The trouble of zero

What better time to contemplate the conundrum that is zero than the start of a new year? Zero is a fairly new concept in human history and even more recent as a number. It wasn't until around the 7th century that zero was used as a number. That's when it showed up in the records of Indian mathematicians. Since then, zero has, at times, been met with some fear — at one point the city of Florence, Italy banned the number. Today, scientists seek to understand how much humans truly comprehend zero — and why it seems to be different from other numbers. That's how we ended up talking to science writer Yasemin Saplakoglu https://www.yaseminsaplakoglu.com/ in this encore episode about the neuroscience of this number that means nothing. Read more https://www.quantamagazine.org/how-the-human-brain-contends-with-the-strangeness-of-zero-20241018/ of Yasemin's reporting on zero for Quanta Magazine. Plus, check out https://www.npr.org/2024/01/03/1198909057/brain-struggles-big-numbers-neuroscience our episode on why big numbers break our brains. Interested in more math episodes? Let us know what kind of stories you want to hear from us in 2026 by emailing [email protected] mailto:[email protected]! Listen to every episode of Short Wave sponsor-free and support our work at NPR by signing up for Short Wave+ at plus.npr.org/shortwave http://plus.npr.org/shortwave. See pcm.adswizz.com https://pcm.adswizz.com for information about our collection and use of personal data for sponsorship and to manage your podcast sponsorship preferences. NPR Privacy Policy https://www.npr.org/about-npr/179878450/privacy-policy

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• 0:00Speaker 00

  This message comes from Planet Visionaries. Host Alex Honnold sits down this season with extraordinary doers creating real climate solutions. Listen or watch wherever you get your podcasts. You're listening to Short Wave from NPR.

• 0:17Regina Barber?

  Hey, Short Wavers. It's Regina Barber. Happy New Year!

• 0:22Regina Barber?

  The new year is all about blank slates, new beginnings, starting from scratch. And so we thought, what better time than now to focus on the number that signifies origin points, literally starting from nothing, zero?

• 0:35Speaker 02

  So zero was invented relatively late in history. It was first thought to be invented around like 2,500 years ago by Babylonian traders in ancient Mesopotamia, actually.

• 0:46Regina Barber?

  That's Yasmin Soplikolu. She's a science writer at Quantum Magazine.

• 0:51Speaker 02

  Back then, they used the symbol like two slanted wedges on clay tablets. But at the time, it wasn't a number yet. It was really used as a placeholder so that you can distinguish between different types of numbers like 20 or 250 or 205.

• 1:06Regina Barber?

  And Yasmin says that this idea of a placeholder wasn't totally unique. The ancient Maya, for example, had a little shell symbol that they used in a similar way. But zero didn't really become a number on its own until around the 7th century.

• 1:21Speaker 02

  There were Indian mathematicians who came up with a couple of ways to use zero as a number, and they were the kind of first to figure out that zero could be a digit, just like the other numbers, like 1 and 2 and 3. After that, it kind of went out from India to the Arab world. And then, you know, in the 13th century, Fibonacci actually picked up the idea during his travels in North Africa, and he brought it back to medieval Europe, you know, along with the base 10 number system.

• 1:54Regina Barber?

  But in medieval Europe, not everyone was thrilled about this concept of zero.

• 1:59Speaker 02

  People had difficulty with accepting it. It was kind of scary. People were confused by it. Some thought of it as like the devil's number. It challenged, like, really deeply held ideas. And, you know, because of the influence of the church, like philosophers and theologians associated nothing with like chaos and disorder.

• 2:20Regina Barber?

  One city, Florence, Italy, actually banned the number zero altogether.

• 2:26Speaker 02

  It's a weird concept if you even think too deeply about it. It's like we're describing something that doesn't exist. Right? We like see three chairs or we see four birds and we can count those and they're, you know, physically there, but we don't see zero birds or zero chairs. We just know that they're absent, but that is zero. That's, you know, an extra level of abstraction from the other kinds of numbers that we see around us all the time.

• 2:56Regina Barber?

  And that abstraction actually makes it harder for our brains to process.

• 3:03Regina Barber?

  So today on the show, the neuroscience of the number zero. How do humans think about the concept of nothing? How do we find out? And what does that mean for our brains? You're listening to Short Wave, the science podcast from NPR.

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  This message comes from Planet Visionaries. If you're looking for a dose of optimism, Planet Visionaries is the podcast you need. Host Alex Honnold sits down this season with extraordinary doers creating real climate action. It's a lineup that proves hope isn't naive, it's fuel for change. In partnership with the Rolex Perpetual Planet Initiative, this is Planet Visionaries. Listen or watch wherever you get your podcasts.

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• 4:40Regina Barber?

  Okay Yasmin, before we get into the complexity of zero, let's just start with the neuroscience of numbers in general. You've done some writing about this, like how our brains comprehend small numbers differently than large numbers. Can you tell us more about that?

• 4:54Speaker 02

  Right, so this is actually kind of cool. We have what are called number neurons in the brain. So there are neurons that are tuned to specific numbers. There are neurons that favor, for example, the number five. And there are other neurons that favor the number seven, and so on. So that means that for the neurons that favor the number five, they'll fire more. Like if it sees five items on a table, it'll fire more than if it sees four or, you know, six. It'll still fire for four and six, but less. And then even less for, you know, three and seven.

• 5:30Regina Barber?

  Yeah, so these neurons are specifically like for that number. They like really like that number.

• 5:34Speaker 02

  Yeah, yeah, it's kind of neat that we have all of these. And there's a lot of questions surrounding it still. Like, we don't know if there are neurons that fire for like 1,505. That seems like there would be a lot of neurons in the brain then for the various numbers. I'm sure there's some other kind of mechanism there. And yeah, there was this research recently that found that the brain actually analyzes small numbers different than it does larger numbers. So there's a weird boundary around the number four. There seems to be some sort of double mechanism that's happening. So the brain processes numbers that are smaller than four

• 6:17Speaker 02

  in a more precise way than it does for numbers larger than four.

• 6:22Regina Barber?

  Yeah, we did an episode about this way back at the beginning of last year. And like how if you get above four, you're not counting, you're actually comparing. And when you're below four, that's when you're literally, like your brain is counting.

• 6:34Speaker 02

  Yeah.

• 6:35Regina Barber?

  So you're not counting anymore past four.

• 6:37Speaker 02

  So interesting, right? I think about this all the time where it's like, why is it four? Like, why not five? But it's four.

• 6:44Regina Barber?

  Yeah.

• 6:45Speaker 02

  And when I reported that piece, a couple of experts that were talking to me about how it's also weirdly related to working memory or awareness. So people can only really hold a certain number of objects.

• 6:58Regina Barber?

  Right.

• 6:58Speaker 02

  In their awareness, and that's four. So they think that maybe there's some sort of connection there between, you know, how we're processing numbers and working memory.

• 7:10Regina Barber?

  Yeah, it's like phone numbers, right? We're in chunks of three and four to like, for us to remember. Same with like, you know, social security number and stuff like that.

• 7:20Speaker 02

  Right.

• 7:20Regina Barber?

  So fairly recently, these like two researchers were like, hey, if zero is special like in math and history, maybe, and this is what you were saying, maybe it's special in neuroscience. Maybe we think about it differently. One group looked at patients with epilepsy. They already had these like electrodes in their brain. So the researchers were able to see like how individual neurons were firing.

• 7:42Speaker 02

  Yeah.

• 7:42Regina Barber?

  And the other one?

• 7:43Speaker 02

  The other group looked more at populations of neurons. So it was kind of a larger scale. They used a magneto- and so I'm gonna botch this. They used a magneto-encephalography scanner.

• 7:57Regina Barber?

  That sounds right. That was impressive.

• 7:59Speaker 02

  Long word. And basically, that means that, you know, as the neurons fire, they generate voltages, which creates magnetic fields that the machine can detect. And by analyzing the magnetic fields, the researchers were able to kind of probe what the neurons were doing when the participants were prompted to think about zero.

• 8:20Regina Barber?

  That's so cool.

• 8:21Speaker 02

  Yeah.

• 8:21Regina Barber?

  So these researchers, they're looking at neurons either specifically or as a group, you know, firing. What did they find? Was there like a new discovery on how we think about zero?

• 8:33Speaker 02

  So they actually, they were looking for something called the numerical distance effect, which is basically a phenomenon that occurs when the brain processes non-zero numbers. And it means that it can more easily distinguish numbers that are far apart from each other than those that are close together. So the brain has a little bit more difficulty distinguishing between like seven and eight versus seven and 10, for example, or seven and 11.

• 9:00Regina Barber?

  Got it, okay.

• 9:00Speaker 02

  So the idea for both these groups was that we should see if zero also is part of this numerical distance effect, because if it is,

• 9:08Regina Barber?

  Right.

• 9:09Speaker 02

  then the brain might be seeing zero, just as it does the other numbers, just a normal number.

• 9:15Regina Barber?

  Just a normal number, yeah, yeah. Probably not.

• 9:19Speaker 02

  Kinda.

• 9:20Regina Barber?

  What happened?

• 9:21Speaker 02

  Yeah, so the first group, the one that looked at a bigger scale,

• 9:25Regina Barber?

  Right.

• 9:26Speaker 02

  found that the brain processes zero similarly to other numbers. Basically, it puts zero at the start of a mental number line, like it's before one.

• 9:37Regina Barber?

  Excellent.

• 9:37Speaker 02

  It showed the numerical distance effect, which is what they were looking for. So

• 9:42Regina Barber?

  Okay.

• 9:43Speaker 02

  their conclusion was there's no difference in the way that the brain sees zero than the other numbers. Zero in terms of both the digit zero and like zero objects. The second group also found that the brain puts zero before one on the mental number line, but they found subtle differences that still made zero special in the brain.

• 10:07Regina Barber?

  Okay.

• 10:07Speaker 02

  So for example, they found that more neurons had zero as their preferred number than other small numbers. That suggested to them that the brain might be representing, you know, this empty set with more accuracy than it does for other small quantities. But this was only true for quantity zero. For the digit zero,

• 10:29Regina Barber?

  Okay.

• 10:29Speaker 02

  they did not find any difference. Like the brain saw the digit zero like it does the other digits, like one, two, three.

• 10:37Regina Barber?

  So in, as you're doing this reporting, do you find that these like, these conclusions are complementary? Do you think that they're like fighting each other? What do you think?

• 10:47Speaker 02

  Yeah, so I actually, um, it was funny because I had both groups kind of look at each other's results. And I was like, what's going on here? Why is this slightly different? And they both said that they think, you know, their results are complementary, actually. And the reason for the discrepancy was most likely just scale. And, you know, they're hopeful that future experiments will be able to kind of tease apart, um, you know, what the nuances of this are.

• 11:14Regina Barber?

  So like, what other, um, like, research did they, um, did the researchers talk about? Like, that they would like to do?

• 11:20Speaker 02

  Yeah, I think that, I mean, there's a lot of directions you can go from here. Like, it's how the brain comprehends zero. This was kind of the first, uh, step into that. And now, you know, one of the groups, actually, they're hoping to go more in the direction of, um, understanding how the brain comprehends absence. Because they think that if they can kind of compare how the brain is, uh, processing zero and processing absence, they might be able to see how, like, evolutionarily, how the, the steps toward understanding zero happened. And then the other group, they're more interested in the numbers aspect of things. So they are hoping to look more into, um, some of these maybe stranger numbers.

• 12:04Speaker 02

  But, for example, like, no one looked at the written word, zero, which would be a really interesting thing to look at, too. Like, would that look different in the brain than the digit zero? Or than it would for empty sets?

• 12:17Regina Barber?

  Right. What, what did you, like, take away from this reporting? Like, you're, you're working on this, you know, you're learning about zero and the history. Like, what was your, like, big takeaway when you're talking to all, all of these researchers?

• 12:29Speaker 02

  I think my big takeaway is how incredible and complicated and big the brain is. I just, I think my mind is still blown that we have neurons that are tuned to specific numbers and ways to comprehend these abstract, you know, ideas. Because numbers, and zero especially, is an abstraction. And we somehow have figured out a way to comprehend it, which is incredible to me.

• 12:58Regina Barber?

  Yeah. Yasmin, thank you so much for bringing us this story on Zero.

• 13:03Speaker 02

  Of course. Thank you for being interested. It was super fun to report, so I'm glad. I'm glad others find it cool, too.

• 13:10Regina Barber?

  If you want to hear more about how numbers can be tricky for us to comprehend, that episode is called "How Big Numbers Break Our Brains." We'll link to it in our show notes. This episode was produced by Hannah Chin and edited by showrunner Rebecca Ramirez. Tyler Jones checked the facts. Jimmy Keeley was the audio engineer. Beth Donovan is our senior director and Colin Campbell is our senior vice president of podcasting strategy. I'm Regina Barber. Thank you for listening to Short Wave from NPR.

• 13:45Speaker 00

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