch line. Part of the reason that I'm nervous about this is that I didn't totally make the video for people who are already sympathetic to the Bible.
Yeah. I tried really, really, really hard to tap into my skepticism, my questions. A long period of time that I went through in my own life of not really being on firm footing in terms of what I believe about God or about anything. I know what it's like to come at the Bible like that and I tried to, is this making sense?
I tried to take that person into account and not just make it for the home team. Yeah. Absolutely. And so I'm especially concerned that the algorithm will not know what to do with it or who it's for.
But that's my swing. That's what I'm trying to do. You've worked for over a year on this first video, which is Genesis. So what's the plan moving forward?
Are you going to start rolling out other ones? I really like, by the way, I really like the way you've stylized it with photos of you and color. People will just have to figure out what I'm talking about later. I think that's cool.
But what's your plan? Are you going to roll that out for Exodus next or how long you think it's going to take? I don't take another year because clearly you built this system. No, no, no, no.
Yeah. We got a good chunk done on Exodus already. But my plan is that we will mill around in Genesis for a little while. So there'll be one main video that is just trying to explain what is in this ancient book and what does it mean.
And then you do with it whatever you want. It's just a really good, understandable, for normal people summary of what is in there, with no instruction for what to do. It's not a sermon. It's educational.
Yeah. And then there's going to be a shorter version of this Genesis video that is totally, it's different words, it's different images. And this one just sort of focuses on the theme. And it's much shorter, like maybe four minutes.
When you say shorter, I mean, are you playing the shorts game with this stuff too? Are you going to roll shorts out? I am. Yeah.
Okay. But it's not just going to be different iterations of the same thing. There are little vignettes and little nuggets that it works really well to pinch zoom in on real fast, 20 seconds, 40 seconds. And what I found is that shorts right now on YouTube, that's the best way in the world to get outside of your own little algorithmic bubble and talk with people who aren't like you, who don't think the same things as you, who don't click on the same things as you.
And so if you want to have a conversation with somebody from a completely different tribe, shorts are a good way to do it. You just keep making good shorts and firing them off. And it seems like that's where I'm meeting the most people who aren't like me on the internet. So I've got right now six little sub 60 second vertical shorts that I'm going to try out with this as well.
So there's one main video and then short video, a handful of literal shorts that I'm just going to try to use to see if I can connect with different people. More power to you, man. I'm still anti shorts. I don't like them, but maybe it's just because of the way I do things.
I don't think they make sense for what you do. I don't think so. I don't think strategically there's any advantage for what you do. I don't find anybody out there, no matter how short their attention span is, I think it makes sense for this, for what you're doing.
I'm trying to find people, even who don't have any interest in believing or in God, or thinking there's anything to the Bible, but they're highly empathetic and they have people in their lives who do highly value the Bible, their Christians, and they would like to understand what they think better. And so I've kind of crafted some of these shorts to try to connect with that crowd to be like, hey, you can learn more about what these people in your life or you care about think and believe and what your neighbors believe without having to really sign up for anything. So, okay, you're about to launch it tomorrow? Is that right?
That's my hope. Where do people go see it on your YouTube channel? Yep. The YouTube channel is Matt Whitman in the 10 minute Bible hour, or, you know, just search my name and always comes up.
Okay. Sounds good. Well, looking forward to it, you will get at least a view from me, my friend. Please, my mom.
Yeah. So, my mom, that is two. That's right. Now, I'm looking forward to it.
I know you've worked really hard on this. That was why I first reached out to you, because I could tell you were doing a thing and you didn't care how it performed. Like the very, very first time I called you and you ignored me was I could tell you were working hard on a thing, even though it wasn't performing super well in the algorithm, but you were being faithful and continuing to do it. It's fun to see you on this side of that equation.
Like, you nervous about it, you know, because I didn't get to meet that version of you. You know what I mean? Well, this is the first time I'm meeting this version of me. Oh, yeah?
You think so? Yeah. I just felt this way before. Well, I'm looking forward to it.
So go check out the Genesis video and you know what you're going to call it yet. Genesis, colon, what's in it and what does it mean? You haven't decided yet. I haven't decided.
Genesis, colon, lightning summary. Genesis, something. Summerized? Yeah.
My recommendation is the first two hours it's going, you just keep changing it and you figure out what gets the most clicks and just stick with that. That's my recommendation. That's the game. I'm going to do it.
I think it's Genesis, colon, how many orphans does it take to summer? No, no, no, no. Don't do that. Don't do that.
I'm going to get clicks. Take the nonzish one here. All right, buddy. I'm excited for you.
It's been a long time coming. So I'm looking forward to seeing it and I hope everybody in the third year checks it out. Thanks, man. What else do you have?
You have other tricks like this? Yeah, this may be not a trick, but here's a question. Let's say somebody says, all right, I want to get a square on your floor. You're going to design something for your floor and it should be a two by two square.
So it's going to be an area four, right? So that's two feet by two feet area, four square feet, right? And you work very hard and you go to your smarter, every day, place, and you know them questions lab, you cut out a square like this and it's a two foot by two foot square. And while you're at it, you make a whole bunch of them because you're not going to just have one.
You're going to fill the floor with this thing in sort of this bathroom time kind of way. You got the picture. You're filling your bathroom floor with these square tiles, each size four square feet, right? Got it, Matt?
Yeah, sure. This seems very straightforward so far. All right. Now, actually, you look back and you realize, oh, actually, oh, I made a mistake.
I don't want something of four square feet. I want something of eight square feet. And you've already made all this these tiles, right? And you're like, oh, my goodness, I screwed it all up.
Well, here's the question. Is there something you could do to get a square of area eight square feet from what you did? Now, there's lots of things you could do, of course, but, you know, just now, I don't brainstorm it. What, um...
It has to be a square. Yeah, it has to be a square. It's going to be an area eight. Okay.
So we got two foot by two foot, yep, four square foot squares. Yup. And you're telling me that you want me without making any more cuts to align these in such a way that they would give me eight square foot squares? Um, what I want is to be able to draw a square of area of eight, eight square feet on that grid.
Oh, my. I'm thinking. Well, nine square feet is very easy. Yes.
Four square feet is very easy. Sixteen square feet is very easy. So if you're sixteen square feet, how would you do that? I would just double everything.
Right. Double everything. Right. Two of my boxes next to each other.
And I'd be four total boxes instead of one box. And you'd have to get a 15. Right. Now, here's the thing.
What the problem that you're running into is when you double the length, what happens to the area? It quadruples. It quadruples, right? This is kind of not what we want.
We want the area to double. So, hold on. I was working on this over lunch. Yeah.
This is crazy. Literally. Okay. Now, let me explain this another way, my friends.
So today, I got lunch with my friend Austin who owns Armadillazite Spring shopping downtown that is getting some lovely flights. Yeah. Austin got three bids for three different types of umbrellas to help provide shade to customers. We spent lunch trying to figure out which would be the most cost efficient and which most provide shade for customers.
The various increments are similar to what we're talking about. And what we were having to figure out is how much would we have to stretch this proposed umbrella to double the square footage of shade that would be created by it. I literally just had to figure this out before lunch immediately before we got on this fall. And you'll be proud to know I did not figure out how to do it.
Well, I'm going to take a stab at it. So, if I have a unit square, the hypotenuse is square root of two. Right. So, one by one, if I draw a diagonal angle from corner to corner, it's square root of two.
And so, I feel like if we were to turn the squares 45 degrees and start stacking things in there, so that's I feel like we cut them on diagonals or something. That's exactly right. You got it. You got it.
But I don't know how to do it. Yeah. So, let's unpack a little bit of what's going on here. I don't know what's going on here.
Because I'm really. So, he started with this grid of two by two squares, right? Yeah. The four by four ones actually kind of useful.
Imagine you had the four by four and that's made up of a bunch of two by two squares. That's before those, right? One upper left, upper right, lower left, lower right. What I want you to do is make a diamond.
You're going to start from the top of the middle of the top of your four by four square, then go diagonally to the left in the middle of the left side. Oh, we cut the corners off each square. Yes. Ah.
And you go from there to the bottom, in the middle of the bottom edge, then to the middle of the right edge and back to the middle of the top edge. And that means the diamond, right? Yes. But that's actually a square.
It is. And so now the hypotenuse of each one is still one. Is that right? Well, you don't have to use my thigrene theorem.
All you need to do is notice this. Look at the upper right, right, right, right. All you need to do is look at this. The upper left two by two square, you cut that in half, right?
You just cut it like diagonally, like you might do to a sandwich. Okay. And so the amount that's in your diamond is half of what you had. Likewise, for the lower left, you cut diagonally and the part that you're going to keep is half of the total.
There you go. And one of the upper right and the bottom of that same thing, you've gotten half of your 16. Got it. And then you just use those little inner squares.
Yeah. This is the math that goes into making mosaics. Yeah. This is how you get your dimensions right.
This is how you mark out your scale with your chalk line or whatever. And you cut from squares to get the proportions that you want. Oh, man. Oh, gosh, that makes so much sense.
And I was intimidated when you're like, well, you're going to run the Pythagorean here. And I'll probably somebody knows up top their head, but square root two is. No. No.
No. No. No. So Matt, do you like Plato?
Plato's dog. That would be enjoyable child substance promoting for the philosopher. The philosopher in the age of Greek philosophy. So I was doing the software.
Yeah. I am right now holding my Alexander the Great Coin in my hand. Alexander the Great was suited by Aristotle. Aristotle was suited by Plato.
Yeah. Like I got a connection with him right here in my hand. Good. Look up, Meno, M-E-N-O, dialogue with Meno in the middle.
OK. Yeah. He has a boy comment that they're discussing how to be learning things. And he brings this boy up and they asked this exact question that I've asked you.
And walks the boy through this, through the argument that I just gave you. We're talking ancient Greece doing exactly what we just did. Really? Yes.
And this is, yeah, that's interesting. So when you think of math, Kevin, do you think more of just numbers and how things line up on grids and stuff? Or do you think philosophically about it? Or do you think geometrically, how does your brain work?
All the above, you know, when you're working on a math problem that you don't know how to solve, you kind of pull everything. Sometimes you're dealing with numbers and you say, OK, well, I know how to deal with numbers and you work with that. Sometimes you're dealing with geometric things and you try to pull up your geometric intuition of what's going on. A lot of it though, once you start doing college level and graduate level math major stuff, you're thinking about big ideas and you're thinking, OK, why is this true?
And you're thinking, well, if this is true here, how does that apply there? And that's a lot of what math is. Math, originally, we studied numbers, counting strings, we've got three apples, five stones, and as well as geometry, we're going to measure this building here, trying to build a pyramid. It was very early on, understood that these two things are two sides of the same coin.
But since then, people have been thinking about the mathematics of symmetry, the mathematics of tiling, the mathematics of games, the mathematics of economic exchanges, a lot of different areas that tie into math. And so math is not just about counting things and not just about geometric figures. It's about a lot of different things that have a lot of structure that you can study on an abstract level. So let me mention that this problem could go on with the problem that I just gave you about finding the square of area eight.
You could ask, OK, what size can make a size of a big enough square? So that's where it's double the size that that side length, you want maybe that to have a whole number of the whole number, right? So we had a square of area four that had side length two, we had where of area nine that had side length three, square of area 16, and square it had length four. But these diagonal ones, those were not whole numbers.
Can we get one that is a whole number? And the Pythagoreans, ancient Greek cult, basically thought a lot about number. And according to their ideas, numbers measured length and numbers, as far as they were concerned, were whole numbers. Hold on.
I thought there was a guy named Pythagoras. Probably. Wait, hold on. You're saying it was a cult?
Yeah, I mean, yeah, there was a whole, well, I mean, maybe we would call it maybe a cult today. It was a group of people who followed Pythagoras. Supposedly, we don't have very many of their writings. They're a secret organization.
They kind of start up in the Greek islands around Samus. And eventually you have to move to an area of southern Italy called Protona. But most of what we know about them is by other people, because they were secretive. You see, so they didn't share anything with you.