[RADIOLAB INTRO]

SOREN WHEELER: This is Radiolab. I'm Soren Wheeler. I'm sitting in for Lulu and Latif today. They will be back next week. But for today's show, we got a good one, and I brought along a friend ...

ALEX NEASON: Hello!

SOREN: ... our editor, Alex Neason.

ALEX: Yeah.

SOREN: All right, so tell us what we're—tell everybody what we're up to today.

ALEX: 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.

LAURA ANDREWS: Yeah.

ALEX: It's like one big gigantic spiral where I'm like, "What are we? Who are we?"

LAURA ANDREWS: I'm sorry.

SOREN: That's okay.

ALEX: So the question came from a woman named Laura Andrews.

LAURA ANDREWS: Yeah. My name is Laura, and I'm a student.

ALEX: Laura is an undergraduate student at the University of Missouri.

LAURA ANDREWS: Mizzou.

ALEX: Mizzou.

LAURA ANDREWS: Yeah.

ALEX: 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.

LAURA ANDREWS: Yeah.

ALEX: I think you had just finished high school, right?

LAURA ANDREWS: Yes. I was a couple months into my gap year. But I hadn't, like, 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 dogsitting once a month or something like that. That was it. And I didn't have any plans.

ALEX: So Laura is just graduated from high school, she's at her parents' house, she's feeding some dogs from time to time.

LAURA ANDREWS: Reflecting on myself and what I'm meant to be doing.

ALEX: Staring into her future. And she starts asking herself a lot of questions.

LAURA ANDREWS: Where do I belong?

SOREN: Sort of philosophical questions.

LAURA ANDREWS: What is my place in the universe?

SOREN: About herself ...

LAURA ANDREWS: Where are we in relation to everything ever?

SOREN: ... about everything.

LAURA ANDREWS: What is everything in relation to everything?

ALEX: And Laura told us that when she started thinking about everything ...

LAURA ANDREWS: The vastness, the bigness.

ALEX: ... she just felt small. But then she thought, "Am I small?"

SOREN: And that led her to the question that she sat down, wrote out and sent to us.

ALEX: And her question turned out to be weirdly mathematical.

LAURA ANDREWS: "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 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's the midpoint between big and small in relation to literally everything ever?"

SOREN: Okay!

ALEX: Okay.

LAURA ANDREWS: [laughs] Okay.

SOREN: Can I ask you, do you have a guess about what the answer might—what an answer might be?

LAURA ANDREWS: One of my thoughts was, like, an apple would be a good size. I mean, you can hold it in your hand.

ALEX: Mm-hmm.

LAURA ANDREWS: You could eat the size of the middle-est thing.

SOREN: Yeah. When I asked my wife she said "toaster," and then we had a ...

ALEX: Toaster?

SOREN: ... like, somebody, I think Annie's friend was like, "Definitely a watermelon."

LAURA ANDREWS: [laughs]

SOREN: He was convinced it was gonna be a watermelon.

LISTENER: The first thing I thought of was an atom.

LISTENER: A grain of sand.

ALEX: So we actually put a call-out to our listeners to see what they thought the middle thing was.

LISTENER: A small rock.

LISTENER: A proton.

ALEX: And we got ...

LISTENER: Maybe Jupiter?

ALEX: ... a huge variety of answers.

LISTENER: The palm of my hand.

ALEX: But mostly what people talked about was ...

LISTENER: How do you ...

ALEX: How do you even start to try to answer the question?

LISTENER: Been really thinking about this question a lot.

LISTENER: Thinking about it more and more ...

ALEX: What are the boundaries?

LISTENER: I don't know.

LISTENER: I don't know.

ALEX: How do you choose the littlest thing?

LISTENER: Quarks and atoms.

LISTENER: Particles.

LISTENER: Neutrinos.

ALEX: How do you choose the biggest thing?

LISTENER: Massive black holes.

LISTENER: Trillions of stars.

LISTENER: Giant supernovas.

LISTENER: The galaxy!

LISTENER: The universe itself.

ALEX: Actually, what even is a thing?

LISTENER: Like, I don't know.

LISTENER: All the things are still made up of atoms, I think.

LISTENER: That's what I think.

ALEX: 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.

SOREN: Yeah. I actually weirdly just immediately thought of a particular person.

STEVE STROGATZ: Hi Soren.

SOREN: Hi, how are you? I can't believe that I feel like the ...

SOREN: Steve Strogatz, 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.

STEVE STROGATZ: And that was fun.

SOREN: Or understand statistics and probabilities.

STEVE STROGATZ: Yeah, time flies.

SOREN: But this time I just got him into the studio ...

SOREN: Well, let's jump in.

SOREN: ... without even telling him what I wanted to talk about.

STEVE STROGATZ: 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 before we talk.

SOREN: Yeah.

STEVE STROGATZ: We're just winging it today. Well, we could see what happens.

SOREN: No, but I mean, I have a very specific thing I want to talk about, actually.

STEVE STROGATZ: Oh. Oh? Really?

SOREN: Yeah, well this was sort of the spark. Here, let me just—let me just tell you ...

SOREN: And so I was like, "Let me just hit you with this question."

STEVE STROGATZ: Okay.

SOREN: Laura Andrews wrote in and said, "What is the most average sized ..."

SOREN: I literally read him the text of Laura's question.

STEVE STROGATZ: Uh-huh.

SOREN: "Where is the midpoint between big and small in relation to literally every single thing ever?"

STEVE STROGATZ: [laughs] Great! What a great question. It reminds me a lot of ...

SOREN: And 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?

STEVE STROGATZ: Huh. Okay. What's in the middle?

SOREN: Yeah.

STEVE STROGATZ: Well first of all ...

SOREN: And right away, Steve was like, "Okay, there's a couple things we gotta do just to get a grip on this question."

STEVE STROGATZ: I think we should measure everything with a common yardstick, let's say meters.

SOREN: Okay.

STEVE STROGATZ: And a meter is approximately the scale of a person, of Laura herself. Depending on how tall she is, she's between one and two meters tall, probably.

SOREN: Right.

SOREN: "And also, to simplify a bit and make the math doable, we're gonna do some rounding."

STEVE STROGATZ: We don't care about numbers like one or two. We're only interested in up to factors of 10.

SOREN: And in particular Steve said, like, if we're gonna talk about really big and really little numbers, the easiest way to do that is to talk about powers of 10.

ALEX: Remind me what powers of 10 mean?

SOREN: I mean, really, it's just like a math-y way of saying numbers like 10, 100, 1,000. Like, you talk about how many zeros come after the 1.

ALEX: Okay.

SOREN: So 10² has two zeros after the one, which is just like a—that's a hundred. And then 10³, the power of 3 has three zeros after the one, which is just a thousand.

STEVE STROGATZ: Sort of like when people talk about salaries. Are you making a four-figure salary or a five-figure salary?

SOREN: So each step going up is just times 10. 10 times each step.

ALEX: Gotcha.

SOREN: And then you can do this in the other direction, like, of 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 tenth, that's 10^-3.

ALEX: Okay. Okay.

SOREN: And then in that case, you're just talking about the number of zeros that are on the other side of the decimal point.

ALEX: Okay. I believe you.

SOREN: [laughs] Okay, so—so that's what we're gonna do. We're gonna think about what the biggest and smallest things are using powers of 10.

STEVE STROGATZ: But—so back to Laura's question, though. I ...

SOREN: Which immediately took us into some very weird spaces.

STEVE STROGATZ: People say that the smallest conceivable thing—a 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.

SOREN: Integrity?

STEVE STROGATZ: Something called the Planck 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 Planck length, space would be made of grains of space.

SOREN: Just dots.

STEVE STROGATZ: 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.

SOREN: Okay.

STEVE STROGATZ: Yeah.

SOREN: Anyway, the Planck length ...

STEVE STROGATZ: That's 10^-35 meters.

SOREN: Okay. [laughs] So that's just a decimal point and then 34 zeros and a one.

STEVE STROGATZ: It's about a trillionth of a trillionth of a trillionth.

SOREN: Of a meter.

STEVE STROGATZ: Of a meter.

SOREN: So if we start with a meter, which is roughly a person, we have to zoom in to a freckle on that person's cheek, like 10², into tiny blood vessels, then a cell in the blood, then the coiled molecules of DNA inside that cell, then down to an atom.

STEVE STROGATZ: Yeah, much smaller than an atom.

SOREN: How big is an atom?

STEVE STROGATZ: Around 10^-10

SOREN: Oh! We're not even close—we're not even close to an atom.

STEVE STROGATZ: Way, way smaller than that.

SOREN: Apparently if an atom was the size of the Earth, then the Planck length would be the size of an atom on that Earth. So we had 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.

ALEX: Er ...

SOREN: And it's still like a billionth of that.

ALEX: Wow!

STEVE STROGATZ: But anyway, that's what we currently think is the smallest conceivable thing.

SOREN: Okay.

STEVE STROGATZ: Now what's the biggest thing?

SOREN: Right.

STEVE STROGATZ: So—and then we're gonna get to what's the middle thing.

SOREN: 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 and dust mites, dolphins, soccer fields, which are, like, 10², oceans, the Earth, about 10⁷, the solar system. Then galaxies and clusters of galaxies. And then out, out, out to include all the vast empty spaces between everything.

ALEX: Wow!

STEVE STROGATZ: It's the size of the whole universe measured from one end to the other. Now what does that mean? [laughs] 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?

SOREN: Right.

STEVE STROGATZ: 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.

SOREN: Okay.

STEVE STROGATZ: Which okay, now that's not—but we were gonna do things in meters.

SOREN: Meters, right. So how do you go from light years to meters?

STEVE STROGATZ: I think if I do it right, I think in meters that's about 10²⁵ meters. We could quickly ask our cell phones.

SOREN: Okay.

STEVE STROGATZ: [laughs] Right? You could say, "Hey, Siri?" Should I do it?

SOREN: Yeah, sure.

STEVE STROGATZ: All right. Hey Siri, how big is the diameter of the universe measured in meters?

[SIRI: Okay. I found this on the web for what's the matter, what's the diameter of the universe measured in meters? Check it out.]

SOREN: Oh, she's just gonna send you to a web page.

STEVE STROGATZ: She's sending me somewhere.

SOREN: She's like, "Here's the internet, Steve." [laughs]

STEVE STROGATZ: [laughs] Oh, man! Well, all right. I'm gonna try using—without asking her, I'm gonna type into my phone "Diameter of universe in meters." Okay, this says it's about 8.8 x 10²⁶ meters.

SOREN: Wait. So that—is that 14 billion light years, and that's just changed into meters? Because does that come out right? It's—14 billion light years would be ...

STEVE STROGATZ: 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.

SOREN: Oh.

STEVE STROGATZ: Okay? So ...

SOREN: So that's—that's how you get your number, which is 8.8 x 10²⁶, which I guess with the 8 is really just 10²⁷ for our purposes.

STEVE STROGATZ: Yeah. That'll get you to 27.

SOREN: I mean, if that's what the smarties are saying ...

STEVE STROGATZ: Let's go with that.

SOREN: 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.

STEVE STROGATZ: All right. So we're ready to do it.

SOREN: Yeah. Okay, so we just have to take the big and the little and figure out what the average thing is.

STEVE STROGATZ: Well, I think we should be careful about the word "average."

SOREN: Hmm.

STEVE STROGATZ: Because there are lots of kinds of averages.

SOREN: Mm-hmm.

STEVE STROGATZ: You know, kids are taught median, mean. There's all these ...

SOREN: Can you—can you remind me what those are?

STEVE STROGATZ: 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.

SOREN: So we'd need to know how many big or little or medium things there are.

STEVE STROGATZ: Right. For a median, we'd have to count up all the objects in the universe ...

SOREN: Okay.

STEVE STROGATZ: ... and then put them in a line from smallest to biggest.

SOREN: Okay.

STEVE STROGATZ: 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.

SOREN: Yeah, because every—every big thing is made of little things. So if you add a big thing, you've also added a bunch of little things, I guess.

STEVE STROGATZ: Yeah. So I don't know ...

SOREN: Yeah, it seems like it would drag it to the—to the little stuff.

STEVE STROGATZ: 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—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."

SOREN: 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—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.

ALEX: Got it.

STEVE STROGATZ: Okay.

SOREN: Okay.

STEVE STROGATZ: We're ready to answer now.

ALEX: Go time.

SOREN: Yeah, except we're actually gonna take a quick little break. But when we come back, Steve and I actually get to an answer that honestly felt to me—I mean, it sort of freaked me out, but also I felt like maybe we had actually landed in the center of everything.

***

SOREN: Hey, I'm Soren Wheeler.

ALEX: I'm Alex Neason. This is Radiolab. And we're back doing the math my eighth grade algebra teacher always swore we would use.

SOREN: [laughs] They were right, though! They were right.

ALEX: [laughs]

SOREN: I don't think they knew what we'd be using it for, but we are here with mathematician Steve Strogatz, using that math to figure out what the middlest-sized thing in the universe is.

STEVE STROGATZ: All right, so we're ready to do it. We're ready to answer now.

SOREN: Yeah, so we got ...

SOREN: So before the break, we had decided that the smallest thing you could measure is the teeny, tiny, beyond-comprehension Planck length, which is 10^-37 meters. And then the biggest thing is the unknowable enormity of the universe itself, which is 10²⁷ meters wide. And to find the middle, Steve actually does this very simple bit of math, almost to the point of being anti-climactic.

STEVE STROGATZ: Okay.

SOREN: Just a good old-fashioned mean of two numbers.

STEVE STROGATZ: So we got 27 on the upside.

SOREN: He just takes the two powers ...

STEVE STROGATZ: And negative 35. So I should add them together.

SOREN: adds them up, 27 plus -35.

STEVE STROGATZ: That gives me -8.

SOREN: And then because we want the average of just two things, he divides them by two.

STEVE STROGATZ: Divided by 2 is -4.

SOREN: So the middle ...

STEVE STROGATZ: So think 4 below 0 is—4 orders of magnitude below 0 is the middle.

SOREN: So that's—that's 10^-4, which is a decimal point and then three zeros?

STEVE STROGATZ: Yeah.

SOREN: So wait. Is that—that's a milli ...

STEVE STROGATZ: That's a 10th of a millimeter.

SOREN: That's a 10th of a millimeter.

STEVE STROGATZ: Yeah.

SOREN: So like a—wait, a millimeter would be like a grain of sand?

STEVE STROGATZ: Yeah.

SOREN: So it's a tenth of a grain of sand.

STEVE STROGATZ: It's a very little tiny dusty. A little piece of dust.

SOREN: Dust particle.

STEVE STROGATZ: Very little piece of dust.

STEVE STROGATZ: Now if I take a bacterium, say, a cell, you know, that's a single-celled organism.

SOREN: Yeah.

STEVE STROGATZ: A big bacterium is something like 10^-5

SOREN: Okay. So that's a—that's a little small, but ...

STEVE STROGATZ: So ...

SOREN: Maybe a—a particularly large cell might get close to ...

STEVE STROGATZ: Yes, maybe.

SOREN: It would probably still be a couple steps—a step ...

STEVE STROGATZ: It's a good question. I think a eukaryotic—let's see.

SOREN: That's a cell with a ...

STEVE STROGATZ: A nucleus.

SOREN: The kind of cells we're made of.

STEVE STROGATZ: Right. I'm gonna look that one up. "Diameter of a eukaryotic cell." Look at that, Soren. It says here, "Diameter of eukaryotic cell: 10¹⁰⁰ microns." So a micron is 10^-6 meters. And 100 of those is 10^-4 meters. So the biggest eukaryotic cell is our happy place in the middle.

SOREN: Hmm. So it's a small—it's a small bit of us.

STEVE STROGATZ: Yeah. Now some people would say this is just an exercise in circular reasoning on our parts.

SOREN: That's what I keep on wondering.

STEVE STROGATZ: That it's gonna come out that—yeah. We're gonna—because of our perceptual limitations, we're gonna tend to see things centered on us.

SOREN: Like a living—a perceiving thing is gonna see out in each direction about the same and thus call itself an average?

STEVE STROGATZ: That's sort of plausible, isn't it?

SOREN: Yeah.

STEVE STROGATZ: But I feel a certain amount of confidence in all of this. I don't think it's just anthropocentric.

SOREN: Yeah. I mean, we are using science that stretches our senses as much as we, you know, have to.

STEVE STROGATZ: Right. Yeah.

ALEX: Yeah. I mean, yeah, it still makes you wonder.

SOREN: But if you—but, like, what if you—like, set that aside for just a beat, if you can manage to set that aside, what we have here is the idea that the middle-est thing is the most fundamental unit of life.

ALEX: Right.

SOREN: Of complicated life.

STEVE STROGATZ: Yeah. It's a big eukaryotic cell.

SOREN: Which I—I mean, I think it's kinda—I think that's kinda cool.

ALEX: 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.

SOREN: Yeah.

ALEX: I'm just not sure if the universe counts as a thing.

SOREN: Yeah. I was—I was actually thinking the same thing when I was talking to Steve.

SOREN: Well, this—so now to be fair, Laura I think might have asked a question that we were scared to do. [laughs]

STEVE STROGATZ: Okay, all right.

SOREN: Which is fine, because—because I think—I like what we did too but, like—but we have now figured out the middle of all measurables. Or something like that.

STEVE STROGATZ: That's right.

SOREN: 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 to, like, what's the largest thing that you could consider its own object?

STEVE STROGATZ: That is such a peculiar framing, 'cause I don't think there—what is a singular thing?

SOREN: Well ...

STEVE STROGATZ: 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 superstrings.

SOREN: But we do certainly walk around objecting things all the time, and we do—we could say ...

STEVE STROGATZ: We do.

SOREN: ... that's a sun—that's the sun.

STEVE STROGATZ: That's the sun.

SOREN: Yeah.

STEVE STROGATZ: Right. Okay. Well, let's go with it. But a galaxy ...

SOREN: So then we just started trying to figure out, like, what is the biggest thing? If you just think of a normal idea of thing.

SOREN: Do you know pulsar or black holes? Black holes, like, they have a lot of mass, but they're actually sort of small.

STEVE STROGATZ: Yeah, I—I sort of think a big star under her definition is the biggest thing.

SOREN: Right.

STEVE STROGATZ: You know, like a red giant.

SOREN: Do you have a guess about—well, let me just look it up.

STEVE STROGATZ: You can look it up. You got the whole world right there in front of you.

SOREN: This—this show is just gonna be like Steve and Soren Google.

STEVE STROGATZ: [laughs]

SOREN: What's the biggest single [laughs] cosmic record holders. Largest exo—no. Largest empty spot? That's weird. Largest star?

STEVE STROGATZ: Yeah.

SOREN: It's called UY Scuti.

STEVE STROGATZ: Really?

SOREN: I'm sure I'm saying that wrong.

STEVE STROGATZ: Did not know that.

SOREN: So that's 10¹² meters.

STEVE STROGATZ: Uh-huh.

SOREN: Which—whoa! Is apparently so big, you could fit almost five billion of our suns in it.

STEVE STROGATZ: Okay.

SOREN: So I guess for the smallest thing, currently the smallest physical size ...

SOREN: And after a lot more Googling and Googling, turns out the idea of measuring sizes of things that are that small gets really dicey, but we eventually ended up settling on 2,000 times smaller than a proton or a rough estimate of the size of, like, a quark.

STEVE STROGATZ: 10^-20 meters?

SOREN: Yeah.

STEVE STROGATZ: Yeah, that sounds to me in the right ballpark for Laura's question.

SOREN: So we had our littlest thing thing and our biggest thing.

STEVE STROGATZ: Right. Okay, so the middle ...

SOREN: So we've got our same thing, 12 and -20, and we add them up and get -8 divided by two, we get -4.

STEVE STROGATZ: That's the same damn answer! We're back to our—to our big, big eukaryotic cell.

SOREN: That might be the first time I've been spooked in a while.

STEVE STROGATZ: I'm looking at Soren. He's folding his arms.

SOREN: [laughs] I had to lean back.

STEVE STROGATZ: [laughs] He's leaning back. His mouth is hanging open.

SOREN: It's—it seems very odd to me that we got the same—I mean, like, hmm.

STEVE STROGATZ: Well, okay. I don't know what to make of it either. Sort of—I think it's—it's interesting. [laughs]

SOREN: Yeah. All right. So the basic unit of complicated life is the middle.

STEVE STROGATZ: Yes. That's nice! It's the thing that we have in common with all the life on this planet, whether plant or animal.

SOREN: Yeah. Like, complex life.

STEVE STROGATZ: Uh-huh. I think this is the answer to Laura.

LAURA ANDREWS: It's smaller than I expected.

ALEX: Does it feel satisfying for the answer to be a cell that's in us?

LAURA ANDREWS: It feels like it should be profound.

SOREN: [laughs]

LAURA ANDREWS: I mean, I'm not having, like, a mind-blown kind of reaction like I thought I would.

SOREN: I love that. No. Yeah.

ALEX: [laughs]

LAURA ANDREWS: But it—it feels like I should have more of a reaction.

SOREN: What if we were to put some music underneath? [laughs]

LAURA ANDREWS: I mean, it would be more dramatic for sure. [laughs]

SOREN: I love—I totally get that. I—I totally get that.

LAURA ANDREWS: Yeah.

SOREN: But let me see if I can at least offer you this.

LAURA ANDREWS: Okay.

SOREN: 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, like, 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.

LAURA ANDREWS: Right.

SOREN: So there are certain kinds of physical events that happen differently if you're small than if you're big.

ALEX: Hmm.

SOREN: 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 out waste 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—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.

ALEX: Well, when you put it like that ...

LAURA ANDREWS: [laughs] I mean, yeah, when you put it like that, it's more profound, for sure.

SOREN: [laughs] Okay, we're making progress!

LAURA ANDREWS: Yeah. I mean, I guess the most comforting part of it is that we're bigger than we seem.

SOREN: We're maybe not so kind of tiny as we sometimes feel.

ALEX: Yeah.

SOREN: Yeah.

LAURA ANDREWS: Yeah. Right.

SOREN: Well, thank you Alex for sticking with me and bringing me this one, and going on the journey with me. And not giving up.

ALEX: And thank you to Laura for sending us on the journey.

SOREN: Yeah.

ALEX: 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.

SOREN: Yeah. She is—Laura is not small to us.

ALEX: For this episode, she was the center of our universe.

SOREN: [laughs] Yes. Yeah, exactly. This episode was reported by me and Alex Neason. It was produced by Annie 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 Strogatz. 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 Radiolab.org.

ALEX: That's it for us today. Thanks for listening.

SOREN: Lulu and Latif will be back next week.

[LISTENER: Radiolab was created by Jad Abumrad and is edited by Soren Wheeler. Lulu Miller and Latif Nasser are our co-hosts. Dylan Keefe is our director of sound design. Our staff includes: Simon Adler, Jeremy Bloom, Becca Bressler, Rachael Cusick, Ekedi Fausther-Keeys, W. Harry Fortuna, David Gebel, Maria Paz Gutiérrez, Sindhu Gnanasambandan, Matt Kielty, Annie McEwen, Alex Neason, Sarah Qari, Anna Rascouët-Paz, Sarah Sandbach, Arianne Wack, Pat Walters and Molly Webster. With help from Andrew Viñales. Our fact-checkers are Diane Kelly, Emily Krieger and Natalie Middleton.]

[LISTENER: Hi, this is Susanna calling from Washington, DC. 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.]

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