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用数学解读犯罪与恐怖主义 – 译学馆
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用数学解读犯罪与恐怖主义

The Mathematics of Crime and Terrorism - Numberphile

我们谈谈跟犯罪有关的数学
We’re talking about the maths of crime
—犯罪?—是的!
– Crime? – Yeah!
对于那些不了解你的人来说 你是个数学家
For people who don’t know, you’re a proper mathematician
我们都很喜欢你的研究
And we’re really getting into your research.
是的 事实上 我还和我的一位博士生一起做过一篇论文
Yup. We’re gonna… In fact, even look at a paper that I’ve even done with one of my PhD students.
所以 是的 我是个真实存在的人
So yes, I am a real person.
这是你擅长的领域?
This is your area of expertise?
额 是的 是的
Ahh… yeah. Ahh… yeah.
想要了解犯罪 或者恐怖主义这样的事 有一点很重要
One of the things…. That’s important to know about crime… or terrorism… things like that…
即事情会什么时候发生
is when it’s going to happen.
以前的数学研究
There’s a bit of old maths
多少可以帮助我们开始理解这样的事
that kind of helps us start off understanding that.
我要说的是“泊松分布”
and that’s something call the Poisson Distribution,
它以泊松的名字命名
named after a guy called Poisson.
跟鱼没关系?
Nothing to do with fish? 🙂
没关系 不过我的一些学生也把它称作“鱼类分布” 这就……
I don’t think so, although some of my students call it the Fish Distribution, which is…
“泊松分布”的要点是
But the main point about the Poisson Distribution
嗯 它第一次的实际应用是用来分析普鲁士军队
…umm…its first practical application was looking in the Prussian army
当时许多士兵被马踢死
There were lots of soldiers who were dying from being kicked by horses
这种情况持续了好些年
over a number of years.
被他们自己的马踢死?
By their own horses?
是的 被他们自己的马踢死
By their own horses, yeah.
马儿们拒绝被用作战马 也许是这样的
Horses objecting to being used as an army horse, perhaps.
所以在1898年 有一个叫Bortkewitsch的人
And so… there was one guy called Bortkewitsch in 1898
被指派调查
who was tasked with looking into
马攻击军人的频率 马踢人的频率
how frequently these horse attacks were happening… these horse kick attacks were happening
马攻击军人?这怎么听都不可思议!
Horse attacks? They sound more dramatic all the time!
我知道 抱歉 但我确实是在说很严肃的事
I know it does, and I’m sorry, and it is actually quite a serious thing.
我想说的是
The point is… is that
我倾向于认为 马踢军人一般都是
I like to think anyway… horse kicks are…
独立事件 是吧 马儿不会彼此沟通
generally independent, right, horses don’t sort of… ‘collude’ with each other
然后决定它们要在某个特定的日子引起一场骚乱
and decide that they’re going to kick up a ruckus on a particular day.
所以如果你仔细看看事件的时间线
So if you look at a timeline of incidents then
你也会认为这些事件 马踢军人事件
you would sort of expect your incidents, your horse kick incidents to be
在这整件事里是基本上是随机分布的
kind of randomly distributed across this thing
也许有时候也是几起事件一起发生的
So maybe you’d have a couple very quickly after each other
这意味着你能做的是
But what that means you can do is
如果你选取一段时间间隔 比如说一定数量的年份
if you take a time interval, so a set number of years perhaps
然后你再去看某个特定数字在那段时间间隔里的出现频率
and you look at the chances of a particular number of incidents in that interval
你会发现它遵循这条很平滑的分布曲线
then it follows this really nice neat distribution
像这样的
which looks like this
这个叫作…… 横轴是事件发生概率
and this is called… this is your probability
竖轴是事件的发生次数
and this is your number of incidents
这个就是你的“泊松分布”
and this is your Poisson Distribution
你可以根据这个预见一年里事件发生的平均数量
so that means that there’s an average number of incidents that you expect in a year, say
这个平均数量的事件量是最有可能发生的
and that average number of incidents is the most likely thing to occur
有着最高的发生概率
and has the highest probability of all
所以这可能意味着 在1890年
so it might mean that, you know, in 1890
只有一个事件发生
you only have, you know, one incident perhaps
然后1891年 有巨大数量的事件发生
and then in 1891 you have a huge number of incidents
但出现这些情况的可能性非常低
but also very low probability
在大多数的年份 你还是会看到
But… that most years you’re going to expect to have
事件的发生率在这个平均数左右
something around the average rate of incidents
这说明你可以开始着眼于不同事件的发生时间
It means that you can start looking at the time between different events
你可以从中看出各种事件的易感性
and you can start coming up with sort of a susceptibility for events
但这种曲线漏掉了一件很重要的事
But there’s one really crucial thing that this stuff is missing
这个泊松分布遗漏了一件很重要的事
that the Poisson Distribution is missing
即事件 或者犯罪 或者恐怖袭击
which is that events, and crime, and terror attacks
或者诸如此类的事
and things like that
它们并不是完全独立的
they’re not completely independent, so…
如果一件事发生了 那么另一件事会马上发生的概率
if one happens, the chances of another one happening very soon after
会增加 而泊松分布无法考虑到这个
really increase, and the Poisson Distribution can’t take that into account.
所以最早研究非完全独立事件的
So the first people to look at events that weren’t completely independent
是研究地震的科学家
were scientists who were studying earthquakes
你会说 也许地震是随机的
Now you could say that perhaps earthquakes were random
是完全随机的 并且呈泊松分布
were completely random and Poisson distributed
所以每一次地震都是相互独立的事件
so each earthquake was independent of every other
但事实是 如果某地发生地震 那么接下来很可能还有余震
But the thing is, is that if you have one earthquake you’re going to be really likely to have aftershocks
对吧 这就相当于在同一个地方发生了一系列的地震
Right, so a series of earthquakes
并且是一个接着一个地发生
in the same place, in quick succession of one another
[播音员]持续的余震使得人们不敢放松
[Announcer] continual aftershock are keeping everyone nervous
科学家和数学家发展出了一种叫“霍克斯过程”的理论
Scientists, and mathematicians developed something called ‘Hawkes Process’
我想也许是以霍克斯的名字命名的 应该是的
which I think might be named after Hawkes actually
所以他们提出了“霍克斯过程”
So they came up with something called the Hawkes Process
把非完全独立事件也纳入了考量
which takes into account the fact that events aren’t completely independent of one another
所以发生地震的时候
So instead if you were looking at an earthquake
情况更有可能是这样的
you’d expect to have something much more like this
某地发生地震 那么可以预见在短时间内
One earthquake happened and then you’d expect a few more smaller earthquakes to happen
还会有一系列的小型余震发生
within a really short space of time
然后也许在后面一段时间里
and then perhaps you’d go a little while
有一个地震是不带余震的
you’d have one with no aftershocks
再后面的地震又是紧随着一些余震
and then another, but with another few, uhh, sort of, aftershocks tagged on quite quickly afterwards
我觉得地震更有可能是按照这样的模式在发生的
I mean things kind of take a bit more of this pattern
但这种模式的好处在于
But the thing that is nice is that
额 说“好”也许不恰当
uh… well, ‘nice’ probably isn’t the right word, uh…
但……犯罪的发生也遵循同样的模式
But… is that crime follows this same pattern.
我们拿盗窃做个比方
So if you take burglaries for example,
任何曾被盗贼光顾过的人都知道 他们短时间内
anybody who’s been burgled will know that your chances of being burgled again
再次被盗的概率会极大的增加
within a really short space of time hugely increases.
这叫作“重复被害”
This is something called ‘repeat victimization’.
原因是 小偷作案后会知道你家房子的布局
And the reason is, is that burglars get to know the layout of your house
也清楚你会把值钱的东西放在哪
they get to know, um, where you keep your valuables.
还知道你家周围的各种情况
They get to know all sorts of things about your local area.
所以你再次被盗的概率会上升
So your chance of being burgled again increases.
你的邻居被盗的概率也会增加
But so does your neighbours’,
还有你邻居的邻居
and your neighbours’ neighbours’,
以及邻居的邻居的邻居的邻居……
and neighbours’ neighbours’ neighbours’ neighbours’ and so on
整条街都不能幸免
as you go along down the street.
所以霍克斯过程可以把短时间内发生的事件
This Hawkes Process then, of seeing events as connected
关联起来 这意味着我们可以将
in time, means that you can then model
发生的盗窃事件系统建模
what happens with burglary statistically.
不仅仅是说“噢 你知道的 事实显然就是那样的”
It goes beyond just sort of saying ‘Oh well, you know, obviously that happens’
因为我们确实可以用数字和方程式
because you’re actually able to describe it and capture it
描述它 找到它背后的规律
using numbers and using equations
一旦我们可以这样做
And as soon as you can do that, then
我们就可以将数学策略应用于真实世界
you can start actually implementing genuine strategies back into the real world.
比如 这里有一份我和一位博士生一起做的论文
So, for example, this is a paper that I wrote with one of my PhD students
论文研究的东西和今天的主题差不多
and this looks at, um, a very similar story
是关于IRA在北爱尔兰的袭击(事件的模式)
about attacks from the IRA in Northern Ireland
你们可以看到 这是袭击的发生模式
and you can see here, this is… the events as they go along
袭击基本上是按照图上的模式在发生的
This is really similar to this graph here.
你们可以看到如果发生了一次大的袭击 那后面还会跟上一系列的小的袭击
So you’ll have one big event and then you’ll have sort of a cluster of events afterwards.
然后中间一段时间熄火 接着又是一连串的袭击
And then a gap for a little while and then another cluster of events going through.
这意味着 袭击事件背后是有固定的模式的
But what this means knowing that there’s this model that sits behind the scenes
我们可以按照模式来算出数量
is that you can actually assign numbers.
这里有一个方程式可以用
There’s a proper equation for this.
所以我们可以根据以往的事件概率(来得出将来的事件概率)
So you have your kind of background rate, so this is…
第一个符号是什么意思?
I don’t know what that first symbol is!
这是lambda 它是希腊字母
Oh, it’s lambda, Greek lambda.
这是mu 也是希腊字母
Umm.. and that’s a ‘mu’… another Greek letter
所以这个是我们后面会谈到袭击事件的频率
So this one here… this… you’re going to be talking about your ‘intensity’ of attacks.
即短时间内某个事件发生的
How likely it is for an event to occur
可能性有多大
within a short space of time.
我们知道以往事件发生的概率 但不确定的因素仍很多
So you have some sort of a background rate, so this is like your randomness,
因为事件的发生还会受一些完全随机的因素的影响
cuz there is still some element of complete randomness in this…
然后 每次发生一个事件 我们加一个代表“kick”的“k”
But then, every time an event happens, you have a little ‘kick’.
这又会导致另一个事件发生的概率会上升 所以再加一个代表“boost”的“b”
So your chances of another event get a little ‘boost’.
像这样
And that’s what this thing here does.
但最后 “boost”持续的时间不会太长
But then finally, this ‘boost’ it doesn’t last for very long,
所以它会像这样
so it looks like this…
当一个事件发生 另一个事件发生的概率会上升
So your little ‘kick’, your chance of another event happening
然后短时间内又回复平静
boosts up and then dies away quite quickly in time.
我们将过去某一事件的发生次数加起来
You’re effectively… you’re summing over all of the incidents that have happened in the past,
根据每一个可能发生的事件得出“kick”值
and you’re working out your ‘kick’ from every possible incident .
当某户人家被盗 或某地发生爆炸袭击
When a house gets burgled, or a bombing happens,
或任何诸如此类的事发生时
or anything like that…
这些代入方程式的数字告诉了我们什么?
numbers are being fed into equations that tell us what?
是的 它们告诉我们 它们抓住了
Yeah, well, so they tell us, they tell us… they capture…
这些事件背后的模式
sort of the process that’s going on behind the scenes.
而且计算的过程在某种程度上不受主观情绪的影响
But they do it in a way that’s sort of free from emotion,
也不受个人能力的影响
and free from ‘hand-wavy-ness’.
所以如果我们把北爱尔兰的袭击事件
So if you apply this to something like the Troubles in Northern Ireland
以及IRA的袭击频率代入这个方程式
and the frequency of IRA incidents
我们可以看到这里有5个袭击事件发生的时间段
there were 5 actual different phases of attacks
我们可以看到 这个方程式
and you can see here with this equation
在整个过程中不同的的时间点里不同参数的值
the different values of these different parameters at different points throughout the process.
这里是“mu” 这里是Kο(boost)
So you’ve got mu there, k-nought (the ‘boost’) there,
这里是omega 它代表事件平息的速度
and omega, which is how quickly things died away back down to normal.
这个表格有趣的地方在于
And what’s really interesting about this, is that
它给我们对比不同事件过程
this allows you to come up with a comparison between different processes,
或者冲突中不同阶段的机会 从而进行量化分析
or different stages in a conflict and actually to quantify it.
我想问一下 这些都是事后统计 还是事先预见?
Hannah, is this all hindsight, or does this give, like, predictive powers?
还是说这些只是你根据已发生的事得出的结论 你就像“噢 是的 我可以看见……”
Or is this just something you apply afterwards, like ‘oh, yeah, I can see…’
嗯 这个例子是回溯性的
Well, so this example is all retrospective,
但我觉得这些理论令人兴奋的地方在于 你也可以把它们应用于当下
but what I think is really exciting about these ideas is that you can also apply them in real time.
特别是盗窃事件
So with burglary in particular,
通过这个方程式 我们可以看到过去怎样影响现在
umm… if you’re just looking at how the past influences the present
又会怎样影响将来
and will influence the future
这是通过对盗窃案的发生频率及
which this allows you to do, by talking about intensity
易感程度的分析得出来的
and susceptibility of burglaries
这意味着 在眼下 你可以根据这些方法及时挑出
what that means is that in real time you can pick up
某个特定的区域 甚至某个特定的街道
on a particular area, or even a particular street
并知道其在未来一段时间更有可能成为盗窃的热点区域
that is more likely to be the centre of our burglary hotspot going forward in time by using these methods.
有一家叫做PredPol的美国公司
So there’s a company in America called PredPol who were the first
他们是第一家将这些方程式
to take these equations
很巧妙地打包进一个ipad应用里的公司 非常有效率
and wrap it up neatly into sort of an iPad app, effectively.
他们将应用给全美的各种警察机关
So that they can give it to different police forces across the U.S.
警察再根据这个应用
and the police forces will then get a printout
得出一张犯罪地图 类似红场地图 就可以知道
on basically a map with like a red square, saying
今晚这里是最容易发生盗窃案或盗车案的地区
here is where is where is most likely to be victims of burglarly or car theft tonight
所以只是通过将这些非常简单的方程式
So just by looking at these, just these really simple equations
嵌入各种不同的系统
putting in the numbers of the system
然后根据数学计算的结果做出应对
and reacting to what the maths tells you
就使得美国一些区域的盗窃案降低率达到32%
they’ve reduced burglarly by up to 32% in certain areas of the States.
这个像放罪预防机制 像《少数派报告》
It’s like a pre-crime, this is like ‘Minority Report’.
是的 是的 他们称这个为“预测警务”
Yeah, yeah, ‘predictive policing’ that’s what they call it. Yeah.
感谢audible.com对今天节目的赞助
Thanks to audible.com for supporting today’s episode
audible有数以千计的主题的有声书
Audible has thousands and thousands of titles in stock
一定也有你喜欢的
and they’re bound to have something that you’ll enjoy
其中也有今天视频的主角Hannah Fry的“The Mathematics of Love”
and among them, is ‘The Mathematics of Love’, by Hannah Fry — who you’ve just been watching.
我有Hannah的这本书 是纸质版本的
Now I’ve got Hannah’s book. Here’s my ‘dead tree’ version.
但我觉得有声书更好一些
But I think an audio book’s even better
因为你可以随时听
because you can enjoy it on the go,
比如开车的时候 或者遛狗的时候
such as like in your car, or walking the dog
更重要的是 你可以听到Hannah亲自读它
or more importantly, you can hear it read by Hannah herself.
[Hannah]你是否想知道为什么我们都对某人有多迷人津津乐道?
[Hannah] Have you ever wondered why we’re all so obsessed with how ‘hot’ a person is?
听作者亲自读他或她的书 总是很有趣
It’s always really interesting to hear an audio book read by the author, his or herself,
我知道Hannah花了很多时间录这本书
and I know Hannah spent a lot of time in a studio doing it,
所以我确定她也很喜欢这本有声书
so I’m sure she’d appreciate it as well.
如果你想尝试有声书 我建议你可以尝试一下 我一直都在听有声书
If you’d like to give Audible a try, and I recommend it. I use it all the time.
欢迎点击audible.com/numberphile
Go to audible.com/numberphile
这样网站就知道你是从这里点进去的
that way they know you came from here
点进去以后 你可以获得30天的免费试用
and when you’re there, you can then join for a 30-day free trial,
首次下载推荐Hannah的“The Mathematics of Love”
and, why not make Hannah’s ‘The Mathematics of Love’ your first download?
所以 随着当局办公越来越智能
So, as the authority’s get smarter,
警察越来越聪明 并开始运用数学
and the police get smarter and start using mathematics
你知道的 打击犯罪
so, you know…. fight crime,
那罪犯会开始用数学来组织犯罪吗?
could criminals start using mathematics to plan crime?
……笑……
…chuckles…
好吧……
Well…
我希望不会
I hope not.
……额……
…ummm….
我希望不会
I hope not.

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视频概述

用数学找到犯罪和恐怖主义的发生规律,以提前防范。

听录译者

收集自网络

翻译译者

祐子祐

审核员

审核团HN

视频来源

https://www.youtube.com/watch?v=lCjspXB5F4A

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