[RADIOLAB INTRO]

LATIF NASSER: Well, first, am I imagining that Jad already knows about—because we just talked about it when I was promoting my show, right?

JAD ABUMRAD: About Benford's Law?

SOREN WHEELER: Just go. Just tell him that. Remind him.

LATIF: Okay, so ...

SOREN: He knows, but he forgets.

JAD: Yeah, just ...

LATIF: Okay. Well, I think ...

LATIF: Hey. I'm Latif Nasser. This is Radiolab. And today, in the week after the election was called for Joe Biden, but in this sort of weird middle space when Donald Trump has refused to concede, our editor Soren Wheeler and I sat Jad down because we wanted to tell him about something from our past that has come back to haunt us.

JAD: Okay.

LATIF: So a few months ago, you may remember I was telling you about the Netflix show I made.

JAD: "Connected," right?

LATIF: Right. And I was telling you about one of the episodes, which is about something that, before my time, Radiolab had also separately done an episode about, which was this thing called Benford's Law.

JAD: Yes. Yes.

LATIF: This kind of funny, nerdy, little bit mystical, mathematical law that's kind of stupendously broadly applicable?

JAD: Stupendously broadly applicable.

LATIF: Yeah.

JAD: It's one of those.

LATIF: But so, you know, in my head, I feel like I parked it in the, like, fun, silly, nerdy category of stuff that's more sort of interesting than it is important. But then all of a sudden, over the last week, it became very important.

JAD: Oh, boy.

[ARCHIVE CLIP: Benford's Law. What is Benford's Law? And how is it relevant to the 2020 election?]

LATIF: It was all over Twitter, Facebook.

[ARCHIVE CLIP: It's mathematics. Add clarity and ...]

SOREN: I think some of the first things I saw about it were YouTube videos.

[ARCHIVE CLIP: In layman's terms, it's the mathematically and statistically provable point that ...]

LATIF: Then it shows up on all these fringe news sites—Newsmax, Boston Herald, Gateway Pundit.

SOREN: And then conservative podcast people like Dan Bongino start to talk about it.

[ARCHIVE CLIP, Dan Bongino: What if I told you when you look at some of the voter data in Wisconsin, that Benford's Law is saying it's not possible?]

LATIF: And ...

[ARCHIVE CLIP, Scott Adams: Benford's Law is what we're talking about.]

LATIF: ... Scott Adams, the cartoonist Scott Adams, who's a big Trump supporter, he was talking about it.

[ARCHIVE CLIP, Scott Adams: Votes don't conform to the natural arc.]

LATIF: There was so much stuff going around online that Twitter actually started flagging mentions of Benford's Law.

JAD: Wait. Why?

LATIF: Because suddenly there were just, you know, a lot of people online trying to use Benford's Law to parse the 2020 election returns to say that the votes for Joe Biden were fraudulent votes, and Benford's Law proves that.

JAD: Huh! That's funny because, like, we're all waiting—like, you know, there's all this talk about fraud. And everybody's like, "Okay, show us the fraud. Where's the fraud?" You're saying Benford's Law of all things is what people are using to try and say that there's fraud?

LATIF: Yeah.

SOREN: And then the big hit is that, like, on Twitter, people would be like, "By the way, check out Radiolab. It's totally true."

LATIF: Right. So ...

SOREN: Or, like, "Go see "Connected." Like, this is the real deal."

LATIF: Yeah.

JAD: Wow.

LATIF: It almost felt like we got pulled into this—into this fight.

JAD: You never know where your stuff's gonna end up. But I assume from what you said about Twitter that there is no there there in terms of Benford proving fraud.

SOREN: No, definitely not. I mean, if you talk to the people who know the math, do the math, they say, you know, like, all these guys are wrong.

LATIF: But interestingly, the way that they're wrong, the way that all these people are sort of fighting about it on Twitter is actually kind of interesting.

JAD: But can you just remind me what Benford's Law is? I mean, I have this vague memory of this from one of our shows. But, like, what is it again?

SOREN: So tell you what, let's play a part of the old piece, and we'll come back to the election battle in just a second. But this was, like, 11 years ago. We did a whole show about numbers. It was actually during your paternity leave with Amil.

JAD: That's right. This was my paternity leave, yeah.

SOREN: So what we did was sort of brought you back into the studio to work you into the piece.

[ARCHIVE CLIP, Jad: I'm Jad Abumrad.]

[ARCHIVE CLIP, Robert Krulwich: And I'm Robert Krulwich.]

[ARCHIVE CLIP, Jad: This is Radiolab.]

[ARCHIVE CLIP, ROBERT: We're still talking about numbers. Now we're gonna switch ... [laughs]]

SOREN: It was definitely a while ago, and it felt a little bit like a simpler time, but we're gonna play it real quick. So the story that we told basically came from an interview that Robert did with a guy named Mark Nigrini, who's a business professor at The College of Jersey.

ROBERT: And his favorite story that numbers tell actually starts back in 1938. So imagine an office.

MARK NIGRINI: In Schenectady, New York. At the GE Research Laboratories.

ROBERT: And in that office is a man and he's sitting at his desk.

MARK NIGRINI: Mr. Frank Benford.

ROBERT: And Mr. Frank Benford is a physicist, so he's doing some difficult calculations and he's hunched over a book—probably actually the—one of the most boring books you could imagine. This is a book of logarithmic tables.

ROBERT: This is a book of logarithmic tables.

JAD: What are logarithmic tables?

MARK NIGRINI: So log tables were a very convenient way of doing multiplication in the early part of the last century.

ROBERT: So remember, this is before there were calculators. So if you wanted to multiply something like 145 times 3,564, you could just go to this book and look it up. So each starts with numbers you might want to multiply by—1 to 100 on the first pages, then 101, 2, up to 200 and 300. And the back of the book is, like, 900s. The further you go, the higher and higher the numbers you use to multiply.

MARK NIGRINI: That's right.

ROBERT: So our Benford fellow, he's sitting there, doing his calculations. And he's looking at the numbers, flipping through the book.

MARK NIGRINI: He's staring at the pages, and ...

ROBERT: He notices something kind of weird.

MARK NIGRINI: He noticed that the first few pages were more worn than the last few pages.

ROBERT: Meaning more smudgy and darker and oily, as if he was using the front of the book ...

MARK NIGRINI: More than the last few pages.

ROBERT: And he wondered, why is this happening?

MARK NIGRINI: Strange.

ROBERT: "I'm not aware of favoring one part of the book over the other. Am I doing something a little odd? Or maybe it's something bigger." And that's when it hit him.

MARK NIGRINI: He thought maybe in this world, there are more numbers with low first digits than with high first digits.

ROBERT: What? More numbers that start with one or two than numbers than start with seven, eight or nine.

JAD: Just because his book is worn?

ROBERT: That's what started him thinking, so here's what he did.

STEVEN STROGATZ: He compiled some tens of thousands of statistics.

ROBERT: That's Steve Strogatz, mathematician at Cornell University.

STEVEN STROGATZ: Just anything he could think of that was numerical: molecular weights of different chemicals, baseball statistics, census data.

MARK NIGRINI: The revenues of all the companies listed on the main stock exchanges in America.

ROBERT: And everywhere he looked, in all these different categories, it seemed yes, there were more numbers beginning with one and twos than eights and nines.

JAD: Wait, really?

ROBERT: Oh, yeah. This has been checked out again and again and again. And it's true.

STEVEN STROGATZ: Size of rivers.

ROBERT: Wow.

MARK NIGRINI: Earthquakes and things like that.

STEVEN STROGATZ: Populations or number of deaths in a war. Areas of counties.

MARK NIGRINI: Streamflow data in the United States.

JAD: What if you were to, say, get all the people in New York together and look at their bank accounts?

MARK NIGRINI: Ah. Bank account balances follow Benford's Law nearly perfectly.

ROBERT: Meaning that if you just look in at the amount of money that people have matter of factly in all the bank accounts, you'll find they begin with one more often than they begin with two?

MARK NIGRINI: Perfectly, yes.

ROBERT: Yes?

MARK NIGRINI: Actually, they begin with one 30.1 percent of the time. They'll begin with a two 17.6 percent of the time. They'll begin with a three 12.5 percent of the time.

JAD: That's a big difference!

MARK NIGRINI: And the ...

JAD: Why would three be—I'm sorry. Keep going. Yeah.

MARK NIGRINI: And the poor nine would only occur as a first digit 4.6 percent of the time, which actually would make the one approximately six times as likely as the nine. And it is quite amazing.

JAD: What?

ROBERT: That is more than quite amazing. That's deeply suspicious.

STEVEN STROGATZ: I mean, this is crazy, what I'm telling you. And I can't give you good intuition why it's true, but ...

ROBERT: Steve and Mark and many, many, many mathematicians will tell you, despite what you may think, there is a preference— a deep preference in the world, it seems, for number sequences that start with ones and then twos and then threes.

SOREN: So that was how we did it. There's more, but ...

JAD: I feel like I'm re-experiencing the weirdness of this law again. Is that—at the risk of tracking us off, why is that, that you would get more ones than twos and all that?

LATIF: Like, this is, yeah, the question I had, too. Is it, like ...

SOREN: Do you want the Radiolab explanation? Because I remember it ...

JAD: [laughs] Yeah, what did we say back then?

SOREN: ... when we did this originally. This was a classic move. It's like, we get to the end of the piece. You ask this very question.

JAD: Huh. You still haven't addressed the central mystery here. Why in the world would there be more ones than nines? Shouldn't they be equi ...

ROBERT: Equicoincident?

JAD: Yes.

ROBERT: Well, the answer is actually very complicated and deeply mathematical. The simple answer is ...

JAD: Is there an answer, though?

ROBERT: Yes, there is an answer, and it has to do ...

JAD: Do you understand the answer?

ROBERT: No, just too numeric for me to explain it to you. [laughs]

JAD: [laughs] Okay. All right.

ROBERT: But I will now.

JAD: [laughs] Right.

SOREN: And then we laugh our way out of the room.

LATIF: The best explanation I heard was about if you imagine a lot of things grow, right? They, like, grow and get bigger, right? And so let's say you're a one, right? And you want to get to grow to be a two. You have to grow 100 percent to get to a two. So it takes you a long time to get from being a one to being a two. If you're an eight and you want to grow to become a nine, right? That's just an eighth of you that needs to grow again, right?

JAD: Right.

LATIF: So it's like, you're gonna be in that eight zone way shorter than you were in the ...

JAD: Right. That's interesting.

LATIF: ... between—in the one to two zone. Yeah.

JAD: I see. So it's like—it's kind of like some kind of a logarithmic situation.

LATIF: Exactly, exactly.

JAD: Jumping from one to two is huge, two to four is huge, four to eight is huge. And that's why the hugeness of those jumps means you—I lost the end of that sentence.

SOREN: It's sort of why we couldn't in the first—but, you know, the point of the piece, like, even though we didn't explain that, what the piece did do was sort of—and this is the whole reason we did the piece—was go on to talk about how you can actually use Benford's Law in these really pretty consequential ways.

LATIF: Right.

ROBERT: When Mark Nigrini first ran across Benford's Law, he thought, "Maybe I can use this law to bust people."

MARK NIGRINI: For payroll fraud, tax return fraud.

ROBERT: You thought, "Hey, we can use this to catch a thief?"

MARK NIGRINI: That's right.

JAD: Huh? How?

ROBERT: Well, Nigrini figured ...

SOREN: And so, you know, basically, we explain that if books are cooked, like, financial books are cooked, they will not be following Benford's Law. So real books would follow the law, cooked books don't. So you can spot a thief. And we gave a bunch of examples of that, you know, little stories.

DARRELL DORRELL: Ran Benford's, and boom!

JAD: Oh, busted!

DARRELL DORRELL: She eventually pled.

ROBERT: Or the guy with a $40 million Ponzi scheme.

DARRELL DORRELL: Ran Benford's, and boom!

SOREN: And then at the end of the piece ...

ROBERT: Well, almost boom. I mean, Benford's was an element in all these cases. It wasn't the clincher. But still ...

DARRELL DORRELL: It was a very compelling argument. And then 10 years from now, it'll be the equivalent of a fingerprint.

SOREN: Which is, you know, a strong statement. But I mean, at the same time, we didn't say anything about elections. And we weren't even thinking about elections.

JAD: Right.

LATIF: But when we come back from break, we're gonna go right into Benford's Law and election data specifically, which is where the trouble begins.

[LISTENER: Howdy. This is Blake Fraser from Nashville, Tennessee. Radiolab is supported in part by the Alfred P. Sloan Foundation, enhancing public understanding of science and technology in the modern world. More information about Sloan at www.sloan.org.]

[JAD: Science reporting on Radiolab is supported by

Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.]

LATIF: I'm Latif Nasser. This is Radiolab. We're talking about Benford's Law and the 2020 presidential election.

JAD: Well, let me ask you, have any smart statistics, knowledgeable people actually tried to use Benford's Law to see whether there's election fraud in any election anywhere?

LATIF: Yeah. Yes. Yeah. And for me in particular, like, I mean, you guys were mostly talking about, like, taxes and forensic accounting, and it was about money and numbers. But in the Connected episode I did, I totally talked about elections.

[ARCHIVE CLIP, Latif: Well, there is one moment when our millions of personal decisions all get channeled in the same direction, when free will is in full flower—or at least it's supposed to be.]

LATIF: There's a whole segment about here's how Benford's Law can potentially relate to elections. And in fact ...

[ARCHIVE CLIP, Latif: Walter?]

[ARCHIVE CLIP, Walter Mebane: Oh, hey. How are you, Latif?]

[ARCHIVE CLIP, Latif: Hi. How you doing?]

LATIF: ... the guy I talked to in that show is the guy that a lot of these people online, it's his work that many of these folks are citing. So I was like ...

WALTER MEBANE: It is now recording, it says.

LATIF: ... I better call him back up.

WALTER MEBANE: Okay, sure.

LATIF: Introduce yourself for me. Just tell me who you are in a line.

WALTER MEBANE: Walter Mebane at University of Michigan in Ann Arbor.

LATIF: So—okay, so what has happened between now and the last time we talked?

WALTER MEBANE: Well, the last time we talked ...

LATIF: And he had seen all of this stuff online. He knew all about it because he'd been getting all these emails in the last week.

WALTER MEBANE: So the trickle turned into a flood. And my students start to write me and say, "Hey, you know, this is going on, so ..."

LATIF: Saying, "Hey look, Benford's Law and your work, people are using it basically to claim fraud."

WALTER MEBANE: I was originally pointed to a Twitter post, and then there was another Twitter post, and then I found a YouTube video. And I don't know which one came first.

LATIF: So basically, what a lot of people are doing is they're taking these, like, precinct tallies and saying, "Okay, look. We're entering all the precinct tallies. We're taking the first digits from all the vote tallies for each of the candidates in each of these precincts, and then we're checking how often it starts with one, how often it starts with two and so on.

SOREN: Take Chicago, right? They did Chicago, didn't they, Latif?

LATIF: They did, yeah.

SOREN: It's not a swingy one. It's one that Biden won by a lot. But let's just do this real quick. Chicago. How many voting precincts are in Chicago?

LATIF: There's—I think there's something like hundreds, if not thousands of them.

SOREN: Yeah, let's just say a thousand.

LATIF: Okay, sure.

SOREN: You just take the votes for Donald Trump in each of those precincts. Here he got 238. Here he got 462. Here he got 521. And then in another column, you take all the totals for—that Joe Biden got in those same precincts. 266 here, 892 here, 326 here. And what it is that's popping up is oftentimes basically just a little graphic. Two little curves with the vote counts. It's like, here's Trump's curve. Look at all the ones and a little less twos, a little less threes. Nice sweeping little curve.

LATIF: Yeah.

SOREN: Oh, here's Biden's. So it's that weird—there's a bunch of sixes in that bumpy curve.

LATIF: Right. Right.

SOREN: And they're just like, "Look at these two. See?"

JAD: I see.

LATIF: And the way that they see it—so this one is from some data from Michigan. It's like, okay, there's less ones than there should be. There's way less twos than there should be. There's more threes than there should be. There's more fours, way more fives, more sixes, more sevens, more eights and less nines. So it's like—it's all over the curve, right? Is the claim.

JAD: Hmm. So they're saying that the Biden numbers are ...

LATIF: They look cooked.

JAD: They don't fall according to this pretty Benford curve.

LATIF: Right.

JAD: Therefore ...

LATIF: Something's amiss.

JAD: ... probably somebody was just, like, keying them in on some ...

SOREN: Right. Some fake adding—some kind of false, fraudulent adding of numbers.

LATIF: Yeah.

JAD: I see.

LATIF: Because the idea is that random numbers follow this pattern, but human-created numbers don't.

JAD: This is a way of seeing human meddling.

LATIF: Right.

JAD: I see.

LATIF: That's the idea.

JAD: That's the claim.

LATIF: But ...

WALTER MEBANE: All this is completely ridiculous.

LATIF: ... Walter was just like, "You just can't do this with precincts."

WALTER MEBANE: Because it's very well known the first digit of precinct vote counts are not useful for diagnosing frauds or anything else.

JENNIFER GOLBECK: So I started jumping into those threads, correcting people and explaining. Which didn't win me a lot of friends on Twitter. [laughs] At least among that audience.]

LATIF: So once this thing blew up online, another person I talked to on my show ...

[ARCHIVE CLIP, Latif: Jennifer Golbeck. Professor at the University of Maryland's College of Information Studies.]

[ARCHIVE CLIP, Jennifer Golbeck: As a researcher who studies social media ...]

LATIF: She's, like, on Twitter, like, fighting, battling with people.

JENNIFER GOLBECK: Yeah, so ...

LATIF: Are you getting nasty DMs and stuff?

JENNIFER GOLBECK: Yeah. I mean, not the worst that I've gotten, right? More ...

LATIF: Right.

JENNIFER GOLBECK: ... you know, people cross a threshold where they don't understand where I'm—what I'm saying anymore, so then they just start calling me names, which is okay. [laughs]

LATIF: Right. Right.

JENNIFER GOLBECK: I mean, it's for sure not a dumb idea to wonder if we can do this. And part of the attraction for Benford and why people really like it here is that it's super surprising when you first learn about Benford, right? My mind was blown the first time I learned about it. And ...

LATIF: On Radiolab, right?

JENNIFER GOLBECK: Yeah, on Radiolab. That's right.

LATIF: Yeah.

JENNIFER GOLBECK: I mean, it is what got me started doing research in this space was, like, listening to that Radiolab and not being able to stop thinking about it, you know, for weeks.

LATIF: Yeah.

JENNIFER GOLBECK: There are papers out there that say, look, Benford could be really powerful for doing this, but it's not the way anybody on Twitter was doing it.

LATIF: The problem is when you're looking at precinct data, these precincts are basically purposefully made just for counting the election data. And the reason that those are helpful is because they're all the same size.

JENNIFER GOLBECK: Normally when Benford works, you've got lots of orders of magnitude. So say we're looking at, like, the length of all the rivers in the world. We know that that follows Benford. So there's some really short rivers, and there's some super, you know, continent-long rivers. So there's a lot of changes in the orders of magnitude. You have some ...

LATIF: But the precincts do not have multiple orders of magnitude.

JENNIFER GOLBECK: Precincts tend to be kind of the same size.

WALTER MEBANE: And the first digit is primarily determined by the size of the precinct. It has nothing to do with anything about the behavior of the voters or the officials or the vote counters. It's just a matter of the design of the precincts.

JAD: Wait. How so? How would the first number have to do with the size of the precinct?

LATIF: Well, Walter put it this way.

WALTER MEBANE: Imagine that all the precincts are about a thousand in size, which is roughly a convenient number, but put whatever you like. And imagine the two candidates get about 50 percent of the vote.

LATIF: Which was true in a lot of the, you know, swingy precincts that this data was based on. And if you look at the Trump-Biden totals in those places ...

WALTER MEBANE: Then the first digit everywhere is gonna be a four or a five.

SOREN: You're gonna get 500 to this guy, 500 to this guy.

LATIF: Right.

SOREN: 400 to this guy, 600 to this guy.

JAD: Yeah.

SOREN: You're probably never gonna get a one in front of anything unless it's a blowout.

JAD: So—that's interesting. So they're skewing—because of the way that the precincts are drawn up, you're skewing towards the middle, I would imagine. You're gonna get a whole bunch more fours and fives and sixes.

LATIF: And that's exactly what that chart I was telling you about before that's sort of gone a little bit viral, which is like, that's exactly what it shows. So it says that Michigan data, where it's like, oh, look: The highest numbers are for fours, fives and sixes.

JAD: Oh, that's funny.

LATIF: So you're like, oh. So, like, that makes sense that Biden would have gotten fours, fives and sixes, right? And then Jen pointed out, okay, now take another thousand-person precinct, and say this is one where Biden has a really big lead.

JENNIFER GOLBECK: So if Trump gets 150 votes, then Biden's gonna get 850 votes. He's gonna get the rest, right? So if Trump follows a Benford's Law distribution, Biden necessarily will not follow that distribution because he's getting the other part, right?

LATIF: Oh! But then shouldn't Biden's votes be the exact oppos—like, the mirror of the curve or something close to it?

JENNIFER GOLBECK: So if it were the situation where we had, like, a thousand people in every precinct, that would totally be true. In reality, there's, like, variation. And so if you look at the plotting of this, what you actually see is that Biden's curve pretty much matches the curve of how many people are in the precinct.

WALTER MEBANE: So that's not Benford's Law. That's just because the precinct sizes are the way they are.

JENNIFER GOLBECK: Yeah. I mean, I don't think there's any reason to expect anybody's gonna look like Benford or not because this first significant digit analysis of Benford in elections doesn't work, period.

LATIF: Now there are definitely statisticians out there who say that you cannot Benford-ize elections at all. But Walter, the thing that's interesting about him is that he thinks—and this is, you know, a lot of the work that he does—that you can look at elections if you look at not the first digit, but at the second digit. This has become his thing. So he's, like, looked at elections in Kenya and Russia and Germany and Turkey and Mexico and Iran. And often, he is using Benford's Law on the second digit.

JAD: The first digit is going to be a function of how big the precinct is ...

LATIF: Exactly.

JAD: ... which is a human construct. But the second digit, that's gonna be more subject to the laws of randomness and whatever, yada, yada, yada. That is not a human construct, not in quite the same way.

LATIF: Probably, hopefully.

JAD: Hopefully, right.

LATIF: So, yeah.

SOREN: Super stupid caveat: Most mathematician total-freakout geeks will say the thing happening with the second digit is not strictly Benford's Law. It's just a very Benford-like thing that's a pattern that you can spot.

JAD: Got it.

LATIF: Yeah. And he uses phrases like "Benford-inflected" or "Benford-like." Or Benford-like—it's like ...

SOREN: Flavored.

LATIF: That kind of thing.

JAD: I see. I see.

LATIF: And Walter also makes clear that even if you do look at the second digit ...

WALTER MEBANE: Even then, it's not a perfect signal for fraud.

SOREN: He'll do the Benford thing right, but he also has this whole, like, sort of tool belt.

LATIF: A toolkit, right.

SOREN: ...A toolkit. Right. That he's made of all these other different statistical things that you bring to bear on it because it's super complicated and backgrounds and expectations, and then you do this with a regression to the—blah, blah, blah. So he's gonna bring the whole suite of many complicated I-am-a-super-smart-person tools to bear on this.

LATIF: Right. And the tools that he's sort of picked up in literally 20 years of studying elections statistically for fraud. But anyway, okay, so those are kind of in general the reasons why he looks at all the stuff that sort of these kind of amateur Benford's Law analysts online are throwing up. He looks at that and he's like, "That's ridiculous." And then so then he was like, "Okay, I'm—" over the weekend, he was like, "I'm just gonna run this myself."

WALTER MEBANE: And I produced a working paper, which I think you have the link for.

LATIF: Yup.

WALTER MEBANE: And it has the diagnostics not only for the second-digit Benford's Law stuff—Law-like stuff—but the other diagnostics that I've developed over the past decade and a half.

LATIF: And what did you find in running that stuff, the second-digit stuff?

WALTER MEBANE: There's nothing. I mean, there's no sign of frauds of any kind.

LATIF: It was like this is a totally ordinary—in fact, it seems pretty exemplary.

WALTER MEBANE: As far as I've seen, there's nothing bad that happened anywhere. This has been miraculous. This election has been so smooth.

JENNIFER GOLBECK: You can't just plug some numbers into your Excel spreadsheet after you've read a Wikipedia page and do it. But people who feel like, "Look, I can see the difference, and a bunch of these look the right way and one looks the wrong way, so forget what you're saying about it being complicated; it must be true," those are hard people to convince.

LATIF: It's just common sense enough, but it's just obscure and complicated enough that it feels like it's, like, a piece of evidence that could—you know, it could take on a—yeah, sort of a life of its own. It could be this thing that then—you know, there's a certain—admittedly small but—segment of the population that's like, now whenever they talk about the 2020 election, they're going to be like, "Oh, and Benford's Law shows that it's all—it was all bogus." You know?

JAD: Yeah. Yeah.

SOREN: Yeah. It strikes me as like, is it gonna go to court and win the day? No. Is it the kind of thing that maybe next Tuesday Donald Trump would say in a press conference? Yes.

LATIF: Probably, yes.

SOREN: Yes.

JAD: Yeah. It's also—like, it's the kind of thing that steps into the breach of a very uncomfortable phenomenon. And we all experienced this, right? Which was election night, you had one result, and then you had this weird, creeping, slow tilt over the next three or four days. And even though we ourselves did a story about how that tilt was coming, the tilt still felt surprising and non intuitive in some emotional way. And so then that is fertile ground for these Benford-esque ways of explaining the irregularity.

SOREN: Yeah. But then even though the people who actually know what they're talking about say it doesn't explain the irregularity.

JAD: No, but see, this is the problem with the world we live in, is that there's never been more distrust of leadership and expertise. But you're asking us, in a moment when we're very unlikely to—to trust experts to explain this thing.

LATIF: Which is all to say, like, it does feel like it's hard to explain. It's gonna be hard for a lot of people to explain, like, why—especially if they're not resorting to experts to help explain it, like, how did it go this way when everybody I talked to, you know, seems to have wanted the opposite to happen?

JAD: Yeah, totally. I find myself wanting to do sort of, like, a cost-benefit on Benford's applications in the world.

SOREN: Well, the upside would be financials. The upside would be ...

LATIF: Well, not just financials. So there's—yeah, financials is a big one. I mean, tax fraud, like ...

JAD: Okay. Okay.

LATIF: But also, another thing is—and this is something that Jen uses in her other research, which is her main research—is how you use Benford's in social media. So you can use it to detect bots online. You can see ...

JAD: Really?

LATIF: And she has done that very thing.

JAD: How do you ...

LATIF: You can also use it ...

JAD: No, keep going. Keep going. Then I'm gonna double back.

LATIF: No, so you—literally, you count—and this is cool because people can do it at home, too. You count up not—so all the follower numbers of your followers on Twitter, Facebook, whatever. And you can see, based on the followers of your followers, if you just take those first digits, it should follow Benford's Law.

JAD: Oh my God. That's incredible.

LATIF: And if it doesn't—yeah.

JAD: That's wild.

LATIF: And then there's ...

JAD: Is that—so wait, does Twitter use that to prune bots, as they do from time to time?

LATIF: I don't know if Twitter officially uses it. She—Jen definitely uses it. And then not only that, but also, you can use—and this is another thing in the TV show that we did. I did an interview with former Radiolab guest, also my—one of my former college professors, Hany Farid. You can use it to basically sniff out deepfakes, and you can use it to sniff out manipulated media in an era when it's getting way harder to tell the truth.

JAD: Really?

LATIF: You basically look at these embedded number values in a single picture, and you can see whether that picture has been edited or how many times it's been saved.

JAD: Oh, wow.

LATIF: Or kind of things like that. So it's actually—like, I mean, it definitely is a force for chaos and doubt, and it's also sometimes a kind of superhero for truth.

JAD: If only we could understand it. [laughs]

LATIF: Right.

JAD: All right. Thank you, Latif and Soren, for taking me back into the past and forward into now.

SOREN: Of course.

LATIF: No problem.

JAD: Definitely go check out Connected, Latif's show on Netflix. You can find it there. It's amazing. The episode with the Benford stuff is called "Digits."

LATIF: And also in addition to that, you can go back into the deep past and listen to the Radiolab show called "Numbers," which has not only all that Benford goodness but also a love story, some babies and even a little Johnny Cash. It's a great episode.

JAD: I'm Jad Abumrad.

LATIF: And I'm Latif Nasser.

JAD: Thanks for listening.

[LISTENER: This is Mark Schondorf from Highland Park, Illinois. 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. Suzie Lechtenberg is our executive producer. Our staff includes: Simon Adler, Jeremy Bloom, Becca Bressler, Rachael Cusick, David Gebel, Tracie Hunte, Matt Kielty, Tobin Low, Annie McEwen, Sarah Qari, Arianne Wack, Pat Walters and Molly Webster, with help from Shima Oliaee, Sarah Sandbach and Jonny Moens. Our fact-checker is Michelle Harris.]

 

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