# The Mathematics of Crime and Terrorism – Numberphile

We’re talking about the maths of crime Crime? Yeah! For people who don’t know, you’re a proper mathematician. And we’re really getting into your research. Yup. We’re gonna… In fact, even look at a paper that I’ve even done with one of my PhD students. So yes, I am a real person. This is your area of expertise? Ahh… yeah. Ahh… yeah. One of the things…. That’s important to know about crime… or terrorism… things like that… is when it’s going to happen. There’s a bit of old maths that kind of helps us start off understanding that. and that’s something call the Poisson Distribution, named after a guy called Poisson. Nothing to do with fish? 🙂 I don’t think so, although some of my students call it the Fish Distribution, which is… *giggles* But the main point about the Poisson Distribution …umm…its first practical application was looking in the Prussian army There were lots of soldiers who were dying from being kicked by horses over a number of years. By their own horses? By their own horses, yeah. Horses objecting to being used as an army horse, perhaps. And so… there was one guy called Bortkewitsch in 1898 who was tasked with looking into how frequently these horse attacks were happening… these horse kick attacks were happening Horse attacks? They sound more dramatic all the time! Ok… I know it does, and I’m sorry, and it is actually quite a serious thing. The point is… is that I like to think anyway… horse kicks are… generally independent, right, horses don’t sort of… “collude” with each other and decide that they’re going to kick up a ruckus on a particular day. So if you look at a timeline of incidents then you would sort of expect your incidents, your horse kick incidents to be kind of randomly distributed across this thing So maybe you’d have a couple very quickly after each other But what that means you can do is if you take a time interval, so a set number of years perhaps and you look at the chances of a particular number of incidents in that interval then it follows this really nice neat distribution which looks like this and this is called… this is your probability and this is your number of incidents and this is your Poisson Distribution so that means that there’s an average number of incidents that you expect in a year, say and that average number of incidents is the most likely thing to occur and has the highest probability of all so it might mean that, you know, in 1890 you only have, you know, one incident perhaps and then in 1891 you have a huge number of incidents but also very low probability But… that most years you’re going to expect to have something around the average rate of incidents It means that you can start looking at the time between different events and you can start coming up with sort of a susceptibility for events But there’s one really crucial thing that this stuff is missing that the Poisson Distribution is missing which is that events, and crime, and terror attacks and things like that they’re not completely independent, so… if one happens, the chances of another one happening very soon after really increase, and the Poisson Distribution can’t take that into account. So the first people to look at events that weren’t completely independent were scientists who were studying earthquakes Now you could say that perhaps earthquakes were random were completely random and Poisson distributed so each earthquake was independent of every other But the thing is, is that if you have one earthquake you’re going to be really likely to have aftershocks Right, so a series of earthquakes in the same place, in quick succession of one another [Announcer] continual aftershock are keeping everyone nervous Scientists, and mathematicians developed something called “Hawkes Process” which I think might be named after Hawkes actually So they came up with something called the Hawkes Process which takes into account the fact that events aren’t completely independent of one another So instead if you were looking at an earthquake you’d expect to have something much more like this One earthquake happened and then you’d expect a few more smaller earthquakes to happen within a really short space of time and then perhaps you’d go a little while you’d have one with no aftershocks and then another, but with another few, uhh, sort of, aftershocks tagged on quite quickly afterwards I mean things kind of take a bit more of this pattern But the thing that is nice is that uh… well, “nice” probably isn’t the right word, uh… But… is that crime follows this same pattern. So if you take burglaries for example, anybody who’s been burgled will know that your chances of being burgled again within a really short space of time hugely increases. This is something called “repeat victimization”. And the reason is, is that burglars get to know the layout of your house they get to know, um, where you keep your valuables. They get to know all sorts of things about your local area. So your chance of being burgled again increases. But so does your neighbours’, and your neighbours’ neighbours’, and neighbours’ neighbours’ neighbours’ neighbours’ and so on as you go along down the street. This Hawkes Process then, of seeing events as connected in time, means that you can then model what happens with burglary statistically. It goes beyond just sort of saying “Oh well, you know, obviously that happens” because you’re actually able to describe it and capture it using numbers and using equations And as soon as you can do that, then you can start actually implementing genuine strategies back into the real world. So, for example, this is a paper that I wrote with one of my PhD students and this looks at, um, a very similar story about attacks from the IRA in Northern Ireland and you can see here, this is… the events as they go along This is really similar to this graph here. So you’ll have one big event and then you’ll have sort of a cluster of events afterwards. And then a gap for a little while and then another cluster of events going through. But what this means knowing that there’s this model that sits behind the scenes is that you can actually assign numbers. There’s a proper equation for this. So you have your kind of background rate, so this is… I don’t know what that first symbol is! Oh, it’s lambda, Greek lambda. Umm.. and that’s a “mu”… another Greek letter So this one here… this… you’re going to be talking about your “intensity” of attacks. How likely it is for an event to occur within a short space of time. So you have some sort of a background rate, so this is like your randomness, cuz there is still some element of complete randomness in this… But then, every time an event happens, you have a little “kick”. So your chances of another event get a little “boost”. And that’s what this thing here does. But then finally, this “boost” it doesn’t last for very long, so it looks like this… So your little “kick”, your chance of another event happening boosts up and then dies away quite quickly in time. You’re effectively… you’re summing over all of the incidents that have happened in the past, and you’re working out your “kick” from every possible incident . When a house gets burgled, or a bombing happens, or anything like that… numbers are being fed into equations that tell us what? Yeah, well, so they tell us, they tell us… they capture… sort of the process that’s going on behind the scenes. But they do it in a way that’s sort of free from emotion, and free from “hand-wavy-ness”. So if you apply this to something like the Troubles in Northern Ireland and the frequency of IRA incidents there were 5 actual different phases of attacks and you can see here with this equation the different values of these different parameters at different points throughout the process. So you’ve got mu there, k-nought (the “boost”) there, and omega, which is how quickly things died away back down to normal. And what’s really interesting about this, is that this allows you to come up with a comparison between different processes, or different stages in a conflict and actually to quantify it. Hannah, is this all hindsight, or does this give, like, predictive powers? Or is this just something you apply afterwards, like “oh, yeah, I can see…” Well, so this example is all retrospective, but what I think is really exciting about these ideas is that you can also apply them in real time. So with burglary in particular, umm… if you’re just looking at how the past influences the present and will influence the future which this allows you to do, by talking about intensity and susceptibility of burglaries what that means is that in real time you can pick up on a particular area, or even a particular street that is more likely to be the centre of our burglary hotspot going forward in time by using these methods. So there’s a company in America called PredPol who were the first to take these equations and wrap it up neatly into sort of an iPad app, effectively. So that they can give it to different police forces across the U.S. and the police forces will then get a printout on basically a map with like a red square, saying here is where is where is most likely to be victims of burglarly or car theft tonight So just by looking at these, just these really simple equations putting in the numbers of the system and reacting to what the maths tells you they’ve reduced burglarly by up to 32% in certain areas of the States. It’s like a pre-crime, this is like “Minority Report”. Yeah, yeah, “predictive policing” that’s what they call it. Yeah. Thanks to audible.com for supporting today’s episode Audible has thousands and thousands of titles in stock and they’re bound to have something that you’ll enjoy and among them, is “The Mathematics of Love”, by Hannah Fry — who you’ve just been watching. Now I’ve got Hannah’s book. Here’s my “dead tree” version. But I think an audio book’s even better because you can enjoy it on the go, such as like in your car, or walking the dog or more importantly, you can hear it read by Hannah herself. [Hannah] Have you ever wondered why we’re all so obsessed with how “hot” a person is? It’s always really interesting to hear an audio book read by the author, his or herself, and I know Hannah spent a lot of time in a studio doing it, so I’m sure she’d appreciate it as well. If you’d like to give Audible a try, and I recommend it. I use it all the time. Go to audible.com/numberphile that way they know you came from here and when you’re there, you can then join for a 30-day free trial, and, why not make Hannah’s “The Mathematics of Love” your first download? So, as the authority’s get smarter, and the police get smarter and start using mathematics so, you know…. fight crime, could criminals start using mathematics to plan crime? …chuckles… Well… I hope not. …ummm…. I hope not.

and Hydra was born

This is a description of the algorithm that will be the core of the machine that shouts "PUT DOWN YOUR WEAPONS… YOU HAVE TEN SECONDS TO COMPLY" at crims before gunning them down using automatic gunfire…. then "gamboling on the ashen skulls" of its enemies.

2:53 doubt the first instance will increases the probability of another instance to occur. seems more likely the current sociopolitical state in the surroundings increases the probability of both instance one and two independently = increased frequency of independent instances = more likely to occur in close succession.

Her voice makes me want to get some tea.

I graduated with a political science degree and now I REALLY regret not looking more into maths. Thank you this is fantastic.

Thanks, I'm a criminal. Now I could implement another methods to confuse police and society. It would no longer earthquake moves. Maybe I would develop moving tornado patterns or tsunami.

Pynchon used Poisson distribution.for pattern of impacts from V2 in Gravity's Rainbow coinciding with SLothrop appearences

Yes or no, did you ever have a math (or maths for non-Americans) teacher who looked like this?

What math looks like in a multicultural society

isnt that gauß´ probability curve

Hannah I'm sorry but your lambda seems a bit off

What's the point in burglaring the same house you allready burgled if you have taken the valuables they won't be there again unless you didn't get it all. Burglars do work on areas tho so your probability is higher if someone in your area has.

I like to think that one is the perks of being a doctor is that you're allowed to have terrible handwriting. An MSc would never get away with a lambda like that.

Hannah is the sexiest mathematician youtube has to offer

"his or herself", what an awkward and pointless construction

Marry me

Interesting but could definitely do without the banter coming from behind the camera.

So a numberphile burgler would turn this around and do deeds in the area where likelyhood is minimal…

?

Now math is politically correct!

Can we access the datasets Hannah used ? I’m quite interested in these for personal projects …

Hannah is so perfect! <3

The Provisional IRA were not terrorists they were freedom fighters against Protestant aggression

isn't it the exact opposite , if someone is robbed and they discover it then they will beef up the security hence the burglars will not target immediately due to higher risk of getting caught.

This is essentially machine learning. A predictive model built from data.

Absolutely fascinating that police forces are using this and it works

Hannah is good ASMR

Well great, now I have to start doing the math to figure out where police using this app are less likely to be so that I can then sell that app to burglars.

Minority report wants in plot device back

There's literally 2 earthquakes in January 2018 and an earthquake in Dec 2017 in my region.

war about big wars or wars in generals? it can be used too?

heißßßßßßßßßß

your to ugly to present videos,

This is why Prussia is no more… They got the horseshit kicked outta them

And there is one more way for insurance companies to charge exorbitant premiums

Deart Hannah. May I ask a question. Im'm a painter. LOVE composition. And ofcourse, you've heared of root angels. We use them a lot. BUT. Can you mzkr z root angel OF a root angel. And how?

F(h)=(Hannah)e^-ky=FAP

The Simpson's must use this equation to predict stuff

if you,ve prevented crime by predicting it , where do you get the info to assess where the next spate of crime will occur? surely interfering with the prediction needs to be accounted for in the prediction or its not the right prediction anyway.

I will watch the entirety of any video that Hannah is in. I'll learn anything that smile and laugh wants to teach me!

Why do all of the people on this channel write on this cartoon thing.

Doesn't the fact of preventing the events from happening change the numbers in a way that the equation becomes less effective? In a particular area for example, the fact of reducing the number of crimes would on the short term boost the probability of a crime happening right after it (because it lowers the average) and then, on the longer term, build an average that is lower than what would happen when prevention focusses on another part of the city?

The burglars nick your telly, then give you time to make the insurance claim and get a new one. Then they steal the new one.

…ok. "Every time a burglary happens, another one is likely to happen nearby". That'll be £100 per hour for every employee in a consultant fee for a large insurance company over many many years, please.

bella

Hannah Fry of the PreCrime police department

The problem with the app is that once the police starts intervening by following its advice, the new data does not follow the same random process anymore and so the predictions will get worse and worse. It's called "Lucas critique " in economics, and it affects all problems associated with policy making and econometric estimation.

Your paper on the Provo's may have taken into account the actions of the BSF and that is excellent, however I think it is necessary to take into account the attacks against them (and the people that they protected) by the DUP, the Orange Order and others like them.

It seems that a model to predict the full scope of such activities could be useful for all manner of militia versus militia violence, such as gang / cartel violence, guerrilla / insurgency attacks and other things.

However, looking at the actions of the Provo's in a vacuum or even just the two groups PIRA versus BSF is an incomplete model at best. It would be like trying to track earthquake related building damage without tracking the underlying earthquakes that caused it.

Factors such as the march season could and did trigger the desire for counter actions. This can be demonstrated if PIRA attacks increased during the march season especially in areas where marchers, not BSF were guilty of violence against Catholics. The escalation event in these cases would not be a successful attack by the PIRA, but rather the initial anti-Catholic violence by a third party. It seems to me that this would of needs require a change in your modeling less you draw erroneous conclusions with your data.

I wonder if there is a fractal relationship.

I just finished Isaac Asimov's "Foundation" for the first time, and watching this video (even though it's years since its upload) is very reminiscent of Seldon's psychohistory.

Pre crime is evil people.

I wonder that it would help in these terrible mass shootings in the U.S. 🙁

An interesting question: Is there a correlation between how widely known these equations and principles are, and how effectively they can still be implemented? I mean, if burglars know these equations, would they change their behavior such that it no longer fits the equations?

"for people who don't know, you know, you're a proper CRIMINAL" is what i thought you were going to say. got my hopes up.

Have Hannah Frye and Diane Spencer been seen in the same room? Thought not!

This was very well explained! Thank you 🙂

I want to be Mr. Whobitmyname Frye.

Imagine the business cards!

Minority Report! 🙂

The mathematics of terrorism? Like how many more virgins you get in paradise if the building you fly your hijacked airplane collapses afterwards? I guess I'll have to watch the video if I want to find out.

The Precrime iPad app should publish crime maps on a public website; kind of like weather forecast websites.

Horses don't colute with each other … keep on dreaming, Hannah!

I <3 her handwriting…

I would actually enjoy a follow on where Hannah (or anybody) looks at whether criminals could use this.

Predictive policing (mentioned at the end of the video) is used by police forces to justify targeting minorities of many kinds. The equations suggest an area is likely to have crime, so more police are sent there, inevitably catching more criminals

because more police were sent there. This then feeds back into predictive policing algorithms making them more likely to justify the biases of the humans who have to act on them.This is very very interesting, the idea that you can apply math to the subject of crime in such a way never appeared to me.

How come almost every single mathematician interviewed is always full of energy and in a jovial mood right from the beginning?

tbf, this is nowhere near the specificity of minority report. this is just a heuristic / probabilistic approach to where crime might arise based on historical frequency values, etc.

also, criminals and terrorists are not unthinking geological phenomena… they can and probably will (eventually) adapt to the statistical approach and modify some of their behaviours. nonetheless, it could help minimise losses meantime.

What’s the difference between the Poisson distribution and the Bell curve?

Make a video about the maths of mine warfare. That would be cool!

That's why trump built that wall.

The Mathematics of Makeup should be an interesting topic. If the effects are measurable, then pi, e and the golden ration should pop up all the time when applying quantities, qualities and distribution of various products. The Zero Measurement is no makeup, of course. And whither then? Only math can tell. And observations.

me less moroner than before

This is like weather forecasting for crime. Awesome

I admire you Hanna, you are brilliant. Lov ya!

LOL "I hope not, I hope not…" I'm not gonna lie, I had the same question arise very quickly. And its not petty crime that could take advantage of this, but large-scale-crime type activity that could benefit. If a computer program is deploying the police force based on algorithms centered around recent crime, it would not be hard to stage a few well-timed distractions to divert patrolling away from a desired area.

Police bias and what would an anarchist think of this and a philosopher of ethics? None of this sounds very responsible.

Decriminalise crimes

i,e if you've been burgled….tell all your neighbours and form a lynch mob for the next few days to get a better chance of getting the twokers

Nice visual – lose the mumbling

I'm not sure if I like grimes or Hannah's videos more. Grimes just acts ridiculously excited about math which makes me happy but Hannah does useful math which I like

I’m so bad at math, but this is like my 20th numberphile video. I feel like a genius. Go ahead and ask me about the Riemann Zeta function, fool. The fibonacci sequence, the most irrational number. I’ll tell you nothing about it except that I know of it…

Will criminals start using mathematics to commit crime?! They already do! They're called "bankers".

9:01 REALLY SIMPLE EQUATIONS.

As Crocodile Dundee would say…"that's not a lambda, THIS is a lambda λ."

The paper was by S. Tench et al. Hope their math doesn't stink.

The rate of the cameraman's questions follows the same pattern.

Thumbs up for typing in "Hannah Fry" for a Youtube search!

That explains the terrorist attacks in the past year

Speaking as a terrorist..many thanks!

can u explain more? and get into the details?

this video deserves a clickbait title due to the relevance of what it eventually talks about: minority-report through maths.

This comment section:

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So beautiful , so smart !!! ❤️❤️❤️❤️❤️

Why is Math plural outside of the US?

Yes, but it's not random, it's human behaviour, even if i had 5 tails in a row on a fair coin flip, the chance of a head or tail is still around 50/50 on my next flip, it's independent, humans don't act the same way, we mostly all live on the same schedule, sleep and eat around the same time and we read the news and use calendars, so the pattern is mostly based on behaviour mix with probabilistic events, it's not entirely mathematical and I think it makes it easier to predict a terrorist attack ….. let's say I meet someone I haven't seen in 10 years in a mall, what a coincidence!! not really, we all go the the same 2-3 malls, usually the week-end, between noon and 4 pm, in a place where there are thousands of people, so the behaviours people have makes it easier for that probabilistic event to happen

I hate when mathematics doesn't have any numbers, just letters. Btw not even understandable letters!

so an over complicated way of saying " don't comeback to the crime scene "

Shame there is no way to deal with Poisson-like processes without lowering the base rate.

Harry Seldon would have been so proud.

Watched a doc on the BBC (that Hannah may have presented actually) where this was applied to find the location of where Jack the Ripper might have lived during his killing spree. We'll never know if the location and person they honed in on was indeed the killer, but this obviously works in other areas of crime today and is fascinating.