Ideas - 4 is a rule maker and rule breaker | The Greatest Numbers of All Time

Episode Date: June 26, 2026

From the medicine wheel to the building blocks of DNA, the number four has represented structure and stability. But four is also a troublemaker: a portal to realms like the fourth dimension. Our series, The Greatest Numbers of All Time explores how the number four helps us understand the world — both by making the rules, and by breaking them. More in the series:Listen to The Curse of 13Listen to 12 is SublimeListen to 27 Club LoreListen to The 33,000 Horsepower GamechangerGuests in this episode:Joyce Perreault is an Ojibway Anishinaabe children's book author and elementary school teacher at Donald Ahmo School in Crane River, MB.Brian Katz is a composer, instrumentalist, improviser, and guitar instructor at University of Toronto and York University.Lauren Fink is a professor of cognitive neuroscience at McMaster University.Alex Fisher is a professor of musicology and area coordinator for early music at the University of British Columbia.Tyrone Ghaswala is an assistant professor teaching stream with the Centre for Education and Computing (CEMC) and an adjunct professor in the Pure Mathematics department at the University of Waterloo. Wenran Jiang is the founding director of the China Institute at the University of Alberta. Stephan Reuter is an associate professor for plasma physics and spectroscopy at the Engineering Physics Department of Polytechnique Montréal Sarah Hart is professor emerita of mathematics at Birkbeck College and author of "Once Upon a Prime: The Wondrous Connections between Mathematics and Literature."

If you sold somebody a loaded gun who you knew was in a vulnerable state and they shot themselves. I think it is murder. Just because you're using the internet doesn't mean you get away with murder. I'm Damon Fairless, host of Hunting Warhead. This season, I take you inside the business of suicide, and the places desperate people go when they can't find what they need in the real world. Hunting the Suicide Salesman. Available now wherever you get your podcasts.

This is a CBC podcast. Welcome to Ideas. I'm Nala Ayyed. As a percussionist, how do you feel about 4-4-Time? It's fun to play. 4-4-time. It's the most popular time signature in Western music. One in three tend to be stronger beats, 2 and 4, these backbeats. So much so that we refer to it as common time. 4-4-4-time is great for me.

many, many things. It creates a very specific feel. For those of us who grew up immersed in it, 4-4 is familiar and reliable. 4-4, I think, gives us a sense of stability because the even subdivision. It's symmetrical, if you want to think of it that way. And the same is true of the number four itself. It's got that balance, it's got that symmetry, that literally squibrate. awareness. But for all its reliability, four can take us to some unexpected places. Within 4-4, just by changing how you syncopate something or changing the rhythmic layers you have, you can really

create so many different feels. We can instinctively feel what 4 is about, but then it's a tipping point that takes us to the beginning of something more complex. The attitude, Towards the number four actually changes over the centuries and is very different now than it was 700 years ago. Ideas producer Annie Bender brings us this installment in our series on the greatest numbers of all time. Are you ready to go? Is this cool? Okay.

We're calling it Rulemaker, Rule Breaker, the wondrous number four. For people who don't have the music background at all, how would you explain what 4-4 time actually is? So imagine that you're listening to music. It's got a nice little beat like just think about where you might want to bob your head to. So this feeling of wanting to move to the music or how your mind is sort of organizing the music

is what we might call musical meter. Hi, I'm Lauren Fink. I'm a professor of cognitive neuroscience here at McMaster University. It's something that actually a composer might notate. and there are many meters, so 4-4 is just one meter. 4-4 may be one of many, but this rhythmic structure, 4 beats to a bar, has become so ubiquitous that for many of us, dividing music by 4 feels instinctive. It feels like it's part of the music.

So even when there might not be an acoustic event, meaning like hitting on a downbeat of 4-4-time, we still perceive a beat in our minds even when it's absent. When we hear complex rhythms from other cultures, we still tend to impose a 4-4 on it, even though it might not be how people that grew up in those traditions think about the music. In our culture, 4-4 is very much everywhere on the radio

and in a lot of classical music too. And so we're pretty good at imposing this 4-4 grid on things. And this affinity for 4 extends far beyond the drum kit. We like to divide things into fours. In ancient Greece, it was believed that there were four elements that made everything, earth, air, fire and water. And then maybe our temperament as a person, our moods, were explained by the four humours that we had.

My name is Sarah Hart. I'm Professor Emeritus of Mathematics at Birkbeck University of London and Fellow of Gresham College London. We've got the four corners of the world, the four winds. There were four rivers of parliaments. paradise traditionally. It seems to be a way that we instinctively want to categorize different types of object of concepts. In fact, an instinct for four seems to be written into our biology. So if you show someone a picture with just a few dots on it, if there are four dots,

you instantly, no, you don't have to count even. You can just see that there are four. So we can somehow instinctively, without even counting, we can recognize the number. one, we can recognize two, three and four. But above that, we have to start counting them. We have less of an instinctive, instant appreciation for what the number is. The same phenomenon has been found across the animal kingdom, in monkeys, crows, even fish. In 1995, scientists at the Queen Mary University of London proved that even,

Even honeybees have an innate recognition of four. It's this transitional point, really, from instant understanding and grasp of what the number is intuitively, we just all know what a fourness feels like, to then bigger numbers that we start to have to count with our, perhaps the more intellectual side of our brain, the analytical side. We can see some dots and we can count them and say there are 12, but we can't see the 12ness straight away. But we can with four and smaller numbers. Four seems to hit a sort of sweet spot between complex information and simple intuition, which brings us back to four-four time. Lauren Fink. It's definitely in a sweet spot of working memory that we can hold four items in mind.

It's in a sweet spot of this duple or bipedal two-step feeling. And then I think four compared to two maybe allows for more playing around. It's giving you something else. Rather than just the duple feel, you have like kind of layers of that duple feel. Right. It's simple without being too simple. Exactly. I think as human beings, we like to categorize things,

but a simple binary is too simple. It doesn't give us enough nuance. So instead of just having winter and summer, we've given it a bit more subtlety and have four seasons. It's a doubling to get us a little bit more subtlety. but not so much that we start to not really hold it in our heads. You know, I bet most people will talk about night, day, but also twilight, you know, in dawn. So these liminal times that we get when we expand from a binary to a four

just gives us those transitional points that are often the most intriguing and entertaining. And the same thing with the moon, right? that's sort of four phases of the moon from new moon, then it's waxing and getting bigger, and then full moon, and then it's waning, and then back to new moon. Again, that's four. So we've got the extremes, and then we've got something in between, a market point in between, that gives us a little bit more subtlety and understanding. Small enough to grasp without effort, but big enough to keep us intrigued. It's no wonder that four has become such a powerful presence.

not just in music and not just in Western culture. In our belief, it's not just a coincidence that nature and human experience can be divided in the poor part sacred. Anin-bojo, my government name is Joyce Perot. My spirit name is Onagoschikonukkwe. I am Ojiboi, Nishnabe, and I work as a teacher at Donald Amo School

on Ojijakazi B, which is located in Crane River, Manitoba, and I teach Anishnaab M-O-N, kindergarten to grade 8. How do you say the number four in your language? Nijwin. In Ojibwe and Nishnabi culture, as in many indigenous cultures in North America, Nijwin, or four, is woven into everything. The number four is sacred to many Native Americans. There are four directions. four sacred plants, four times of day or night.

The number of order in the universe is four, the four elements, earth, air, fire, water. And there's emotions in the number four, too, mental, spiritual, physical, and emotional selves. And it always comes back to the medicine wheel as to why the number four is sacred to the indigenous people. Joyce Perrault published a children's guide to the medicine wheel in 2018. The book, like the Medicine Wheel itself, is full of fours.

The Medicine Wheel has four sacred colors, and each of those sacred colors has a meaning using the number four. The east is the yellow, south is the red, the west is the black, and then the north is the white. Every time we start talking about the medicine wheel, we always start with the east. And the reason why is because where does the sun rise? rises in the east and it always brings a brand new day. We live in a world where you can navigate by four directions and any combination of those will get you to anywhere, anywhere on the surface of the world. So it's really grounded.

It helps us really to position ourselves both actually, literally and metaphorically as well. Across time and across cultures. The number four has given us both a literal compass and a way to, order the world. Early Islamic thinkers said that the creators formed things into tetras, into fours. So you've got, for instance, yes, four elements that were then believed to be existing for humours, four seasons, four directions, four winds. But then everything in creation is one of four things.

So it's either a kind of inorganic mineral of some kind, that's one option, or it's a plant, or it's an animal, or it's human beings. So everything's one of four options. But we encounter this in everyday life as well. I mean, traditionally towns or cities, villages would be divided up into four areas or quarters. So we still get that word, you know, this quarter of a city, the Latin quarter, whatever. And the town square was once genuinely a square, you know, with perhaps four, roads leading out of it, but we still use that in our conversation. I actually looked up the word quarter in the dictionary this morning and it had 25 different meanings. So it's crazy.

25 meanings, one for every cent in a quarter of a dollar. Exactly. So we've got it in our coins and you've got the old Latin word for the army subdivision of quarter was quadra and from that we get the word squadron. So it's there in so many words and concepts that in some we don't necessarily become aware of and then we think about it. Oh, yeah. But these ideas and the fourfold division is so, so important to the way we think about everything. If we look past the English dictionary and Western pop percussion, beyond the beliefs of the Ojibwe Anishnabe, early Islamic thinkers and the ancient Greeks, we can find at least one more

prominent culture that relies on fours for structure. Guitar culture And if I'm going to sing a little something For strong winds that blow lonely Seven seas that run high All those things that don't change Come with me Great Canadian song

For Strong Winds by Ian Tyson Made famous by the great folk duel Ian Sylvia I'm never back this way. I'm Brian Katz. I'm a musician, guitarist, pianist, composer, and educator. I've got some friends that I could go working for. How important is the number four to the guitar?

It's very important in terms of the tuning. But we've been through this a hundred times or more. Four strong. Standard guitar tuning is defined by the number four. With just one exception, the strings are tuned in fourths, meaning they are all four notes apart in pitch. So we have a fourth between E and A, EFGA, we have A, B, C, D, C, D. We have D, EF, G, and then we have a major third, G-A-B, and then we have another fourth, B-C-D-E.

And according to Brian, it's that tuning that has given the guitar its classic open string sound. You know, the guitar before it was like a concert instrument. You know, its essential role was really an accompanying instrument where you're using chords. People call it cowboy chords, like in a cute kind of way. And everybody's heard like these simple chords, you know, CFG, right? People talk about rock and roll, three chords, etc. and a lot of folk music and just tons of music. And it's not just the chords.

There's something qualitatively very, very different than hearing those chords on a piano or a guitar. Because here I got the open strings. And the open strings are like, they're so attractive to the ear. Yeah, they're very harp-like. For strong winds that blow lonely, seven seas that run high.

All those things. If you've ever enjoyed a campfire sing-along, you can thank cowboy chords and the perfect force. I'll look for you if I'm never back this way. And given all the kumbaya moments that campfire circles bring about, you might say there's a harmonious quality to four, one that goes well beyond music. There's also this saying fair and square. It's almost like there's a sense of justice associated with four. Yeah. So in ancient Greece, the Pythagoreans had very much an association of four with fairness and justice.

And that came from their belief, which of course I agree with, that the universe is based on number. Everything in the universe is mathematical and it comes from mathematics. And so they had explorations that they made into music, for example. where they've found that you can make very pleasing combinations of sounds using the numbers 1, 2, 3 and 4. So music is all about the numbers 1, 2, 3 and 4. But then also 4 itself, it's kind of even more even, if you like, than the number 2. So 2 is the first even number and you can break two exactly in half, of course, and that's where we get binary concepts from. But 4 is doubly even. And they call it even, even. It's so even. You can break it up.

in twice two ways. And so it was associated with harmony, with justice, with fairness. So is that where the term perfect fourth came from? Does it stem back to Pythagoras and ancient Greek theories of four? Absolutely. I mean, the perfect fourth was considered to be one of the perfect mathematical ratios that was especially prized by ancient Greek theorists and continued to be prized by theorists and musicians of the Middle Ages. My name is Alex Fisher. I'm a professor of musicology at the University of British Columbia in Vancouver, B.C. The ancient Greeks had a very strong idea that music was kind of a sonic equivalent or sonic analog for the structure of the cosmos. And so the perfect fourth was one of those fundamental ratios that can be heard and appreciated

in music, but it can also be observed in the relationship of the sun and the planets in their respective orbits. For the ancient Greeks, four was the bedrocked. of the universe. It was the basis of the Pythagorean system of numbers that everything was based on the numbers 1 to 10, right? You can make them into a triangular form, 1 plus 2 plus 3 plus 4. If you sort of build those up in layers, you get this nice triangle, which they call the tetractus. And on the bottom, on the base of everything, holding everything up is this 4. And then you build the other numbers on top of it. So it's really absolutely instrumental. to how the world is put together

and how Earth is put together so that they believe that those four elements, Earth, Air Fire and Water, Earth was associated with a cube structure so they had a shape for every element. Earth was cube because you can stack cubes together. You can build things with cubes so that solidity of Earth is represented again

by this concept of four. Wow, four really becomes a building block in so many ways. Well, and the Greeks didn't know this, but actually it really is a building block even for life itself, because now we know the structure of DNA is built entirely of four things. There are four nucleotide bases, right, which are labelled A, C, G and T that pair up and make the double helix of DNA. So life itself is based on four. And yet, despite all the ways that four orders our world,

the so-called perfect fourth is a bit of a troublemaker. Over the centuries, the fourth became problematic and had to be disciplined in certain ways because it has certain properties and practical music making that make it rather difficult to use. Now, what was a common practice in the Middle Ages, people in the churches, they would spend all day singing Gregorian chant, which are just these single line melodies. No later than the 9th century, people realize that they could make their church music sound better by adding another voice to that chant. And so the simplest is.

if you double the musical line at the octave. The next most simple way of doing it would be to sing the same musical line at the interval of a perfect fifth. That works extremely well, but we begin to have a problem with the fourth. And the reason for that is if you think about the musical scale, A fourth between C and F is perfectly good. No problems with that. A fourth between the notes D and G is perfectly fine. A fourth between E and A is perfectly fine. But on the piano, if you are to play F with the white key B natural together, you get an awful sound.

And that is called the tritone. So the tritone is a particular flavor of the fourth that has actually a wider interval as opposed to the perfect fourth. And it sounds terrible. In the Middle Ages, they thought it sounded terrible. They actually called it the devil's interval. So from the Middle Ages on, engaging. with Floor was a dance with the devil. Theorists and musicians in the Middle Ages had strategies to eliminate the tritone and replace it with

a perfect fourth. In fact, the origin of the note B-flat is one of those solutions. Wait, they invented a note? Wait, you can't invent a note. They actually thought that you could invent notes. and that inventing a note was actually a rather daring thing to do. And in fact, there were no flat notes in this original scale. So we actually have the fourth to think for the fact that we have flats in the musical system to begin with because it was invented essentially in the 11th century as a way to conceptualize the musical system so that you could avoid that terrible interval.

And music isn't the only realm where four has proven itself a little less perfect and a little more subversive. Along with all these nice ideas like the four seasons and the four phases of the moon, we also have slightly scary ideas like the four horsemen of the apocalypse who come galloping in and bring chaos to the four directions by just seeding trouble all over the world. Pestilence and plague and war, you know, those bring us into the realms of chaos.

And if you open the door to the realms of chaos, anything might happen. How would you describe the personality of the fourth dimension relative to the other dimensions? Oh, this is like a black sheep kind of, yeah, dimension where things don't work as you want them to. at all. It sounds as though

four is about to break all the rules. Our documentary about the number four is from producer Annie Bender. This is Ideas. I'm Nala Ayad. If you sold somebody a loaded gun who you knew was in a vulnerable state

and they shot themselves, I think it is murder. Just because you're using the internet doesn't mean you get away with murder. I'm Damon Fairless, host of Hunting Warhead. This season, I take you inside the business of suicide, and the places desperate people go

when they can't find what they need in the real world. Hunting the Suicide Salesman. Available now wherever you get your podcasts. Since at least the time of Pythagoras in ancient Greece, the number four has been viewed as a beacon of harmony. But among its musical peers, four has a bit of an edge. Very different quality. It's that quality that has made for a bit of a loose canon in certain cultural and scientific circles.

In contemporary terms, it's definitely being avoided. There's a certainty about counting up to four, and then we start to get this there be dragons. We're just glimpsing into the unknown. It becomes really complicated very quickly. It's very, very hard to control. We're calling this episode Rulemaker, Rulebreaker, The Wondress number four. Okay, let's start with your license plates. Producer Annie Bender takes it from here.

What do your license plates say and why? What is the fun play? The number eight and number nine, these in Chinese tradition, culture, are considered extremely lucky numbers. And so I have license plates that's ending in three-eighths or four-nines. But would you ever consider a license plate that had the number four in it? I would definitely try to avoid it. Wen Ren Jiang is a retired political science professor and founding director of the China Institute at the University of Alberta.

And he's not the only one avoiding the number four. It is definitely the case in Chinese contemporary culture that number four is avoided to the extent that many agencies are taken number four out of the license plates. Commercial real estate marketing is not in favor of number four. So therefore, they often skip the entire floor of fours, 14s, 24s, etc. instead either not to have them at all or replacing them by, say, 3A, 13, A, 20, 3A, etc. In fact, the well-known high-speed rail train models in China skipped the ending number four altogether in terms of their serial numbers. What is it about the number four that makes it so unappealing in Chinese culture?

Well, number four is associated with the sound of s, which is death, and therefore people tend to avoid it. This superstition, sometimes referred to as tetrophobia, is common across East Asia, but it hasn't always been that way. In Chinese ancient history up to modern times, number four, in fact, symbolizes structure, stability, completeness, and cultural excellence. It is actually having a very strong cosmic and philosophical foundation. For example, the four symbols in the Book of Changes, I Ching, east, south, west, and north. They're saying about heaven and earth's four directions are called the universe, right? So these are very strong traditional symbols about balance. From balance and stability to bad luck and even death,

the number four's spectacular fall from grace in China echoes the medieval fate of the perfect fourth. There's kind of the pros and cons historical dimensions and contemporary twists regarding number four, you know. And speaking of twists, huh, you know what, I'm just realizing as I speak to you that my house number is 44? Well, 44 does have a negative connotation,

but you can make a twist of it. Oh. Four plus four is eight, which is a lucky number. Oh, thank you for that. And the wild and twisted world of four is about to get even wilder. Wow, I see a book already here called

The Wild World of Four Manifolds, four manifolds, and Kirby Calculus. That book's hard. I should have you introduce to yourself, actually. So my name's Ty. Tyrone Gaswala. I'm an assistant professor teaching stream in the Center for Education and Mathematics and Computing

at the University of Waterloo. In a coincidence too perfect to ignore, Thai is also a dad with four kids. When the third one comes along and the fourth one comes along, the complexity escalates rapidly. There's a lot more of them forming a society themselves without as much control from us, I think. We'll see.

But no, I mean, I love having a full house at home. It's a lot of fun. But that's not why I reached out to Ty. Okay, so we're here to talk about the fourth dimension. Yeah, I think a lot of really interesting mathematics happens there that doesn't happen in higher or lower dimensions. Very interesting. There's something about the fourth that's kind of unique.

Yeah, so the standard sort of punchline mathematicians use for this is that there's enough space for things to go wrong in four dimensions, but not enough space for them to correct themselves. This is, yeah. So like you get enough space that things, surprising things can happen, but there's not enough space for those surprising things to untwist themselves. Well, that sounds almost kind of sinister. Yeah, I think so.

It's pretty mysterious. Before we can get to the mysteries of the fourth dimension, we need to define our terms. What is the fourth dimension? So a standard response that people will give is that the fourth dimension is time. So we're familiar, we live in a three-dimensional space. And what do we mean by this is that if I want to tell you a point to meet in space, I need to give you three numbers.

I need to say how far in the sort of forward and backward direction, how far left and right, and how far up and down. With those three pieces of information, I can identify a point. But now, let's say I want to say meet here at this time. I have to give you a fourth piece of information. If I'm interested in including time in this picture now, now it's a four-dimensional thing. And this is often why people say that, you know,

we live in a four-dimensional world or universe. Right. In some sense, if the fourth dimension is time, we already live in a four-dimensional world. So why don't we think of ourselves as being four-dimensional? Yeah, so I think when humans usually think about dimensions for the extent that they do, we're usually thinking about spatial dimensions. And here we've stumbled upon yet another place

where four sits right on a knife's edge between the intuitive and the counterintuitive. Okay, so it's possible to think of the fourth dimension as time and in that scenario, we are ostensibly four-dimensional beings that perceive things in four dimensions, but there are other ways that you can conceptualize a fourth dimension in space where things are a little wilder. Is that fair?

Do things get a little weirder when you start to think about the fourth dimension as a spatial dimension? Yes, certainly. I mean, this is true, I think, emotionally and mathematically. Well, now, when a situation gets mathematically and emotionally weird, there's no better guide than Sarah Hart. What would it look like if a four-dimensional being came traipsing into the studio here in our three-dimensional world? It would have a possibly infinite number of ways that it could manifest to us.

And the best way to think about this is to make an analogy of what if you and I, three-dimensional beings, went into a two-dimensional radio studio and we manifested. So the first thing we could do is if we were just kind of walking at all, into a two-dimensional place, so a flat plane, we could put our bodies into that space in any number of ways. So if I started to move through that, just imagine a kind of a slice through space. If I started to move my body through it, well, you might first see the bottom of my feet, right? So you might think, oh, this is a being that's made of two vaguely long, overly shaped things. And then gradually, as I'm descending into that space, we're looking at cross-horisional, like cross-sections of my body. So then, you know, it gets bigger, it gets smaller.

And then at some point, I'm completely all the way through and my head just disappears out of the bottom of the plane and the poor mystified people are going, what on earth is happening? This creature can just change shape and size at will. So that's a really curious thing about the fourth dimension. When you go up a dimension, we're only seeing a slice of that being. So we don't know that we can't.

visualize the whole thing, if they're really four-dimensional. All we can see is what does it look like if we took slices of it? So, and in fact, the fourth dimension had been postulated as a way to explain the existence of ghosts. Because in the 19th century, this was genuinely put forward, it was postulated that perhaps ghosts could move in the fourth dimension. And that would be how they could walk through walls. because it can just go up a dimension, go to the other room and then come back down and appear to us. So this is why ghosts can walk through walls, possibly. Another story I read had someone being able to rob a bank because they could go into the fourth dimension

and then come back down inside the safe, you know, of the bank, take the diamond necklace and disappear. So you can have all sorts of fun if you have a fourth dimension of space. From Arbiter of Truth and Justice to Bank Heist Co-Conspirator, for all that Four helps us organize the world, if you follow it out of that tidy box, things get messy fast. You can pass a loop out of itself by going up into the fourth dimension and then bringing it back down again. So you can untie any knot and free yourself from any bounds.

You can do things like turn things inside, out, take a three-dimensional sphere and completely turn it inside out. You can look inside a three-dimensional object without any problems. Medical imaging would be completely different. For instance, if someone needed to have their appendix removed,

you wouldn't need to make any cuts with a scalpel. You could just go into the fourth dimension and remove whatever you needed to do, easily done, so surgery gets revolutionised. I can't really visualize living inside a four-dimensional world, but I have tricks.

there's a thing called a hypercube. Isn't that kind of a visualization of the fourth dimension? Yeah. I don't know how to describe it. It doesn't lend itself to radio very well. But you imagine a cube sitting inside another cube and then the corners are sort of joined together. But that's only really one shadow, a projection is what the mathematical term is, of the four-dimensional space. In sort of the same way, maybe if you had a three-dimensional object inside a room, but you could only see its shadows onto like the front wall, the back wall, the side wall and the top wall. Maybe you could stitch together what this object looked like just from the shadows. I find it hard to listen to you describing this sort of hypothetical cube like four-dimensional shape

and not feel like I'm dimensionally challenged in some way that there's something out there around me that I just can't see. Yeah, I think this is absolutely right. So the mathematics that we do, when we're talking about these things, they are as real as the things I can visualize. It's a really interesting philosophical point that the mathematics we do applies to the universe, is motivated by the universe that we live in, but somehow exists, is very real, but exists in its own universe. And when we're doing mathematics, at least from the point of view of doing pure mathematics,

which is what I do, we're just exploring that universe. and even though I can't visualize this hypercube, to me and to dwell in mathematics, it's as real as a cube that I can see and hold. Because I can describe it mathematically, and it's absolutely there. It's just, yeah, I'm exploring this universe as a human, which is restrictive because I only have three dimensions to think about.

But I guess the thing I'm really kind of so curious about that you can't actually answer for me, but that I want you to, that I wish you could, is like, are there four-dimensional beings? Like, do you think there are four-dimensional? Like, it's such a crazy question. It's kind of like asking you, are there aliens? I think that's exactly the same question.

Yeah. I don't know. I'm willing to say that we don't have evidence of any. But, you know, anything's possible, I guess. Is this where you thought the interview was going to go? No, it's not. To be honest, it's nowhere I thought we were going to go. Talking about four-dimensional aliens or anything like this.

Just one more unexpected coordinate on the endlessly twisting road of four. And there's one more place where four offers us a bridge between the familiar and the extraordinary. It can take on many forms. It always will emit some kind of light. It will usually look purplish or orange and glow very strongly. It looks a little bit like from science fiction. If you think of spaceship engines, you always imagine this glow that you have. And it sometimes looks like a fluid.

It can move in ways that it would seem like a liquid gas sometimes. Wow, that sounds kind of ethereal almost. Yes. Stefan Reuter is a physicist and professor at Polytechnique, Montreal, and the ethereal substance he's describing here, plasma, is the fourth state of matter. The fourth state of matter, plasma, is an ionized gas, a gas that consists of negatively and positively charged particles such as electrons and ions. When I was growing up, I did not know that there was a fourth state of matter.

We learned about the first three, and then there was just kind of radio silence. No one happened to mention that there was a fourth state of matter at all. Why do you think that is? Why is it that we're so unfamiliar with? I think the reason is, yes, we are surrounded by the normal three states of matter every day. And in elementary school, plasma is, it's really not that much talked about because it's not so much part of our everyday life. We don't touch it.

We don't interact with it. Can you touch it? Yes, you actually can. Given how little we tend to hear about it, you'd be forgiven for assuming the fourth state of matter was a rarity, but the opposite is true. We can observe it in nature, lightnings, and also at the Aurora Borealis,

it's often said 99% of visible matter is plasma state. You zoomed out, you see our galaxy here, and you see the Milky Way. This light, this is surely almost all coming from, plasmas. We see the stars, we see our sun. Our sun is entirely a plasma. And if we zoom out further, we see astro-nebolas, so clouds in space that are made to a large part from plasma. So if stars are made of plasma and all the atoms in our bodies are famously made of stardust, does that mean we're all in some sense born from plasmas? I would actually say so, yes, that's a

way to put it. Everything that has become solid matter has been created in stars to a degree. And yes, we've been created in a plasma burner. That's a nice way to put it. Oh, so does that mean that, do you think there's some case to be made then that perhaps plasma should be the first state of matter? Oh, wonderful. Yes, I would love that. That would be perfect. Like so many aspects of the number four, the fourth state of matter turns out to be at the foundation of it all. And remarkably, you can literally conjure it from thin air. Most plasmas in nature are very, very hot, millions of degrees. But you can actually also create plasma without heating up the gas. And how does that work? You can supply energy, for example,

by taking electrodes and applying an electric field. So you can create what's called cold plasma. You can even create plasmas that have temperature around freezing temperature. And with those plasmas, you can do exciting stuff. You talk about almost being able to turn plasmas on and off. Absolutely. You can just take a power supply. You have a switch. And when you switch it on, your plasma starts to be there.

And when you switch it off, the plasma stops. Huh. It sounds kind of magical. Yes. Sometimes it does feel that way. But like four itself, the fourth state of matter can be fickle. It sounds like plasmas are a little bit fragile or tenuous. Like they're not a reliable state of matter.

They require some finagling to kind of keep them around. They require care, yes. What makes plasma different, I guess, in that sense, from a gas or a liquid? Well, gas and liquid, they are stable at equilibrium. A plasma always requires an energy input. I work with cold plasmas that we have atmospheric pressure. in your normal surrounding, and they're filamentary, they're random, they appear quickly, and they disappear quickly.

It's funny that something that's so prevalent in the universe can also be so hard to keep around. Yes, that's what makes it fun. The fourth state of matter may not always be easy to contain, but when it's harnessed, remarkable things can happen. We can create the same molecules that are responsible for, for communication between cells. For example, there is a molecule nitric oxide, and nitric oxide is an important signaling

and messaging molecule in the human body. And with plasma, we can make these molecules and we can apply plasma to skin. For example, to trigger healing of chronic wounds. These molecules that are created trigger a signaling process in the human body that tells the body, oh, there's something wrong. The immune system is triggered,

and the human body can then recognize this wound again as an active wound that needs to heal. Well, that's amazing. What you're describing is plasma almost telling the body to heal itself. Yes, exactly. It sounds a little bit like Star Trek, but it's not going so fast. But there are other applications. We can use electricity and air and water to create fertilizer in agriculture.

And it's a clean technology. We don't need any fossil fuels. And we can just create it when we need it and how much is needed. Oh, that's just really interesting. So can you just unpack that for me a little bit more? You would take water and air and you would, use plasmas to somehow add nutrients out of thin air in and make a fertilizer? Literally, yes. So when you make an air plasma, you do the same thing that lightnings and

thunderstorms do. You break the oxygen and nitrogen molecules apart. And with these, you can make molecules that are needed for plant growth. So it's a process that happens in thunderstorms. And we can replicate that in the laboratory by taking electricity, taking the air, and then putting nitrogen nutrients for plants in water. What you're describing sounds like it could be a game changer in terms of, you know, sustainable agriculture. There's just a tiny hitch. Darn it. Yes. It's not as efficient as the current technology that creates nitrogen fertilizer.

So solving the energy problem might also solve this problem that we can use clean fertilizer. All right. All we need to do is to solve nuclear fusion and then we'll be all set. Yes, exactly that. Nuclear fusion, of course, also relies on the fourth state of matter, as does pretty much all our energy here on Earth. Our sun is entirely a plasma and gets its energy from nuclear fusion. and we want to bring plasma on earth in a controlled way that we can actually use it to create energy in fusion reactors.

Sometimes I joke and say plasma can save the world and you can get clean energy. So fusion plasmas work basically with hydrogen and diuterium to create helium. And hydrogen, it's in water. So we take water and we make energy from it. And this is a very, very clean and exciting way to create electricity. So when we will have fusion plasmas that create electricity,

we will have solved almost the entirety of the energy problems that we have. On the one hand, four is central to everything we know. It's not just in our DNA. It's our life force, the sun. But it's also a portal to a world beyond our grasp. There's something about it that it's outside of the bounds of the nose. And then, you know, we get the Four Horsemen of the Apocalypse bringing in the change over from things we understand to things that are different or that we don't understand. It's going beyond. It's breaking a boundary. And that's really exciting.

And just so really come full circle here. The same boundary breaking quality that makes four so interesting to mathematicians and scientists has also given it something of a redemptive, arc in music. We've come back into, you know, particularly in the jazz and improv world, loving the fourth more. Brian Katz. The John Coltrane group of the early 1960s with Coltrane on sex and McCoy Tyner on piano, Jimmy Garrison on bass and Alvin Jones on drums, the classic Coltrane quartet pioneered a whole new sound and a big piece of that sound was McCoy Tyner's chord.

built and stacked perfect force. I think it really just speaks to that we need different intervals at different times. You know, why did Coltrane McQuay-Machner embrace this idea of these force, this kind of sound? Well, one could also talk about that in terms of, you know, the civil rights movement and it's punchy. It's like really speaking out.

In music and mathematics alike, the unpredictability of four might just be its biggest asset. Let's sit down. Sure. Mathematician Tai Gasuala. There's been this unreasonable effectiveness of mathematics in the natural sciences, is the exact quote, I think. And what's the quote trying to say is that we do all this abstract pure mathematics,

which seems to be done for its own sake, not motivated by real world problems at all. And then every now and then, more often than it ought to, it turns out to exactly describe the real world in extremely powerful ways. So in this four-dimensional context, a lot of the understanding of how space curves, how you describe curvature, it turns out that this was exactly the mathematics that Einstein needed in 1915, almost 50 or 60 years after it was created and set down, to describe his theory of general relativity, which is what now allows us to navigate the stars. have GPS be as accurate as it is.

The curiosity with the fourth dimension might seem like it's a unmotivated thing, but the history of society and humans has been built upon pure mathematics for its own sake, and then it turns out to be exactly the foundations for technology and understanding and advances in science and things like this. Even when four propels us far outside our comfort zone,

it still manages to help us see the world a little more clearly. Do you think of the number four of us having a personality if it was a character in a novel you were writing? What traits might it have? If four was an actor, I think it would be Pedro Pascal if I was making a movie of another. No, because sort of roles he plays. As soon as we don't hear a truck, we move fast as we can.

It's someone who's completely reliable and dependable, but also is not afraid and they can lead you into the chaotic world, beyond. Because you can always rely on, four gives you the directions, the cardinal points, the compass points. With four, you can find your way into the wilderness, but you can also find your way home. An agent of chaos and a guide through the storm. That is the wondrous power of four. That was Ideas producer Annie Bender with her documentary called Rulemaker, Rule Breaker, the Wondress Number 4. It was part of our occasional series,

the greatest numbers of all time. Technical production, Sam McNulty, Orande Williams, Hannah Barker, and Emily Carvezio. Our web producer is Lisa Ayuso. Senior producer Nicola Luxchich. Greg Kelly is the executive producer of ideas, and I'm Nala Ayyad. For more CBC podcasts,

go to cbc.ca slash podcasts.