How small is the world, really?
世界何其小，真的吗？
Last week’s finding by a team of data scientists at Facebook that everyone in the social network is connected by an average of 3.5 “intermediaries” has renewed interest in the longstanding “Six Degrees of Separation” hypothesis: that everyone in the world is connected by some short chain of acquaintances.
上周，一个脸书数据分析专家小组发现，社交网络中的每个人都可经由平均3.5个“媒介好友”而联系起来，这一发现刷新了之前长期流行的“六度分隔”理论，即世上任何两人皆可通过某条较短的熟人链条连接起来。
Not surprisingly, the attention has focused on the plausible assertion that online social networks like Facebook have made the world smaller: that what used to be six degrees is now almost half that. But really what it has revealed is how little we understand this intriguing phenomenon and what it might mean for our world. Not surprisingly, the attention has focused on the plausible assertion that online social networks like Facebook have made the world smaller: that what used to be six degrees is now almost half that. But really what it has revealed is how little we understand this intriguing phenomenon and what it might mean for our world.
无出意外，人们的注意力被吸引到了一个看似可能的判断上：像脸书这样的社交网络让世界变得更小：以前的六度现在一半就足够。但它真正揭示的是，对此令人神迷的现象和它对我们世界的意义何在，我们的理解何等浅薄。
This “small world” hypothesis, as it is known in sociology, has been percolating in popular culture for a long time. Almost a century ago the Hungarian poet Frigyes Karinthy wrote a short story called “Chain Links” in which he claimed he could reach anyone in the world, whether a Nobel Prize winner or a worker in a Ford auto factory, through a series of no more than five intermediaries.
在社会学领域内，大家都已了解，这个“小小世界”假说久已渗透进我们的文化之中。早在一个世纪前，匈牙利诗人Frigyes Karinthy就写了一则题为“链接”的小故事，文中他声称可以通过一系列不超过5个的“媒介”，联络到世界上任何人，无论是诺奖得主，或是一名福特工厂的工人。
Subsequently, writers like Jane Jacobs, John Guare, and Malcolm Gladwell have periodically reinvigorated the idea with their own colorful characters and fantastical speculations about who really runs the world.
此后，像Jane Jacobs, John Guare, and Malcolm Gladwell等等作家时不时的通过他们自己书中丰富的人物重塑了这一假说，并天马行空的猜测究竟是谁在真正掌控这个世界。
But arguably no one has had more impact on the question of how small the world is than Stanley Milgram, a Harvard psychologist who in the 1960s conducted an ingenious experiment to test it (Milgram is even more famous for another experiment of his, on obedience to authority, but that’s for another day).
但是，毋庸置疑，没有人对此“小小世界”问题的影响超过1960年代任教于哈佛大学的心理学家史丹利·米尔格拉姆，他进行了一个原创试验来测试此理论（米尔格拉姆其实有另一个更加有名的试验，“权力服从研究”，这个我们改天再谈）。
In brief, Milgram chose a single person, an acquaintance of his who was a stockbroker living in Sharon Mass, just outside of Boston, to be the “target” of the experiment. In addition he chose roughly 300 others — 100 from Boston itself and the other 200 from Omaha Nebraska, which Milgram figured was about as far away from Boston, socially and geographically, as one could get within the US.
简言之，米尔格拉姆选择他的一位朋友作为其实验的“靶标”，他是一位股票经纪人，住在波士顿城外的Sharon Mass。另外，他还另外选择了约300名实验对象——其中100名来自波士顿，其他200名来自内布拉斯加的奥马哈市，米尔格拉姆认为，就美国境内而言，奥马哈无论在社会关系上还是在地理上，都距离波士顿足够远。
Milgram then sent these 300 subjects special packets containing a good deal of information about the target — his name, address, occupation, etc. — and also instructions that they were to try to get the packet to him. But there was a catch: they could only send the packet to him if they knew him personally, meaning on a first-name basis.
随后，米尔格拉姆为这300名实验对象送出了特殊的包裹，其中包涵他这名股票经纪人（靶标）的许多信息——他的名字，地址，职业，等等——以及一些让他们试着将包裹寄给他的提示。但是，这儿有个坑：他们只能在个人直接认识他的情况下才能寄出包裹。
In the overwhelmingly likely event that that they did not, they were instead to send to someone they did know on a first name basis and who was closer to the target than they were themselves. These new participants would then get the same packet with the same instructions, and the process would repeat until — hopefully — some of the packets reached the target.
而实际上，在绝大部分情况下，他们不满足这一条件，所以只能将包裹寄给某位他们直接认识并且和靶标的关系距离更近一层的人。而这个收到包裹的新参与者，得到的是同样的包裹和提示，这一过程会一直持续循环下去，直到——幸运的话——有些包裹能顺利到达“靶标”。
Milgram’s question then was: for successfully delivered packets, how long would the chains be? Curiously, before he ran the experiment Milgram asked lots of people to guess the answer. Many assumed it wasn’t possible while others figured it would take hundreds of steps. So when Milgram found that not only did 64 packets, roughly one fifth of the initial sample, reached the target, but that the average length of the successful chains was just 6, he knew it would surprise many people.
米尔格拉姆接下来的问题是：如果包裹递送成功，那么这些链条有多长呢？有趣的是，在米尔格拉姆进行此实验之前就让很多人猜过答案。一些人表示根本不可能送达目标，另一些则认为至少得通过成百上千个步骤。所以，当米尔格拉姆得知不仅64个包裹（占初始样本的五分之一）到达了靶标，而且这些成功链条的平均长度仅仅为6。他知道这会让许多人咋舌。
In many ways, it still does. Although the phrase “Six Degrees of Separation” has become a cliché, when pressed many people still find it difficult to imagine how they could really reach anyone — not just someone like them or someone near to them, but anyone at all in the whole world — in something like six steps.
从许多方面看，这仍然令人惊奇。虽说“六度分隔”已经成了陈词滥调，但这一结果发布之后，许多人仍难以相信自己仅仅只需六步即可链接到世界上的任何人——不仅是自己一个圈子的人，或是周边的人，而是整个世界的任何人。
Understandably then, the Facebook result also attracted some resistance: “Facebook is an unrepresentative sample of the population;” “Facebook friends aren’t real friends” and so on. But although these critiques may have merit, they miss the point. In reality, the 3.5 number is simply incomparable to Milgram’s 6 for three reasons.
所以不难理解，脸书的研究结果发布后吸引了许多反对声音：“脸书是个不具代表性的人口样本；”“脸书的朋友并非真朋友”等等。虽说这些批评也许有可取之处，但是他们没抓住要点。实际上，这个3.5不能和米尔格拉姆的“六度”直接对比，理由有三：
First, the number 3.5 counts intermediaries not degrees of separation. If I am “one degree” from someone I know them directly; there are zero intermediaries between me and them. Likewise, there is one intermediary between me and my “two degree” neighbors, and so on.
首先，3.5这个数字计算的是“媒介”的数量，而不是分隔度数。如果我是某人的“一度”友邻，我就直接认识此人；我和他们间没有“媒介”。类似的，我和我的“二度”友邻之间存在一个“媒介”，以此类推。
In general, therefore, an average of 3.5 intermediaries corresponds to 4.5 degrees of separation, which is almost exactly what Facebook itself found when it performed a similar exercise a few years ago. Conversely, Milgram’s six degrees result corresponds to five intermediaries, which is actually the number he reported in his original paper with Jeffery Travers. So already the difference is one less than it appears.
因此，平均3.5个“媒介”对应的是“4.5度分隔”，这和几年前脸书自己通过类似实验得出的发现几乎相同。反之，米尔格拉姆的“六度”所对应的是5个“媒介”——其实他和Jeffery Travers发表的文章中所用的正是这个数字。所以上述差异比表面看起来就已经少了1 。
Second, though, Milgram’s experiment was a subtly but importantly different test than the one run by Facebook. Whereas the latter measured the length of the shortest possible path between two people — by exhaustively searching every link in the underlying Facebook graph — the former is simply the shortest path that ordinary people could find given very limited information about the underlying social network.
第二，虽然米尔格拉姆的试验很巧妙，但是，和脸书做的这个测试有重要差异。后者度量的是两个人之间的最短可能路径的长度——通过穷举搜索脸书关系图上的每条链接，而前者则是普通人基于其所掌握的极为有限的社会关系信息而能够找到的路径长度。
There are, in other words, two versions of the small-world hypothesis — the “topological” version, which refers only to underlying network structure, and the “algorithmic” version, which refers to the ability of people to search this underlying structure.
换言之，其实“小世界假说”有两个版本：“拓扑版”，它度量的是社会关系网络结构，和“算法版”，它度量的则是人们在此网络中进行搜索的能力。
From these definitions, it follows that algorithmic (search) paths cannot be shorter than topological paths and are almost certainly longer. Saying that the world has gotten smaller because the shortest topological path length is 4.5 not 6 therefore makes no sense — because the equivalent number would have been smaller in Milgram’s day as well.
从这些定义得出，“算法版”（搜索）路径不可能短于“拓扑版”。仅仅因为最短拓扑路径的长度是4.5而非6就说世界变小了，这么说毫无意义——因为米尔格拉姆时代的相应数字同样小于6。
Finally, the number 6 is also in some respects too small. As has been pointed out many times since Milgram’s experiment, only about 20% of the letters made it to their target. More importantly, these letters were almost certainly on shorter paths than the ones that didn’t make it, meaning that estimates of path length that don’t take into account the missing data are almost certainly biased downwards.
最后，从某些角度看，数字6也太小了。因为自从米尔格拉姆试验后就被很多人指出，仅有20%的信封送到了靶标。更重要的是，这些信所通过的途径几乎肯定短于那些没有到达靶标的，这就意味着那些投递失败的长链条在估算链条长度时没有被计算在内，这肯定会造成向下偏差。
Fortunately it is possible to correct for this bias using standard statistical methods. In a 2009 paper my colleagues and I performed exactly this analysis both on Milgram’s original data and also on our data from a similar — but much larger — experiment that we had conducted ourselves in 2003.
有幸的是，我们可以通过标准的统计算法来更正这一偏差。在2009年的一篇论文中我和我的同事们对米尔格拉姆的原始数据和我们自己在2003年做的一个大得多的类似试验的数据进行了恰如上面所述的分析。
Remarkably we found that after the correction, both experiments yielded similar results: the median shortest path was 7, meaning that 50% of chains should complete in 7 or fewer steps while the other 50% would be longer. Many people find this result surprising because it seems so clear that the world has gotten smaller in the last 50 years.
我们惊喜的发现，在矫正了数据后，两个试验得出相似的结果：最短链条的中位值是7，即50%的链条会7步或少于7步时完成，而另外50%则会更长。许多人觉得这个结果不思议，因为过去50年世界变得更小了这个事实看起来如此明白无误。
Yet this apparent stability is exactly what one would predict from my early theoretical work with Steven Strogatz back in the late 1990’s. In a nutshell what we showed is that it is easy to turn a “large” world into a “small” one, just by adding a small fraction of random, long-range links, reminiscent of Mark Granovetter’s famous “weak ties.”
但这一明显的稳定性正是我和Steven Strogatz在1990年代后期的理论研究中预见到的。简言之，我们要证明的是，只需要在“大”世界中加入一小部分随机的“长范围”链接，就可以把世界变“小”，这让人联想起马克·格兰诺维特著名的“弱关系”理论。
The flip side of our result, however, is that once the world has already gotten small — as it was already by the 1960’s — it is extremely hard to make it smaller. Obviously Facebook did not exist in 2003 so possibly since then something has indeed changed. But I suspect that the difference will be small.
实际上，这一结果反过来说就是，一旦世界变小之后——其实它在60年代已经变小了——想要把它变得更小就极为困难。很明显，脸书2003年并不存在，所以有可能某些东西真的已经改变了。但是我估计这个变化是微小的。
Why does any of this matter? There are three reasons. First, the two versions of the small-world hypothesis — topological and algorithmic — are relevant to different social processes. The spread of a sexually transmitted disease along networks of sexual relations, for example, does not require that participants have any awareness of the disease, or intention to spread it; thus for an individual to be at risk of acquiring an infection, he or she need only be connected in the topological sense to existing infectives.
何以见得这些差异是要紧的呢？理由有三：第一，两个版本的“小世界假说”——拓扑版和算法版——关乎不同的社会过程。例如，就像性病通过两性关系而传播，这并不需要参与者意识到疾病的存在或者拥有传播它的意图，而仅需要他或她在拓扑上链接到既有的感染者即可。
On the contrary, individuals attempting to “network” — in order to locate some resources like a new job or a service provider — must actively traverse chains of referrals, and thus must be connected in the algorithmic sense. Depending on the application of interest, therefore, either the topological or algorithmic distance between individuals may be more relevant — or possibly both together.
相反，若是个人想要“建立链接”寻找资源，比如找工作，寻找服务商，则必须积极的遍历中间人链条，因而必须在算法上建立链接。所以，根据实际应用中的关注重点，有些情况下个体之间的拓扑距离更切题，有时则算法距离更切题，或者两者同时切题。
Second, whereas the topological hypothesis has been shown to apply essentially universally, to networks of all kinds, the algorithmic hypothesis is largely (although not exclusively) concerned with social networks in which human agents make decisions about how to direct messages.
第二，拓扑版小世界假说已经表明普遍适用于所有类型的网络结构，而算法版假说则大致上量（虽然不完全）适用于社交网络，在这些网络中，人类主体就如何引导信息流向做出决定。
And third, whereas the topological version is supported by an overwhelming volume of empirical evidence — hundreds of studies, if not thousands — have found that nodes in even the very largest known networks are connected by short paths, the practical difficulty of running “small-world” experiments of the sort that Milgram conducted in the 1960s has meant that much less is known about the algorithmic version.
第三，鉴于“拓扑版”得到了压倒性数量的经验证据——来自数百甚至数千项研究——支持这些证据表明，即使在最大的关系网中，节点之间也可通过较短路径相连接，进行像米尔格拉姆在1960年代所做的那种“小世界效应”试验的实际困难意味着，我们对“算法版”的情况其实所知不多。
On this last point, for example, our 2009 analysis also found evidence that some of the longer paths could be much longer than the median, adding weight to the skeptics’ claims that in spite of the small-world phenomenon, some people remain socially isolated.
有关最后这一点，（例如）我们2009年的分析同样发现了证据表明，一些长路径可以远远长于中位值，这为那些怀疑者的主张提供了依据：即使存在小世界现象，总有些人在社会关系上是保持孤立的。
Given the importance of social networks in determining life outcomes, it would be extremely interesting and useful to understand better who these people are and why they are isolated. Is it something to do with their underlying networks or is it that their search strategies are somehow less effective?
考虑到社会关系网在决定生活质量上的重要性，研究并理解这些孤立者是谁，为何变得孤立，将是件极为有趣且有用的事情。这跟他们的下层关系网有关？【编注：此处underlying networks应是指亲戚、邻里等个人被预先给定的被动关系，相对于个人主动寻求建立的社会关系】还是他们的搜索策略不够有效？
Could it be, as my coauthors and I speculated many years ago, some kind of self-fulfilling prophecy, in which the perception of social isolation discourages one from searching one’s network, and that the resulting lack of success reinforces the original perception of isolation?
有没有可能，正如多年前我和我的共同作者所推测的那样，是某种自我实现的预言？即，对社会孤立的感知，使得个人不愿意搜索自己的关系网，由此导致的关系建立失败进而强化了对孤立的最初感知？
Answering these questions would require new experiments that are only now just becoming possible. But the answers would not only be of academic interest — they could also potentially help many people access currently inaccessible reserves of “social capital” thereby improving their lives. Far from being settled, the small-world problem still has much to teach us about the world, and ourselves.
要回答这些问题需要更新的试验，而此类实验直到最近才变得可行。但是，这些问题的答案不仅仅是满足学术兴趣——它们同样可能帮助很多人得以访问目前对他们来说还不可触及的“社会资本”储备，从而来改善他们的生活。 小世界问题还远未解决，在未来，它仍将为我们带来有关这个世界以及我们自身的诸多教益。
Duncan Watts is a principal researcher at Microsoft and author of Six Degrees: The Science of a Connected Age (WW Norton, 2003).
邓肯·J·瓦茨是微软首席研究员和《六度分隔理论》作者
翻译：龟海海
校对：辉格(@whigzhou)
编辑：辉格@whigzhou