Radiolab - The Middle of Everything Ever

Episode Date: December 9, 2022

After graduating from high school, without a clear plan for what to do next, Laura Andrews started asking herself a lot of questions. A spiral of big philosophical thoughts that led her to sit down and write to us with a question that was… oddly mathematical.  What is the most average size thing, if you take into account everything in the universe. So, along with mathematician Steven Strogatz, we decided to see if we could sit down and, in a friendly throwdown of guesstimates and quick calculations, rough out an answer.  Special thanks to all the listeners who sent in their responses to this question. Episode Credits:Reported by - Soren Wheeler and Alex NeasonProduced by - Annie McEwenwith mixing help from - Arianne WackFact-checking by - Natalie A. Middletonand Edited by  - Alex Neason Citations: BooksYou can find links to many books by Steven Strogatz here: https://www.stevenstrogatz.com/all-books MediaAnd the podcast he does for Quanta Magazine, The Joy of Why, here: https://www.quantamagazine.org/tag/the-joy-of-why/ Our newsletter comes out every Wednesday. It includes short essays, recommendations, and details about other ways to interact with the show. Sign up (https://radiolab.org/newsletter)!Radiolab is supported by listeners like you. Support Radiolab by becoming a member of The Lab (https://members.radiolab.org/) today.Follow our show on Instagram, Twitter and Facebook @radiolab, and share your thoughts with us by emailing [e-mail].   Leadership support for Radiolab’s science programming is provided by the Gordon and Betty Moore Foundation, Science Sandbox, a Simons Foundation Initiative, and the John Templeton Foundation. Foundational support for Radiolab was provided by the Alfred P. Sloan Foundation.

Wait, you're listening to Radio Lab from WNYC. This is Radio Lab. I'm Soren Wheeler, I'm sitting in for Lulu and lots of today. They will be back next week. But for today's show, we got a good one and I brought along a friend. Hello, our editor, Alex Nieson. Yeah. All right. So tell us what we're, tell everybody what we're up to today.

Yeah. So we're here because a little while back, we got a question from a listener. It seemed like a pretty simple question, but the more we got into it and tried to figure out how to answer it, the more it just dragged us into the middle of everything. Yeah. It's like one big gigantic spiral.

Like, what are we? Who are we? I'm sorry. That's OK. So the question came from a woman named Laura Andrews. Yeah. My name is Laura and I'm a student. Laura is an undergraduate student at the University of Missouri.

Mizzou. Mizzou, okay. But when she sent us this question almost a year ago now, she was standing kind of on the precipice at a very particular transition moment in her life. Yeah. I think you had just finished high school, right? Yes, I was a couple months into my gap year.

But I hadn't applied to any colleges. I had planned to, but some personal things went on that just kept me from doing that. So I was living with my parents. The most that I was ever doing was dog sitting. Once a month or something like that, that was it. And I didn't have any plans. So Laura is just graduated from high school.

She's at her parent's house. She's feeding some dogs from time to time. Reflecting on myself and what I meant to be doing. Staring into her future, and she starts asking herself a lot of questions. Where do I belong? Sort of philosophical questions. What is my place in the universe? About herself? Where are we in relation to everything ever? About everything. What is everything in relation to everything ever. About everything. What is everything in relation to everything? And Laura told us that when she started thinking

about everything, the vastness, the bigness, she just felt small. But then she thought, am I small? And that letter to the question that she sat down, wrote out, and sent to us. And her question turned out to be weirdly mathematical. What is the most average size that a thing could be in the universe? If one were to take the size of the largest singular thing, be it a star or a black hole or something, rather than a cluster of stuff like a galaxy, and the size of the largest singular thing, be it a star or a black hole or something, rather

than a cluster of stuff like a galaxy, and the size of the smallest thing, my guess would be an electron or something of the sort. And found the exact median size, how big would that be? I've tried to work it out myself, but I'm good at neither math nor science, and my answers always seem to be entirely too large. Where is the midpoint between big and small in relation to literally everything ever? Okay. Okay. Can you ask, do you have a guess about what the answer might, what an answer might be? One of my thoughts was like an apple would be a good size.

I mean, you can hold it in your hand. You can eat the size of my middleist thing. Yeah. When I asked my wife, she said toaster. And then we had to go, like somebody, I think Andy's friend was like definitely a watermelon. He was convinced it was a watermelon. The first thing I thought of was an atom.

A grain of steam. So we actually put a call out to our listeners to see what they thought the middle thing was. A small rock-haired pro-tron. And we got a huge variety of answers. The problem with my hand. The sun, yeah. But mostly what people talked about was how do you...

How do you even start to try to answer the question? I'm really thinking about this question a lot. Thinking about it more and more. What are the boundaries? I don't know. I don't know. How do you choose the littlest thing? Courts and atoms. Particles.

The neutrinos. How do you choose the biggest thing? Massive black holes. Trillions of stars. Giant supernovas. The Dalitsy. The universe itself. Actually, what even is a thing?

But I don't know. All the things are still made up of atoms, I think. Blacks with I think. That's what I think. And I have to say, I spiraled out in exactly the same way. So much so that I wasn't actually sure if we could answer this question at all. I actually weirdly just immediately thought of a particular person. I saw her. I saw her. I can't believe that I feel like the Steve Strogat's a mathematician at Cornell, an old friend of the show.

In the past, we've called him up to help us untangle impossible logic puzzles. Yeah, and that was fun. Or understand statistics and probabilities. Yeah, time flies. But this time, I just got him into the studio. Well, let's, let's jump in, because there's without even telling him what I want to just talk about.

Yeah, I mean, I do feel a little off as far as our usual thing, because usually I've had something to think about hard. Just before we talk. We're just winging it today. Well, we could see what happens. No, but I mean, I have a very specific thing I want to talk about actually. Oh, oh, really?

Yeah, well, this was sort of the spark here. Let me just tell you. And so I was like, let me just hit you with this question. Okay. Laura Andrews wrote in and said, what is the most average I literally read him the text of Laura's question? Where is the midpoint between big and small

in relation to literally every single thing ever? Ha ha, great. What a great question. It reminds me a lot. He was into it, so I was just like, I don't know, do you think we could just right here on the fly right now rough it out? Huh.

OK. What's in the middle? Yeah. Well, first of all, I did use it. And right away Steve was like, OK, there's a couple of things we get to do just to get a grip on this question. I think we should measure everything

with a common yardstick, let's say meters. OK. And a meter is approximately the scale of a person of Laura herself, depending how tall she is, she's between one and two meters tall, probably. Right. And also to simplify a bit and make the math doable, we're gonna do some rounding.

We don't care about numbers like one or two, we're only interested in plus, you know, up to factors of 10. And in particular, Steve said, like if we're gonna talk about really big and really little numbers, the said, if we're going to talk about really big and really little numbers, the easiest way to do that is to talk about powers of 10. Remind me what powers of 10 means? I mean, really, it's just like a mathy way of saying numbers like 10, 100, 1000. Like you talk about how many zeros come after the one.

So 10 to the 2 has 2 zeros after the one, which is just like that's 100, and then 10 to the three, power three has three zeros after which is just a thousand. Sort of like when people talk about salaries, are you making a four figure salary or a five figure salary? Right. So each step is just going up times 10, 10 times each step. God. And then you can do this in the other direction, like I'm getting smaller, so you just do divided by 10 divided by 10. So if you take one and divide it by 10, you get a 10th. That's 10 to the negative one. Okay.

Okay. And then in that case, you're just talking about the number of zeros that are on the other side of the decimal point. Okay. I'm going to read you. Okay. So that's what we're going to do. We're going to think about what the biggest and smallest things are using powers of 10.

But so back to Laura's question, though, I think. Which immediately took us into some very weird spaces. People say that the smallest conceivable thing, the physicist will tell us nowadays, the smallest conceivable thing is a unit of the size of space at which space is thought to lose its integrity. Integrity. Something called the plank length.

This is a pretty far out thing. No one has experience with this in their daily life. But emptiness, the ordinary space between your hands, when you hold your hands apart before you clap them together. Emptiness itself has a fabric to it. And at the scale of the plank length, space would be made of grains of space. Just dots. Yeah, dots. Kind of pixelated.

And what we don't know is are they neat little pixels like checkerboard squares. Or is it that space itself starts to kind of rip apart? We have reason to think that because in quantum theory, everything gets very jittery. Things pop into and out of existence. Okay. Yeah. Anyway and out of existence. Okay. Yeah.

Anyway, the plank length, that's 10 to the minus 35 meters. Okay. So that's just a decimal point and then 34 zeros and a one. It's about a trillionth of a trillionth of a trillionth. Of a meter. Of a meter. So if we start with a meter, which is roughly a person, we have to zoom into a freckle

on that person's cheek, like 10 to the negative 2, into tiny blood vessels, then a cell in the blood, then the coiled molecules of DNA inside that cell, then down to an atom. Yeah, much smaller than an atom. How big is an atom? We're on 10 to the minus 10. Oh, it's way close. We're not in close. Way way smaller than that.

Apparently, if an atom was the size of the Earth, then the plank length would be the size of an atom on that Earth. So we have to keep going into the tiny bits of the nucleus of the atom, the protons and the neutrons, and then to the smallest fundamental particles that we know of. And it's still like a billionth of that. Wow.

But anyway, that's what we currently think is the smallest conceivable thing. Okay. Now, what's the biggest thing? Right. So then we're going to get to what's the. Now, what's the biggest thing? Right. And then we're gonna get to what's the middle thing. So for the biggest thing, we have to, of course, zoom back up through protons and neutrons and up to the atom, then out to molecules, dust mites, dolphins, soccer fields,

which are like 10 to the two oceans, Earth, about 10 to the seven, the solar system, then galaxies and clusters of galaxies, and then out, out, out to include all the vast empty spaces between everything. Wow! The size of the whole universe. Measured from one end to the other. Now what does that mean? Okay, we don't know if there's an end to the universe.

It's possible the universe itself is spatially infinite, but all we can really observe is how far can light travel since the beginning of the universe. Right. So if you use that estimate, you'd say the universe is something on the order of 14 or so billion light years in diameter. Okay. Which, okay, now that's not what we were going to do things in meters. Right. So how do you go from light years to meters? I think if I do it right, I think in meters that's about 10 to the 25th meters. We could quickly ask our cell phones.

Okay. You could say, hey Siri, should I do it? You sure? All right. Hey Siri, how big is the diameter of the universe measured in meters? Okay, I found this on the web. For once the matter, once the diameter of the universe measured in meters, check it out. Oh, she's just going to send you to a webpage. She's sending me somewhere. She's like, here's the internet, Steve. Oh, man. Well, all right, I'm going to try using without asking her, I'm going to type into my phone diameter of universe in meters. Okay,

this says it's about 8.8 times 10 to the 26 meters. Wait, so is that 13 billion light years, and that's just changing the meters? Because is that come out, right? It's 14 billion light years would be. Well, you may want to get a physicist or an astrophysicist because they say that's not actually the diameter of the universe. They're now quoting a number that is much bigger than that, 93 billion light years. And they say it has to do with the expansion of the universe at the very beginning

in this process called inflation. Oh. Okay, that's. So that's how you get your number, which is 8.8 times 10 to the 26, which I guess with the eight is really just 10 to the 27 for our purposes. Yeah, that gave you a 27.

I mean, if that's what the smarties are saying. Let's go with that. Let's go with that. So that's a one with 27 zeros behind it, which just means that we've taken one meter and times it by 10 27 times. All right, so we're ready to do it. Yeah, okay, so we just have to take the big and little

and figure out what the average thing is. Well, I think we should be careful about the word average. Because there are lots of kinds of averages. You know, kids are taught median mean. There's all these. Can you, can you remind me what those are? Well, the mean, the way you compute it is you add up all the numbers and then divide by how many of them there are. So we need to know how many bigger, little or medium things there are. Right. For a median, we'd have to count up all the objects in the universe. Okay. And then put them in a line from smallest to biggest. And like all the quarks that there's so many of, they'd all be in line. So there'd be a lot of quarks lined up. Yeah, because every

big thing is made of little things. So if you had a big thing, you've also added a bunch of little things, I guess. Yeah, so I don't know. Yeah, it seems like it would drag it to the little stuff. So I'm just saying there's a lot of different concepts of middle, and depending on the context, one is more appropriate or convenient or useful than another. But I sort of, when I hear Laura's question about what's in the middle of the universe, I think of this might be an off-putting word, what we would call the geometric mean. So Steve said he thought the most intuitive and simplest thing we could do, what we would call the geometric mean. So Steve said he thought the most intuitive and simplest thing we could do because we now had the biggest and smallest

numbers as powers of 10 is just figure out what the average of those two numbers is in a way that would tell us from the middle, it would be the same number of times 10s up as it would be like divided by 10s down. So that's the one that we're gonna go for. Got it. Okay. We're ready to answer now. Go time.

Yeah, except we're actually gonna take a quick little break. But when we come back, Steven and I actually get to an answer that honestly felt to me, I mean, sort of freaked me out, but also I felt like maybe we had actually landed in the center of everything. What's the point of being a real man?

What's the point of being a real man? What's the point of being a real man? Hey, I'm Soren Wheeler. Malak Sison, this is Radio Lab, and we're back doing the math, my eighth grade algebra teacher always swore we would use. They were right, though. They were right. I don't think they knew what we'd be using it for, math, my eighth grade algebra teacher always swore we would use. They were right.

They were right. I don't think they knew what we'd be using it for, but we are here with mathematicians Steve Strogas using that math to figure out what the Middle East size thing in the universe is. All right, so we're ready to do it. We're ready to answer now. So we've got, so before the break, we had decided the smallest thing you could measure is the teeny tiny, beyond comprehension plank length, which is 10 to the negative 35 meters, and then the biggest thing

is the unknowable enormity of the universe itself, which is 10 to the 27 meters wide. And to find the middle, Steve actually does this very simple bit of math, almost to the point of being any climatic. Okay. Just a good old fashioned mean of two numbers. So we got 27 on the upside. He just takes the two powers and negative 35. So I should add them together. Add them up 27 plus negative 35. That gives me negative 8. And then because we want the average of just two things, he divides them by two. Divide it by two is negative four. So the middle.

So the four below zero is four orders of magnitude below zero is the middle. So that's that's 10 to the negative four, which is a decimal point and then three zeroes. Yeah. So is that that's a mill. That's a tenth of a millimeter. That's a tenth of a millimeter.

Yeah. So like a millimeter would be like a grain of sand. Yeah. So it's a tenth of a grain of sand. It's a tenth of a millimeter. Yeah. So like a millimeter would be like a grain of sand. Yeah. So it's a tenth of a grain of sand. It's a very little tiny dusty, a little piece of dust. Dust part of it. Very little piece of dust. Now if I take a bacterium, say a cell, you know, that's a single cell organism, a big

bacterium is something like 10 to the minus 5 meters. That's a little small. So maybe a particularly large cell might get close to. Yes, maybe. But you still be a couple steps. It's a good question. I think a eukaryotic, let's say. That's a cell with a nucleus.

The kind of cells we're made of. Right, I'm gonna look that one up. Diameter of a eukaryotic cell. Look at that, Saren. It says here, diameter of eukaryotic cell. Look at that, Soren. It says here, diameter of eukaryotic cell 10 to 100 microns. So micron is 10 to the minus 6 meters. And 100 of those is 10 to the minus 4 meters. So the biggest eukaryotic cell is our happy place in the middle. So it's a small bit of us.

Yeah. Now some people would say, this is just an exercise in circular reasoning on our part. That's what I think it's going to come out that, yeah, we're going to, because of our perceptual limitations, we're going to tend to see things centered on us. Living a perceiving thing is going to see out in each direction about the same and thus call itself an average. That's sort of plausible, isn't it? Yeah. But I feel a certain amount of confidence in all of this. I don't think it's just anthropocentric.

Yeah, I mean, we are using science that stretches our senses as much as we know how to. Yeah. Yeah, I mean, yeah, it still makes you wonder. But what if you set that aside for just a beat, if you can manage to set that aside, what we have here is that the idea is that the middleist thing is the most fundamental unit of life.

Right. Of complicated life. Yeah, it's a big eukaryotic cell. Which I think is kind of cool. But you know, I'm not actually sure if we've answered Laura's question, though, because she was asking about things. What's the middle-sized thing? And what you and Steve are talking about is space, I guess.

Yeah. I'm just not sure if the universe counts as a thing. Yeah. I was actually thinking the same thing when I was talking to Steve. Well, to be fair, Laura, I think might have asked a question that we were scared to do, which is fine because I think I like what we did, too. But we have now figured out the middle of all measurables, or something like that. That's right.

She did seem to, like, let me just return to the text. If one were to take the size of the largest singular thing, and she says rather than a cluster of stuff like a galaxy, so she really is trying like, what's the largest thing that you could consider its own object? That is such a peculiar framing, because I don't think that what is a singular thing? Well. Isn't that a fiction? Is anything a singular thing?

Aren't we all multitudes? A star is made of electrons. Electrons are made of super strings. But we do certainly walk around objecting things all multitudes. A star is made of electrons. Electrons are made of super strings. But we do certainly walk around objecting things all the time. And we could say, we do. That's the sun.

That's the sun, right? Okay. Well, let's go with it. But a galaxy is not a thing either. You can see that. So then we just start trying to figure out like what is the biggest thing. But do we call it?

Okay, it's it. If you just think of a normal idea of thing, do you know pulsar or black holes? And black holes, they have a lot of mass, but they're actually sort of small. Yeah. I sort of think a big star under her definition is the biggest thing.

Right. You know, like a red giant. Do you have a guess about, well, let me just look at it up. You can look it up. You've got the whole world right there in front of you. This show is just going to be like, Steven Soren, Google. What's the biggest single?

OK. Cosmic record holders. Largest ex-open-o. Largest empty spot. That's weird. Largest star. Yeah. It's called UY Scoody. Really?

I'm sure I'm saying that wrong. Did not know that. So that's 10 to the 12 meters, which, whoa, is apparently so big you could fit almost 5 billion of our sons in it. Okay. So I guess for the smallest thing, Currently the smallest physical size. And after a lot more Google accelerator and Googling, quarks are smaller and turns out the idea of measuring sizes of things that are that small gets really dicey. But we eventually ended up settling on 2000 times smaller

than a proton or five, a rough estimate of the size of like a quark. 10 to the minus 20 meters. Yeah, that sounds to me in the right ballpark for Laura's question. So we had our littlest thing thing and our biggest thing. Right. Okay. So the middle.

So we've got our same thing. Yeah. 12 negative 20 and we add them up and get negative 8 divided by 2, we get negative 4. It's the same damn answer. We're back to our big, big eukaryotic cell. That might be the first time I've been spooked in a while. I'm looking at Soren, he's folding his arms. I had to lean back. He's leaning back.

His mouth is hanging off. It seems very odd to me that we got the same. I mean like, hmm. Well, okay, I don't know what to make of it either. Sort of, I think it's, it's, it's interesting. Yeah. All right, so the basic unit of complicated life is the middle. Yeah, that's nice.

It's the thing that we have in common with all the life on this planet, whether plant or animal. Yeah, complex life. Uh-huh. I think this is the answer to Laura. It's smaller than I expected. Does it feel satisfying for the answer to be a cell that's in us? It feels like it should be profound.

I mean, I'm not having like a mind blown reaction. Like I thought I would. But it feels like I should have more of a reaction. What if we were to put some music underneath this? I mean, it'll be more dramatic for sure. I totally get that. I totally get that. Yeah.

But let me see if I can at least offer you this. Because there's a little bit of a feeling that like I don't know being small or average or a little bit whatever in the middle, it makes you feel sort of insignificant or something. But size is actually like a weirdly interesting thing because when something gets bigger, it's not just a bigger version of the same thing. Like when you get bigger and bigger and bigger, the physics, the physical stuff actually works differently. Mostly because a really large thing has more volume compared to its surface area and

a small thing has more surface area compared to its volume. That's why you can get salt or sugar to dissolve in water if it's in little grains, but if you had a big cube of sugar it would take forever. So there are certain kind of physical events that happen differently if you're small than if you're big. And there's an argument out there that like cells being the basic unit of the way life functions, which has to do with like making energy and getting outwaste and doing all the things that a body needs to do, you can't be much bigger than the cells are because

you have to have the right amount of surface where you're like sending things out and bringing things in and interacting with the world, given like what you've got going on inside. So it might be that this average middle size is actually ideal to allow this very rare, precious thing, which is life, to even happen in a cold, cold bit of empty space. Well, when you put it like that, I mean, yeah, when you put it like that, it was more profound for sure. Okay, what is making progress? Yeah. I mean, I guess the most comforting part of it is that we're bigger than we seem. Or maybe not so kind of tiny as we sometimes feel. Yeah. Yeah. Yeah. Right. Well, thank you, Alex, for sticking with me and bringing me this one and going on the journey with me and not giving up. And thank you to Laura for sending us on the journey.

We love getting questions from our listeners and Laura spent so much time talking to us about the question, about the method to find the answer and again about the answer itself. So we appreciate you. Thank you. Yeah. Laura is not small to us. For this episode, she was the center of our universe. Yes. Yeah, Laura is not small to us. For this episode, she was the center of our universe. Yes, exactly.

This episode was reported by me and Alex Niesen. It was produced by Andy McEwen with mixing help from Arianne Wack. And I gotta say, if you're gonna talk about math and space on a podcast, get yourself a Steve Strogas. Steve, by the way, in addition to being a great podcast, get yourself a Steve Strogas. Steve, by the way, in addition to being a great mathematician, is also a great writer, and his books on math are gorgeous, and yes, they have math, but they're also easy to read, fun to read, funny, and full of humanity. He also now has a podcast that he does called The Joy of Why, where he talks to some big

name scientists of all kinds about their work, but also about their lives. You can find a link to that on our website at radielab.org. That's it for us today. Thanks for listening. Lulu and Lethith will be back next week. Radio Lab was created by Jad Abinrock and is edited by Sauron Wheeler. Jack next week. Radio Lab was created by Jack Abberrod and is edited by Soren Wheeler. Lulu Miller and Latif Nasir are our co-hosts. Dylan Keath is our director of Sound Design.

Our staff includes Simon Adler, Jeremy Bloom, Becca Bressler, Vétu Q6, Aketty Foster Keys, W. Harry Fortuna, David Gabel, Maria Pasco, T.R.S, Sindhu, Nana Sanban Dan, Matt Q.T., Anima Q.N., Alex Nisen, Sarekari, Anna-Rasquit-Bas, Sarah Sandbach, Aryan Wack, Pat Walters, and Molly Webster, with help from Andrew Vinyales. Our fact checkers are Diane Kelly, Emily Krieger, and Natalie Middleton. Hi, this is Susanna calling from Washington DC. Leadership support for Radio Lab Science Programming

is provided by the Gordon and Betty Moore Foundation, Science Sandbox, Assignment Foundation Initiative, and the John Templeton Foundation. Foundational support for Radio Lab was provided by the Alfred P. Sloan Foundation.