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Beautiful Maths

Media – Cubers

John Dickson (Studio)

That’s a couple of ‘cubers’ being interviewed by the BBC at a three-day World Championship cubing competition in Glasgow. And it demonstrates just how compulsive the Rubik’s Cube can be for some. There are speed tests for standard cubes, mini cubes, pyramids, dodecahedrons—12-sided beasts—and then there are one-handed races and, I kid you not, blindfolded competitions. The cube is an example of the daunting complexity of mathematics. There are 43 quintillion possible positions (that’s 43 million million millions) … and only one solved position. Producer Kaley and Director Mark are so committed to the Undeceptions project that they decided to learn the Rubik’s Cube just for this episode. Kaley can now solve it in under four minutes. Mark… can’t. Me? I gave up cubing on the very day I first tried it. For me, cubing and mathematics have always belonged together. I was, of course, forced to do mathematics through to the end of high school, but I gave it up the day I walked out of Mosman High. I can still almost feel the relief. I had a brief return to a mathematics career… when my first son was learning it. But I gave it up when he surpassed me… in about Year 7. One of my guests today says that almost everyone can remember the exact moment they gave up on mathematics. But he insists that the very subject so many of us abandoned isn’t merely useful. It’s beautiful. Obviously, mathematics is practical. The modern technological world is built on it. But my guest insists it has a beauty beyond its application in the world. The mathematician’s circle is perfect: every point lies exactly the same distance from the centre. You can describe it perfectly. You can never actually draw it. You and I are stuck in three dimensions. But the mathematician can think and play in a limitless number of dimensions. Mathematics is a language. Some even call it “the language of God.” But first … a trigger warning for my American friends. From this point on, I’ll be shortening “mathematics” to “maths”. I love almost everything about the United States … but saying “math” is just wrong. And I can prove it.  The word isn’t mathematic—which would shorten to “math”. It’s mathematics. So it shortens to “maths”. Take the related discipline “statistics”. No one—not even an American—calls it “stat”. It’s “stats”.QED. Mathematics = maths. Here I stand. I can do no other. I’m John Dickson, and this is Undeceptions.

Undecetiopns theme

Media – John checking out Satyan’s laboratory

John Dickson (Studio)

I’ve travelled across the US to California to meet this guy – Dr Satyan Devados, the Fletcher Jones Professor of Applied Mathematics and Professor of Computer Science at the University of San Diego, which is a lovely historic campus. He’s a fellow of the American Mathematical Society and the recipient of two teaching awards from the Mathematical Association of America. He writes technical pieces, of course, but his popular writing has appeared in the Washington Post, the London Times, the Chicago Tribune, and plenty of other places. He’s also written several textbooks, a mythical storybook aimed at introducing kids to unsolved maths problems, and he’s been involved in numerous mathematical collaborations with artists – one producing a two-ton metal, wood and acrylic sculpture for Burning Man, the annual desert arts festival in Nevada. He’s cool and clever. And he’s dedicated himself to making maths accessible for learners from all backgrounds. I could tell that from the moment I entered his maths play room.

John Dickson:
Tell me about this room, because it, it looks like I’ve gone into a, you know, preschool. And there’s lots of things I could play with.

Satyan Devadoss:
That’s right. So, on one side is a glass wall and outside a wall to wall chalkboard. We could talk a lot more about why chalk is one of the greatest gifts god’s given us, uh, and the demonic work of the whiteboard. That’s a separate conversation if you want to. And behind me is, uh, um. Basically a little spot for some books, like a little library, but it’s a wall-to-wall craft store, Popsicle sticks, toothpicks, um, origami paper, uh, yarn, you know, scissors cutting. Like all elastic bands, paper clips. Like anything. Basically you could, you could resupply this entire place for about a hundred dollars, right? Because you could just run out of glue and get some more glue. And it’s, and the idea, um, and the idea is simple. Which is, I was, I usually do do things when I, when I’m, when I get upset, right? Like when, when I feel like there’s a sense of injustice. And so it felt like almost every discipline had laboratories, had places of creation. So if you think about a historian, well they might actually need to go to Edinburgh to look at the original documents and you know, be there. You could imagine photographers and you could imagine, like literary scholars or working in manuscripts. Archeologists. Archaeologists certainly. But even if you think of the sciences, they have labs going back to the math and the sciences being put together again, like the biologists have a lab, the chemists have a lab physics, physicists dealing with physical things and they have labs. And of course within those areas you could be, in the theoretical end, you could be thinking theoretical. Um, talking about theoretical ideas behind chemistry. Or you could actually be on the laboratory side of it, it doesn’t matter. But still, there’s just playfulness. And in math, I’ve never heard of a mathematical laboratory, a studio. And so the idea when I, when I came here to San Diego about a decade ago was what happens if we had one? So in my contract with three things, a salary, a chalkboard guaranteed to be in my office and a space to build a math laboratory. So I struggled with the name ’cause it’s truly not a laboratory because it hasn’t been around for generations to know what we’re doing as a biology or a chemistry lab. The reason we have a laboratory in college, much less in high school, is that biology has advanced so much that we can now be able to communicate and share how biologists create and push the boundary of biology, that we could bring that down to a college level, much less a high school level. Here’s some buns and burners, here’s some test tubes for chemistry and all these things. And so I don’t wanna call this a laboratory ’cause in math, nobody’s had one. So we don’t know what to do with our hands and our bodies yet. And the question that this place, which is now called the playroom, just a chance to play. It’s simply asking is if math has advanced so much with our mind alone, how much more can it advance if our body’s also involved? That’s it. And the reason you had alluded to it, John, about it kind of being like a, like, like a playroom or just, you know, like you just want to get up and touch things, is simply because, um, I am a big believer in the fact that we are embodied and so at the end of the day. Things we see with our eyes, things we hear with our ears, right? Things we can touch, impact, and make knowledge acquisition and creation better. I mean, this is, this is nothing new, right? It’s been done everywhere. There’s been an incredible amount of data all over the place. Um, even Stanford, uh, maybe about a couple of decades ago, came up with something called the D School, the Design School, which is this notion of rapid prototyping. If you bring big companies like 3M or Apple or Microsoft and they want to redesign a cell phone, you don’t start by looking at the computer and drawing sketches on this, you actually start in 3D. You, they said, you know, the best way to do it is get some blocks of, uh, paper, crumple it up, put some duct tape around it and give it to somebody and go, does this feel like a phone? ‘Oh no, I want it to be skinnier’. Okay, let’s squish it. You know, let’s squish it around, make it skinnier. And, and so once you have this kind of rapid prototyping, everybody can play and you can give that idea that I’m thinking in my head to you because it is not in my head. Physically give it to you and you could like add an antenna, delete an antenna, make the screen bigger. This is what I mean. And uh, and once that rapid prototyping is done and you could play with it a little bit more, then you could make it a little bit more rigorous. Then you could get to 3D printing if you, if you have some more of the dimensions, and then you can get into processing later on. So I just wanted everybody to come and play with mathematics.

John Dickson (Studio)

Sure, let’s play – but what exactly are we playing with? What is mathematics? It seems like a simple enough question to answer – it’s about numbers, right? But what is the study of mathematics aiming at?

John Dickson:
Have you got a definition of mathematics? You quickly took it out of the realm of science for me before I opened my mouth, so what is the definition of mathematics?

Satyan Devadoss:
I think it is, um, that’s a great question. I, there are those who study the history and philosophy of mathematics itself in the larger realm. I’m, I am I’m a fool, right. I’m just, I’m, I just know a little bit about the world of shapes, about geometry, anthropology, but I’d say mathematics is really interested in capturing and studying structure and patterns. That’s what we really want. Mm-hmm. And we don’t care if the structure and patterns are on a zebra or in our minds, right? Like how do you, how do you do that thing? And one of the simplest ways to find structure and patterns is just counting, right? Like, you know, one chair, two chair, three ch. That’s one of the fundamental things. Oh, I have two parents and I have three siblings. You just this as a child, you’re building some structured patterns. Some are tall and some are short. And to me, I actually like the word discrimination or discriminate because what mathematics is trying to do is to say ‘What is the same and what is different’, and I’m not putting weight and a and a value system to it. I would just say, oh, there are eight chairs here, and the rest of the things here are not chairs. So I am discriminating by saying what are not chairs and what are chairs? And so I would say, oh, this is a prime number. Five is a prime number, but four is not a prime number. And for us to add more value to, well, won’t four feel sad that it’s not prime? I mean, shouldn’t we all be primed? Well, that’s silliness, right? Because the goal is to discriminate and be clean. Now in the world today, you could turn up the heat and put a value system and say, oh, I’m discriminating between men and women and saying, oh, men are thus worth more. Well, then you have problems, right? But in mathematics, we don’t deal with values at all, right? We’re just dealing with the simple number of measurement. How would you say what is equal? Are two triangles equal? If one is a little bit bigger than the other one, what if I scaled one into the other one? They’d be equal. So this all this notion of equality, discrimination, measurement, uh, comparison. This is what mathematics is trying to do.

 John Dickson:
So what is a mathematician doing? I mean, I understand at a university a Mathematician is teaching other students to do math, and obviously kids do mathematics here, so they can be engineers and chemists and other things. But once you pass all the levels of using maths, what does a mathematician do?

Satyan Devadoss:
That’s a great question. To me, the most poisonous. Word in the sentence you had just mentioned is used. Of course.

John Dickson:
I knew you were gonna say that, but

Satyan Devadoss:
To me, I mean it, it’s, if I think of a marriage or think of my children, think of my friendships and say, oh, our relationship is great ’cause they can use you to do something. It’s like you’ve just deprived the joy out of that thing. Right? So I think math, the fact that math is actually useful is quite stunning to me. Because I am not interested in the world. I’m just playing in my own mind, right? And so all of a sudden an engineer’s like, oh, I like what you’re playing with. Can I take some of those tools and bring it to engineering or bring it to the real world? Oh, you mean people actually care about this and science? It’s amazing. And so there have been papers written about the fact that mathematicians take an idea and do whatever they want with it, generalise it, and ask ridiculously unrelated, useless questions to the world, but incredibly beautiful questions to a mathematician. And it turns out that that kind of question asking i kind of parallel. This is stunning to how the world is working. And so the fact is, as you keep going more and more in abstraction, you still find connections. So let me give you a simple example. You could, um, take the Rubik’s cube or just a simple cube mm-hmm.

John Dickson:
Which you have over there.

Satyan Devadoss:
Yeah. And then you could, uh, you could look at symmetries of the cube, for example. If I rotated a little bit, kinda looks the same. If I, if I color the cube in different ways, like a Rubik’s cube would, if I rotate a cube four times. It comes back to the way it was before, right? And if I rotated, uh, maybe in a different axes, four times, it comes back. So you could, you could rotate in different combinations and see what it’s doing, and you can keep track of how the colours change as you rotate and the x, y, and z axis in different ways. And you can keep track of a multiplication table of all the ways colours change. Great. Mathematicians were kinda interested in this and then they said, you know what? Why are we talking about a cube? This multiplication table of weirdness is actually what the structure’s about. What if we come up with rules from multiplication tables of just random symbols? Like A times B times C equals B times C times D square?  Just some abstract with some rules, right? Just what if we come up with the, there’s some rules for the cube. What if we do this generally? And we came up with something called group theory, like abstract algebraic systems. And the physicists first said, well, we like the whole thing about the cube thing ’cause it’s really important to us. And chemists were saying, well the structures of these other shapes are good for proteins and you know, these structures we’re building. These abstract rules of silliness. You’re just coming up with a study of the rules, not the studying of the object. It feels useless and it turns out about 150 years later, this became the foundation of quantum mechanics when Einstein was keeping track of particles and how they interact it turned out that group theory was the way it interacted. So this thing that you would think you’re just doing in incredibly silly things to it becomes, again, comes back down again.

John Dickson:
And yet that isn’t the justification of the doing.

Satyan Devadoss:
Exactly. That’s the utility is not what drives us right now. It might be nice to say if I’m, if I’m trying to get a grant from the government or something, right, just to say, Hey, mm-hmm This impact we’re gonna make is something bigger, but most of the things we do is for the sake of ourselves. So what does a mathematician do? So in my classroom, my job is one of two things. One is to cover the topic at hand. So if it is about group theory, to tell the students about how to build their own groups and how to play with this, and a little bit of history, and if it’s about calculus or all these things, that’s one. But the second thing is to give them an in, like instill in them what, how a mathematician thinks. So if I’m, if the goal is to teach them how to do something, it turns out YouTube videos or computers, all these things, you know, books are written exactly for this thing, but this installation of the sharing of joy through an embodied experience like you are in watching me perform, you’re, I’m giving you worksheets designed to curate the questions you have. I’m trying to answer because I’m not trying to just tell you how something is working. I’m telling you why we thought of it this way in the first place. And that comes because we as humans are curious. So you can ask me like, what are you curious about in math? I’d be happy to tell you all those kind of things. But in general, we’re just curious about things. And you could talk about curious about chapstick. Oh my gosh, my chapstick keeps cracking. I wonder if there’s a way that could last if I forget about my Chapstick in my backpack. Five, you know, five weeks. If I come back, maybe it’ll still be fresh to use. So you can be curious about those questions. I am absolutely curious about shapes. I love pictures, and I love to draw. So all of my mathematics is asking me about questions about shapes and finding truth statements there.

John Dickson (Studio)

The more I sat and talked with Satyan, the less I felt triggered by this subject I hated at school. I wish I’d had him as a teacher! It turns out, there’s more philosophy in maths than we usually recognise. 

Satyan Devadoss:
So, uh, let me, let me give you a rough idea of how I think mathematics works. Most people think mathematics is related to the sciences. You know, you, you have a department, department or a division, mathematics and the sciences, right? You have humanities and the arts. And to me, I don’t think they don’t belong to each other at all. To me, science is deeply connected to nature and you’re asking questions about the natural world, physics about physical things. About chemical things, biological things, and, and, uh, wonderful math is simply caring about truth. That’s it. So it has actually, the things we study in math are not real. Like if, if you, somebody says, let’s consider a triangle. Triangles don’t exist in the world. It’s not infinitely thin. You have nothing called perfect sides and perfect lines and perfect angles, right? It’s completely make-believe. So math actually comes from the world of philosophy. Philosophers, were interested in truth and logic, right? You’re making these amazing arguments. Socrates, much so, I mean, go back to India and China, the deep thoughts, but. And then instead of dealing with issues of death and friendship and love and mercy and incredibly hard questions, you ask things about numbers and primes and triangles, you ask much simpler sillier questions. And because you’re asking simpler questions, you could make a lot more progress in it. So now instead of talking about whether euthanasia’s good or if it’s healthy, or you know, like these deeper philosophical questions, one way or the other, you could actually prove that the sum of the angles of a triangle is 180 or you know, like these handful of things like this. So mathematics is, is in the line of philosophy and neither one, in some sense is directly interested in nature. Of course nature’s there and you can get motivated by it. So to me, what mathematicians do, we’re just pr, we’re just truth seekers. That’s all we want. 

John Dickson (Studio)

Satyan is motivated by the beauty of mathematics. And he’s not the first. More than two thousand years ago, Indian scholars studying poetry noticed a remarkable numerical pattern while analysing rhythms of long and short syllables. Over the centuries, other mathematicians refined it into the famous sequence where each number is the sum of the previous two:

1, 1, 2, 3, 5, 8, 13, 21…

Most of us know it as the Fibonacci sequence. But that’s a little unfair. It was described in India centuries before the thirteenth-century Italian mathematician Leonardo of Pisa made it famous in Europe. Ever since, mathematicians have found this elegant sequence turning up in all sorts of unexpected places—from pure mathematics to patterns in the natural world, like sunflower seed spirals and pinecones. There’s the point. Mathematics isn’t just about solving practical problems. Sometimes, it’s about discovering beauty and reality, and beautiful realities. One of those beautiful realities was noticed by the great German astronomer and mathematician Johannes Kepler. He realised that if you divide one Fibonacci number by the previous one — 13 by 8, 21 by 13, 34 by 21, and so on — you keep approaching the same remarkable number:

1.618033…

Mathematicians call it “Phi”, or the Golden Ratio. It’s one of those strange discoveries that feels more like uncovering something than inventing it. Artists, architects and designers have been fascinated by Phi for centuries. It’s even been suggested that the Mona Lisa was composed around the Golden Ratio—though we’ve got no one to verify that. Ditto claims about the architecture of famous buildings like the Parthenon or the Taj Mahal. Whatever the case, mathematics keeps revealing elegant patterns that no one expected to find. Which brings us back to Satyan. For him, mathematics isn’t just a tool for building bridges or writing computer code. It’s a way of glimpsing the deep order of reality.

John Dickson:
You have written the full splendor of mathematics is so glorious, so majestic that we are all children when it comes to exploring it. It almost sounds religious.

Satyan Devadoss:
It it is, it is the foundation of so many machines that both move the economy and give our life some form of semblance of happiness for a little bit, right? The newest iPhone is based on foundationally mathematics, which influences engineering, which influences, right? And eventually we have this like technological wonder in our hands. And so we love mathematicians ’cause they feed our addiction to these toys we have. So having said that in one piece, that’s one thing, but the second piece is that there’s this notion that you must be good at math today in order to be employed. So there is incredible pressure from families, from parents and from kids on themselves to be good at math and it always  cracks. And let me let tell you what I mean by that. The second thing that happens when people meet me, other than telling me that I’m smart, is telling where they failed. It truly feels like I am a priest and I’m listening to confession, right? Oh my gosh, you’re a mathematician. You must be smart. Let me tell you, I was good in algebra, but I stopped the geometry. I mean, everybody can know. The day their life in mathematics ended. This is not true for English, for literature. This is not true for, what is the last history class you took? Oh, I don’t know. Cold War? Or was it, you know, was it the Civil War? Like, what was it? European? I don’t remember, but like, what was the last math classOh, I remember May 17th. I turned in that final exam and I will never, you know, and so there’s this, there’s this painful thing, so I, I always think of this as math and trauma. And the way you deal with this trauma is to realize that you failed at this, at climbing this mountain, right? Like, oh, the mathematicians are able to do it, but I’m not able to climb. I, I’ll tell you exactly where, up on the mountain I was able to climb to. I, I got to calculus and I stopped. I got to differential equations and I stopped. Even those who got doctorates- I got a PhD, but I didn’t become a professor, and I didn’t publish that many paper. And there’s always this notion of failure and my, there’s two ways of handling this from a teacher perspective, right? Which is one, encourage them and say, no, no, no, no, you are great, but I don’t believe in this because, uh, my way of encouraging it is to say, I agree with you. You have failed in math. But I want to then encourage by saying, but so have I. Because it’s almost as if somebody can say to Mount Everest, I fully get this mountain now .That’s ridiculous. At the end of the day, you might be at base camp and I may be four feet above you, but compared to the beauty and the wonder and the splendor of what math is, we are nothing. So it’s almost like somebody saying, I finally get God. Then you just know either their God is nothing. It’s a foolish God, or they’re foolish, like something’s up. And I know having looked at math enough, it is incredible. It’s beyond us. And anything you solve. If you think about this in your own life, John, any problem that you’re able to understand and go, oh my gosh, if I used this tool for it, I’m able to get it. The moment you’re able to solve something, it it allows you to ask 10 new questions you’ve never asked before. Solutions don’t close the problem up. They open it to more problems. So most of the ideas in math people think are, oh, it’s this finite kind of a field. And at the end of the day, you’re gonna figure it out. But it’s just the opposite. It’s vast and infinite. We’re just scratching the surface.

John Dickson (Studio)

So, primary school beginner or PhD brainiac, we are all tiny sailors on a giant sea of numbers. And it’s a very ancient story …  Stay with us!

Break

Media – Hidden Figures

John Dickson (Studio)

There are lots of great maths films—A Beautiful Mind, Good Will Hunting, The Man Who Knew Infinity. This is another recent one. Hidden Figures, the true story of the brilliant Black American women mathematicians whose calculations helped launch the early space age, despite working in a segregated NASA. Those women helped make possible everything from John Glenn’s orbit of the Earth to the Apollo missions that eventually took Neil Armstrong to the Moon. That’s just one recent chapter in the remarkable history of maths. The history of maths is crowded with giants. Around 3000 BC, the Babylonians developed base-60 arithmetic—the reason we still divide hours into 60 minutes, and circles into 360 degrees. Ancient Egyptians mastered fractions, areas, and volumes. In India, the seventh-century mathematician Brahmagupta gave the first systematic rules for treating zero as a number in its own right. In China, the fifth-century mathematician Zu Chongzhi produced the best approximation of pi the world would see for almost a thousand years. The Greeks gave us Pythagoras, Euclid, and Archimedes. Contrary to popular myth, Christian scholars preserved, developed, and transmitted this classical tradition – we have the receipts in people like John Philoponus in sixth-century Alexandria, and Hunayn ibn Ishaq, the Syriac Christian scholar in ninth-century Baghdad. Muslim scholars then took this combined Classical and Christian inheritance and supercharged it in what can rightly be called the Islamic Golden Age. One of its greatest mathematicians was Muhammad ibn Musa al-Khwarizmi, whose work gave us algebra. The word algorithm even comes from his name. Then Europe produced thinkers like Nicole Oreme, Isaac Newton, and Gottfried Wilhelm Leibniz, laying the foundations of modern science. But this brings us to the Enlightenment. And Satyan reckons something unhelpful happened at this point.

John Dickson:
You’ve said that the enlightenment wrongly divided the intellectual world between science and they put maths there. And art and music. Poetry. What’s wrong with that?

Satyan Devadoss:
In one sense it is incredibly important because it has given me a job, right? Like it has allowed me to live in my own corner. So the problem with, I think if you pull back to a certain degree, I think of the problem with enlightenment is not the division of these pieces, because as we get deeper and richer and, uh, stronger in understanding. Nobody can be a full generalist, right? We’re not there anymore. Everything is so deep that I am not good at math. I’m not good at, I’m just good at the speck of a speck of a speck of a problem about mathematics, right? So the enlightenment kind of brought division here. The thing I disagree with. The enlightenment is the weighting of the system to say that, okay, I, I, I get it. This is what a musician does. And this is what an artist does, and this is what a mathematician does, but the mathematician’s better. 

John Dickson (Studio)

It’s not exactly that the Enlightenment raised mathematics up. It divided it from other things – like music, philosophy, poetry, and theology – and then demoted those other things as not really belonging to the ‘truth’. The earliest scientists, like Galileo, thought philosophically and theologically, as they went about their maths. “Nature is written in that great book which ever lives before our eyes … it is written in the language of mathematics.”  Early scientists believed in two books of truth – the Bible and Nature. After the Enlightenment, thinkers like Bertrand Russell talked like there was only maths. Ultimately, if you can describe the universe mathematically, you have explained it – and so explained away the need for a Creator. Did maths kill God? We’ll be right back. 

Break

Media – Hitchhiker’s Guide to the Galaxy

John Dickson (Studio)

Yep …  The Hitchhiker’s Guide to the Galaxy – and author Douglas Adams’ answer to life, the universe and everything. A number. Incidentally, Director Mark tells me that Adams chose the number 42 because he said it sounded funny. But it’s a punchline with serious implications because it suggests that mathematics is the ultimate answer to life, the universe and everything. There are serious versions of the same idea.

John Dickson:
Stephen Hawking, who was pretty good at maths. He, he sort of felt maths did away with God cause we can explain all the things. Mm. Mathematically. Therefore, in the beginning was maths not God. I happen to know. You don’t really buy that. Yeah. Line of reasoning. Why not?

Satyan Devadoss:
Well, I remember the last book that, uh, Hawking wrote, if I remember correctly, it opened with a preface. It simply said, philosophy is dead. And I found that absolutely hilarious because that’s a philosophical statement, right? So he’s, he’s claiming philosophy is dead by talking about a philosophical. So this is, again, this issue of the Enlightenment that I have a struggle with. True, Hawking was brilliant talking about black holes, cosmology, and the mathematics needed to understand those things. Stay in your lane. The moment you leave that lane and say, I can also play the role of a historian to understand how the world works, I could play the role of an anthropologist to talk about how humans are thinking about, I could play the role of a linguistic scholar to see how the great text in the world, whether it’s the Quran or the Bava Gita, or the Christian Letters of Paul to the brilliant Hebrew narratives that we find, like all, all of that can be explained in math, tells you that this person has no clue about this great spread and but the enlightenment has shattered him into his own discipline, that he’s just naval gazing it. To say that a cosmologist can understand these other [00:22:30] disciplines is ridiculous. And so I, I would love to have Stephen Hawking say it. You know, actually, I have worked about 30 years of my life really focusing on history and the historicity of the resurrection. Something that I, and here are some reasons, let me tell you why, but that’s not what he did. You just wave your hand. Why should I trust Stephen Hawking as a cosmologist who studies black holes to tell me about literature? And so to me, that doesn’t drive me at all. That’s number one. The second thing, mathematically, mathematics isn’t interested in the world. It’s just interested in creating our own structure and patterns of what truth is right within the rules that we come up with. For example, when I draw a curve, and I say, how does the curve change over time? Well, that’s a mathematical principle, the derivative. But that curve is an arbitrary, abstract concept. You could say, well, the hill can be approximated with a mathematical curve. So this notion of like pulling things from reality and bringing it into the math world, that’s what we do. And so all of a sudden, Stephen Hawking has the power, or someone has the power to talk about the notion of forgiveness, the notion of wonder, the notion of tears, the notion of fear, the notion of death, and these huge ideas that artists have struggled with, the poets cannot express except through small chips of many tweaks of, you know, poems and their words. If you look at the sonnets of Shakespeare, right, it’s playing off of some of these incredibly complicated ideas, funny ideas, goofy ideas, gorgeous ideas. And so I find that very weird, uh, to be able to wash all that away because you are really good at understanding black holes.

John Dickson (Studio)

Let’s press pause. I’ve got a five-minute Jesus for you. There’s not much maths in the Bible. A Galilean Jew like Jesus probably didn’t have mathematics lessons as a boy—unlike Jews in places like Alexandria in Egypt. Philo of Alexandria, who lived at the same time as Jesus, certainly studied mathematics at school. But numbers were still important to ancient Jews—and to some biblical authors. I may have mentioned before the amazing number symbolism in the book of Genesis. The all-important number seven is everywhere. Seven was the number of perfection—the divine. The opening sentence has seven words in Hebrew. The crucial phrase “And it was so” appears seven times. The words “and it was good” also appear seven times. The whole chapter is structured around seven days—or seven scenes. Then the multiples of seven keep coming. The word God occurs thirty-five times—that’s five times seven. The two halves of the created order—earth and heaven/sky—each appear twenty-one times, or three times seven. And so on. Then there’s a whole class of number plays—as distinct from word plays—called gematria, the Aramaic form of the Greek word geometry. The idea is simple. In Hebrew and Aramaic, letters also function as numbers. The first ten letters of the alphabet stand for the numbers one to ten. The next nine stand for twenty, thirty, forty, and so on up to one hundred. That means any number can be written with combinations of letters. It also means every word has a numerical value. And numbers can stand in for words. One cool possible example is the most famous number in the Bible: 666, in the book of Revelation.

Reading

He required everyone—small and great, rich and poor, free and slave—to be given a mark on the right hand or on the forehead. And no one could buy or sell anything without that mark, which was either the name of the beast or the number representing his name. Wisdom is needed here. Let the one with understanding solve the meaning of the number of the beast, for it is the number of a man. His number is 666.

Revelation, Chapter 13

John Dickson (Studio)

Many scholars have pointed out that 666 may be a gematria reference to the emperor Nero. The great Revelation scholar David Aune writes: “If the name of ‘Nero Caesar’ is transliterated into Hebrew from the Greek to form nrwn qsr, the numerical value is 666: nrwn = 306 plus qsr = 360, making 666 … And (Aune says) most scholars agree that this is the most likely solution.” My favourite example, though, is in the opening of Matthew’s Gospel. It probably seems pretty boring to us that Matthew begins with a long list of names—a genealogy—from Abraham, to King David, to Jesus. By the way—and I don’t mean to pick on my American friends again—but the word is genealogy, not geneology. It’s an a, not an o. That’s just for free today.

Anyway…

Matthew divides his genealogy into three groups of fourteen generations, all hinged around King David.

Reading

This is a record of the ancestors of Jesus the Messiah, a descendant of David and of Abraham:

Abraham was the father of Isaac.
Isaac was the father of Jacob.
Jacob was the father of Judah and his brothers.
Judah was the father of Perez and Zerah (whose mother was Tamar).
Perez was the father of Hezron.
Hezron was the father of Ram.
Ram was the father of Amminadab.
Amminadab was the father of Nahshon.
Nahshon was the father of Salmon.
Salmon was the father of Boaz (whose mother was Rahab).
Boaz was the father of Obed (whose mother was Ruth).
Obed was the father of Jesse.
Jesse was the father of King David.
David was the father of Solomon (whose mother was Bathsheba, the widow of Uriah).
Solomon was the father of Rehoboam.
Rehoboam was the father of Abijah.
Abijah was the father of Asa.
Asa was the father of Jehoshaphat.
Jehoshaphat was the father of Jehoram.
Jehoram was the father of Uzziah.
Uzziah was the father of Jotham.
Jotham was the father of Ahaz.
Ahaz was the father of Hezekiah.
Hezekiah was the father of Manasseh.
Manasseh was the father of Amon.
Amon was the father of Josiah.
Josiah was the father of Jehoiachin and his brothers (born at the time of the exile to Babylon).
After the Babylonian exile:
Jehoiachin was the father of Shealtiel.
Shealtiel was the father of Zerubbabel.
Zerubbabel was the father of Abiud.
Abiud was the father of Eliakim.
Eliakim was the father of Azor.
Azor was the father of Zadok.
Zadok was the father of Akim.
Akim was the father of Eliud.
Eliud was the father of Eleazar.
Eleazar was the father of Matthan.
Matthan was the father of Jacob.
Jacob was the father of Joseph, the husband of Mary.
Mary gave birth to Jesus, who is called the Messiah.

John Dickson (Studio)

And just in case we missed the pattern, Matthew concludes in verse 17: 

Reading

All those listed above include fourteen generations from Abraham to David, fourteen from David to the Babylonian exile, and fourteen from the Babylonian exile to the Messiah.

John Dickson (Studio)

Did you hear that? Fourteen. Fourteen. Fourteen. Why is that important? Especially since every reader of the Old Testament knows Matthew has deliberately omitted several generations to make the numbers come out exactly right. The answer lies in one of Matthew’s great themes: Jesus is the promised descendant of King David who would, according to the Old Testament prophets, rule forever. The name David is spelled with three Hebrew letters: Dalet, Vav, Dalet. Those letters are also numbers: 4. 6. 4. Even my primary-school mathematical brain can work out that 4 + 6 + 4 = 14. Matthew’s repeated emphasis on the number fourteen is really an emphasis on David. Jesus is the fulfilment of all the hopes attached to David. I’m not making this up. The great Matthew scholars Davies and Allison write:

“In a genealogy of 3 × 14 generations, the one name with three consonants and a value of fourteen is also placed in the fourteenth spot. When one adds that this name is mentioned immediately before the genealogy (1:1) and twice at its conclusion (1:17), and that it is honoured by the title ‘king’, coincidence becomes effectively ruled out. The name David is the key to the pattern of Matthew’s genealogy.”

Matthew takes the simple historical fact of Jesus’ descent from King David…and turns it into the anthem of his genealogy. You can press play now.

I spoke to John Lennox last week for an upcoming episode about his extraordinary life. But, given he also happens to be a professor of Mathematics at the University of Oxford, I thought I’d throw in a kind of ‘phone a friend’ for this episode. John, as usual, was a good sport! 

John Lennox:
Is mathematics discovered or invented? The answer to that is a resounding yes. I really think it’s both and both from a practical experiential point of view and from a Christian perspective. God the Creator has done something rather remarkable. He has put together in one entity both intelligence and consciousness, and he has made us in his image and part of that image is the capacity to create. In the world of ideas, in the world of machines, in the world of art and music, literature, everything else. So on the one hand, I’m with the famous Paul Urdosch, one of the most prolific mathematicians that ever existed, who’d turn up on every mathematician’s doorstep and he would knock the door, and he would smile and say, ‘My mind is opened’ he would immediately be invited in because everybody knew that before he left the house he’d have written a joint paper with that person and therefore increased their academic output. So that we have this wonderful concept of an Urdush number. If I write a paper with you, and you’ve written a paper directly with Urdush, my Urdish number is two, which it is actually, but the paper wasn’t written with you. So Urdish used to say of all mathematics, ‘it’s in the book, it’s in the book’. That is, we are discovering something that’s actually there. And I think that was the impression of many of the brilliant pioneers of mathematics and physics, particularly Newton and Kepler and others. The phrase thinking God’s thoughts after him, that the amazing thing about mathematics is it appears to work. It appears to be describing something out there that is independent of your brain or mind, so that the study of it becomes an internationally agreed phenomenon in a sense, and it was so impressive to people like Einstein that he formulated it by saying the most incomprehensible thing about the universe is that it’s comprehensible. I share that. I think the mathematical describability of the universe is one of the evidences that this is a word-based universe, as I would say is the genetic discovery of the information-carrying macromolecule DNA. This is a word-based universe. And that resonates with in the beginning was the word or the simpler language of Genesis, and God said, a word-based universe. 

Reading

In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. In him was life, and that life was the light of all mankind.”

Gospel of John, Chapter 1

John Lennox:
…and we have the evidence of it out there. But in that, in our exploration, and after all, I think it’s not just a straw in the wind, but the fact that God who created the universe started biology off and indeed started science off, according to the Genesis record, by telling humans to name the animals. And that discipline of taxonomy as common to all intellectual activity is a very good indicator because, strikingly, in the book of Genesis God names several things: the heavens, the earth, the sea. And the fact that he doesn’t name everything means this is a job for you humans to do. Be creative. Get on with science and all the rest of it. So I do feel not because I’m an Irishman, but because I perceive it that way, that it’s both and rather than either or. And what human minds come up with has to be tested in some way against our perception of reality. And of course, that goes to the heart of science. If you do not believe that the universe is in some sense independently ordered and not by you, you’ll never do science because science has that built-in assumption that the universe is going to be at least in part rationally intelligible. So that for me actually comes to form a solid base for theism.

John Dickson (Studio)

Satyan took our conversation in a different direction. He isn’t convinced maths points to God – not because maths is too powerful to leave room for the divine, but because maths is too weak to find God. Maths deals with simple things; science deals with complex things; philosophy and theology deal with the most significant things. It’s things outside of maths that deal with our embodied life – those are more likely to point the way.

 

Satyan Devadoss:
When I was a kid, I lived, I was born and raised in India, and I came to the States when I was around seven or eight years old. And around nine or 10 when we finally had, we were able to afford a tv, I was watching it as a kid, we would watch, um, maybe a half an hour of Sesame Street where they would have these puppets talk about, you know, the letter A and the letter B and the letter C and the numbers and all these different things. Maybe talk about how the postal system worked and all these things. And then we would have Mr. Rogers ‘ neighbourhood, and he would come in and he’d take off a sweater and sing a song as he took off his shoes. And for the whole half an hour, I learned nothing. Like this guy wasn’t talking about letters or numbers.

John Dickson (Studio)

Just for our non-American listeners, Mr Rogers’ Neighbourhood is a children’s show hosted by Fred Rogers that ran from 1968 to 2001 – 912 episodes over 31 seasons! It was a gentle, thoughtful children’s show that treated kids like intelligent people … most kids wanted to be Mister Rogers’ neighbour. Satyan wasn’t sure back then. 

Satyan Devadoss:
He’s talking, he’s he moose. Well make believe, land of puppets, and they talk. I don’t even, oh my gosh. It just felt like a waste of time. Whereas at least for the first half an hour I was getting something. And I say this because in my forties I finally realised what was going on. Sesame Street was giving me information, but Mr. Rogers was dealing with emotion. He’s saying, ‘I’m going to deal with loss. What if your parents are going through a hard time? You know what’s gonna happen if you turn on the channel and listen to me. I’ll be faithful to you. I will always put on a sweater. I’ll always take off those shoes. I’ll be here over and over again if the world is shaking. You could trust me to do the same actions.’ And I say that because the amount of measurable movement of knowledge was almost nothing for Mr. Rogers. But the depth of emotion and faithfulness he’s able to come with is off the charts. ’cause he’ll, he’s dealing with something far more complicated. So, as somebody again who yelled at Stephen Hawking a little bit and picked on this genius, I do wanna say that I don’t wanna put myself in the shoes by saying I finally have some tools to defend God. Those aren’t my tools, those aren’t my toolkits, but the reason notions of faith and notions of something bigger are exciting to me. It is because science doesn’t deal with anything outside of this world. It is only designed to measure things in the world. Math makes its own world, so that’s not it. But linguists, historians, artists, musicians, and my own life and my friendships- this embodied life that we live, those are other pointers to far more complicated than beautiful things.

John Dickson (Studio)

It’s a lovely thought, actually. He’s saying embodied thought and experience – over pure intellect – are more likely point toward a Creator God, a God that purposed matter and our bodies themselves. 

Satyan Devadoss:
I guess I would say that the reason that I’m putting my chips in the theist bucket is not because of mathematics, but mathematics does have confirmation towards many of these things.

John Dickson:
Okay. I’m really interested in that. Right. Yeah.

Satyan Devadoss:
So in some sense, when I, when I see going back to maybe the earlier conversation we were having about the fact that. The scientists are worrying about questions of science and math makes its own world and we’re un not interested in science at all. We might be motivated by it, but uninterested and as both of these unrelated worlds pursue their own adventures, you would think that they would start in the same point, but move to very far off corners, right?  Like I’m becoming more and more unrelated. In fact, the more maths you do. The more you cannot relate to the scientist ’cause we both started by talking about the cube, but we’re asking incredibly different questions about it. And the scientist is stuck in three, maybe four dimensions of space and time, maybe 11 dimensions of strength theory. But mathematicians are not interested in 11. We can talk about 800 dimensions without batting an eye. Right? Dimensions are, are not related to the physical world. They’re constructs we make. So naturally, my students and I always think about 800 dimensions and see what happens. That’s, that’s not a weird thing for us. So you would think that the balls rolling down the hill would land at two very different spots, but the balls continue to be parallel. So it’s interesting that even after 150 years, Einstein is asking some questions that mathematicians are going, ‘oh, we’ve been thinking about that’. So this connection between the real world and the mathematical world is fascinatingly close to one another. And so to me there’s, that’s something really interesting. I could. That’s something interesting that moves me to say that something else is going on. Now to say that, would I then say, well, clearly it has to be theism and there’s a God isn’t enough. But, there are these pointers, right? And also the pointers, I would say another pointer is, um, it’s this notion of kind of glory. That there’s something bigger than us. I think a theist might say, maybe a, a Christian might say like, you know, you are, you’re called to worship something. There’s, you know, we’re just created beings. And when you are able to get glimpses of the beauty and the glory of mathematics, oh my gosh, you are close to seeing the face of God. It’s the closest I can say it’s, I could see the, this movement is, is [00:33:30] being at a phenomenal football game with a hundred thousand people cheering on or at a concert and you’re crying because this event that is happening. It’s beyond you, right? It’s, it’s you’re, you’re involved in a bigger process of community and I would say this notion of coming up with a new mathematics that’s never existed before, this notion of a new creation, one could say co-creating, right? One could say, you know, you’re, you’re bringing with the part of the community of mathematics, you’re creating something else that’s a different taste of glory. That’s like listening to the, your favorite album and then crying in the car, right? Or holding a baby for the first time or enjoying ice cream and a meal with friends and remembering that again, or, you know, any one of those glorious high points in life or just a vacation. Those phenomenal. I think that’s, that’s the best of those is how I’d attribute to creating new mathematics. It is glorious to me, it is appointed to something bigger.

John Dickson (Studio)

Albert Einstein knew a thing or two about maths. Like Satyan, he didn’t really think maths pointed directly to God … but he agreed it was a little spooky and points to bigger realities. I quoted Satyan earlier … “The full splendour of mathematics is so glorious, so majestic that we are all children when it comes to exploring it.” Einstein made exactly the same point in his 1929 interview with the great journalist and author George Sylvester Viereck. It’s a fun read, because Viereck talks about making his interview subjects squirm until they gave up their fundamental philosophy. Einstein’s reply is awkward but beautiful. It seems a fitting place to end.

Reading

“Your question is the most difficult in the world. It is not a question I can answer simply with yes or no. I am not an Atheist. I do not know if I can define myself as a Pantheist. The problem involved is too vast for our limited minds.

“May I not reply with a parable? 

“The human mind, no matter how highly trained, cannot grasp the universe. We are in the position of a little child, entering a huge library, whose walls are covered to the ceiling with books in many different tongues. The child knows that someone must have written those books. It does not know who or how. It does not understand the languages in which they are written.

“The child notes a definite plan in the arrangement of the books, a mysterious order, which it does not comprehend, but only dimly suspects. That, it seems to me, is the attitude of the human mind, even the greatest and most cultured, toward God.

“We see a universe marvellously arranged, obeying certain laws, but we understand the laws only dimly. Our limited minds cannot grasp the mysterious force that sways the constellations.” – Albert Einstein

Undeceptions theme