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六度分割理论的科学 – 译学馆
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The Science of Six Degrees of Separation

我有个朋友叫Sammy 在2000年代初 在他的MySpace(社交网站)首页上写了点代码
I have a friend named Sammy who back in the early 2000s wrote some code for his MySpace page.
任何人访问了他的首页 代码就会把他的照片
And what the code did was anybody who visited his page would have his picture and
连同一行标语 “Sammy是我的英雄” 复制到他们的首页上
a tag line that said, “Sammy is my hero,” copied over to their homepage.
这么玩了一会儿之后 Sammy想再加点功能
And that was a bit of fun for a while, but Sammy wanted more. And so he tweaked his code so that no
于是他改了一下代码 不单是照片和标语 还把代码也复制过去
only the picture and the tag line were copied over, but also the code itself.
然后它就爆炸式扩散了 九小时内他传染了480个账号 13小时后升到8800个账号
And now it exploded. In just nine hours he had reached 480 accounts. In 13 hours he was up to 8800.
仅仅18小时后 他就传染了一百万个账号 这是当时MySpace账号总数的1/35
And in just over 18 hours he had hit a million accounts, which was a full 1/35th of all the
他一下子慌了 当时想删掉自己的页面
accounts on MySpace at the time. So in a panic, he tried to delete his page. And when he was
successful he actually took down the whole of MySpace with it. He was arrested and convicted
然后他就被捕了 判以非法侵入计算机罪 三年内不得接触计算机
of computer hacking and ordered not to touch a computer for the next three years.
But I think what this story really tells us is just how connected we all are.
假设你有44个朋友 他们之中每个人又都有44个你不认识的朋友
Imagine you have 44 friends and each one of those friends has 44 friends who are not also
你朋友的朋友中每个人又都有另外的44个朋友 其中每个人又都有44个朋友
your friends. And each of them has an additional 44 friends, each of whom has 44 friends who
后者又有44个朋友 后者还有44个朋友 仅通过一条六级的链
again has 44 friends and they have 44 more. Then in a chain of just six steps you would
你就联络了44的6次方即72.6亿人 这比今天地球总人口数都多
be connected to 44 to the sixth or 7.26 billion people, more than are alive on earth today.
其实在有MySpace之前很久 人类就已经思考过我们的联络有多紧密的问题了
And we have contemplated how closely connected we area since long before MySpace even existed.
早在1929年 一位名叫Frigyes Karinty的匈牙利作家兼诗人写了一个短篇故事叫做《链》
Back in 1929 a Hungarian author and poet named Frigyes Karinthy wrote a short story called
故事中某人向其他人发起一个挑战 要求他们找到另一个人
Chains. And in it, one of the characters challengers the others to find another person on earth
that he cannot connect himself to through fewer than five intermediaries. This is the
origin of six degrees of separation.
如果这个理论是正确的 它就意味着你只需通过6步就能联络到女王或汤姆克鲁斯
If the theory is correct, it means that you would be connected to the Queen or Tom Cruise
不过他们可能算比较容易联络的 如果是这家店的老板或者是蒙古羊放牧人呢?
in just six steps. But they may be the easy ones. What about this shop owner or the Mongolian
sheep herder? What the theory really means is that any two people picked at random from
anywhere on the earth would be connected by just six steps.
这个概念一直处于假想阶段 直到1960年代 哈佛大学的心理学家Stanley Milgram
The idea remained just fiction until in the 1960s a Harvard psychologist, Stanley Milgram,
尝试对它进行验证 他把下面这种现象称为小世界实验
attempted to test it. He called it the small world experiment after that phenomenon where
你在聚会上碰见一个陌生人 意识到你们有一个共同的朋友 然后你就感叹:哦 这世界可真小
you are at a party, you meet a stranger and you find out that you have a friend in common
这位心理学家所做的 就是先把300个包裹寄给
and you remark: Oh, it is such a small world. What he did was he sent out 300 packages to
住在波士顿和内布拉斯加州的人 然后他希望他们自己想办法
people both in Boston and in Nebraska. Now what he wanted those people to do was try
把包裹送到位于波士顿的终极收件人 但他们不可以将包裹直接寄回给他
to send their package to a target person in Boston, but they weren’t allowed to send
it directly to him. They had to send it to someone they knew on a first name basis who
觉得有可能认识终极收件人的朋友那里 后者可以用同样的方法
they thought had a better chance of knowing the target and they could forward it on in
the same way.
也许你猜到了 多数包裹并没能最终送达 但是有64个包裹送达了
Now, as you might expect, most of the packages never made it, but 64 did and the average
而且平均路径数是5.2 所以六度分割在实验上确认了 确实如此吗?
pathway was 5.2. So now six degrees of separation had experimental confirmation. Or did it?
如果再仔细观察Milgram的例子 你会发现 这300人之中
If you look more closely at Milgram’s sample, you will find that of the 300 people, 100
有100人位于波士顿 终极收件人本来就住在这儿 另外100人是股票经纪人 与终极收件人有相同职业
were located in Boston, the actual city where the target lived. Another 100 were stockbrokers,
which was the same profession as the target. So only 100 people lived in a different state
and had a different job. And of them only 18 of their packages made it to the target.
So we are talking about a sample size of 18 is all the evidence there was for six degrees
of separation.
所以实验性证据很难得到 但是 再早十年(1950年代)
So experimental evidence was tough to come by. But a decade earlier, a mathematician
一位名叫Paul Erdos的数学家已经研究了类似这些的网络的理论属性
named Paul Erdos had tried to work out the theoretical properties of networks like these.
但他并不清楚实际的社会网络结构 所以他决定
But he didn’t have any information on the structure of real social networks, so he decided
to work on networks where the connections between nodes were all completely random.
And we can actually simulate a network like this using buttons and thread where we just
这里我们只是把纽扣随机地连起来 Erdos发现
connect up the buttons at random. What Erdos found is that when the number of
当每节点的联络数较小时 网络是分裂的 任意拿起一颗纽扣
links per node is small, the network is fragmented. Pick up any button and few others will come
其它几颗会连带着一同起来 但只要平均每节点的联络数超过1
with it. But once you exceed an average of one connection per node, the behavior the
网络的特征就会产生显著变化 它们会几乎全部连起来变成一大串
network changes dramatically. They almost all link up forming a giant cluster. Now if
现在如果你把任意一个纽扣提起来 剩下的几乎所有纽扣都会一起跟着它起来
you pick up any button almost all of the rest will come with it. This change happens rapidly
这种变化发生得十分显著 有点像物理中的相变 现在你可以把这个叫作一个小世界网络
and it resembles a phase transition in physics. Now you could call this a small world network,
since the path between any two buttons is short.
关于随机网络 它天生就是小世界网络
The thing about random networks is that they are naturally small world networks, because
you are just as likely to be connected to someone here in Manila as you are to someone
但是显然 随机网络并不能够充分地描绘现实生活
in your own town. But obviously a random network doesn’t represent real life very well. So
那么现实世界的网络看起来是什么样的呢?好 想知道答案 我们就需要看看经验数据
what do real world networks look like? Well, for that, we need to go to the empirical data.
1994年 几个大学生发明了一个游戏叫《Kevin Bacon的六度》
In 1994 a couple of college kids invented a game called six degrees of Kevin Bacon in
游戏里 你要想办法只用6步就让Kevin Bacon通过他的合演者联络到任意一位演员
which you try to connect any actor to Kevin Bacon through just six steps through his costars.
后来 几名社会学学者研究了一个含有25万名演员的数据库
Now a couple of sociology researchers got access to their database of a quarter million
对这个网络分析之后 他们发现它是一个小世界网络
actors and they analyzed the network and what they found was that it was a small world network,
也就是说 任意2个演员之间都只需要很少的几步联络
meaning between any two actors there were only a very small number of steps. And that
这与随机网络已经很相近了 但与随机网络不同的是
is very similar to a random network. But unlike a random network, the actor network also showed
演员的网络表现出高度的聚集 因为他们经常在一个个小团队里一起工作
a high degree of clustering, that is, they often worked together in small groups.
因此 你如何在任意两个演员之间同时找到这种群组行为(一种高度聚集)
So how do you get both this grouping behavior, a high degree of clustering, and the short
以及很少的联络步骤呢?好吧 为了弄清楚这一点 他们考虑了两种极端
number of steps between any two actors? Well, to figure this out they looked at two different
假如有一圈节点 现在如果你任意连接它们
extremes. Imagine a circle of nodes. Now if you connect them at random you get the same
就会得到和Erdos一样的实验结果 任意两个节点之间存在短路径 但是很少聚集
outcome as Erdos, short paths between any two nodes, but little clustering. Now consider
connecting up the nodes only with their nearest two neighbors on each side. Now clustering
这时候聚集度就高了 但是任意两个节点之间的路径变长了
is high, but path lengths are long for two nodes picked at random.
但是如果你按照第二种方法做 再把少量的节点任意连接
But what if you take this set up and rewire just a small number of connections randomly.
你会发现路径长度短了很多 而聚集度仍然很高
What you find is that the path length drops rapidly, but clustering still remains high.
因此 将真实的社交网络模型化的关键 就是要有大量的聚集行为
So the key to modeling real social networks is to have a lot of clustering behavior—that
也就是说 你的朋友不仅还是别人的朋友——也有少量随机的泛泛之交
is, your friends are also friends with each other—but also to have a few random acquaintances.
And the importance of those acquaintances can’t be overstated.
There was a researcher named Granovetter in the 1970s who published a paper called “The
题为《弱联系的强度》 在这篇论文里他指出:相比通过密友找工作
Strength of Weak Ties,” in which he points out: You are much more likely to get a job
通过那些泛泛之交找到工作的可能性更大 如果你也这么想
through those random acquaintances than through your close friends. And if you think about
是在情理之中 因为你和你的密友认识相同的人
it, that makes sense, because you and your close friends all know the same people and
有同样的信息 只有通过随机的泛泛之交
have the same information. It is through the random acquaintances that you can get connections
你才能和那些与你的社交圈相隔甚远的人取得联系 从而你能找到新工作 新的居住地
with people very far from your social circles. So you can find new jobs, new places to live
and you can be connected to the outside world.
归根到底 是那些随机的泛泛之交实际上促成了六度分割理论
So, in fact, it is those random acquaintances that make possible six degrees of separation.
So when I want to…
I am told the degrees have dropped in recent years.
…to like four degrees.
说说看 我们怎么知道这个的?我不知道怎么他们怎么测量计算的
Tell me about that. How do we know this? I don’t know how they measure it, but
到我试验过了 我认为这种下降基于多少人
I have tested it and I think it actually has dropped based on how many people have friended
在Facebook上和别人是好友 这种朋友圈扩大了 不是说他们是知心朋友
one another on Facebook. The friendship circle has grown, not that they are bosom buddies,
但他们是你接触到的朋友 这是重点
but they are people you have access to. That is the point.
那…你认识这个人 他又认识另一个人 因此我能认识这些陌生人?
And it is… do you know this person who then knows that so that I have access to these
所以我得知这一程度下降了 我们从六度分割降到了
other people? So I am told that it has dropped. As much as the six degrees, we are down to
四度分隔 至多五度分割
four, at most five.
我认为Neil DeGrasde Tyson可能是对的 在2011年Facebook分析了他们的数据
I think Neil DeGrasse Tyson might be right. In 2011 Facebook analyzed their data and they
他们发现92%的用户彼此要有所联系 只需要五步
found that 92 percent of their users were connected through just five steps. And that
这一数字正随着时间推移而减少 六度分割理论已经
number is decreasing over time. The concept of six degrees of separation has
使人们为之痴迷了近一世纪 我认为这不只是因为它有多出人意料
fascinated people for nearly a century. And I think that is not only because of how counter
intuitive it is, but also how comforting it is to know how closely we are all linked,
not in some kind of abstract, ill defined way, but through hard scientific data.
只需要六次握手 你就能和这个星球上的任意一个陌生人去的联系
Just six handshakes will connect you to anyone else on the planet.
现在 我为你准备了一项挑战 本着六度分割理论的精神
Now I have a challenge for you. In the spirit of six degrees of separation I want to try
我想做个实验 我想让你试着给我发邮件 但是除非你认识我
an experiment. I want you to try to get an email to me. But you can’t send it directly
否则你不能直接给我发 所以假设你不认识我
to me unless you know me. So assuming you don’t, I want you to send it to a friend
我想让你把邮件发给你的一位朋友 一位你不太熟悉
of yours, someone you know on a first name basis who you think has a better chance of
而又有可能把邮件发到我这里来的朋友 如果你的邮件最终通过一系列人发到我这里来了
getting that email to me. If your email eventually gets to me through a chain of people, I will
我会在邮箱里给你发一封明信片 如果我们真的能在六步或几步做到的话
send you a postcard in the mail and I will tally up if we were able to get that done
in six links or not.
那么让我们试着做吧 看看我们能不能联系上相应的做法已经描述过了
So let’s try to do it and see if we can connect. The instructions are in the description.
Veritasium系列由 Fine Brothers 官方授权
This episode of Veritasium was inspired by the Fine Brothers, Ben and Rafi Fine who are
Ben 和Rafi Fine 都是我的朋友 因此我们之间只有一度分割
friends of mine. So we are connected through just one degree of separation. Now they have
现在他们成了TruTV上播放的电视剧品牌 叫做《万物的六度分割》
a brand new TV series launching on TruTV. It is called The Six Degrees of Everything
是一个剧情紧凑的喜剧 旨在为我们展示我们认为毫无关联的六个事物
and it is a fast paced comedic show that tries to show us how six things that we don’t
但实际上有所关联 这包括漫画 歌曲自以及真实的电视机
think are connected actually are. It involves sketch comedy and songs and reality TV. I
am really looking forward to seeing how they are going to do this. So you can check it
所以你可以在周二的9:30或8:30锁定TruTv 观看我太期待它了
out Tuesdays at 9:30 or 8:30 central on TruTv. I am so looking forward to it.
感谢Fine Brothers对此系列视频的赞助支持 那么我要去检验
And thank you to the Fine Brothers for sponsoring this episode so I could check out the science
of networks.