Connected: The Hidden Science of Everything (2020) s01e04 Episode Script
Digits
1
[clock ticking]
[Nasser] I need to tell you about a code.
A pattern of numbers.
When you first hear about it,
it seems trivial.
But then you start seeing it
over and over.
Hidden in plain sight
in the chaos all around us.
The stock market, street addresses,
the numbers in this morning's paper.
Each clue leads you one step closer,
possibly to insanity,
but possibly to unlocking a secret
about human society
that's so big, so profound,
so powerful, that the US government
doesn't want you to know it.
You have no idea just how deep this goes.
[suspenseful music playing]
[upbeat music playing]
I'm Latif Nasser,
and this is a show about
the astonishing connections all around us.
Connections
between you and me and our world
that'll make you see that world
in a whole new way.
Welcome to the US Naval Observatory,
official residence of the Vice President
of the United States,
home to the telescope that discovered
the two moons of Mars,
and rumor has it,
but no one here will verify,
site of a top-secret underground bunker.
But I don't care about any of that.
I'm here for the library
because here, 140 years ago,
is where our mystery began with a book.
It's a logarithm book from the late 1800s.
It's basically what people used
as a calculator before calculators.
Think about it as a giant, old book
of multiplication tables.
Admittedly dull stuff.
So, here's what happened:
an astronomer named Simon Newcomb,
that guy,
was working here,
looking at a book a lot like this one,
and he noticed something kind of weird.
If you look at the early pages,
what you'll see is that they're all worn.
But if you look at the later pages,
they're much less so,
as if people were only using
the first few buttons of the calculator.
Kind of random, right?
But then he looked at another logbook
and saw the same thing.
And another,
and another and another.
Every time. First pages worn.
Back pages, good as new.
But what Newcomb stumbled upon
was the first clue
to a profound and secret order
to the world all around us.
One that could pop up
in everything from your favorite sport
to your favorite song,
even to the way you're gonna die.
Once you see it, you can't unsee it.
It's everywhere.
But I'm getting ahead of myself.
Let's go to clue number two.
Your taxes.
[film narrator] The average taxpayer
is hardly concerned
with all the intricacies
of the far-flung IRS computer system.
There's a "good" tape,
and there's the "error" tape.
Looks like this one is deducting
for medical payments covered by insurance.
So all this started
because I heard this rumor
that somehow governments around the world
have turned Newcomb's discovery
into a secret weapon against tax cheats.
That using this mysterious pattern,
they can just look at the entries
on your tax form
and magically tell if you're lying.
Is it true? Is that even possible?
And if so, how?
I decided to just go ask them myself.
Of course,
I couldn't get the IRS to talk to me.
So I had to find someone
who would talk to me.
[keyboard clicking]
[clicking continues]
[woman] Sir, Randy will see you now.
Thanks.
First of all, thank you so much.
I tried to go talk to the IRS,
and they would not talk to me.
This is Randy Shump,
former Senior Attorney for the IRS.
If anyone can explain
the inner workings of the IRS, it's him.
So I heard about
this 150-year-old statistical technique
that maybe gets used to analyze taxes.
It has to do with this old logbook,
and there are, like,
dirty pages at the front.
I think you're talking
about Benford's law.
-Oh really?
-Yeah.
[Nasser] Okay, yeah. That's the thing.
That's the thing I read about.
It has a name: uh, Benford's law.
Okay, so that's
what this episode is about.
[Nasser] So let me just ask you
straight out.
Does the IRS use Benford's law?
I'm not permitted
to disclose that information.
The IRS doesn't make
that information available.
I don't know what it is.
And even if I did,
I wouldn't be able to say so.
Turns out it's illegal for IRS employees
and even former IRS employees
to disclose certain tools they use.
So, I'm not going to say
that the IRS uses Benford's law,
but I'm also not not going to say that.
Anyway, that's what it's called:
Benford's law.
About 50 years
after Newcomb discovered it,
an engineer named Frank Benford
discovered it again,
and he's the guy everybody remembers.
But I don't care who discovered it
or when or what it's called.
I want to know how it works.
And since it's virtually a crime
to talk about it here in the USA,
I need to go somewhere
a little less secretive.
Turns out the European Union is not only
open about using Benford's law,
they're flaunting it.
[instrumental music playing]
[Nasser] Thank you.
[Nasser] There's an entire conference here
devoted just to Benford's law.
So I figured I'd just sneak in here,
blend in amongst the mathematicians
and law enforcement folks,
and learn their nerd secrets.
I presume the bank is very eager
to figure out a way to solve this.
Yeah, yeah. Of course. Of course.
[Nasser] How important or how widely
prevalent a tool is Benford's law?
For some features we apply Benford's law
because if Benford's law
says it doesn't fit,
something strange might be going on.
[announcer in Italian] The conference
is starting in the next five minutes.
Alright. I guess it's time to go.
[Nasser] Wow, okay. Here we go.
Benford's law. It's showtime.
[drums playing]
[lecturer] We say a sequence
is equidistributed mod one
if it falls evenly.
More explicitly, you choose
any subinterval of zero one,
and the fraction of the time
in the limit that I land in there
is just its length.
And this will be very important shortly
in proving Benfordness.
Then n times beta
is equidistributed mod one
We can write it as a significant
So I chose
a semi-random irrational number
So we take logs of both sides,
we'll get the log of x
So, let's quantify this.
Throw away the integer part
Fibonacci numbers The logarithm
Fibonacci numbers are between
[mouthing] I have no idea what's going on.
It makes sense of this intermediate
[Nasser] Okay, so that didn't work.
I needed the "for dummies" treatment,
so I bought keynote speaker Ted Hill
a mocktail
and got him to explain it to me.
The conversation
went to some weird places.
"When you encounter
the first extragalactic potato,"
he said, "how many atoms
do you think will be in it?"
What? That might be
the greatest question I've ever heard.
Okay, so
[Nasser] But I finally got him
to explain Benford's law to me.
Imagine you have a big batch
of random numbers.
Any numbers between one and 999,999.
Now pick a random number
out of that batch of random numbers.
What's the first digit of that number?
What does it start with?
If it's a random number,
it should be random, right?
It could be a five, could be a seven,
could be a one
Who knows, right? All equally likely.
But turns out it's not.
If I told you that there's
more numbers in the world
that start with a one than a two.
More than that, if I told you
about 30 percent start with a one
-That's I--
-About 17 percent start with a two.
-Okay, now
-[chuckles]
When you first see that, you go,
"Whoa, wait a minute. That's just crazy."
[Nasser]
Okay, so I'm going to go over this again
because it's so counterintuitive,
I'm not even sure I understand it.
Start with a big batch of numbers.
Could be basically anything.
New York City apartment prices.
The GDPs of countries.
The winning bids
for sports tickets on eBay.
Whatever it is,
if you take all those numbers,
strip away everything but the first digit,
and it'll generally follow a pattern.
You'll have more ones than twos,
more twos than threes,
more threes than fours,
and so on.
And not just a few more. A lot more.
And a precise amount more.
About thirty percent of those numbers
will be a one,
and less than five percent will be a nine.
And if you graph it out,
it makes this pretty curve.
The curve is decreasing like this,
logarithmically.
Uh-huh.
Benford's law does not sound right.
-It sounds wrong.
-That's right.
It's hard for me to believe too,
just like it is you.
So I did this experiment.
I'd just come back from Australia.
And I went to my shelf,
and I got a fact book on Australia.
And I just started
I said, "I'm just going to collect data."
And I went through the fact book.
I'd pick a page at random,
take ten numbers off it,
pick a different page at random,
airline distances,
pick a different page at random,
temperatures
But when you wrote all these down and saw,
gee, about 30 percent started with a one.
About 17 percent started with a two.
I said, "Holy cow."
I said, "There's got to be
a theorem there."
I came up with a theorem,
and even that is such a screwy idea
that I had a little trouble
getting it published,
because people were going, "Aw, come on."
[Nasser] But Ted's paper
did make its way to this guy:
Mark Nigrini.
I'm an accountant and I'm an auditor.
And first of all I was a policeman
in law enforcement.
So this sort of idea of using this as a
not quite a lie detector
-Okay.
-wasn't foreign.
Huh! So you were like, here's the thing.
Let's see if I could use it
to catch some bad guys.
Quite right.
[Nasser] Nigrini had already
been tinkering with Benford's law,
figuring if real-world numbers
follow this pattern,
what would happen if you applied it
to books that were cooked?
And then, news hit of some
of the biggest book-cookers of all.
[Nigrini] Enron broke loose,
and now we actually had something,
a big headline, with fraud and
-[Nasser] Right.
-[Nigrini] And this was all very exciting.
I sort of analyzed Enron's numbers,
but with hindsight.
And the patterns were quite obvious,
that they were pushing the boundaries
and making their numbers
look, cosmetically, as good as they can.
[Nasser] Weird. Why?
Because they wanted to puff up
their numbers.
They wanted to just match
these thresholds.
20 billion in revenue,
40 billion in revenue,
100 billion in revenue.
[Nasser] Whoa!
[Nasser] Mark could see all of that
simply by looking at that curve.
How did it feel? What did it feel like?
It was almost like magic.
-It was sort of an exciting discovery.
-Yeah.
It was like, "Wow, this actually works."
There is structure to those digits.
Those digits have a regularity
which is Benford's law.
-Like, hidden inside them?
-Yes.
Like a little lost fingerprint. [chuckles]
Benford is just there.
Benford is with us every day in every way.
Okay, so, what?
So, it's a spellcheck for your taxes?
Oh, no, no. It's much more than that.
[classical music playing]
[Nigrini] I read that the music
of Beethoven, Bach, Schubert, and the like
had some Benfordness
in their intrinsic pattern.
-How so?
-It was very interesting.
What the authors did
was they took some of these pieces,
and they measured
how long each note is played
cumulatively over the course of the piece.
[Nasser] They literally just took
the durations of each note,
and looked at the first digit.
[Nigrini] And out popped Benford.
So why? Why?
Out popped Benford every single time.
Like, is that something
about the way we hear patterns?
Is it something about our ears?
Is it something about our brains?
Is it something about the strings?
Like, wh--wh-- How does that
It is a bit puzzling to me too, in fact.
[chuckles]
Good, good. I'm glad. Finally.
'Cause I feel like
this is all puzzling to me.
Every part of it is puzzling to me.
It's like blowing my mind.
Like, the world is random. It's random.
Do you think Could you Benford Beyoncé?
[chuckles]
[Beyoncé music playing]
I would almost think yes.
-Yes?
-Yes.
Really?
I would think if anything does work,
then it probably--
Is Beyoncé.
[classical music playing]
Like, okay, so it's a pattern.
It's a pattern we're making,
and it's a pattern we make
because it's good for our ears,
but it also happens to be a pattern
that fits this other pattern
that makes this pretty curve.
Yes.
Well, how Is that a coincidence?
Is that not a coincidence?
I don't think it's a coincidence.
[eerie music playing]
Okay.
Yes. I-- I think this pattern
is pleasing to our ear,
and Benford's law
is just this regularity that hides behind
the music of Tchaikovsky, Beethoven
Beyoncé.
[chuckles] Beyoncé and the like.
[Nasser] Yeah.
[upbeat music playing]
It's neat, but
It's neat, but when you think about it,
it's not so surprising
that there's a pattern there.
What are accounting and music
if not patterns, right?
But what happens
if you apply Benford's law
to a realm where patterns shouldn't apply?
When you think about it,
athletes aren't trying to make patterns.
They're trying to break patterns.
To get out in front of the pack,
to zag, when their opponents
expect them to zig.
They're trying to go faster, further,
higher than anyone ever has before.
Still, take all kinds
of sports statistics:
career basketball points,
tae kwon do kicks,
badminton rallies,
number of runs per batter in cricket,
number of touchdowns per player
in American football,
number of passes before an interception
in soccer
You can go on and on.
Benford's curve appears every time.
Sports often come down to one athlete
making a split-second decision.
Should I pass or shoot?
But we all make decisions like that
all the time.
Could Benford's law apply
to the rest of us?
Even the lazy ones?
[Nigrini] City populations, also,
would follow Benford's law.
On average, it's Benford's law.
Each city might have bumps and hiccups,
but when I take all nineteen and a half
thousand cities in America together,
it'll come out Benford's law.
-[Nasser] It does? It works?
-It works absolutely beautifully.
[Nasser] But it's
that's blowing my mind.
It's kind of eerie.
A city's population.
It looks like a number, but it's not.
It's the aggregate
of millions of highly personal decisions.
Like someone over here
decides to move to take a new job.
Someone over here decides not to renew
her birth control prescription.
A couple here decides to retire early
and retreat to the mountains.
Each of these feels like
it's a personal decision
that we're making freely.
So you could take the populations
of these nineteen and a half thousand
towns and cities
-Yeah.
-in 1912,
and you can take it in 2012.
It'll still follow Benford's law.
Why? That's so weird.
[Nigrini] It's amazing.
The town and city populations
are not random.
[Nasser] But But but, like
I-- I just I feel like I now don't even
understand what random means.
[Nasser] Even though some things
may feel super random,
like being the victim of a crime,
they're not.
FBI data collected over 43 years
from 18,000 law enforcement agencies
across the United States
held to Benford's law almost perfectly.
Even breaking the law
follows Benford's law.
And we don't just live by Benford's law,
we die by it too.
It's been applied to cancer rates,
infectious disease cases,
even the intervals between your heartbeats
when you're about to go
into cardiac arrest.
Like, we're all these robot lemmings.
Like, we just have this illusion
that we have agency,
but really we all just fit tidily
into this mathematical formula.
Like, don't box me in, Benford.
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.
-Walter.
-Oh, hey. How are you, Latif?
-Hi. How are you doing?
-Good to see you.
-Thanks for meeting me here.
-Yes. Delighted.
Yeah, so I guess for what you study,
this is sort of
the belly of the beast here.
Ah, in some sense. I look at elections
not just in the United States,
but certainly this is a place.
[chuckles] Where it all happens.
[Nasser] Political scientist Walter Mebane
remembers
the 2000 US presidential election
the way the rest of us
remember our first date.
Everything was awkward.
Nothing went the way it was supposed to.
The news called Florida for Gore,
then Bush,
then said it was too close to call,
until finally it went back to Bush.
[crowd chanting] Revote!
[Nasser] In the aftermath, a lot of states
tried to revamp their voting systems
to prevent a similar debacle
in the future.
And the tool they thought would help them
do that
[Walter] Electronic voting machines.
[Nasser] So if someone
is monkeying with the results,
you need another way.
You can't just look at the papers
and see, you know,
there might be a problem here.
Like you need another way
to figure that out.
Well, that's what led me
to Benford's law in particular.
I had in mind, "Can we use this
to address the issue
of no-paper paper trails?"
[Nasser] So Walter did an experiment.
He started by analyzing voting data
from a clean election
and applying Benford's law
to all the individual vote tallies.
And it fit.
Then, he tried to mess it up.
Beginning with a perfectly Benfordy
election data set,
he started to switch votes
between candidates.
So I simulated fraud in those data.
What if they just steal two percent
because the Florida election
was really close in 2000,
and there's lots of allegations
about that amount of fraud.
Suppose that was there.
Could it detect that?
So, I ran a simulation
and with one percent of the votes
switched between the candidates,
this Benford's-law-motivated test
triggered.
-One percent?
-One percent.
[Nasser] With a tool this sensitive,
it should be easy to either root out,
or rule out, fraud, right?
Not quite.
Benford's-law-like tests
are a little too sensitive
to all kinds of things.
-Right.
-Not merely fraud.
Huh.
[Nasser] As Walter looked deeper
into his data, he noticed something else.
Benford's law wasn't just flagging
weirdness that takes place
in some polling station,
but also weirdness
that takes place in your own head,
when you strategically vote for someone
other than your first choice.
[Walter] And so if you have people
deciding not to vote for a candidate
because they think that candidate
has no chance.
And that may mean I'm voting
against my first, second and third choice
to go down to four. I'll hold my nose
and vote for this person.
That may trigger
departures from Benford's law.
What? So it's like
if everybody just voted their heart,
it would fit Benford's law.
But if everybody's, like, gaming it out,
puzzling it out--
Doing what people do in real politics
That doesn't fit?
That's like spooky and weird.
It's like a lie detector test
or something.
Well, something like that.
It's either telling us about fraud,
people who are, like, maliciously
trying to steal an election,
or it's telling us
that all the people who are voting,
like, there's an extra layer of thinking
that they're devoting here.
And hopefully it can help to,
with other data maybe,
disentangle what they're thinking.
[Nasser] There was one last thing
I had to ask Walter.
Sort of the elephant in the room.
So, did you find any evidence of fraud
in the 2016 elections?
I would say there's no evidence
of bias in the vote counts.
Frauds can be many other things.
Certainly, the claimed
Russian information attack on the US
did happen.
One of the most poisonous kinds of frauds
that can happen in a democracy.
If you can't rely on elections,
then, to me personally,
there's basically nothing else.
[Nasser] So, this all started
because I was curious
what they were doing with my taxes,
but then it got so much bigger.
I saw it in other number patterns,
like music,
in non-patterns, like sports,
and, eeriest of all, in some
of the most intimate moments of our lives.
I hate being so predictable.
But that very thing
might help save our society
from some of its biggest threats.
Like the undermining of our elections
and a lot more than that.
Which brings me to my new friends,
Venkman, Hopper, and Riley.
They're basically celebrities.
No big deal.
[Golbeck] They're very popular
on the internet.
They have a Twitter account, Instagram,
YouTube, Snapchat. [chuckles]
-They're all over the place.
-Oh, my God.
[Golbeck] And we have,
like, 75,000 followers on Twitter.
The whole squad. Wow.
That's way more than I have.
-Me too. Way more than me.
-Okay. Wow. Yeah, that's a lot. Wow.
[Nasser] But I'm really here
to talk to their owner,
a celebrity in her own right.
Jennifer Golbeck,
professor at the University of Maryland's
College of Information Studies.
As a researcher who studies social media,
it's been so interesting
to see, oh, you can use Benford's law
for finance,
but we can also detect
basically fraud on social media too.
Wow. How exactly do you apply it?
Like, what does that even mean
or look like?
So, for Benford's law,
you gotta look for numbers.
What are the numbers that we have?
We have "How many friends do you have?"
-Okay. Simple, clear. Yeah.
-Right? That's the number.
So, you only have your friend count,
but you have all your friends.
-So look at their friend counts.
-[Nasser] Uh-huh.
[Golbeck] You take your 500 friends online
and you take all their friend counts,
30 percent of them are going to have
a friend count that starts with a one,
just like you'd expect.
So if you take all the Facebook users,
it fits that pattern,
but then if you even take
my friends' followers,
-it'll still follow that.
-Exactly.
Ah!
And does it follow that pattern? It does.
And it does
on every single social network.
No.
So I went out and I was just pulling data
from Facebook, from Twitter,
from Pinterest, from all these places.
Were you the first person
to look for that?
This was one of the most exciting
research moments of my life because I was.
And so I'm sitting
in my little rental house,
and I'm like, "I know a thing
that nobody else on Earth knows,"
and it's so exciting
and I love it so much
and I could not wait
to tell everybody else.
[Nasser] But as thrilling as it was
to notice Benford's law
lurking in your friend count,
my friend count,
even in Cardi B's friend count,
Jennifer discovered something else,
something sinister.
I had 50,000 Twitter users
that I'd randomly picked.
All of them
look exactly like Benford's law,
but there were, like, a hundred
at the bottom of my list
that didn't look
anything like Benford's law.
And it's Twitter, so it's public.
I was like, well, let's go look
at these accounts and see what's up.
And every single one of them
was a Russian bot
-[gasps]
-operated by the same person.
[Nasser] For the two people who don't know
what bots are, Mom and Dad,
they're computer programs that can
look and sound like real people online.
Sometimes they're harmless.
Other times,
they can wreak all kinds of havoc.
[Golbeck] So, I started with them.
They'll randomly follow legitimate people,
and then they follow each other.
And then looked at who they follow.
We ended up with about a hundred,
hundred fifty thousand bots
in this network.
I had no idea I was going to find this.
[Nasser] What were those bots doing?
So they would tweet in Russian,
and they basically would tweet
sentences out of novels
or technical manuals.
They had these stock-photo
profile pictures.
They'd occasionally throw in an emoji,
and they would like each other's tweets.
They would follow each other.
-[Nasser] Huh.
-[Golbeck] They would retweet each other.
Now, what was that for? We don't know.
And sometimes people set up
these huge botnets
just to have them, so they can use them
for something in the future.
They kind of look legitimate,
and then when they want to send spam,
they want to influence elections,
they already have these hundreds
of thousands of bots out there.
And then they'd go from tweeting
about Tolstoy or whatever
to tweeting about, like, you know,
this sex scandal
that is totally made up or something.
Exactly.
Part of their purpose in the last election
and in Brexit and in the time since,
has not been necessarily
to support one side or the other,
but to get us mad at each other.
And that's exactly what they're doing.
You need a little bit of tech skill
and a lot of creativity.
You can have a huge impact.
-Oh, my God, this is terrifying.
-[laughs]
[chuckles] Oh, man.
[Nasser] But maybe a little
less terrifying thanks to Benford's law,
which isn't just helping us
unmask bots online,
it's also helping us
see through the lies they spread.
Do you ever wake up
and you just go look at yourself
in the mirror,
and you think,
"I look way better than usual today"?
Like, I look movie star good.
Yeah.
Like, I could be Brad Pitt.
Yeah.
Yeah. Yes, I could.
But then you realize
No, I I look nothing like Brad Pitt.
I I
That's It's all just a deepfake.
[Nasser]
Meet computer scientist Hany Farid.
He's kind of a Sherlock Holmes
for the age of the Instagram filter.
Journalists, courts,
and even intelligence agencies come to him
to sort the fake images
from the real ones.
He also happens to be
my old college professor.
So I dropped in on him,
to hear how he uses Benford's law.
Hello?
Last time we spoke,
things got a little tense.
-Hey, how you doing?
-How you been?
-Good to see you.
-Is it possible that it's ten years?
It's been about
-Yeah. Beautiful view here.
-Not bad.
-It's not terrible. [chuckles]
-Pretty good.
I don't know if you remember,
the last time we met,
the last time we talked,
we got into an argument,
and it was kind of awkward, actually.
It was a little testy.
And the argument was, you said
fake images on the internet
are going to be really bad.
-It was apocalyptical.
-Yeah.
You also thought that very soon
we would not be able to tell
the difference
between real images and fake images
on the internet.
-I said that you were being paranoid
-Yeah.
that there was no way. We'd always
be able to tell the difference.
I probably was being paranoid,
and I probably was calling it early,
but something very dramatic has happened
in the last few years
in our ability to trust
what we see and hear online.
The ability to manipulate digital content
has accelerated.
It's not a game anymore.
[Nasser] Most of us have seen
these celebrity face mashups
because they're hilarious.
and then Tom Cruise walks in,
and even those guys are like, "Whoa."
And he's super stoked
to be there, you know? [chuckles]
He's like, "Yeah! Boom." You know?
[Nasser] But it's genuinely scary
when you realize that this could easily
be done on public figures,
on heads of state,
on you.
So, what we've been
in the business of doing
is developing techniques
to distinguish real images,
real video, real audio from fake ones.
Let me show you how we do some of that.
-Show me.
-Okay, good.
-I actually teach about Benford's law.
-Okay.
And I thought, "I wonder if images
exhibit Benford's law."
So now you have to start thinking about
what are you going to analyze in an image?
-[Nasser] Take a photo.
-All right, hold on.
[Nasser] Any photo.
[camera clicks]
If it's digital,
that means it's really made
of millions of tiny number values.
If you take an image, jpeg compress it,
and you look at the underlying
representation, it follows Benford's law.
-Okay.
-Okay, good.
If you then take that image,
stick it into Photoshop and do something.
And then what do I do when I'm done?
-You save it.
-Save it. Good.
So now the image has been saved twice.
It has gone through two compressions.
Benford's law gets violated.
No.
-Yes! Isn't that great?
-It works.
[Nasser] Huh. So, the more you manipulate
an image, the more you save it,
and the more you save it,
the less it adheres to Benford's curve.
And then when you do an unnatural image,
it looks something like this.
So it's sort of Benfordy,
it sort of falls off a little bit,
but not nearly with the right ratio
that you would expect.
Does it make you more suspicious,
the lower this one value goes?
Yeah, yeah, and that's because
as you keep compressing and compressing
The ones go down.
It gets worse and worse.
And the first thing I do,
as a forensic analyst,
when somebody asks me,
"Is this image manipulated?"
The first question I ask is,
"Has it been saved more than once?"
Look for double compression.
Here's a physical analogy.
Police officer goes to a crime scene,
collects some physical evidence,
puts it into a bag and seals it,
and puts a stamp on that.
If that seal is broken,
we have a problem, right?
Because it means that bag was opened,
and it opens up the possibility
that evidence was manipulated.
-Right. And why was that opened?
-And why was it opened?
Because we're going to a court of law
and it's evidence.
But digital evidence
should be treated the same.
If I save an image as a jpeg,
and if I open it and re-save it,
well, why did you do that?
It's evidence, right?
You shouldn't do that.
[Nasser] For all his techniques
in the war on fake news,
Benford's law is one of the first tools
that Hany turns to.
Still, Hany is under no illusion
that he'll be able to stop
all doctored images on the internet.
The way I think about it is,
I'm going to continually raise the bar
so that it is more difficult,
more time-consuming, and more risky,
and take it out of the hands
of the average person
to create a compelling fake.
[Nasser] And that need,
to keep compelling fakes off the internet,
has never been greater.
The real threat is when
nobody is going to believe anything,
whether it's real or not,
because now, any image, any video,
any audio recording,
any text can be it's fake.
That's the real threat here.
Once it's in the psyche
that we can't tell the real from the fake,
it's sort of game over
because that's all it really takes.
So, it's not about thinking
the fake is true.
Yeah.
It's about thinking
the true might be fake.
That's exactly what it is.
It's a wildly improbable journey
from an obsolete
nineteenth-century reference book
to a high-tech,
cutting-edge forensics tool
that we can use to safeguard ourselves,
our democracy,
and even the idea of truth
in the age of Photoshop.
Not bad.
But why does this distribution of numbers
apply so widely in the first place?
Is it something about us and the way
we divide up and count the world?
Or is it about the world itself?
Is it about the nature of numbers?
Or is it about the nature of nature?
It's hot.
Oh!
[indistinct chatter]
[Nasser] There's a first time
for everything, and for me right now,
that thing is
riding a hot-air balloon over a volcano.
God. It's pretty in every direction.
[man] But we are going
to the center of the crater.
[Nasser] I'm flying over
the Garrotxa Volcanic Zone Natural Park
in Catalonia, Spain.
Woof. Yeah.
I love how this
is literally just a wicker basket,
a flame thrower, and a plastic bag.
Yeah, but probably are safe.
[both laughing]
[Nasser] It's a range of 40 volcanoes
about an hour and a half's drive
from Barcelona.
It's also the home away from home
for volcanologist Joan Martí.
This is a volcano?
[Martí] Yeah, this is another volcano,
Santa Margarida.
The largest one in terms of size
of the crater, of the area.
Oh, wow.
And that was created
by a very strong explosion.
-When would that have been?
-Thirteen thousand years.
So, 13,000 years ago,
there was an enormous explosion.
Yeah. Enormous explosion.
-Right here?
-Right here.
This area's dormant right now,
but maybe, I don't know, tomorrow,
they will be active again.
-Tomorrow? It could be literally tomorrow?
-Yeah, could be.
Tomorrow Well, not tomorrow literally,
but maybe the day after tomorrow.
-The day after tomorrow.
-[laughs]
-It's gonna surprise you.
-Yeah.
When it comes to volcanoes,
surprises are a bad thing.
[Martí] The main problem
is the ash that goes into the atmosphere.
[Nasser]
And that ash can become a global problem.
The relatively small Iceland eruption
in 2010
grounded transatlantic flights
for almost a week
and cost the global economy
nearly five billion dollars.
No one even saw it coming.
So, what makes it so hard
to forecast a volcano going off?
We started doing monitoring
or systematic monitoring on volcanoes
three decades ago.
[Nasser] That may sound like a long time,
but in geological terms, it's nothing.
[Martí] We don't have, still, enough data
to prepare for eruptions
In the end, even geology is numbers.
[Nasser] And given the stakes
of volcano prediction,
the numbers you do have
had better be right.
In volcanology, we have to use
these mathematical tools
that help us to see if the numbers we have
are correct or are not correct.
Joan works with Adelina Geyer
at Barcelona's
Institute of Earth Sciences.
She's the one in charge
of all of that data.
So, one of the main questions, always,
is how reliable are our databases,
how complete they are,
and just by chance,
I assisted to one of the conferences
about Benford's law.
When you first heard about that idea,
what did you think? How did it strike you?
I was feeling like
this is like a kind of magic. [chuckles]
I felt like a bit mystic,
I don't know, esoteric.
Like, is this going to work?
So, just when I arrived home,
I started to look at our databases.
[Nasser] Adelina analyzed
one database in particular:
volcano sizes from across the globe.
And surprise, surprise, it worked.
I was really excited.
[Nasser] Sure enough, it fit the curve
as if Benford's law is literally
baked into the structure of our planet.
I think that's what's extraordinary,
but also spooky to me a little bit.
There's an order where we weren't looking
and we didn't expect there to be an order,
and it's there.
But what does that tell you?
What it tells you, I think,
is that nature works in the right way.
In the right way, yeah.
It doesn't do things
that are inconsistent.
That nature is something
which is much more regular than we think.
But I don't know, like,
I feel like that the world is chaos.
Like we make seemingly arbitrary decisions
all the time.
These volcanoes, sometimes they go off,
sometimes they don't.
But somehow you've found underneath there,
there is this order and simplicity.
I think sometimes we don't want
to discover that things are simple.
So we think that, "Oh, things
need to be more complicated." No.
I mean when you deal with
natural systems, uh
you should look
for the simplest explanation, always.
If there is a volcano that has to erupt,
it's because that volcano has to erupt
to equilibrate the energy, the balance,
the energetic balance
that it has in its interior.
So, nature is not spending
more energy than it needs.
But it sounds like,
if I'm getting you right,
what you're saying
is that the Earth is a system.
-It's an ordered system.
-Uh-huh.
And in a way,
it's like Benford's law is a clue
to that order,
of the giant planetary system.
Yeah.
There is a relationship
between all these processes
that occur in our planet
concerning and related to
the internal geology of our planet.
Before you go to bed at night,
when you're putting your head down
on your pillow,
and you, that day, have found
this little nugget of order,
and it says something,
maybe just about your data set,
but maybe also about the whole world,
what do you--
what does that make you feel?
-Small.
-[laughs]
-I feel small. I feel really small.
-That's true.
[Geyer] I mean, we work for planet Earth,
mainly. So our big boss is planet Earth.
It's like, I'm not even sure we understand
a million part of what is going on.
We think we understand a lot,
but there are so many questions
still open.
[Nasser] And here's the really crazy thing
about Benford's law:
it works all over the natural world,
whether you're looking
at the depths of earthquakes,
the distance traveled
by tropical cyclones,
even the weights of atoms.
And that is why I'm back here,
back where we started,
at the US Naval Observatory.
I didn't come here just for the library.
There's one last thing I want to show you.
Turns out Benford's law
isn't just baked into our planet.
It's baked into all the planets,
and the stars-- Oh.
And did I mention the galaxies?
If you measure the distance
from here to all the galaxies
that we've measured,
the first digits of those distances
will follow that same pattern.
But here's where it really gets me:
whether you measure it in light years,
kilometers,
yards, inches,
my height, your height,
the length of your dog's tail
No matter how you measure
those galactic distances,
Benford's law will apply
every single time.
Imagine, all this started
with one person noticing something curious
about a library book.
A hundred and fifty years later,
we know that that simple observation
suffuses our whole universe.
For all the chaos and randomness
and clamor of our lives,
there's a mathematical order at play here.
And no one really knows why
or whether it had to be there.
All the tax cheats and the Twitter trolls
and the tectonic plates
and the polling data
and the pop stars
and the pulsars
and you and me,
we all fit
onto this gorgeously simple curve.
And in that way, we're all connected.
[upbeat music playing]
[clock ticking]
[Nasser] I need to tell you about a code.
A pattern of numbers.
When you first hear about it,
it seems trivial.
But then you start seeing it
over and over.
Hidden in plain sight
in the chaos all around us.
The stock market, street addresses,
the numbers in this morning's paper.
Each clue leads you one step closer,
possibly to insanity,
but possibly to unlocking a secret
about human society
that's so big, so profound,
so powerful, that the US government
doesn't want you to know it.
You have no idea just how deep this goes.
[suspenseful music playing]
[upbeat music playing]
I'm Latif Nasser,
and this is a show about
the astonishing connections all around us.
Connections
between you and me and our world
that'll make you see that world
in a whole new way.
Welcome to the US Naval Observatory,
official residence of the Vice President
of the United States,
home to the telescope that discovered
the two moons of Mars,
and rumor has it,
but no one here will verify,
site of a top-secret underground bunker.
But I don't care about any of that.
I'm here for the library
because here, 140 years ago,
is where our mystery began with a book.
It's a logarithm book from the late 1800s.
It's basically what people used
as a calculator before calculators.
Think about it as a giant, old book
of multiplication tables.
Admittedly dull stuff.
So, here's what happened:
an astronomer named Simon Newcomb,
that guy,
was working here,
looking at a book a lot like this one,
and he noticed something kind of weird.
If you look at the early pages,
what you'll see is that they're all worn.
But if you look at the later pages,
they're much less so,
as if people were only using
the first few buttons of the calculator.
Kind of random, right?
But then he looked at another logbook
and saw the same thing.
And another,
and another and another.
Every time. First pages worn.
Back pages, good as new.
But what Newcomb stumbled upon
was the first clue
to a profound and secret order
to the world all around us.
One that could pop up
in everything from your favorite sport
to your favorite song,
even to the way you're gonna die.
Once you see it, you can't unsee it.
It's everywhere.
But I'm getting ahead of myself.
Let's go to clue number two.
Your taxes.
[film narrator] The average taxpayer
is hardly concerned
with all the intricacies
of the far-flung IRS computer system.
There's a "good" tape,
and there's the "error" tape.
Looks like this one is deducting
for medical payments covered by insurance.
So all this started
because I heard this rumor
that somehow governments around the world
have turned Newcomb's discovery
into a secret weapon against tax cheats.
That using this mysterious pattern,
they can just look at the entries
on your tax form
and magically tell if you're lying.
Is it true? Is that even possible?
And if so, how?
I decided to just go ask them myself.
Of course,
I couldn't get the IRS to talk to me.
So I had to find someone
who would talk to me.
[keyboard clicking]
[clicking continues]
[woman] Sir, Randy will see you now.
Thanks.
First of all, thank you so much.
I tried to go talk to the IRS,
and they would not talk to me.
This is Randy Shump,
former Senior Attorney for the IRS.
If anyone can explain
the inner workings of the IRS, it's him.
So I heard about
this 150-year-old statistical technique
that maybe gets used to analyze taxes.
It has to do with this old logbook,
and there are, like,
dirty pages at the front.
I think you're talking
about Benford's law.
-Oh really?
-Yeah.
[Nasser] Okay, yeah. That's the thing.
That's the thing I read about.
It has a name: uh, Benford's law.
Okay, so that's
what this episode is about.
[Nasser] So let me just ask you
straight out.
Does the IRS use Benford's law?
I'm not permitted
to disclose that information.
The IRS doesn't make
that information available.
I don't know what it is.
And even if I did,
I wouldn't be able to say so.
Turns out it's illegal for IRS employees
and even former IRS employees
to disclose certain tools they use.
So, I'm not going to say
that the IRS uses Benford's law,
but I'm also not not going to say that.
Anyway, that's what it's called:
Benford's law.
About 50 years
after Newcomb discovered it,
an engineer named Frank Benford
discovered it again,
and he's the guy everybody remembers.
But I don't care who discovered it
or when or what it's called.
I want to know how it works.
And since it's virtually a crime
to talk about it here in the USA,
I need to go somewhere
a little less secretive.
Turns out the European Union is not only
open about using Benford's law,
they're flaunting it.
[instrumental music playing]
[Nasser] Thank you.
[Nasser] There's an entire conference here
devoted just to Benford's law.
So I figured I'd just sneak in here,
blend in amongst the mathematicians
and law enforcement folks,
and learn their nerd secrets.
I presume the bank is very eager
to figure out a way to solve this.
Yeah, yeah. Of course. Of course.
[Nasser] How important or how widely
prevalent a tool is Benford's law?
For some features we apply Benford's law
because if Benford's law
says it doesn't fit,
something strange might be going on.
[announcer in Italian] The conference
is starting in the next five minutes.
Alright. I guess it's time to go.
[Nasser] Wow, okay. Here we go.
Benford's law. It's showtime.
[drums playing]
[lecturer] We say a sequence
is equidistributed mod one
if it falls evenly.
More explicitly, you choose
any subinterval of zero one,
and the fraction of the time
in the limit that I land in there
is just its length.
And this will be very important shortly
in proving Benfordness.
Then n times beta
is equidistributed mod one
We can write it as a significant
So I chose
a semi-random irrational number
So we take logs of both sides,
we'll get the log of x
So, let's quantify this.
Throw away the integer part
Fibonacci numbers The logarithm
Fibonacci numbers are between
[mouthing] I have no idea what's going on.
It makes sense of this intermediate
[Nasser] Okay, so that didn't work.
I needed the "for dummies" treatment,
so I bought keynote speaker Ted Hill
a mocktail
and got him to explain it to me.
The conversation
went to some weird places.
"When you encounter
the first extragalactic potato,"
he said, "how many atoms
do you think will be in it?"
What? That might be
the greatest question I've ever heard.
Okay, so
[Nasser] But I finally got him
to explain Benford's law to me.
Imagine you have a big batch
of random numbers.
Any numbers between one and 999,999.
Now pick a random number
out of that batch of random numbers.
What's the first digit of that number?
What does it start with?
If it's a random number,
it should be random, right?
It could be a five, could be a seven,
could be a one
Who knows, right? All equally likely.
But turns out it's not.
If I told you that there's
more numbers in the world
that start with a one than a two.
More than that, if I told you
about 30 percent start with a one
-That's I--
-About 17 percent start with a two.
-Okay, now
-[chuckles]
When you first see that, you go,
"Whoa, wait a minute. That's just crazy."
[Nasser]
Okay, so I'm going to go over this again
because it's so counterintuitive,
I'm not even sure I understand it.
Start with a big batch of numbers.
Could be basically anything.
New York City apartment prices.
The GDPs of countries.
The winning bids
for sports tickets on eBay.
Whatever it is,
if you take all those numbers,
strip away everything but the first digit,
and it'll generally follow a pattern.
You'll have more ones than twos,
more twos than threes,
more threes than fours,
and so on.
And not just a few more. A lot more.
And a precise amount more.
About thirty percent of those numbers
will be a one,
and less than five percent will be a nine.
And if you graph it out,
it makes this pretty curve.
The curve is decreasing like this,
logarithmically.
Uh-huh.
Benford's law does not sound right.
-It sounds wrong.
-That's right.
It's hard for me to believe too,
just like it is you.
So I did this experiment.
I'd just come back from Australia.
And I went to my shelf,
and I got a fact book on Australia.
And I just started
I said, "I'm just going to collect data."
And I went through the fact book.
I'd pick a page at random,
take ten numbers off it,
pick a different page at random,
airline distances,
pick a different page at random,
temperatures
But when you wrote all these down and saw,
gee, about 30 percent started with a one.
About 17 percent started with a two.
I said, "Holy cow."
I said, "There's got to be
a theorem there."
I came up with a theorem,
and even that is such a screwy idea
that I had a little trouble
getting it published,
because people were going, "Aw, come on."
[Nasser] But Ted's paper
did make its way to this guy:
Mark Nigrini.
I'm an accountant and I'm an auditor.
And first of all I was a policeman
in law enforcement.
So this sort of idea of using this as a
not quite a lie detector
-Okay.
-wasn't foreign.
Huh! So you were like, here's the thing.
Let's see if I could use it
to catch some bad guys.
Quite right.
[Nasser] Nigrini had already
been tinkering with Benford's law,
figuring if real-world numbers
follow this pattern,
what would happen if you applied it
to books that were cooked?
And then, news hit of some
of the biggest book-cookers of all.
[Nigrini] Enron broke loose,
and now we actually had something,
a big headline, with fraud and
-[Nasser] Right.
-[Nigrini] And this was all very exciting.
I sort of analyzed Enron's numbers,
but with hindsight.
And the patterns were quite obvious,
that they were pushing the boundaries
and making their numbers
look, cosmetically, as good as they can.
[Nasser] Weird. Why?
Because they wanted to puff up
their numbers.
They wanted to just match
these thresholds.
20 billion in revenue,
40 billion in revenue,
100 billion in revenue.
[Nasser] Whoa!
[Nasser] Mark could see all of that
simply by looking at that curve.
How did it feel? What did it feel like?
It was almost like magic.
-It was sort of an exciting discovery.
-Yeah.
It was like, "Wow, this actually works."
There is structure to those digits.
Those digits have a regularity
which is Benford's law.
-Like, hidden inside them?
-Yes.
Like a little lost fingerprint. [chuckles]
Benford is just there.
Benford is with us every day in every way.
Okay, so, what?
So, it's a spellcheck for your taxes?
Oh, no, no. It's much more than that.
[classical music playing]
[Nigrini] I read that the music
of Beethoven, Bach, Schubert, and the like
had some Benfordness
in their intrinsic pattern.
-How so?
-It was very interesting.
What the authors did
was they took some of these pieces,
and they measured
how long each note is played
cumulatively over the course of the piece.
[Nasser] They literally just took
the durations of each note,
and looked at the first digit.
[Nigrini] And out popped Benford.
So why? Why?
Out popped Benford every single time.
Like, is that something
about the way we hear patterns?
Is it something about our ears?
Is it something about our brains?
Is it something about the strings?
Like, wh--wh-- How does that
It is a bit puzzling to me too, in fact.
[chuckles]
Good, good. I'm glad. Finally.
'Cause I feel like
this is all puzzling to me.
Every part of it is puzzling to me.
It's like blowing my mind.
Like, the world is random. It's random.
Do you think Could you Benford Beyoncé?
[chuckles]
[Beyoncé music playing]
I would almost think yes.
-Yes?
-Yes.
Really?
I would think if anything does work,
then it probably--
Is Beyoncé.
[classical music playing]
Like, okay, so it's a pattern.
It's a pattern we're making,
and it's a pattern we make
because it's good for our ears,
but it also happens to be a pattern
that fits this other pattern
that makes this pretty curve.
Yes.
Well, how Is that a coincidence?
Is that not a coincidence?
I don't think it's a coincidence.
[eerie music playing]
Okay.
Yes. I-- I think this pattern
is pleasing to our ear,
and Benford's law
is just this regularity that hides behind
the music of Tchaikovsky, Beethoven
Beyoncé.
[chuckles] Beyoncé and the like.
[Nasser] Yeah.
[upbeat music playing]
It's neat, but
It's neat, but when you think about it,
it's not so surprising
that there's a pattern there.
What are accounting and music
if not patterns, right?
But what happens
if you apply Benford's law
to a realm where patterns shouldn't apply?
When you think about it,
athletes aren't trying to make patterns.
They're trying to break patterns.
To get out in front of the pack,
to zag, when their opponents
expect them to zig.
They're trying to go faster, further,
higher than anyone ever has before.
Still, take all kinds
of sports statistics:
career basketball points,
tae kwon do kicks,
badminton rallies,
number of runs per batter in cricket,
number of touchdowns per player
in American football,
number of passes before an interception
in soccer
You can go on and on.
Benford's curve appears every time.
Sports often come down to one athlete
making a split-second decision.
Should I pass or shoot?
But we all make decisions like that
all the time.
Could Benford's law apply
to the rest of us?
Even the lazy ones?
[Nigrini] City populations, also,
would follow Benford's law.
On average, it's Benford's law.
Each city might have bumps and hiccups,
but when I take all nineteen and a half
thousand cities in America together,
it'll come out Benford's law.
-[Nasser] It does? It works?
-It works absolutely beautifully.
[Nasser] But it's
that's blowing my mind.
It's kind of eerie.
A city's population.
It looks like a number, but it's not.
It's the aggregate
of millions of highly personal decisions.
Like someone over here
decides to move to take a new job.
Someone over here decides not to renew
her birth control prescription.
A couple here decides to retire early
and retreat to the mountains.
Each of these feels like
it's a personal decision
that we're making freely.
So you could take the populations
of these nineteen and a half thousand
towns and cities
-Yeah.
-in 1912,
and you can take it in 2012.
It'll still follow Benford's law.
Why? That's so weird.
[Nigrini] It's amazing.
The town and city populations
are not random.
[Nasser] But But but, like
I-- I just I feel like I now don't even
understand what random means.
[Nasser] Even though some things
may feel super random,
like being the victim of a crime,
they're not.
FBI data collected over 43 years
from 18,000 law enforcement agencies
across the United States
held to Benford's law almost perfectly.
Even breaking the law
follows Benford's law.
And we don't just live by Benford's law,
we die by it too.
It's been applied to cancer rates,
infectious disease cases,
even the intervals between your heartbeats
when you're about to go
into cardiac arrest.
Like, we're all these robot lemmings.
Like, we just have this illusion
that we have agency,
but really we all just fit tidily
into this mathematical formula.
Like, don't box me in, Benford.
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.
-Walter.
-Oh, hey. How are you, Latif?
-Hi. How are you doing?
-Good to see you.
-Thanks for meeting me here.
-Yes. Delighted.
Yeah, so I guess for what you study,
this is sort of
the belly of the beast here.
Ah, in some sense. I look at elections
not just in the United States,
but certainly this is a place.
[chuckles] Where it all happens.
[Nasser] Political scientist Walter Mebane
remembers
the 2000 US presidential election
the way the rest of us
remember our first date.
Everything was awkward.
Nothing went the way it was supposed to.
The news called Florida for Gore,
then Bush,
then said it was too close to call,
until finally it went back to Bush.
[crowd chanting] Revote!
[Nasser] In the aftermath, a lot of states
tried to revamp their voting systems
to prevent a similar debacle
in the future.
And the tool they thought would help them
do that
[Walter] Electronic voting machines.
[Nasser] So if someone
is monkeying with the results,
you need another way.
You can't just look at the papers
and see, you know,
there might be a problem here.
Like you need another way
to figure that out.
Well, that's what led me
to Benford's law in particular.
I had in mind, "Can we use this
to address the issue
of no-paper paper trails?"
[Nasser] So Walter did an experiment.
He started by analyzing voting data
from a clean election
and applying Benford's law
to all the individual vote tallies.
And it fit.
Then, he tried to mess it up.
Beginning with a perfectly Benfordy
election data set,
he started to switch votes
between candidates.
So I simulated fraud in those data.
What if they just steal two percent
because the Florida election
was really close in 2000,
and there's lots of allegations
about that amount of fraud.
Suppose that was there.
Could it detect that?
So, I ran a simulation
and with one percent of the votes
switched between the candidates,
this Benford's-law-motivated test
triggered.
-One percent?
-One percent.
[Nasser] With a tool this sensitive,
it should be easy to either root out,
or rule out, fraud, right?
Not quite.
Benford's-law-like tests
are a little too sensitive
to all kinds of things.
-Right.
-Not merely fraud.
Huh.
[Nasser] As Walter looked deeper
into his data, he noticed something else.
Benford's law wasn't just flagging
weirdness that takes place
in some polling station,
but also weirdness
that takes place in your own head,
when you strategically vote for someone
other than your first choice.
[Walter] And so if you have people
deciding not to vote for a candidate
because they think that candidate
has no chance.
And that may mean I'm voting
against my first, second and third choice
to go down to four. I'll hold my nose
and vote for this person.
That may trigger
departures from Benford's law.
What? So it's like
if everybody just voted their heart,
it would fit Benford's law.
But if everybody's, like, gaming it out,
puzzling it out--
Doing what people do in real politics
That doesn't fit?
That's like spooky and weird.
It's like a lie detector test
or something.
Well, something like that.
It's either telling us about fraud,
people who are, like, maliciously
trying to steal an election,
or it's telling us
that all the people who are voting,
like, there's an extra layer of thinking
that they're devoting here.
And hopefully it can help to,
with other data maybe,
disentangle what they're thinking.
[Nasser] There was one last thing
I had to ask Walter.
Sort of the elephant in the room.
So, did you find any evidence of fraud
in the 2016 elections?
I would say there's no evidence
of bias in the vote counts.
Frauds can be many other things.
Certainly, the claimed
Russian information attack on the US
did happen.
One of the most poisonous kinds of frauds
that can happen in a democracy.
If you can't rely on elections,
then, to me personally,
there's basically nothing else.
[Nasser] So, this all started
because I was curious
what they were doing with my taxes,
but then it got so much bigger.
I saw it in other number patterns,
like music,
in non-patterns, like sports,
and, eeriest of all, in some
of the most intimate moments of our lives.
I hate being so predictable.
But that very thing
might help save our society
from some of its biggest threats.
Like the undermining of our elections
and a lot more than that.
Which brings me to my new friends,
Venkman, Hopper, and Riley.
They're basically celebrities.
No big deal.
[Golbeck] They're very popular
on the internet.
They have a Twitter account, Instagram,
YouTube, Snapchat. [chuckles]
-They're all over the place.
-Oh, my God.
[Golbeck] And we have,
like, 75,000 followers on Twitter.
The whole squad. Wow.
That's way more than I have.
-Me too. Way more than me.
-Okay. Wow. Yeah, that's a lot. Wow.
[Nasser] But I'm really here
to talk to their owner,
a celebrity in her own right.
Jennifer Golbeck,
professor at the University of Maryland's
College of Information Studies.
As a researcher who studies social media,
it's been so interesting
to see, oh, you can use Benford's law
for finance,
but we can also detect
basically fraud on social media too.
Wow. How exactly do you apply it?
Like, what does that even mean
or look like?
So, for Benford's law,
you gotta look for numbers.
What are the numbers that we have?
We have "How many friends do you have?"
-Okay. Simple, clear. Yeah.
-Right? That's the number.
So, you only have your friend count,
but you have all your friends.
-So look at their friend counts.
-[Nasser] Uh-huh.
[Golbeck] You take your 500 friends online
and you take all their friend counts,
30 percent of them are going to have
a friend count that starts with a one,
just like you'd expect.
So if you take all the Facebook users,
it fits that pattern,
but then if you even take
my friends' followers,
-it'll still follow that.
-Exactly.
Ah!
And does it follow that pattern? It does.
And it does
on every single social network.
No.
So I went out and I was just pulling data
from Facebook, from Twitter,
from Pinterest, from all these places.
Were you the first person
to look for that?
This was one of the most exciting
research moments of my life because I was.
And so I'm sitting
in my little rental house,
and I'm like, "I know a thing
that nobody else on Earth knows,"
and it's so exciting
and I love it so much
and I could not wait
to tell everybody else.
[Nasser] But as thrilling as it was
to notice Benford's law
lurking in your friend count,
my friend count,
even in Cardi B's friend count,
Jennifer discovered something else,
something sinister.
I had 50,000 Twitter users
that I'd randomly picked.
All of them
look exactly like Benford's law,
but there were, like, a hundred
at the bottom of my list
that didn't look
anything like Benford's law.
And it's Twitter, so it's public.
I was like, well, let's go look
at these accounts and see what's up.
And every single one of them
was a Russian bot
-[gasps]
-operated by the same person.
[Nasser] For the two people who don't know
what bots are, Mom and Dad,
they're computer programs that can
look and sound like real people online.
Sometimes they're harmless.
Other times,
they can wreak all kinds of havoc.
[Golbeck] So, I started with them.
They'll randomly follow legitimate people,
and then they follow each other.
And then looked at who they follow.
We ended up with about a hundred,
hundred fifty thousand bots
in this network.
I had no idea I was going to find this.
[Nasser] What were those bots doing?
So they would tweet in Russian,
and they basically would tweet
sentences out of novels
or technical manuals.
They had these stock-photo
profile pictures.
They'd occasionally throw in an emoji,
and they would like each other's tweets.
They would follow each other.
-[Nasser] Huh.
-[Golbeck] They would retweet each other.
Now, what was that for? We don't know.
And sometimes people set up
these huge botnets
just to have them, so they can use them
for something in the future.
They kind of look legitimate,
and then when they want to send spam,
they want to influence elections,
they already have these hundreds
of thousands of bots out there.
And then they'd go from tweeting
about Tolstoy or whatever
to tweeting about, like, you know,
this sex scandal
that is totally made up or something.
Exactly.
Part of their purpose in the last election
and in Brexit and in the time since,
has not been necessarily
to support one side or the other,
but to get us mad at each other.
And that's exactly what they're doing.
You need a little bit of tech skill
and a lot of creativity.
You can have a huge impact.
-Oh, my God, this is terrifying.
-[laughs]
[chuckles] Oh, man.
[Nasser] But maybe a little
less terrifying thanks to Benford's law,
which isn't just helping us
unmask bots online,
it's also helping us
see through the lies they spread.
Do you ever wake up
and you just go look at yourself
in the mirror,
and you think,
"I look way better than usual today"?
Like, I look movie star good.
Yeah.
Like, I could be Brad Pitt.
Yeah.
Yeah. Yes, I could.
But then you realize
No, I I look nothing like Brad Pitt.
I I
That's It's all just a deepfake.
[Nasser]
Meet computer scientist Hany Farid.
He's kind of a Sherlock Holmes
for the age of the Instagram filter.
Journalists, courts,
and even intelligence agencies come to him
to sort the fake images
from the real ones.
He also happens to be
my old college professor.
So I dropped in on him,
to hear how he uses Benford's law.
Hello?
Last time we spoke,
things got a little tense.
-Hey, how you doing?
-How you been?
-Good to see you.
-Is it possible that it's ten years?
It's been about
-Yeah. Beautiful view here.
-Not bad.
-It's not terrible. [chuckles]
-Pretty good.
I don't know if you remember,
the last time we met,
the last time we talked,
we got into an argument,
and it was kind of awkward, actually.
It was a little testy.
And the argument was, you said
fake images on the internet
are going to be really bad.
-It was apocalyptical.
-Yeah.
You also thought that very soon
we would not be able to tell
the difference
between real images and fake images
on the internet.
-I said that you were being paranoid
-Yeah.
that there was no way. We'd always
be able to tell the difference.
I probably was being paranoid,
and I probably was calling it early,
but something very dramatic has happened
in the last few years
in our ability to trust
what we see and hear online.
The ability to manipulate digital content
has accelerated.
It's not a game anymore.
[Nasser] Most of us have seen
these celebrity face mashups
because they're hilarious.
and then Tom Cruise walks in,
and even those guys are like, "Whoa."
And he's super stoked
to be there, you know? [chuckles]
He's like, "Yeah! Boom." You know?
[Nasser] But it's genuinely scary
when you realize that this could easily
be done on public figures,
on heads of state,
on you.
So, what we've been
in the business of doing
is developing techniques
to distinguish real images,
real video, real audio from fake ones.
Let me show you how we do some of that.
-Show me.
-Okay, good.
-I actually teach about Benford's law.
-Okay.
And I thought, "I wonder if images
exhibit Benford's law."
So now you have to start thinking about
what are you going to analyze in an image?
-[Nasser] Take a photo.
-All right, hold on.
[Nasser] Any photo.
[camera clicks]
If it's digital,
that means it's really made
of millions of tiny number values.
If you take an image, jpeg compress it,
and you look at the underlying
representation, it follows Benford's law.
-Okay.
-Okay, good.
If you then take that image,
stick it into Photoshop and do something.
And then what do I do when I'm done?
-You save it.
-Save it. Good.
So now the image has been saved twice.
It has gone through two compressions.
Benford's law gets violated.
No.
-Yes! Isn't that great?
-It works.
[Nasser] Huh. So, the more you manipulate
an image, the more you save it,
and the more you save it,
the less it adheres to Benford's curve.
And then when you do an unnatural image,
it looks something like this.
So it's sort of Benfordy,
it sort of falls off a little bit,
but not nearly with the right ratio
that you would expect.
Does it make you more suspicious,
the lower this one value goes?
Yeah, yeah, and that's because
as you keep compressing and compressing
The ones go down.
It gets worse and worse.
And the first thing I do,
as a forensic analyst,
when somebody asks me,
"Is this image manipulated?"
The first question I ask is,
"Has it been saved more than once?"
Look for double compression.
Here's a physical analogy.
Police officer goes to a crime scene,
collects some physical evidence,
puts it into a bag and seals it,
and puts a stamp on that.
If that seal is broken,
we have a problem, right?
Because it means that bag was opened,
and it opens up the possibility
that evidence was manipulated.
-Right. And why was that opened?
-And why was it opened?
Because we're going to a court of law
and it's evidence.
But digital evidence
should be treated the same.
If I save an image as a jpeg,
and if I open it and re-save it,
well, why did you do that?
It's evidence, right?
You shouldn't do that.
[Nasser] For all his techniques
in the war on fake news,
Benford's law is one of the first tools
that Hany turns to.
Still, Hany is under no illusion
that he'll be able to stop
all doctored images on the internet.
The way I think about it is,
I'm going to continually raise the bar
so that it is more difficult,
more time-consuming, and more risky,
and take it out of the hands
of the average person
to create a compelling fake.
[Nasser] And that need,
to keep compelling fakes off the internet,
has never been greater.
The real threat is when
nobody is going to believe anything,
whether it's real or not,
because now, any image, any video,
any audio recording,
any text can be it's fake.
That's the real threat here.
Once it's in the psyche
that we can't tell the real from the fake,
it's sort of game over
because that's all it really takes.
So, it's not about thinking
the fake is true.
Yeah.
It's about thinking
the true might be fake.
That's exactly what it is.
It's a wildly improbable journey
from an obsolete
nineteenth-century reference book
to a high-tech,
cutting-edge forensics tool
that we can use to safeguard ourselves,
our democracy,
and even the idea of truth
in the age of Photoshop.
Not bad.
But why does this distribution of numbers
apply so widely in the first place?
Is it something about us and the way
we divide up and count the world?
Or is it about the world itself?
Is it about the nature of numbers?
Or is it about the nature of nature?
It's hot.
Oh!
[indistinct chatter]
[Nasser] There's a first time
for everything, and for me right now,
that thing is
riding a hot-air balloon over a volcano.
God. It's pretty in every direction.
[man] But we are going
to the center of the crater.
[Nasser] I'm flying over
the Garrotxa Volcanic Zone Natural Park
in Catalonia, Spain.
Woof. Yeah.
I love how this
is literally just a wicker basket,
a flame thrower, and a plastic bag.
Yeah, but probably are safe.
[both laughing]
[Nasser] It's a range of 40 volcanoes
about an hour and a half's drive
from Barcelona.
It's also the home away from home
for volcanologist Joan Martí.
This is a volcano?
[Martí] Yeah, this is another volcano,
Santa Margarida.
The largest one in terms of size
of the crater, of the area.
Oh, wow.
And that was created
by a very strong explosion.
-When would that have been?
-Thirteen thousand years.
So, 13,000 years ago,
there was an enormous explosion.
Yeah. Enormous explosion.
-Right here?
-Right here.
This area's dormant right now,
but maybe, I don't know, tomorrow,
they will be active again.
-Tomorrow? It could be literally tomorrow?
-Yeah, could be.
Tomorrow Well, not tomorrow literally,
but maybe the day after tomorrow.
-The day after tomorrow.
-[laughs]
-It's gonna surprise you.
-Yeah.
When it comes to volcanoes,
surprises are a bad thing.
[Martí] The main problem
is the ash that goes into the atmosphere.
[Nasser]
And that ash can become a global problem.
The relatively small Iceland eruption
in 2010
grounded transatlantic flights
for almost a week
and cost the global economy
nearly five billion dollars.
No one even saw it coming.
So, what makes it so hard
to forecast a volcano going off?
We started doing monitoring
or systematic monitoring on volcanoes
three decades ago.
[Nasser] That may sound like a long time,
but in geological terms, it's nothing.
[Martí] We don't have, still, enough data
to prepare for eruptions
In the end, even geology is numbers.
[Nasser] And given the stakes
of volcano prediction,
the numbers you do have
had better be right.
In volcanology, we have to use
these mathematical tools
that help us to see if the numbers we have
are correct or are not correct.
Joan works with Adelina Geyer
at Barcelona's
Institute of Earth Sciences.
She's the one in charge
of all of that data.
So, one of the main questions, always,
is how reliable are our databases,
how complete they are,
and just by chance,
I assisted to one of the conferences
about Benford's law.
When you first heard about that idea,
what did you think? How did it strike you?
I was feeling like
this is like a kind of magic. [chuckles]
I felt like a bit mystic,
I don't know, esoteric.
Like, is this going to work?
So, just when I arrived home,
I started to look at our databases.
[Nasser] Adelina analyzed
one database in particular:
volcano sizes from across the globe.
And surprise, surprise, it worked.
I was really excited.
[Nasser] Sure enough, it fit the curve
as if Benford's law is literally
baked into the structure of our planet.
I think that's what's extraordinary,
but also spooky to me a little bit.
There's an order where we weren't looking
and we didn't expect there to be an order,
and it's there.
But what does that tell you?
What it tells you, I think,
is that nature works in the right way.
In the right way, yeah.
It doesn't do things
that are inconsistent.
That nature is something
which is much more regular than we think.
But I don't know, like,
I feel like that the world is chaos.
Like we make seemingly arbitrary decisions
all the time.
These volcanoes, sometimes they go off,
sometimes they don't.
But somehow you've found underneath there,
there is this order and simplicity.
I think sometimes we don't want
to discover that things are simple.
So we think that, "Oh, things
need to be more complicated." No.
I mean when you deal with
natural systems, uh
you should look
for the simplest explanation, always.
If there is a volcano that has to erupt,
it's because that volcano has to erupt
to equilibrate the energy, the balance,
the energetic balance
that it has in its interior.
So, nature is not spending
more energy than it needs.
But it sounds like,
if I'm getting you right,
what you're saying
is that the Earth is a system.
-It's an ordered system.
-Uh-huh.
And in a way,
it's like Benford's law is a clue
to that order,
of the giant planetary system.
Yeah.
There is a relationship
between all these processes
that occur in our planet
concerning and related to
the internal geology of our planet.
Before you go to bed at night,
when you're putting your head down
on your pillow,
and you, that day, have found
this little nugget of order,
and it says something,
maybe just about your data set,
but maybe also about the whole world,
what do you--
what does that make you feel?
-Small.
-[laughs]
-I feel small. I feel really small.
-That's true.
[Geyer] I mean, we work for planet Earth,
mainly. So our big boss is planet Earth.
It's like, I'm not even sure we understand
a million part of what is going on.
We think we understand a lot,
but there are so many questions
still open.
[Nasser] And here's the really crazy thing
about Benford's law:
it works all over the natural world,
whether you're looking
at the depths of earthquakes,
the distance traveled
by tropical cyclones,
even the weights of atoms.
And that is why I'm back here,
back where we started,
at the US Naval Observatory.
I didn't come here just for the library.
There's one last thing I want to show you.
Turns out Benford's law
isn't just baked into our planet.
It's baked into all the planets,
and the stars-- Oh.
And did I mention the galaxies?
If you measure the distance
from here to all the galaxies
that we've measured,
the first digits of those distances
will follow that same pattern.
But here's where it really gets me:
whether you measure it in light years,
kilometers,
yards, inches,
my height, your height,
the length of your dog's tail
No matter how you measure
those galactic distances,
Benford's law will apply
every single time.
Imagine, all this started
with one person noticing something curious
about a library book.
A hundred and fifty years later,
we know that that simple observation
suffuses our whole universe.
For all the chaos and randomness
and clamor of our lives,
there's a mathematical order at play here.
And no one really knows why
or whether it had to be there.
All the tax cheats and the Twitter trolls
and the tectonic plates
and the polling data
and the pop stars
and the pulsars
and you and me,
we all fit
onto this gorgeously simple curve.
And in that way, we're all connected.
[upbeat music playing]