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.
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.
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
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.
Imagine you have 44 friends and each one of those friends has 44 friends who are not also
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
be connected to 44 to the sixth or 7.26 billion people, more than are alive on earth today.
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
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.
If the theory is correct, it means that you would be connected to the Queen or Tom Cruise
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,
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
and you remark: Oh, it is such a small world. What he did was he sent out 300 packages to
people both in Boston and in Nebraska. Now what he wanted those people to do was try
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
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
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
named Paul Erdos had tried to work out the theoretical properties of networks like these.
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
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
with it. But once you exceed an average of one connection per node, the behavior the
network changes dramatically. They almost all link up forming a giant cluster. Now if
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.
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
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.
Now a couple of sociology researchers got access to their database of a quarter million
actors and they analyzed the network and what they found was that it was a small world network,
meaning between any two actors there were only a very small number of steps. And that
is very similar to a random network. But unlike a random network, the actor network also showed
a high degree of clustering, that is, they often worked together in small groups.
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
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
is high, but path lengths are long for two nodes picked at random.
But what if you take this set up and rewire just a small number of connections randomly.
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
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
Strength of Weak Ties,” in which he points out: You are much more likely to get a job
through those random acquaintances than through your close friends. And if you think about
it, that makes sense, because you and your close friends all know the same people and
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.
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.
Tell me about that. How do we know this? I don’t know how they measure it, but
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,
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
other people? So I am told that it has dropped. As much as the six degrees, we are down to
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
found that 92 percent of their users were connected through just five steps. And that
number is decreasing over time. The concept of six degrees of separation has
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.
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
to me unless you know me. So assuming you don’t, I want you to send it to a friend
of yours, someone you know on a first name basis who you think has a better chance of
getting that email to me. If your email eventually gets to me through a chain of people, I will
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.
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
a brand new TV series launching on TruTV. It is called The Six Degrees of Everything
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
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
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