CBC IDEAS at Perimeter - The Numbers That Shape Our Universe

Añadido: 2026-06-01

[00:00:00]Thank you all for being here. Good evening to all of you. What a privilege it is to be here to lead this conversation and to um actually I don't want to overstate that I'm not leading this conversation. I've done dozens and dozens of interviews but I've never sat on a panel with this much intellect so it's a bit daunting for me. If you're not familiar with ideas, um there's a QR code that you could just scan. It's just popped up there. Uh where you can follow our podcast. uh there is no idea under the sun that we will not explore. So follow us and give us suggestions if you have them. Uh without further ado, we can get started here. Um and so good evening to all of you. Thank you for saying yes uh for playing ball with us with ideas. Matt, I want to start with you. How did you first come to appreciate how important certain numbers are to the nature of the universe?

[00:00:53]Yeah. So, I was a challenging youth. Uh, I would say I was not a stellar high school student. And, uh, and then I got to university. I wanted to be a fiction writer. And so, I took this course that integrated in a very creative way fiction writing, ecology, biology, and calculus.

[00:01:17]>> Extraordinary.

[00:01:18]>> And I had never before in my life seen calculus.

[00:01:22]And for some reason, I don't know, it was just so beautiful uh that I wanted to do more. And so, uh I asked my professor, "How do I do more calculus?" And he said, "Oh, you might want to take a course in physics."

[00:01:40]And so then I became very interested in physics through that. Um but really it was through uh just the beauty of calculus this mathematical structure that you could um predict observed physical phenomenon from this structure this mathematical structure was fantastic >> and that's the difference between you and the rest of us who when we saw calculus we thought terrifying not beautiful thank you for that um Mina you said um hi >> hi >> you have said in our conversations preceding this evening that math is the language of the universe >> and I wonder when it was that you kind of realize that fact. When did that hit you?

[00:02:26]>> When when did that hit me? Um well I guess it's a process right? I cannot identify a specific time but let me tell you I guess it's not um maybe it's not um mathematics per se I can tell you an anecdote okay but I like to say when people ask me okay what made you to physics okay so when I was in elementary school in in one of our books there was uh a a chapter that discussed the sun the solar system and it also had the speed of light.

[00:03:03]>> So I calculated how long it took for light from the sun to reach us. Okay. And I calculated it took 8 minutes and um and and and two thing two things made an impression on me from that number. One, eight minutes is a long time.

[00:03:28]So, and and light travels faster than any car, than anything that we know of.

[00:03:33]So, for light to take eight minutes to come from the sun, the sun is far away.

[00:03:40]It's so far away that makes the solar system very large, much larger than we will ever realize.

[00:03:48]Um, and as a result of the universe. So, the earth is actually tiny.

[00:03:54]>> So, that's one. The other thing is that it made me realize that because the speed of light is a is and we probably come back to >> we are gonna talk about the speed of light.

[00:04:03]>> It's it's it's a it's it's a it's a constant. It means that we are bound to the past.

[00:04:10]The concept of simultaneity that we all always see things exactly when it happens. It will never happen. So in some ways we're bound to the past of things just by the fact that light is the fastest thing that travel. the information that we get is uh uh is reaching us at always at a finite time, not at at instantaneously.

[00:04:33]>> What a beautiful and yet confounding kind of idea.

[00:04:36]>> Yeah. Okay. We'll we'll get more into the speed of light um in in a bit.

[00:04:40]>> Yeah.

[00:04:41]>> Ben, you come at this kind of from a somewhat different angle um than Matt and Mina. You're a mathematician by training.

[00:04:48]>> Yes.

[00:04:48]>> Uh and profession. How does that perspective or that perch affect the way you see the world and the universe or how you came to see it?

[00:04:59]>> I know it's a big question.

[00:05:00]>> Yeah. Well, and I I mean I fear all through this I'm going to be like, "Oh, I dispute the premise of your question."

[00:05:07]>> And by the way, >> I don't you know I I don't know that it it affects especially from the standpoint of whether you're a mathematician or a physicist, right?

[00:05:15]Because when when I see the world, I'm still seeing the world through physics, right? Mathematics is in indeed it's sort of a language that you use to think about this. So I mean we you know we had had some discussions beforehand. You know I I got to reveal how the sausage gets made here and you know one of the things you had mentioned was you you sort of wanted to hear about you know personally how did we get into this?

[00:05:38]>> Absolutely. I maybe my story it's it's not quite the same as Matt's cuz you know not not to brag but I was a stellar high school student. Um but you know I the the sort of point that I that came up when I was sort of thinking about that was also a class that I took in college on special relativity cuz you know when when you're when you're a stellar high school student. Um you know you hear explanations of things like relativity on the level of what Mina just said and that all sounds very cool but then you're like what but what does that actually mean? like how wait we're bound to the past but what what do we mean by that and mathematics is the language that lets you actually give that a precise meaning where you can really understand okay this is like what a light cone means and so I I you know took a class on special relativity I think maybe in my second year of university and it was like oh all this stuff that was just words before and words that sounded like kind of interesting concepts no it's formulas right like you know either either your two points in spaceime. Either you can get to them physically possibly by going less than the speed of light or you can't. And there's a formula that tells you whether you can or whether you don't.

[00:06:53]>> Y >> and there are lots of kind of interesting concepts. You know, maybe you've heard about things like uh the fact that people who've been on the International Space Station have aged more slowly than those of us who are on Earth, right? And there are formulas that tell you why that happens, right?

[00:07:10]So if you don't learn the formulas, that's just sort of a statement that you hear and you're like, "Huh, that's kind of cool." And if you want to understand why, you have to know the math.

[00:07:20]>> So keeping in mind that you might dispute the premise of this question, I'm curious um if you could answer that question that Mark put to you in the hallway, what is if you had to think of a favorite formula or a number or a figure, what would that be, Ben?

[00:07:35]>> Yeah, it's interesting. I was thinking about this because I uh I when I tried to do this, I kept coming up with like uh stories about why that's like not a good premise. So one there there's the one I told Mark which may maybe I'll tell you some other time but there was another one I thought of which was so you know there was a very very famous mathematician named Grotenique who you know sort of revolutionized how mathematicians think about kind of let's say equations >> uh you know put this sort of you might not believe that that could be put in like a totally new perspective but it can and there was some very interesting work he was doing where you had to choose a prime number and you were you know everything you were doing depended on this prime number, but it didn't really matter which one it was. You just had to choose one. It was okay. You know, somehow like you want to think about all of them at once, but you got to be working with one at a given time.

[00:08:26]And in a lecture, there was another sort of more f another famous mathematician from the older generation, Zoriski, who was getting very annoyed with him for being so abstract. And he was saying, "Oh, well, you keep writing P. What prime is P?" And Gartendique was sort of like what you want me to name an actual prime number and Suski was like yes what what number is P? And he said oh fine.

[00:08:54]Okay I'm getting a little bit of 57 is not a prime. It's divisible by three. Um and if you look on Wikipedia there's a Wikipedia entry for the Groanddeek prime which is 57.

[00:09:07]>> So that's the number you're choosing.

[00:09:09]>> Sure. Why not?

[00:09:10]>> Okay.

[00:09:12]Fair enough. Um, Mina, >> is there do you have a favorite number or a favorite ratio or a favorite figure?

[00:09:19]>> Yeah. So, so let me go back to numbers.

[00:09:22]Uh, I don't because for me I'm a physicist. So, numbers I have to say they are meaningless. What does it mean for something to be five? Five of what?

[00:09:31]Like five dollars? Five million dollars?

[00:09:33]That sounds better. So, so um so we always talk about ratios and or we always have to measure something for it to have a value or a number. So a great example actually a cute example of this and I think it's a bit timely uh because of something that will happen in August. So the this so the distance so the the moon in size in length is roughly 400 times smaller than the size of the sun.

[00:10:09]At the same time the distance of the earth to the moon is 400 times smaller than the distance of the earth to the sun. So far so good.

[00:10:19]>> Yeah. So what that means is that the angular size the opening the size the part of the sky that the moon covers is exactly the same as the size of the sun.

[00:10:34]So the fact that when you have the fact that we have eclipses is based on this accident. There is no physical reason. There's no physics law that tells you this had to happen. It's just that the size that the moon covers on the sky relative to the size of the sun, they actually match to to one part in a 100 a percent. So that's why we get these beautiful eclipses and there's going to be one in August, right? So the so so the so this type of this tells you that the ratio of the distances that there is this cancellation of the factors of 400 of how big the actual length size of the moon is relative to the distance >> uh to the sun. Yeah.

[00:11:18]>> So you're more interested in relationships between numbers rather than numbers in and of themselves.

[00:11:23]>> Yeah. Exactly.

[00:11:23]>> That makes a lot of sense.

[00:11:24]>> Yeah. And Matt, do you have a favorite number or >> ratio or figure?

[00:11:31]>> Yeah, let's talk about the cosmological constant and that uh >> right into the deep end.

[00:11:37]>> Let's go. Uh so if we want to think about it in terms of ratios or comparisons to other scales, uh one number I could throw out is that the cosmological constant in terms of a density is about four hydrogen atoms per cubic meter. So it's a really tiny density. Uh we could think about it in terms of a distance scale. If I if my ruler is a actual ruler and the distance scale associated with the cosmological constant is about 10 ^ 26 m.

[00:12:15]Uh I could think about it in terms of the size of galaxies and it's like 10,000 galaxies in distance. Uh so it's a really long distance scale. uh and I can think about it in terms of a fundamental unit that we think is associated with the uh quantum nature of gravity. That's a pursuit of physicists for quite a long time. We haven't quite gotten there. And it is 122 orders of magnitude smaller than that scale. Uh so that's a bunch of numbers. Now what do they mean and why is that interesting?

[00:12:52]So those numbers kind of connect to all of the important outstanding questions I would argue in uh fundamental physics today. Uh why is that number so much smaller than this fundamental scale associated with quantum and gravity? Uh in fact you'd predict it to be about one on that unit scale.

[00:13:16]um why is it uh so much bigger than human scales? Yeah. Why is the universe so big compared to how how big we are?

[00:13:27]Um and that number governs sort of the overall evolution of the universe. So the fact that that number is what it is um you know tells us that uh we should just now in the history of the universe be able to start seeing it. Uh so we're extraordinarily lucky in that sense to be alive right now. Um and uh it will tell us how the universe evolves in the future.

[00:13:54]>> So maybe take us back if you can to the story of the cosmological constant.

[00:13:59]>> Yeah.

[00:14:00]>> How did it how did who came up with it?

[00:14:02]And I mean I think it's it also is called the Einstein. Am I right about this? The Einstein cosmological constant. Is that true?

[00:14:10]>> It's well he called it his biggest blunder.

[00:14:12]>> Right.

[00:14:13]>> Uh so uh Einstein came up with our current best theory of gravity called the theory of general relativity. Uh and at the time uh we had not seen out very far with our telescopes in the universe. And the concept was that uh the universe kind of was always the same. It was static. Uh >> that it didn't get bigger or smaller size, >> right? And if I had a universe full of just stuff, matter, um matter attracts.

[00:14:45]And so you'd kind of expect things to be attracting. And uh there was a very natural solution to this problem which was uh in the equation for general relativity to add a constant because that constant what it does in the equations essentially is cause things to want to uh spread apart. And so you had a situation that Einstein presented which was uh okay uh we have attraction we have uh the cosmological constant which wants to push things apart and they can perfectly balance and give you a static universe. And then uh 193 something I can't remember Edwin Hubble observed that no that is not quite right uh in fact things are expanding away from us. So the universe is expanding and then he threw it at he's like okay that was a bad idea obviously this no static universe and so um let's give up on that. Uh and then there was a long period of time where um theoretical physicists uh argued about what it should be. Um the big development was quantum mechanics because quantum mechanics actually told us that um there is an energy associated with empty space. Uh and that that energy is actually really significantly big and it looks just like this thing the cosmological constant. uh and that that's this 122 orders of magnitude difference uh in some fundamental scale we might predict it to be and the uh well what we observe it today but the non-observation of it back then suggested it was really small and so people spent a really long time arguing why it should be zero and there were lots of great theoretical ideas for why it is zero. uh and then in 1998 uh there was an observation of distant supernova and we discovered that the universe was not just expanding but it was expanding at an accelerated rate and ah that's exactly the kind of thing that a cosmological constant would do and so we were back to the cosmological constant but now the puzzle was uh okay it's not as big as we think it should be it's not zero but it's this kind of random really tiny number so why on earth would it be this tiny number uh and and that you know then um that kind of developed into what I would say a very interesting crisis and it had tons of implications. So when I came up as a PhD student, it it was you know a little bit after the discovery that the universe was undergoing accelerated expansion and theoretical physicists who had for a long time tried to argue it is zero or there's you know beautiful theoretical reasons why it should be just so kind of lost their religion. And uh and we we thought man well what if it could just be anything?

[00:17:40]Uh and this gave rise to something called the string theory landscape. Uh and uh and and this was a period where we we we sort of as a community globally gave up a little bit on on there being a fundamental explanatory reason behind this number. It just was anything goes.

[00:18:01]And uh it gave rise to this very uncomfortable situation where we had to explain the number we see because if we lived in a universe with a cosmological constant that was quite a bit bigger, the universe would have expanded so much that we never would get galaxies and planets and us. So there would be no life there to observe it.

[00:18:21]>> Uh and this is something called the anthropic principle. And oh man, scientists were really uncomfortable with the anthropic principle. So this was another crisis. Uh so so ma where did we land where where do you continue your that story?

[00:18:34]>> We haven't landed.

[00:18:35]>> We haven't landed.

[00:18:37]>> So so what do you find interesting or puzzling about the cosmological constant?

[00:18:40]>> I think I think uh Matt na n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n nailed it right on the head. In fact see our theory there is a prediction the moment we discovered quantum mechanics and especially quantum field theory which now is which many people in this building study and it's about what 80 years old now almost. So they um h the so the the the value of the columnological constant is much larger than uh that we calculate is much larger. In other words, if I were to put it in a size, if I were to put it in a size, um, the size of the universe would be that it predicted at best at best it would be this big >> like millimeter size at best. This is best case scenario. Okay. So, can you fit galaxies here?

[00:19:32]and and yeah so the point is that the the ourory made a prediction there was no reason why that prediction is wrong and this is very important we have no dynamic or mathematics we have no mathematics equations that can tell us why this number is so small as as as as Matt said >> so the f so this is a huge huge puzzle continues to be a huge puzzle and in fact the multiverse idea which is the multiverse and um is the best one we have.

[00:20:12]>> So I like in a way the way Matt described how important this number is to the universe. I wonder how what words you would use to describe just how fundamental and important the cosmological constant is to the universe as we know it now.

[00:20:25]>> So if we were to change >> how much matter there is. So if we were to change the cosmological constant even by a factor of let's say 10 which in the grand scheme of things given that we're talking about 120 orders of magnitude a factor of 10 is small potatoes. Okay. So if we were to change it by make it larger by that factor of 10 galaxies would never be able to form. They would have been ripped apart before they had any time to form. So we wouldn't have stars. we wouldn't be around. And this is something that Steven Weinberg found in 1988 and um in his efforts actually to disprove anthropic arguments because this is in fact an anthropic argument tells you this value cannot be any different than what it is otherwise we wouldn't be around. Right? That's the essence of an anthropic argument. So um so that's another way to say it that this is a force so powerful uh that because this energy density can be so large that it can it just rips things apart doesn't allow things to grow. So we'll have to have another panel to discuss where the argument lands between physicists at some stage.

[00:21:43]But just to shift gears a little bit and talk about something that's a little bit more familiar maybe to the people like myself. Yeah. Ben, another one of the most um fundamental numbers is the speed of light, which you mentioned a little bit earlier, about 300,000 kilometers per second. Why is that number so important to how the universe works?

[00:22:04]>> Well, I mean, it sort of uh comes back to what I was saying about special relativity, right? That it's, you know, sort of famously it's it's the speed limit of the universe. If you try to go faster than it, you have to push harder and harder and harder to accelerate. Um, you know, this is all the stuff I learned in this class in college. It's uh all this kind of very paradoxical stuff happens, but it's amazing, right?

[00:22:27]Like you sort of try to break through it and what happens is your mass keeps increasing. You get heavier and heavier and heavier, which is why you have to push so hard to to accelerate and you just can't make it. Um, but I mean it it shows up in uh in lots of other places, right? Um, you know, people always call it the speed of light, but of course that's also the speed that radio waves move, >> right?

[00:22:51]>> Right.

[00:22:51]>> How was it theorized? Like, how do we even know that that is the speed limit of the universe? I mean, I don't know if there's an answer to that.

[00:23:00]>> How was it theorized? What's the story behind how we realized that was the speed?

[00:23:05]I I worry that I'm not the right person to tell this story, but you know this because to to physicists this is sort of like you know oh yeah all of us heard this in college um you know very famously Einstein had all of these kind of crazy thought experiments. So you know what had happened in the late 19th centuries they started getting these strange observations of of what was going on and in particular they in the late 19th century of course the most exciting thing was electricity electric we can use electricity to do things now and um Maxwell came up with these famous equations that describe how electricity and magnetism work and if you sort of look at these equations they don't work properly with the old version of physics that people thought was how the universe worked at the time. So, um you know, this is sort of a common theme, right?

[00:23:59]You'll hear this a lot that you know, everybody in this building, what what we would love to do is kind of take gravity and quantum mechanics and make them work together. Well, before we knew about quantum mechanics and before we knew that gravity was as complicated as it is, it was well, people knew about the old Newtonian physics and they knew about electromagnetism and they needed to get them to work together and Einstein was the one who sort of made that synthesis.

[00:24:23]>> Matt, what do you know about how how this became understood and persuasively so as the speed limit of the cosmos?

[00:24:32]Uh, I don't think I'll answer that question, but I'll talk more about why it's interesting.

[00:24:37]>> Okay. Absolutely.

[00:24:39]>> I mean, the speed of light is fascinating because the it it imposes a uh fundamental definition of causality, right? There are things that can have cause and effect on each other and there are things that cannot because they are simply too far away uh for light to have. you know coming back to Mino's observation >> right >> as a child that it takes 8 minutes you know from the light from the sun to hit her eyes uh the sun you know could have exploded and it took eight minutes took eight minutes for for us to know so um so it imposes this fundamental definition of causality it also illustrates that um empty space has properties that we didn't think it had before it has symmetries we didn't think it that. So if I have perfectly featureless empty space, uh, you know, I could walk around, I could like go different places, looks the same. I could turn my head around different places, looks the same. And the the the constant speed of light tells us that there's actually other symmetries that uh if I um go really fast, it looks the same. uh and in fact it implies kind of a rotation of space and time together and it forces us to think about space and time as this unified object and that really laid the bedrock for uh trying to understand the force of gravity in a in a fundamentally geometric way in Einstein's theory of general relativity.

[00:26:13]So this, you know, it's fantastically interesting. But the other interesting thing is that um the speed of light is not constant.

[00:26:21]And if you've ever seen a rainbow, you know that that's true.

[00:26:24]>> Because the speed of light is is the fundamental constant only in totally empty space.

[00:26:31]>> Uh but when light goes through a raindrop, light of different colors travels at different speeds, right?

[00:26:37]>> And that's why it spreads out and we get to see a beautiful rainbow.

[00:26:39]>> Well, they say that's the speed in a vacuum. Yep. That's the speed limit.

[00:26:43]Mina, you were nodding when we were talking about I'm I'm curious about this moment that you talked about that we live in the past or we see the past even when we look out on the sky.

[00:26:51]>> Yeah.

[00:26:51]>> Can you talk about the role of the speed limit in what we see on a nightly basis in the sky?

[00:26:57]>> Can I talk about the role Can I talk about something else?

[00:27:03]>> I did suggest before we started that that you don't need me tonight.

[00:27:09]No, because there is actually there is something correlated with what the importance of the speed of light and what and what Ben said before about about how we got there and it's not just the equations Maxwell's equations there was an actual experiment people thought that so so Maxwell's equations told us that wave light behaves in similar many similar ways like waves on the surface of a lake but at the same time because people had experience with waves on the surface of a lake they thought okay we need a lake so they said we need something called the ether >> for this wave to to propagating so devised an experiment where they sent light in different directions and they try to measure how the earth should move through the ether so they they were it was some sort of interference of waves so an exper experimented with waves and they were expecting to see a signal that would tell them how fast is the earth moving with respect to the ether. But that experiment found nothing.

[00:28:18]>> Meaning >> meaning that the only way to explain that experiment is with with the Laurens transformations that that Einstein had found >> was talking about.

[00:28:28]>> Yeah. And and and they were coming from Maxwell's equations. So light is actually in fact I I like the speed of light and the properties of it and special relativity because it also tells you something else that in physics there are experiments that give you zero answers. No, nothing interesting is happening. But it may have huge implications about our understanding of how the world works. Right? So of course my question with every one of these is what would our world look like if the speed of light in a vacuum were different?

[00:29:03]Does anyone have an idea? If it was a different number, we wouldn't care. Yes.

[00:29:07]Wouldn't it wouldn't affect >> it is the fact that that there that there is such a thing.

[00:29:12]>> Exactly.

[00:29:12]>> That is the interesting part >> because it's always it's a relative thing. So in our in my calculations in fact and I think in both of these guys calculation the set of speed of light to one it's not uh it's not uh 3 * 10 8 m/s. It's one. So so because we always compare to the speed of a car. So the ratio of the two doesn't have any units.

[00:29:36]You measure how many how many units of the speed of light does a car move. I can tell you it's very little. So um so but but yeah so going back yeah so going back to ratio. So numbers by themselves don't tell you much. It's it's how how do you what do you compare it to >> that makes it interesting?

[00:29:54]>> Okay. So Mina, staying with you. Yeah.

[00:29:56]Speaking of comparisons, >> I'd like to talk about something that might be familiar more familiar to our audience, which is the Higs Bzon.

[00:30:03]>> Okay.

[00:30:05]>> Uh most people in this room probably recall the excitement when the existence of the Higs Bzon was confirmed at CERN, which is the European Organization for Nuclear Research in 2012. But I'd like to venture to say that we may not remember why it was important that its existence was proven. Can you remind us why that discovery was so important?

[00:30:27]So the way it's oh well it's a bit of a long story because it completes everything. So in some ways the hicks completes everything that we'll be doing in the 20th century.

[00:30:41]In some ways the speed of light and lens transformations are a bit 19th century it's called. So uh but quantum mechanics and our understanding of what the force is that uh that that tells us how matter behaves um is uh what got completed with with the discovery of the Higs. So um it gave us two numbers but it was of a theory of that had another 17 numbers in it.

[00:31:14]>> Oh wow. the theory of the standard model of of particle interactions. Okay. And it took and I'm saying it's a journey because it started from I mean and it did start in the 19th century when JJ Thompson discovered the electron and then ratherford discovered the proton and then Fermy did radioactivity experiments and discover the weak force that is responsible for a deactivity and discovered neutrinos and then as we were going we discovered new particles and then we discovered what is the structure of the strong force that keeps um nuclei together um and we started piecing things together and we ended up with we call it simple um because it has three forces. It has these particles called quarks that make up the proton and the neutron and the atom. It has these particles called lepttons that are of three types. There is the electron and two brothers of it, the muon and the tow. Um and uh there is the Higs. Okay. Yeah.

[00:32:20]>> Um, and the way this these these these guys interact with each other. So, so the the the Higs was the last piece we needed which was already needed from the structure of the theory because the the weak force to be unified with electromagnetism, we needed the Hicks.

[00:32:39]>> So really it explains how matter forms, >> how matter interacts and behaves.

[00:32:45]>> Exactly. So it it it was it was we needed it to be there >> and it was there.

[00:32:52]>> I mean it explains why it was called God's particle.

[00:32:55]>> Yeah. I hate that word. I really >> Do you Have you heard of Have you heard of where that came from? God's particle.

[00:33:04]>> Why do you hate it? Why do you hate God's particle?

[00:33:07]Why do we I mean I think I think it has to do with the fact that I mean I want to say this later but it has to do with the fact that that humans always look for meaning >> and we look for patterns and symmetries and I think uh sometimes it's just I mean it's mathematics >> mathematics I don't think mathematics has a god >> so why so what I understood was that The Higs Bzon is roughly 130 times greater the mass of it than a proton.

[00:33:43]>> It's 170 something times.

[00:33:45]>> Why is that number significant? What does that mean?

[00:33:48]>> Oh, good. That's an excellent point.

[00:33:50]It's very important turns out. So that ratio is very important. H because turns out the mass of the proton is not really related to the Higs boson mass. it it has to do with a strong force. So the fact so we know of light right so light is an interaction that's that light is the mediator of the electromagnetic force um light interacts with charged particles like the electron okay now there is the strong force who the analog for for that force the analog of the the photon is the gluon and the point is that because that force is so strong it doesn't allow the particles that carry uh the charge of the strong force to roam around free and the fact that they are glued together carry some energy.

[00:34:43]>> So that energy from the gluing together of the gluon and the quarks is the the mass of the proton. So so it so it is another so the mass actually and and the the proton actually contributes to the weight.

[00:34:59]So the way we interact with gravity is not has nothing to do very little to do with electrons. It has mostly to do with protons and neutrons and nuclei. So that that strong force tells us how strong our interaction is with gravity of a human on the surface of the earth.

[00:35:14]>> Right. And yet as certain as that sounds and as a big deal as it was back in 2012, there's still some uncertainty and controversy over this number as well.

[00:35:24]Matt, is that true?

[00:35:26]>> Yeah. So uh I think that's a case where actually the number is pretty interesting because the beautiful structure of the standard model of particle physics um breaks unless if you know unless there is some new physics that comes in at a scale associated with that special mass of the Higs boson. Um and uh trying to explain uh why that particular number uh connects with an idea that you know another beautiful idea that physicists had been working on for quite a long time super symmetry. Uh and uh this is a way to take the standard model kind of to the next level and try and start to explain some of its properties um at a more fundamental level. Uh and so you know there are there were lots of predictions for what we might find at the Large Hadron Collider that could be new particles associated with this thing called super symmetry and we have not found them yet. Uh and every year we continue to not find them actually makes the the number associated with the mass of the Higs Bzon a little bit less explicable in terms of these beautiful ideas of theoretical physicists. And so it's a bit like the situation with the cosmological constant but not as severe that uh we're being driven to a place where maybe we need to think about the explanation as being this everything goes type explanation and it's a weird place to be in >> but it's a lot more expensive an endeavor than than that of the cosmological constant. Well, actually, I'm not sure. I mean, we we built billiondoll experiments to go out and measure the properties of the universe.

[00:37:21]Uh, and those are the experiments that have allowed us to to measure that that number, the cosmological constant to like 1% precision.

[00:37:30]>> It's interesting because we as a as a lay person, you don't hear about that, but I will always remember the fact that this particle collider at the Swiss French border cost 10 billion dollars.

[00:37:42]It's it's an extraordinary money. Yeah.

[00:37:44]Yeah. But an important number, God's particle.

[00:37:49]>> You're going to keep calling that, right?

[00:37:53]>> Um, moving on to Planck's constant, Ben.

[00:37:58]>> Uh, there are a few numbers that are associated with German physicist Max Plank. And one of them, he's actually one of the fathers of quantum theory and modern physics. And one of those numbers is Plank's constant. If any of you dabbled in physics, you would remember that it gave me nightmares when I took physics. But what is it and why is it so important?

[00:38:22]>> Again, I I fear I'm the wrong person.

[00:38:24]>> Oh, yeah.

[00:38:25]>> You know, the I have to confess I snuck in here. I'm not really a physicist. Um, >> but you know, quantum mechanics uh is just sort of I mean, it's not just Oh god, why why did I say the word just?

[00:38:40]But you know it it tells us that for example the energies that electrons can have inside atoms uh can't be just sort of random right they're they're not in this anything goes position where they could be anything. They have to hit certain levels. Uh and a lot of the interesting phenomena we observe in chemistry for example come from well you know atoms.

[00:39:07]You can only have a certain number of atoms with some energy. And once you have enough of those, you have to have one with a higher energy. Maybe you guys when you took chemistry heard about shells. That's what's really going on in shells is you can only have so many uh electrons with this energy. And plank's constant describes amongst many other things those jumps in energy that particles have to take. So it's sort of >> it's describing some sort of resolution to the universe. You know, it's like like the pixels on your screen where you kind of can't go below that. You can't there's some distance that you can't really sensibly talk about distances shorter than that.

[00:39:45]>> Yeah.

[00:39:45]>> Yeah.

[00:39:46]>> So, it's it's a decimal followed by 33 zeros. Do I have that right?

[00:39:53]>> I'm not going to start reading them because it'll take a while.

[00:39:55]>> If it were bigger, we would notice.

[00:39:58]>> But how was Plank able to determine such a tiny number? Ma, >> you're giving me the history question.

[00:40:04]Any ideas?

[00:40:08]>> Pontin it. Pontinate it.

[00:40:10]>> Punt it. I'm glad you're you're the particle physicist.

[00:40:14]So the task falls on me, I guess. So as so plans constant is important as Ben said because it has to do with quantum mechanics and the wave nature of of everything. Okay. So when you measure a wave, there is a wavelength, right? the distance between two maxima of the wave.

[00:40:36]Um and um what blacks constant tell you that for things like light there is an energy associated with it. So people can measure the wavelength of light and they can measure the energy of light comparing always to some units. Again I will say we set that h bar to one when we do calculations because we always care about ratio >> and c. Yeah, exactly. H bar and CR1. But the point is that yes, so you you relate a length scale, a frequency in other words, to an energy scale.

[00:41:12]>> Okay. So, so this is how it was measured. So, it's basically the the basics of of the fact that quantum mechanics is basically some in in one of the or one of the important properties is the dynamics of waves that everything is a wave to some level. Do you I I'm just curious if there are any numbers that you deal with that are even smaller than plank's constant.

[00:41:38]>> Oh. Uh this the cosmological constant is the one we go back toological.

[00:41:43]Everything goes back to that.

[00:41:44]>> Everything is that I mean uh I mean people can imagine even the multiverse actually I like. So the when people the string landscape as people call it when they found all these solutions where the value of the cosmological constant can change by jumping from world to world and world is a very um is a very um is a very generous statement because it may be very empty. Um the amount of how many worlds does the multiverse have the multiverse have? So people came up with numbers like 10 to the 500.

[00:42:22]I don't even know what that means.

[00:42:23]>> What does that mean?

[00:42:24]>> I don't even I I cannot understand it.

[00:42:26]Maybe Ben can. Uh I mean 10 to the 500.

[00:42:30]We have I I I I I I have trouble even fathoming what that number is.

[00:42:35]>> Yeah.

[00:42:36]>> I want to cover one more constant before we move on to other things. Um and Mina staying with you. There's the fine structure constant. I have to admit I have never heard of this. the fine structure constant.

[00:42:49]>> Yeah, I don't know why actually I forget why they call it that but it has to do with the charge of the electron. Okay.

[00:42:59]And um >> it's one over 137.

[00:43:02]>> Yes, exactly. For in the atom. Okay. And uh it tells you what strong electromagnetism is. Okay.

[00:43:13]Um and it's an important number because in the atom for example the electron and the proton are bounded by electromagnetism and it tells you how big the atom is or how much energy it takes to excite atoms. Uh so it determines their properties or like the the many I mean because we we we are held together by electromagnetic forces are mainly our the way our bodies work are determined by the values of the fine structure constant the electromass and the proton mass um and just to give you an idea because it is a dimensions number let's compare it to gravity that's a very interesting comparison so if you were to calcul calculate the force of gravity in the atom, you would find that it is 40 orders of magnitude smaller than electromagnetism.

[00:44:09]I don't even know how to describe to you what 40 orders of magnitude is. What I can show you is the following. So every time every time you pick up something, okay, what happens? So you're using the electromagnetic forces in your body to overcome the pull of the entire planet.

[00:44:30]Okay, think about this. You cannot eject yourself in space. We're not supermen or super women, okay, or super persons. But we can beat the force of the entire earth by just lifting our hand.

[00:44:46]Okay. And this is related back goes back to the Higs mass and the hierarchy problem. This is another way to say if the natural value for all mass scales is in fact is the plank mass.

[00:45:00]So the fact that the Higs mass is so much smaller than the plank scale um tells you that um if it were at the plank mass the force of gravity would be at the same strength as everything else.

[00:45:11]>> Right?

[00:45:12]>> Okay. So this is another way to say the puzzle of of this hierarchy problem and and why it is a puzzle and why people try to find theories like super symmetry to explain it.

[00:45:22]>> Yeah.

[00:45:23]>> But it's definitely true that the the big ratios >> Mhm.

[00:45:27]>> that's what make the universe interesting.

[00:45:29]>> Exactly.

[00:45:30]>> It would be really boring if everything was the same.

[00:45:32]>> I know this is the thing. So it's like I I I it's it's these imperfections that make our universe interesting. It's like when you have you know that people buy uh diamonds grown in a lab but they are worthless right the valuable diamonds are the one from nature because they have the imperfections and they have color in them all the impurities that they have is what makes them beautiful and in fact it's all these ratios of numbers that make the universe so unique. I was wondering whether I mean three of the numbers that we've talked about are constants and that I'm wondering whether that suggests some kind of coherence or a governing principle. Um just it would seem reassuring that there are um specific numbers underlying the nature of the universe. Does it make it seem more orderly or rational when you look at those numbers?

[00:46:22]>> I I would I'll I'll just punt it back to the to the the relatives. I mean um there are physical phenomena and it's a wonderful thing that we can associate scales with different physical phenomenon uh because that is really something that underlies the explanatory power of physics. Uh if there was no such set of rulers, if there was no such large ratios or differences between scales, um then this thing we call physics would have far less explanatory power. Uh and yeah, the universe would be less orderly in that sense because um a lot of the concepts and ideas that that underly why uh applying mathematics to describing physical phenomenon is so unreasonably effective.

[00:47:18]>> Does come down to that?

[00:47:20]>> Yeah.

[00:47:20]>> Mina, do you have do does that >> Yeah.

[00:47:24]>> Do do numbers make yeah the universe more understandable, more coherent and profound?

[00:47:28]>> It does. And it's both about the beauty of mathematics. As humans as I said we always try to find patterns and purpose and symmetries and uh but the many of the interesting fact comes out of these funny hierarchies right of these funny ratios of small numbers that appear. uh for example uh the Higs gives the mass the Higs particle gives mass to quarks and the the quarks that made up the proton but it's a tiny contribution but at the same time gives the mass to the electron so if I start changing the hicks mass by a little bit then if you calculate what properties of nuclear properties you would get um you would get a universe that's very boring it will either be filled with hydrogen, basically a proton and an electron going around it or some weird doubly charged partner of the proton that no no carbon, no beautiful diamonds, no um h no wood, no humans.

[00:48:34]So, so it is those hierarchies, those those those things that deviate from the natural pattern of what you expect uh that make the the un the universe so rich.

[00:48:49]>> Yeah.

[00:48:50]Perhaps on the less reassuring side, and I guess again this is from the lay person's point of view, um there are some numbers that just don't seem to make a lot of sense on the face of it and like something called imaginary numbers.

[00:49:05]make it even more complicated. But I'll start with you, Matt. Just can you explain what imagin What is an imaginary number?

[00:49:14]>> It is a solution to equations that do not have a solution. If I restrict myself to normal numbers like 1 2 3 4 5, right?

[00:49:26]>> Uh, math quiz. Uh, x2 + 1 = 0. What is x?

[00:49:34]>> x^2 + 1 equals zero.

[00:49:37]>> So I need x^2 to be a negative number for that that that to square.

[00:49:41]>> Yeah. Yeah.

[00:49:44]>> Excellent answer. You get an A+.

[00:49:46]>> Congratulations.

[00:49:48]>> Yeah. So that is I that is an imaginary.

[00:49:51]I is for imaginary. And uh if I have a mixture of real numbers, the ones we're used to, and imaginary numbers, we call that a complex number. Uh and these are just wonderful tools that underly the mathematics allowing us to describe waves for example uh that allow us to describe functions as sums of simpler functions. If you've ever heard something called a forier transform. Yeah. Anyway, it's a wonderful tool. uh and uh the a lot of the mathematics underlying physics uh in particular quantum mechanics relies very heavily on this concept of imaginary numbers. It's a really wonderful mathematical tool that allow us to describe many phenomena in nature.

[00:50:42]>> Ben, as a mathematician here, what do you make of imaginary numbers? Well, I mean, you know, so somewhere around, I don't know, third or fourth year of university, you start assuming that students are are maybe more comfortable with complex numbers than real numbers.

[00:50:57]That's maybe a little early, but you know, at at some point, uh, one of the remarkable things is a lot of mathematical things actually become much easier if you think about complex numbers rather than real numbers. So, for example, right, Matt was sort of saying, oh, well, how do we get complex numbers? Well, we look at x^2 + 1. Well, x^2 minus one, there are two solutions to that 1 and minus 1. x^2 + 1, there's no solutions. Well, that's really upsetting. But if we go to the complex numbers, there are two solutions because our our lovely audience supplied one solution to x^2 + 1, but there's another one which is minus i. Um so once you incorporate complex numbers any polomial equation like that where you have x right what if you had x cubed + one well it's going to be much harder for me to say what the solutions to that are out loud on a radio show but there are three of them um and they're perfectly good complex numbers. So you know sort of and and there are lots of other sort of more complicated con concepts that follow on from that where you know if you try to describe what happens if you use rational numbers you you something very complicated happens right it's a very complicated question when an equation like that has a rational solution rational means a fraction of two whole numbers um or you know real numbers the sort of usual numbers we use that are decimals whereas with complex numbers the the ampl answer is much simpler. So for for I think almost all mathematicians complex numbers are sort of the kind of default kind of numbers to use.

[00:52:38]>> So we have imaginary numbers um that are essential to quantum physics as as you said there are numbers that are foundational to the world as you said Ben like pi and the golden ratio that are irrational numbers numbers that have decimals that go on forever. This is a really big question, Ben, but I'd like to ask you anyway. But what what does it say about the nature of our universe of reality that these numbers are so foundational? These are rational.

[00:53:06]>> I mean, it it just says that geometry is a little more complicated than that, right? So, you know, the Greeks famously wanted everything to be a rational number. And there's even a story about a Greek, you know, jumping off a ship because he was so upset that uh the square root of two was an irrational number. Um but you know, uh yeah, geometry is more complicated. Uh one of these things that's sort of hard to think about now in the modern world or at least for those of us who you know took university classes on this stuff for a long time people thought that like numbers and geometry were separate things. like the the Greeks there's sort of Uklid who you know did many many books on geometry and all his geometry was purely in terms of oh when these two lines intersect and yada yada and then there there were other people doing I think maybe even the same people but they were doing it separately doing you know solutions to algebraic equations and it was like a huge brain wave to be like oh we can describe the points in a plane by pairs of numbers and we can understand geometric shapes by using equations. That that was a huge advance in the 1600s. Um, but once you start doing that, you immediately are like, "Oh, yeah. Irrational numbers.

[00:54:22]They're here to stay. We're not going to get rid of them."

[00:54:25]>> I'm interested in that story. The person that you said jumped into the water because of not getting their head around an irrational number. How have mathematicians dealt with and scientists with these irrational numbers and imagining numbers through the ages? Uh I think there's a saying you know you don't really come to understand things you just get used to them um you know you you have the tools to work with these things you you make sense and you know we get started people started early now right and so it doesn't seem so upsetting that you take a square root and it's an irrational number right >> there's there's a story about Pythagoras I think that >> yeah I'm sorry I should have looked it up beforehand I don't remember >> no worries at all are go ahead >> I don't know the story >> you do or I just need stand up.

[00:55:09]>> I don't know the story. I cannot stand up for the Greeks at first.

[00:55:12]>> All good. Are there numbers that you find confounding that that that are that you can't get your head around? Matt >> beaten the dead horse, but I'm not going to say it again, but the cosmological is my answer. And uh confounding numbers. Yeah. I don't know.

[00:55:32]Yeah.

[00:55:33]>> So, let me ask this. Um, we've talked about so sorry we've been uh talking this evening about why these numbers are so important, but most of us kind of all of us many of us are really kind of blissfully unaware of much of what we've talked about tonight. And I wanted to ask each of you just what are we missing out on but by by not knowing about these these numbers that basically rule our universe? Matt. Yeah, I mean the it it is a beautiful thing that we can use mathematics to understand and predict the world around us. Uh and the the fact that it is so unreasonably effective. Um it just gives you a new perspective on essentially everything. Um and it gives you a framework within which you can try and understand the world around you.

[00:56:38]>> Um and a lot of those concepts, I don't know, I mean you you might apply them to yourself, your your view of the universe, life, everything. Uh it's really a perspective, right? So you're missing out on that.

[00:56:53]>> Yeah. Mina.

[00:56:55]>> Um yeah, that that was very nice, Matt, actually.

[00:57:00]Um yeah to that I would like to add again going back to symmetries and the fact that a lot of the equations in principle you can write equations never talk about numbers you can say my number that I'm missing is x okay and keep it to that so a lot of these funny numbers that we talked about the hierarchies why is the higs master the way it is why is the universe so large it didn't come from the structure of mathematics by itself it came out from observation and observing the rich structure that we see around us doing experiment. So language the language of nature is mathematics but that the way we ask questions to nature is experiment and that's something to remember for us for physics uh those two come together to describe the world around us and it's important to know that if you look and the other thing is yes you have these weird numbers 19 in the standard model you have the cosmological constant how much dark matter there is which we didn't talk about um all the rich structure that you see comes out of these things but it's a small set of numbers um which I find remarkable that as a human race sitting in a little rock going in a vast empty space we did pretty well yes Ben >> uh I mean I guess the sort of thing that came to mind for me is that sort of like uh I I think there's a lot to be gained by just not being scared of numbers.

[00:58:39]Numbers will not hurt you, right? They uh and they they follow very simple rules that that I trust me you can understand. I think you know there is some cultural block believe me having you know gone around for 30 years of my life telling people oh I'm a mathematician and you quite often hear like ah hated math in high school. Um, and you know, I I'm not saying you have to love math, but I I think you should sort of uh do your best to be comfortable with it and sort of not be scared by it.

[00:59:10]>> So, we've kind of done a very brief survey of those numbers that kind that underpin or shape our universe. And I wonder just kind of as a final round to each of you, if you wanted to give the average lay person an entry point of the numbers that we discussed, what you think is the most important or fundamental or most interesting number that you would ask us to uh explore further? What would that be of all the numbers we've talked about?

[00:59:38]What would that be? Ben, >> I mean, I I'm still going to stand up for the speed of light. uh you know I mean planks constant is great of course but the speed of light it's sort of I mean it's so important to what's going on around us right like all of this techn you know like the cell phone in your pocket it wouldn't work if uh if we if the speed of light was not a constant and it was changing right um and I think you know the special relativity it's you know again it can sound a little scary but some really amazing stuff happens um and that's uh you know this discussion about causality, the sort of idea that there are sort of events because of where they are in space and time, they couldn't affect each other. Um, I think that's all stuff that that people can understand and it's uh it'll really expand your mind.

[01:00:26]>> Mina, >> for me, because I know what Matt is going to say.

[01:00:30]>> I'm not on purpose. I'm not going to say it. That's boring. Now, >> I I'm going to say that people should remember that gravity is a very weak force. It doesn't feel like that when you get off the couch some days or you go upstairs every day.

[01:00:47]>> But but but uh it is a very weak force relative to everything else and it's a huge puzzle. It shapes us. Um and it's something that's worth understanding.

[01:01:02]>> Thank you. Matt, should we even ask?

[01:01:04]>> No. Yeah. I'm going to go I'm going to go small. We've gone big. I'm going to go small. I'm going to say uh you should understand H bar because quantum just like special relativity underlies pretty much everything we know about the modern world. And so um you don't have to go as fancy as quantum computers. You could go to the color of a fluorescent light. Uh it's something that you should know about and it's very interesting.

[01:01:38]It's all really just wondrous and I'm just so privileged to have had the chance to speak with you about it. Thank you so much Matt, Mina, and Ben. Thank you. Thanks.