Original subtitles

100 years ago, most lifts were driven by trained operators.

The technology was there to replace them,

but people just didn't feel comfortable

with the idea of automation.

Level one, please.

And then lift designers made some small but ground-breaking changes.

TANNOY: First floor, Christmas lectures.

Add that to a stop button and some relaxing music

and suddenly trust in automated lifts soared.

And here we are today.

But what about today?

Should we trust the machines that surround us

or are we right to be cautious?

CHEERING AND APPLAUSE

Welcome to the Christmas Lectures.

I'm Dr Hannah Fry and tonight we're going to ask

whether we should trust the maths.

Just how far should we be going with our mathematical skills?

And let's demonstrate those mathematical skills first off

because we are joined by Scott Hamlin and your BMX bike. Hello.

And a rather carefully placed ramp just here.

Very careful indeed, to make sure it's absolutely amazing.

And you've been in since 8:00am this morning calculating exactly

where this ramp should be, the shape of the ramp, everything,

because it's quite a short space we've got here. Yes, absolutely.

We need to make sure we can get enough velocity to give us lift

off the ramp and I need to use my personal calculations...

..OK, instincts, to be able to perform my stunts

and stop before we crash into the wall.

And when you say stunts, Scott, what are you going to do?

Well, it depends. It might be a backflip if people want to see one.

Do you want to see a backflip? ALL: Yes!

Yeah, they want to see a backflip.

All right, Scott, you ready to give this a go? You guys ready?

ALL: Yes. Right, here we go.

Come on, then. We'll give you a countdown, Scott,

when you're in place. Cool.

Here we go.

And then I'm going to get really far out of the way.

LAUGHTER

OK, whenever you're happy.

Right, are we ready? Yeah.

You happy, Scott? I didn't hear the kids.

Are you guys ready for this? ALL: Yes!

All right, we're going to give you a countdown, Scott. Go for it.

Five...

ALL: ..four, three, two, one, go!

Wow!

APPLAUSE

Woo!

I'm alive.

Well done, Scott.

That was some tight calculations going on. Yes, it certainly was.

I'm glad it paid off. Thanks to you guys for making the noise.

Well, no, thank you to you. Scott Hamlin, thank you very much.

CHEERING AND APPLAUSE

Now, OK, we all know that maths is amazing at this kind of stuff.

It's out there in physics and engineering.

It's doing a brilliant job, just as long as you do your sums correctly.

But I want to tell you a little story about a bridge

that I think demonstrates how it's quite a lot easier said than done,

because this here, this is the Millennium Bridge in London.

It had its grand opening in the year 2000.

But you might also know this bridge by its nickname.

This is known as the Wobbly Bridge

because of something that happened very soon after it opened.

Now, all bridges, including this one, they're built to move

left and right just a little bit. It's no biggie.

But there was something about this particular bridge

that the designers hadn't thought of.

They'd missed off something quite important in their equations.

Let me explain what happened here with one of these -

a little metronome.

Now, this thing here ticks and tocks in time.

If I wanted to write a set of equations for this metronome,

it would be quite simple - some very straightforward physics.

And if I wanted to write some equations for a number

of metronomes, I'd just do the same thing over and over again.

It's not like these things can communicate with one another.

I can treat each one as though they're completely individual.

But now let's see what happens when they're on a bridge

with just a little bit of movement,

because something rather intriguing happens.

I don't want that to fall too far. Let's go from there. OK.

Let's see what happens when these things are on a bridge

that can move itself left and right just a little bit.

OK, so now that these things can move left and right,

something a little bit unusual happens,

because every time that a metronome is ticking or tocking

in one direction,

that left and right movement means that the whole bridge

will just be knocked ever so slightly left and right.

What that means is that now

these metronomes can effectively start listening to each other.

They're all now connected by the bridge,

which means that very, very slowly,

you just see it moving very slightly left and right

and very slowly they start to synchronise with one another...

..like a creepy metronome army.

Now, this is something that my equations

just wouldn't have taken into account.

But humans, like metronomes, actually have to be handled

with quite a lot of care and so for that I'm going to put you

in the very capable hands of my good friend

and mathematician Matt Parker.

Oh, hey. So, thanks, Hannah.

I'm over here in the library at the Royal Institution

where, instead of very small metronomes,

we have a massive wobbly bridge simulator.

We've borrowed this from the University of Cambridge.

They use it to test things like, well, full-size bridges.

It's a very firm structure with a tray attached to it,

which is able to move a little bit side to side.

We've got two treadmills. I'm joined by Dylan here,

who's going to walk on one of these treadmills with me.

If we turn these on, in theory, we'll start walking,

slowly to start with. There we go.

And then, shall we go up to four? Let's try a speed of four.

So now we are trying to walk on a bridge

which is not staying still at all

and it feels a bit like being on a boat, maybe,

where it's moving around

and you're trying to compensate for that movement,

and it means we have perfectly synched up our walking

and that's causing it to move...

..I'll say a concerning amount.

Yes. You're keeping a brave face but it's terrifying up here.

All our movements is causing it to shift backwards and forwards.

Hannah, you can imagine what would happen if you had loads of people

doing this on a much bigger structure.

Just imagine, indeed.

But it turns out this is precisely what had happened

because the people who designed the Millennium Bridge

hadn't taken into account the fact that people can affect each other

with the way that they're walking.

Those small movements left to right suddenly became a very big deal

and it meant that on the opening day, you had hundreds of people

walking over an £18 million bridge, the beginning of a new millennium,

and every single one of them was hanging on for dear life.

Look at that. That's British ingenuity at its finest, just there.

But there is an important point in all of this,

with wobbly bridges and BMX bikes.

Maths can do an amazing job, but only if your equations

actually match up to the world that you're describing.

Just as long as you've got the right equations for bikes and bridges,

you can be certain of what's going to happen next.

But there are some things that are quite hard to write equations for

in the first place.

OK, let's imagine that it's long into the future and you're trying

to write an algorithm that can help a doctor

work out what's wrong with their patients.

Now, a doctor's job is quite different to that of an engineer

or a physicist because if someone just comes in with a headache,

a doctor can't just take measurements of what's wrong

and end up with an exact answer

because that headache could mean a whole host of different things.

Somehow, the doctor has to use a whole bunch of clues

to build a picture of what might be wrong with you.

Now, this is the difference between calculating the answer

and just making your best possible guess, and no-one had any idea

how to do that in an equation until the 1700s,

when the Reverend Thomas Bayes thought of a very clever game.

Now, we're going to play a version of this game

just with a little bit more fire,

so who would like to come down and volunteer for this?

Erm, let's go... Let's go for you just there.

Round of applause as she comes to the stage.

APPLAUSE

What's your name? Emma. Emma? Yeah.

OK, Emma. Right, what we're going to do is, we're going to play

a version of this game and it involves this red hat,

if you don't mind just popping that on your head.

Now, just so that we can get your view of things. Oh, it's a bit...

Hold on one second. Let me tighten this up.

Now, just so we can get your view of things,

I've also got a version of this red hat over here for this camera

so we'll be able to see what you see.

The other thing that we need for this game is a whole host

of balloons, which is just coming on...just coming on behind you.

If you want to turn around, Emma. Just have a little look...

Just have a little look at these balloons.

What colour are these balloons, Emma? You want to stand over here.

Red. What colour are the balloons? Red. Red. OK.

So if we look through this camera now,

we will be able to see that they do indeed all look red,

and yet... Just step over here. Sorry.

And yet, to everyone in this audience, we can see that, in fact,

what you're looking at are 99 orange balloons and one yellow one.

Now, we all know where the yellow balloon is.

No-one's allowed to give it away.

But your job, Emma, is to try and pop that yellow balloon.

And if you manage it, we're all going to explode in excitement.

And if you fail,

we're going to respond with disappointed silence, OK?

So here we go. You get to pick a balloon at random and pop one.

Which one do you want to pop? You stand here and Matt will do it.

Up? Up?

Down. This one? Yeah.

Perfect. That one there? Yeah.

Ready? Here we go.

That is not the yellow balloon. That's OK.

It's pretty hard in the beginning. I mean, you know...

How can you possibly guess it first time?

What we're going to do is, audience, we're going to help her here.

So, we are going to tell you, on my cue, we're going to tell you,

based on the last balloon that you popped,

whether you should go higher or lower, left or right.

If you think it's higher, say higher.

if you think it's lower, say lower.

If you think it's neither higher nor lower,

I want exactly 50% to say higher, 50% to say lower,

and I'll let you work out between yourselves which one is which.

OK, so, based on her last balloon pop,

should she go higher or lower?

ALL: Lower.

And should she go left or right?

ALL: Left. OK, where do you want to pop?

Erm...

..lower.

Left a bit.

That one. That one. Ready?

Oh, OK. We'll give her another go.

Do you want to go, based on the last balloon pop,

should she go higher or lower? ALL: Lower.

And should she go left or right? MIXED RESPONSES

Oh, interesting. OK, which way do you want to go?

Down.

Down. That one.

Ready?

EXPLOSION

APPLAUSE

You got there. Thank you so much, Emma.

You got there amazingly quickly. OK, do you want to take this...?

Tell me, what was your strategy in the first place? Just pick one.

Just pick one at random? Yes. You were just guessing at random.

Did our clues help you? Yes.

You knew probably where the balloon was by the end. Yeah.

Were you getting more and more confident? Yes. Yes. Perfect.

All right, Emma, thank you so much. Amazing.

APPLAUSE

What Emma was doing there, she was demonstrating something

that's called Bayesian thinking and, actually, it's something

that all of us do instinctively.

But it wasn't until Bayes thought of a version of that game

that the world realised that you can actually write down

that way of thinking into an equation.

I'm really not exaggerating when I tell you that that Bayes theorem

is one of the most important equations of all time,

because, suddenly, it doesn't matter if you're not

completely sure of the answer.

You can still get a really good sense of the right answer,

even from incomplete pieces of information.

And that is something that is incredibly useful.

Let me show you.

So, OK, let's imagine that you are making a driverless car.

Now, it hasn't got a driver in it so you need to make sure

that you know where you are and, OK, you could use GPS to do that,

but GPS isn't perfect.

So, sometimes, your GPS will get your position out

by about a metre or so.

And if you're a human, that's fine. No big deal.

You can work out where you are.

But if you're a driverless car, the difference of a few metres

can mean the difference between driving on the pavement

and driving into oncoming traffic, which isn't ideal.

So driverless cars, they also have cameras on board.

Now, cameras are pretty good at letting you know where you are,

but, again, they're not perfect because skies look a lot like water

and, you know, lorry tarpaulin looks a lot like a clouded sky.

The point about driverless cars is that you don't just have one thing

that gives you exactly where you are.

You have lots of different things that you use as clues

to indicate where you are.

And that is something that is especially important

when you are driving at 200mph.

So, this thing here, this is the world's fastest autonomous car.

It was built for racing and it's got all kinds of different sensors

to help it work out where it is.

It's got little cameras here,

it's got another kind of camera called LiDAR over here.

it's got radar over here at the back.

All of these are the clues for the car,

and GPS within the computer that's just inside here.

Now, this thing is basically a Bayesian machine.

So, that computer, that is the size of just a lunchbox,

is churning through trillions of calculations every second

to make sure that this car knows where it is

and finishes the race as quickly as possible,

all while avoiding other competitors.

I think that's the thing about how these modern inventions work.

That's how they deal with uncertainty.

They don't just have one sensor, they don't just have two sensors,

they have a whole host of sensors that they use to layer up

and give them information.

That's something that's true of driverless cars,

but it's also true of this little guy here,

who I believe is going to follow me into the studio.

There we go.

Come on, then.

Come on. Come on.

CHUCKLING

Hey! Round of applause for our little drone.

APPLAUSE

Oh, that was a lovely landing.

Right, I want you to join me in welcoming to the stage

Duncan and the Skyports drone.

CHEERING AND APPLAUSE

This is quite some drone, Duncan. This is quite a big one.

This is one of our delivery drones, so we can do medical samples

or e-commerce deliveries with this one.

So what kind of things is this used for? We do blood samples.

We can do them between hospitals and medical facilities.

We can do packages. We were flying them in Finland recently.

Basically, anything you can fit in that box, up to about 5kg,

we can fly it. So how does this thing avoid crashing?

It's got a number of systems on it. It's got 4G, like a mobile phone.

It's got a Wi-Fi network of its own.

And it's also got, if all else fails,

a satellite communications network.

What's this thing over here? That's the fail-safe.

So, if everything goes wrong, that's a parachute and that would deploy.

So, for example, if one of the rotors stops

or one of the motors doesn't work, a big alarm goes off,

that will deploy, and it will come down to Earth very safely.

So it needs all of those different systems running in parallel?

It needs them running in parallel. Hopefully you only ever use one.

The rest we call redundancy. It's there in case something goes wrong.

What's the future of drones like this, then?

This is becoming more and more prevalent. We're flying in Africa.

We're doing snake bite anti-venom.

So very urgent stuff, often very bad road networks.

We're flying in the west coast of Scotland,

doing some medical samples again.

Ultimately, it will come into cities,

much more complex environments,

you've got lots more people, lots more buildings,

lots more things to keep out of the way of.

But the technology is good enough now

that you can fly in pretty much any environment.

Talking of people, could I ever get a personal passenger drone? You can.

In fact, you can already.

So this is your company. Personal passenger drones, are they?

Yes, this is a company called Volocopter, and these are live.

They're going through certification now.

Within two years, everybody will be able to get in one and fly around.

Within two years? Within two years. Goodness me.

Wil our skies be full of them in the future, do you think?

The air space is vast. Cities are now very dense.

It's hard to put more infrastructure into cities.

These can fly in our underutilised air. Amazing.

Duncan, a view of the future there, I think.

A big round of applause, if you can.

APPLAUSE

Duncan was talking a lot there about having backups on backups

on backups, just to make sure that if there's ever a problem,

you know that the drone won't crash, and that is something, actually,

that Matt Parker has been thinking about, too.

Yes, and I've brought a comedy oversized slice of cheese.

A slice of cheese? A slice of cheese. All right.

Because when a lot of people are thinking about things like drones

and trying to avoid disasters, they find it's useful to think of it

in terms of cheese. OK.

Things can go wrong with drones.

You can have... One of the motors might break,

the battery might run out of charge.

When that happens, you don't want it to crash and cause a disaster.

So, you imagine these mistakes, these errors, coming at your system

and you put in barriers...

so, like a slice of cheese, to stop them from making it...bear with me,

making it through and becoming a disaster.

So this could be, for example, like, the GPS system. OK.

It's tracking where it is, anything that goes wrong,

it shouldn't be a disaster. What about the holes, though?

Well spotted. So, GPS, as you know, is not perfect.

You could be on the sidewalk, according to the GPS,

and so it might be inaccurate, it might give you the wrong data.

No one layer to try and stop disasters will be perfect.

So this is trying to block disasters from happening,

mostly it works, but just occasionally it's going to fail.

Occasionally a mistake will slip through and GPS won't be enough.

But over here, we've got more cheese.

If you'd like to take a seat here, under the cheese. It's fine.

Are you sure? You trust the maths. Here we go.

I'm not sure I trust you though, Matt. Wise Very wise.

So, this is another slice of cheese and this one is the parachute.

So, if the big drone fails and the GPS is wrong,

the parachute will deploy.

With two layers together... This has got holes in it as well.

That's true, but what we hope is, the holes in this layer

don't line up with the holes in the other layers.

Actually, we can get another layer.

This one's called rules, which doesn't sound very exciting,

but we all need rules.

So, when we brought the drone in here,

we weren't allowed to fly it above a crowd.

That's one of the rules for using a drone.

So even if an accident happens.. Yeah.

..even if the parachute fails and the GPS fails,

at least people won't get hurt.

In theory, if you're following the rules, it'll be fine,

although, of course, sometimes people break the rules

and you hope the other layers will help you out.

And so...I'm going to grab a camera so I can show you a point of view.

Thank you. Can I just...

You know what, Matt, I mean, it's not that I don't trust you...

No, it's literally that you don't trust me. It's literally that. OK.

So if you have a look from Hannah's point of view underneath,

you can see up through some holes, but then, almost straight away,

it's blocked by a different slice of cheese.

And the point of view at the top, here you go.

Again, there are some holes that go partway down, but then they stop.

What we're going to do now is rain some errors down on you.

We've got a whole bucket of errors

and, in theory, if we drip them down,

while they will make it through some of the slices of cheese

they will be stopped by... More errors, more errors.

And so, some of them are being stopped by the first layer,

some of them are getting through the first layer

but they're stopped by the next layer, and so, in theory...

OK, I get it, I get it, I get it.

Yeah, overall... Overall, it's fine, right?

All of these different layers are blocking it from happening.

And so even though any one individual layer,

you're like, oh, look at all those holes in it,

if you sit down and you look through the whole lot at once,

you're like, oh, that's amazing.

From here, I can't see any hole which goes the entire way through.

That's good, but then, Matt,

what happens if the holes do go the entire way through?

That's a good point, because every...

LAUGHTER

You make a valid point.

I think we need more errors. Albeit in an interesting way.

More errors. More errors.

CHEERING

I'm trying to make a serious point here.

Occasionally, your cheese holes will line up

and a few mistakes, normally, will make it through

and become a disaster.

And there's nothing you can do about that? Nothing you can do.

Disasters, Matt, are inevitable. Erm, yep.

I'm coming to terms with that as we speak.

Matt Parker. Round of applause. Thank you very much.

CHEERING AND APPLAUSE

So this is the really big downside of uncertainty.

You have to accept that perfection is impossible.

Mistakes are effectively inevitable.

I think that that raises a very big and important question.

If we know for sure that our algorithms

are never going to be perfect,

do we want to put them in charge of making decisions,

especially in situations where people's lives are at stake,

like in the courtroom?

Someone who's thought about this a lot is Professor Katie Atkinson.

APPLAUSE

Katie, the courtroom, it doesn't feel like a natural place

where you would find mathematics. Well, perhaps not, but, actually,

AI and law researchers are working on building models

of legal reasoning using mathematical models

that are then turned into software programmes

that can help judges and lawyers. Why do they need them?

Why can't the judges just do it all themselves?

Well, the point of using these mathematical models

is that we can get consistent, efficient decisions,

and we know that any kind of unconscious biases are stripped out.

So, judges make mistakes, they have unconscious biases,

and the idea is that using algorithms

can help to minimise that? That's absolutely right.

We're hoping these can help. I understand that you've brought

a little friend along to help us understand what's going on here.

Yes, this is Pepper the robot. Pepper the robot. Hello, Pepper.

All rise for the court that will decide the case of Popov v Hayashi.

So this links us to a legal case that was in the United States

and involved a baseball and people catching and dropping a baseball.

So someone hit a baseball into the crowd

and then two people fought over the baseball,

and this baseball was very valuable, wasn't it? Indeed.

It was worth $450,000 in the end. Oh, crikey!

I can understand why two people were particularly upset. Yeah.

So what we have to do is, first of all, work out what the facts

of the case are and then we have to work out what the arguments are

for the two different sides within the legal case.

And that's what Pepper's going to help us with? That's right.

So the facts of the case are that Mr Popov stopped the forward motion

of the ball once it was hit into the crowd.

He tried to get it under control but he was thrown to the ground

by this mob who were also trying to secure the baseball.

It sounds a bit unfair, really, if you're, you know...

You've caught it and then... It's not your fault. That's right.

That's why he felt that he should have been given the opportunity

to complete the catch.

And then Mr Hayashi found the loose ball on the floor

and he picked it up and claimed it as his. OK.

Well, I mean, he was the one who ended up with it at the end.

That kind of seems like he's got a fair claim, too. That's right.

And, in particular, he wasn't part of this mob

that threw Mr Popov to the ground, so he did no wrong either,

so he shouldn't be punished.

And that's really the facts and the arguments of the case.

So you can take all of those facts and arguments over the case,

put them into equations, compare them to cases

that were like this in the past,

and then, ultimately,

can the algorithm give us a verdict? Yes, that's right.

OK, Pepper, what's the verdict in this case, then?

The decision of this court is that the ball should be sold at auction

and the proceeds split evenly between Mr Popov and Mr Hayashi.

OK, that's very clear. We're having lots of fun with a humanoid robot,

but it's not the intention to actually have humanoid robots

in courtrooms, is it? That's absolutely right.

We're aiming at writing these mathematical models

that we're turning into AI tools that will be on the computer

and helping judges and lawyers

who are set there using these for decision support.

It's all the stuff inside Pepper, not Pepper herself. That's right.

I can't imagine us seeing Pepper in a court any time soon.

If she's sending you off to jail, going like that... No.

This example sounds like a very positive thing.

You could get through, I imagine, a big backlog of cases

with something like this on your side.

But algorithms in the courtroom, they're not...they haven't been

universally positive, have they? Yeah, that's right.

There is a big issue of trust

as well as whether the actual technology works in itself.

Because if you're putting all of history into a series of equations,

I mean, history wasn't exactly fair, was it? That's right.

And we want to make these decisions as fair as we possibly can

and get AI technologies to help us do this. I quite agree.

Katie, thank you very much for joining us. You're welcome.

APPLAUSE

I think Katie made a really important point in all that,

because if all you're doing is just chucking in everything that happened

in the past to your equations, then you're going to perpetuate

all of society's biggest imbalances going forward.

And a machine is only ever as good as the data that it's trained on.

Let me show you what I'm talking about here,

because I'd like you to welcome back to the stage Matt Parker

with a very special shoe-detecting machine.

APPLAUSE

Is that a new shirt, Matt? I bring a range of shirts.

So, this is my shoe-detecting device. OK. You can have a go.

I call it Shoe Do You Think You Are? OK. Very nice.

If you point it at something, it can tell you if it's a shoe or not.

All right. Let me give it a go. Try your face.

OK, that is not a shoe.

Not a shoe. Correct. Thank you very much.

Let's try aiming at your shoes. Yep.

Oh, hang on. It says they're not shoes.

The device is fine. We just haven't trained it yet.

We have to put in some training data.

You were here for lecture two. I was.

So we've got to teach it what a shoe looks like

and then it'll be amazing. OK. All right, then.

So let's get a group of people to help me train this shoe.

So let's get some people from over here.

Let's get that little column up there. And up here.

You guys all want to come down here and help me train this machine.

Round of applause as they come to the stage.

APPLAUSE

OK, so here's what we're going to do.

We'll give you 20 seconds,

and I would just like you to draw a picture of a shoe

that I can scan into the machine.

Here we go.

Two, one, stop.

OK. Let's turn those round. Hold them up to the camera.

We'll have a look. Let's scan these.

We've got some lace-y numbers.

Some nice... A top shot of a shoe there. This is great.

Lots of laces. You hare some trainers there.

This is all perfect. OK, great. Perfect.

It's all... I think it's all trained, Matt.

So let's give it a go.

Let's try your shoes there.

OK. Perfect.

Spotted your shoes. Amazing. It's great. It works.

Is it detecting shoes? Yeah, look. Yeah, perfect.

That's amazing. Can I just pop through and get a closer look?

That's incredible. Oh.

And it's not failed yet on any of these near identical shoes?

No. I mean you did all draw very similar shoes. Give these a go.

Let's try this one.

Oh, no. It's saying no. It doesn't detect your shoes at all.

You need a much more diverse range of training.

I'm very disappointed in all of you.

LAUGHTER

I mean, guys, you did just basically draw your own shoes.

So let's try again.

Turn your paper round, try again,

and this time try and think of as wide a range of shoes as possible.

Off you go.

Three, two, one, stop.

OK. Here we go. Let's get this in scanning mode.

We're ready to go.

Turn it around. Hold it up to the camera. That's it.

It looks pretty much like a shoe. This is pretty good.

This is great. Got some high heels.

Lots of high heels. Got flip-flops, got boots.

We've got some wellies there.

This is lovely. Ballerina shoe. That's great. Perfect.

Matt, I think it's good now. I think it's got to be good now.

Surely this works on all shoes now.

Let's have a closer look at it.

Excuse me. MURMURS IN AUDIENCE

Shoe? Shoe.

Not shoe. Not a shoe?!

I mean... Shoe.

..that's debatable whether that's a shoe. It's definitely footwear.

OK. Let's give it a go.

With the right data it could have detected that as a shoe.

This is true, with the right data.

But I think the point here is that even when you know to draw

as diverse a range of shoes as possible,

it's actually just really hard to think of everything.

Just unbelievable.

Thank you very much, Matt.

A round of applause for our volunteers.

APPLAUSE

Now, there is a really important point in all of this,

because if you don't think through all of the possible situations

that your machine needs to include,

it can end up having very big, real life consequences.

To tell us a little bit more,

please join me in welcoming from the University of York

an expert in image recognition for surveillance,

Dr Kofi Appiah.

APPLAUSE

Hey, Kofi.

Now, Kofi, you've done a lot of work in facial recognition before, right?

That's right. Tell me, how does facial detection work?

So for face detection, all that we need is to be able to pick out

the elements of the face, which is the eye - the key features -

the eye, the nose, the mouth,

and to be able to pick out these features,

there's a big contrast that we can find between the eye

and the eyelashes, the eyelashes and the skin itself.

When it comes to the mouth, the lips, you have an edge there.

So these are the big contrasts that we are able to pick

and as far as we're able to find eyes, nose, mouth, we've got a face.

So is it looking... If I come over here, then, to this one here.

Is it looking for areas of light and dark?

Say, on my nose, for instance? Yes.

It's kind of darker on either side and then lighter down the middle.

That's correct. And if it gets a strip of darker pixels and lighter

pixels, it knows it's found a nose? That's right.

It's looking for these key features.

This is what a face normally will have - the key features.

And that's what we train our systems to use and recognise.

Perfect. Just one thing, though, Kofi, that I'm noticing here.

It's getting my face OK, but...

Right. So it's not able to pick my face,

and it's relating to the data that you just mentioned.

This system has not been trained with enough data.

The contrasting features that you've got between your eyebrows

and the skin texture is different from mine.

And it's not picking it up.

So in this case, I'm going to have this...

It's picking it up as a face because it can pick some

of the salient features that I was talking about.

It's going to put a bounding box around it.

Whereas in my case, no.

But this stuff is actually, you know, it's a really big deal.

It's not just in cameras.

We're now seeing facial detection in all kinds of things.

Passport queues, for instance. That's right, yes.

Obviously, in this case, if you've got a face like me,

unfortunately, it's going to be a long delay for you.

We're using it in law enforcement as well.

An example, if it's not able to pick the right face,

you're going to be prosecuted for something that you've not done.

We're using this facial recognition to be able to unlock phones.

It's like a password now.

So if it's not working right look at the harm that it can do.

Is it improving?

Are the algorithms getting better?

Yes, it's getting better and better.

And what they're trying to do is to make it non-biased

by training with diverse, non-biased data sets.

As you can see, you can pick some of the features,

it can pick mine. And works with a whole different range of faces.

It's trying to fix that.

So it's improving over time and we're getting there.

Obviously, the issues of bias and fairness are incredibly important

when it comes to facial recognition.

But there is another concern that people have when it comes

to this technology, which is that some people don't like the idea

that they can be identified in a crowd

based on their facial features.

Some people don't like the idea of losing their anonymity.

So some people have been experimenting with different ways

to try and trick facial recognition cameras.

And we are lucky to be joined from Glow Up

by make-up artist Tiffany Hunt and Eva.

APPLAUSE

If you come and stand round here.

Now, Eva, you have had, as we can see,

Tiffany has been doing your make-up for a little while backstage.

Looks very remarkable.

Is this the kind of thing that would work to fool facial detection?

Oh, yes. So this kind of system, because it's looking

for that contrasting bit between the eye, the eyelashes, the nose,

but the way the face has being painted now,

it's breaking all the symmetry.

It can't find the nose.

Tiffany, talk us through what you were going for here.

It's quite dramatic!

Just a bit. Just something, like, natural!

Basically, what I was thinking,

was something that was a monochromatic illusion.

I really wanted to break up specific facial features

such as this area in the central area of the face,

which is the area that gets picked up the most.

Also changing the eye shape, the lashes and just really going

for something with colours that are just so different

to your usual skin tone and just changing her face totally, really.

Do you like it?

Yeah. Friday night out.

But the proof is in the pudding. Let's have a look.

So, Tiffany, we're picking you up. If you step to one side.

It's not getting you at all!

I think a big round of applause there for the dazzling make-up.

Very impressive.

To Eva, Tiffany and Kofi. Thank you.

APPLAUSE

We've got some ways now that we know we can avoid being detected

by facial recognition cameras. Might look a little bit crazy

if you're wandering around with that all the time.

But when it comes to protecting our privacy, there are some people

who are worried that even this won't be enough.

There are some people who are worried that with the help

of mathematical algorithms, we are building and processing vast

profiles on each and every one of us,

often without our knowledge.

Now, to explain this, please welcome to the stage

computer scientist extraordinaire, Dr Anne-Marie Imafidon.

APPLAUSE

Anne-Marie, do you think that we're seeing the death of privacy?

In some ways we are, in other ways we aren't.

I know if you go back far enough, we used to communicate with fire

and smoke signals or by yelling things long distance.

Not that long ago, really! Yeah, basically.

But now, with the algorithms that we have and the time

that we spend online, really in-depth profiles are being built up

on all of us continuously.

And it's those profiles that are connecting pieces of information together, right?

That's kind of the big thing. Exactly.

So where those things might not have been private before,

being able to connect them together to build up that picture of someone,

that was harder. Whereas now it's very easy.

And we use things like social media

where we're putting that information out. Voluntarily. Exactly.

So the profiles are pretty complex.

OK. So to give us a sense of these kind of profiles,

I wanted to get, let's say, three volunteers here,

because Anne-Marie's got a little demonstration for us.

OK, perfect. All right.

OK. We'll go for you. You get to come down.

Let's go for... Let's go for you there, in the jumper.

And you there, in the stripy jumper.

APPLAUSE

Let's bring you down to the stage, come on.

What's your name? Natasha.

Natasha, OK, perfect. Natasha, if you want to go there.

What was your name? Kieran. OK, perfect.

Do you want to go there, Kieran? And what was your name?

Caitlin. Perfect. You jump round there.

Anne-Marie is going to talk us through a little demonstration.

Yes. So, each of you have got a website that we've loaded up

for you on your laptop there.

And I want to make sure you've accepted cookies.

And I'd like you to get clicking and browsing on these sites

and doing some cool things.

And as you've accepted cookies, I'm going to give each of you a cookie.

They are rather large cookies.

Thank you very much.

So as your browsing and your clicking around,

you have this cookie in your site, in your laptop,

and there's different data and information that you're putting in.

So I can see you here.

You're about to watch some YouTube videos.

I can see which channel that you're on.

So I'm going to pop a little bit of a chocolate chip there.

That's some data.

I can see the artist that you've got as well.

So I'm going to pop a little bit more data

on your chocolate chip cookie.

I can see you're shopping here.

Brilliant, curtains.

That's a good bit of data.

Just got a new house and she likes blue and white curtains.

So two more bits of data that we've got there.

Fantastic.

I think you've added them to your basket as well,

so we're going to add that into your cookie,

just so when you come back, you don't need to browse blue

and white curtains again.

And just over here, we're looking at your address,

so that's a bit of data.

And I can see you're getting directions to school,

so that's even more data that we've got popped in there.

This is a lot of data now, Anne-Marie.

A lot of data just from browsing and entering information

that is going into these cookies that are stored on their laptops.

Now, if you stop browsing now,

you'll see that we've got quite a lot of data on these cookies.

And these cookies don't just stay within your laptop.

Many of you might have accepted cookies

that have got third party sites as well.

So here's our third party site. What does that mean then?

And you actually get that data as well from their cookies.

So you know it's blue and white curtains that she's looking for.

So if you accept third party cookies, that means another person

can just buy that data and add it to a whole host of other data

that they've got from all loads of other websites

and build this incredibly detailed profile.

That's exactly what's happening.

Do we realise that's what we're really doing when clicking around?

Probably not. OK.

But the thing is, is it's not just the information

that you're clicking on that helps to build this profile of you.

It's also things that you are not clicking on, too.

And so for this, let me welcome to the stage Marc Kerstein.

APPLAUSE

You build websites, don't you? Yes, that's right.

And you in fact built a website for us.

Yes. So, let's have a look at this. Talk us through what you've built.

This is just a web page that I've created that lists

a bunch of animals. OK. Perfect. All right.

So, what I'd like you to do, if it's OK,

is just have a little look through this

and have a little flick through and stop and have a little

read of whichever one you think ends up being particularly interesting.

Happy? Have you stopped on one? Have you picked one?

Yup. OK, perfect. All right. Now, Marc, which one did she pick?

That would be the dog, is that correct? And how did you know that?

Yes, so, it's not just about the information

you're actively putting in,

but it's enough to simply scroll through something to find out

what someone's thinking of, so in this case, this web page,

as you scroll through, you're seeing the different animals that

are being looked at in real time, being transmitted to the server.

So, Anne-Marie, websites aren't just tracking what you're

clicking on, they're tracking on what you're pausing on...? Yeah.

How fast your mouse is moving,

the kind of device that you're using to access the website.

They can even tell the difference between a click and a tap.

But often, there's even more, so things like your IP address,

which might give a clue as to where you are physically browsing from.

Just imagine how much information you could get on someone

if you're a professional company that had been doing it for years.

Exactly, and that's why it's so valuable.

There's so many insights that we can pick up from lots of different

websites. There's so many of us that are using these platforms

and so those cookies are pretty valuable

over time to lots of different people. Incredibly valuable indeed.

Thank you. APPLAUSE

And thank you, Anne-Marie.

Now, with all of this stuff,

we're not saying that it's necessarily bad,

but I think it's important to realise exactly how

much we are giving away

because I think if someone can work out what kind of person

you are, they can use that information to target you

with very precisely tailored messages.

Now, that might be adverts to persuade you to buy something,

but it might also be linked to political messages to

persuade you to vote in a certain way.

And that is something that's been in the news a lot recently.

I think it is important to remember this is kind of how our whole

online world is designed to work, but what makes people

particularly unhappy is when that targeting happens with fake news.

But even there, there is maths hiding behind the scenes.

Because with algorithms on your side, it is

easier to create realistic fake stuff now than it's ever been before

and I want to show you just how easy it can be to create fake stuff.

I want to see if you as an audience are capable of spotting some

fake classical music.

We're going to play a little game that

I like to call Is The Bach Worse Than The Byte?

OK? I was pretty proud of that. Thanks. What they're going to do,

they're going to play you two pieces of classical music.

One of them was composed by the very great Vivaldi and the other

one was composed by a mathematical algorithm in the style of Vivaldi.

What I want you to do is to see

if you can guess which one is which, OK?

So, two pieces of music, your job, spot the real Vivaldi.

OK, here we go, piece of music number one.

THEY PLAY

That was lovely. APPLAUSE

OK. That was piece of music number one.

Here is piece of music number two.

THEY PLAY

APPLAUSE

OK.

But one of those was a fake, OK? So you've got to spot which one.

If you think that the real Vivaldi was the first one, give me a cheer.

THEY CHEER

If you think the second song was the real Vivaldi, give me a cheer.

THEY CHEER

I mean, that's basically 50-50, guys.

Just guessing at random, I see. And the real answer was...? Which one?

Number one. Number one was the real Vivaldi.

Well done, if you got that right. APPLAUSE

Now, OK, that fake Vivaldi was impressive enough to

kind of fool half a room full of people as to which one was real,

but the algorithm itself is actually incredibly simple.

All you do is you take a catalogue of all of the songs that

Vivaldi has ever written and then you give the algorithm a chord

and then it will tell you with what probability the next chord

that was likely to come up in Vivaldi's original music.

So all you do, give it a chord, it gives you a chord back based

on probability, you give it a chord,

it gives you a chord back based on probability,

you chain those chords together, one after the other,

until you end up with something that is entirely original.

But that, I think,

is the real giveaway here about the fact that this is the fake.

Those very simple chord transitions that go on in the background.

And there are other bits though, right?

There was one bit at the end there particularly which

looked like it was quite difficult. I'm afraid there are passages later

on which are impossible to play. Impossible to play? Impossible, how?

At the speed that the artificial intelligence has asked us to play,

you physically can't reach extreme ends of the instrument quick enough.

And I think that's an important point.

Vivaldi, he had knowledge of how to play instruments,

he had knowledge of human hands and human bodies, but the algorithm

doesn't, it just kind of shoves loads of stuff in together.

But I should tell you that it turns out that you can use this

very same idea for lots of other things.

You can use it for music, but you can also use it for lyrics

and because it's Christmas, what I decided to do,

I decided to feed in some classic Christmas carols

and I decided to train my very own algorithm to generate a whole

new carol, and so for this, please welcome to the stage Rob Levey,

and join us for a rendition of a mathematical Christmas carol.

Round of applause for Rob Levey. APPLAUSE

Feel free to sing along.

CHEERS AND APPLAUSE

Rob Levey and the Aeolian String Quartet, everybody!

Thank you very much!

Here's the thing about maths in this very creative way,

it's very impressive way, but it's also not really human

and there is something a little bit uncomfortable about a world

where fakes can fool,

especially when we aren't just mimicking music, but people.

To explain, let's welcome Dr Alex Adam.

APPLAUSE

Now, Alex, you work in an area called deep fakes, right?

That's right. What are they?

So, deep fake algorithms are a special kind of machine

learning algorithm that can take say one person's face,

or their head, or their entire body, or their voice,

and turn it into another person's head.

So, to make people look like they've done stuff in videos that

they've never done. Absolutely.

OK. I mean, that's quite something, right? You can manipulate someone.

Yes, it's quite scary. You can essentially puppet people.

So, how does it work?

So you imagine if I have a video of you and a video of me.

So we take those two videos and we split them

up into their sort of individual frames,

so the images that make up that video,

and we'll show a computer all of those different images of me

and you and what the algorithms will start to learn is they'll start

to learn things like what's the structure of our different

faces and what are the different kinds of expressions that we

make, but critically, they learn how to distinguish the two,

so one of them will know, OK, I can make red hair

and a particular kind of skin tone and the other one will say,

I can make brown hair and a particular kind of skin tone.

But they'll separate out our expressions, so I'll be able

to say, OK, I want to take you smiling and put that smile on to me.

So, you're splitting out what your face looks like

and what your face is doing. That's exactly right.

And then you can put what your face is doing on my face.

Whilst keeping all of your other features the same. OK, all right.

So we've got a couple of puzzles here. So here's a picture of you.

You're doing a little snarl. A bit of an eyebrow raise as well.

OK, so you can make me do this face. Yeah, that's exactly right.

How do you do it? So, if we just flip that over,

so what we can think of is we can think of my expression

as having some kind of abstract mathematical representation,

which I'm sort of thinking of as these puzzle pieces

and what I can do is I can say, well, piece 32 and say 37 over there

correspond to me making this snarl

and what I can do is I can just take those pieces, let's imagine I've got

them over here, and I can just slot them in over here into your face.

You're shuffling my face around, essentially.

Yeah, I'm basically saying,

turn on the bits of your face that will make you make that snarl.

OK, so once you've completed that jigsaw,

if you can flip it over, the idea is...

Ah, there we go.

That's a lovely, snarly face, isn't it? Exactly.

Now we get Hannah with the snarl.

Are there concerns about this kind of technology?

So, like, my day job is a data scientist of faculty

and I work on using artificial intelligence techniques to

sort of detect these sort of video manipulations.

Obviously, there's lots of implications for the fact that you

can just puppet people. I could record a video of myself saying

something and just transform it into some celebrity, for example,

and this has implications for say privacy

but also for say democracy and political disinformation.

So there are lots of sort of concerns about that, which is

why it's important to be able to detect this kind of content online.

There are also many great applications though,

like dubbing, special effects and things like that.

Do you have any top tips for spotting deep fakes?

Yeah, so I think my top tip for sort of spotting deep fakes is

always just if you're watching a video of something

and you sort of suspect that it might be a deep fake,

just ask the question, do you really believe that this person

would do or say these things that the video is portraying?

So that's like my number one suggestion.

My second suggestion would be sort of do some fact checking.

Sort of try to see if you can find that video on some trusted news

outlets, particularly if you found it posted on social media or

something that's harder to verify. And from a technical perspective,

I think it's useful to look for things like objects in the

background of a video, so if as I move you notice objects

in the background of the video moving with me,

that's a pretty strong indication that the video's been manipulated.

They, I think, are some excellent tips that will only serve us

well in the future. Alex, thank you very much indeed. Thank you.

APPLAUSE

Now, we really wanted to show you how this deep fake stuff works,

so what we've done is we've been working with Alex's team

and we've created a deep fake of someone in the audience.

We always look to break boundaries here at the Christmas Lectures.

So, to give this moment the real sense of occasion that it

deserves, I would like to introduce you to a brand-new talk show

because tonight, for one night only,

please welcome your host, it's Matt Parker and This Is Your Face.

CHEERS AND APPLAUSE

Thank you.

Welcome to This Is Your Face. Can you please welcome to the stage

tonight's face? It's Kaya.

CHEERS AND APPLAUSE

Come on down, Kaya. If you'd like to take a seat. Thank you.

So, Kaya, it's great to meet the person behind the face and to

get to know you, my first question is, do you have a favourite food?

Yes, I like pizza and pasta. Pizza and pasta. Yes.

That's pretty uncontroversial. Pizza and pasta?! No.

We're not having that. Let's have another go.

I really like vegetables,

just plain old vegetables.

Especially Brussels sprouts, actually. That's number one.

And often maybe with a side of extra vegetables.

Well, Kaya, that is your face.

My next question, do you have a favourite type of animal? Yeah.

I love cats. You love cats? They're pretty adorable, aren't they? Yeah.

Have you got like a least favourite creature? Erm, probably insects.

You don't like insects? No.

Interesting. Hm, let's see, shall we?

I just love ants. I think they're amazing.

I love the idea of them crawling all over me,

in my hair, up my nose, in my ears.

Just like a massive swarm of ants everywhere.

Oh, Kaya, you'd better talk to your face.

Now, my last question, you've got a younger sister, haven't you? Yes.

Are they in tonight? Yes, just right there. Over there. Excellent.

And you get pocket money. Yeah.

OK, my final question, just hypothetically,

your pocket money, you wouldn't mind giving all of that to let's

say your sister for the next roughly five years?

No! No?

Hm.

That's your sister? Yeah. Don't worry, we've got you.

I've decided to give my sister all of my pocket

money for the next five, ten, 20 years.

I think she deserves it, you know, she can have it.

And she can have all of my desserts too. I don't need those.

And she can also have my phone and my room, which is

where she can keep all of my clothes because they are now hers.

LAUGHTER

Wow! That is your face, so thank you very much for coming along.

No problem. No, not you. Your face!

Thanks, it's been wonderful to be here

and I completely stand by all of my answers.

APPLAUSE Thank you very much, Kaya.

There is a point to all of this

because whether you're talking about deep fakes or driverless cars

or facial recognition, under the surface,

all of these things that have such potential to change our world,

they're ultimately mathematical creations

and maths isn't just about bridges and bicycles and buildings.

Behind the scenes,

it's mathematical levers that are powering the changes to our society.

It's got the potential to change everything, what we know,

how we talk to each other, even how our whole democracy is structured.

Now, don't get me wrong,

I don't think this is about being afraid of the advancement

of machines, but I do think that we need to be honest with

ourselves about the awesome power of mathematics

and I think we need to be careful of the very real

limitations of something that will never be perfect,

but I think if we can be aware of the pitfalls,

if we can work our way around the challenges,

I am optimistic about a future where humans

and machines can work together, exploiting each other's strengths

and acknowledging each other's weaknesses,

a partnership has the real potential to be a force for good.

And so to finish, let's combine human

and machine in a performance of collaboration.

Please welcome the Chineke! Orchestra.

APPLAUSE

Your job is to guess which parts are human

and which were the mathematical algorithm.

Enjoy.

THEY PLAY