The Q&A: Samuel Arbesman
Nov 28th 2012, 13:56 by R.D.A. | LOS ANGELES
IN PRIMARY school Babbage learned that there were nine planets in the solar system. None were known to exist outside it. Since then, astronomers have spotted over 800 planets around other stars (and thousands more "candidates") and demoted Pluto to a mere "dwarf planet". Even a cursory glance at other fields reveals similar patterns.
Samuel Arbesman, a mathematician at Harvard, calls this "The Half-life of Facts", the title of his new book. In it he explains that this churn of knowledge is like radioactive decay: you cannot predict which individual fact is going to succumb to it, but you can know how long it takes for half the facts in a discipline to become obsolete. Such quantitative analysis of science has become known as scientometrics. We talked to Dr Arbesman about how knowledge changes over time, and what this means for the way people consume information.
What is scientometrics?
Put simply, scientometrics is the science of science. It grew out of bibliometrics, the science of books and research papers. In bibliometrics the unit of measurement is a research paper, which are easy to study because you can quantify different aspects of it: who the authors are, who has co-authored papers with those authors, how often a paper is cited, by whom, and so on.
Librarians were some of the first people to do this. In the 1970s people started looking around and noticing that scientific knowledge was growing very rapidly, but papers had not been digitised yet, and libraries were finite in size and had finite resources. And so librarians had to grapple with the question what to carry on their shelves. They had to calculate which fields get overturned really rapidly, in other words, which papers and books people were unlikely to care about in the future.
But bibliometrics is only one subfield of scientometrics. There are all kinds of ways that you can quantify science: you can measure the number of discoveries that are occurring within a particular field, the number of elements in the periodic table, etc. Broadly, scientometrics is about quantifying and understanding how science occurs.
That includes both the social aspects of science and the relationship between science and technology. There is a tight interplay between the capacities of our tools and what we can actually discover. Technology is crucial to the story of science. Science of science is about all these different things. And my book is about how the facts of the world—the stuff we know—grow in number, and how they change.
What does it mean to say that a fact has a half-life?
When I say that a fact has a half-life, I am trying to illustrate how knowledge changes by making an analogy to radioactivity. With radioactivity, if you give me a single atom of uranium, I can tell you it will eventually decay. When it does, it will break down into specific bits and release a certain amount of energy. But I have no way of telling when it is going to decay. It could be in the next half-second or not for millions and millions of years.
But things change when you go from a single atom to lots of atoms. When you have a big chunk of uranium, you can graph out the decay; you can say it takes 4.47 billion years for half of the atoms in a chunk of uranium to break down. You aren't going to know which half, but you know the overall rate of the decay. And the same thing is true for science, and for knowledge in general. Even though I cannot predict what discovery is going to be made or what fact is going to be overturned, there are regularities in how knowledge grows and changes over time.
For example, in the area of medical science dealing with hepatitis and cirrhosis, two liver diseases, researchers actually measured how long it takes for half of the knowledge in these fields to be overturned. They gave a whole bunch of research papers from fifty years ago to a panel of experts and asked them which were still regarded as true and which had been refuted or no longer considered interesting. They plotted this on a graph. What they found is that there is a nice, smooth rate of decay; you can predict that every 45 years, half of this particular sort of knowledge gets outdated.
You can use these same methods with citations in newer papers. There, you look to see how long papers are cited in a field and then derive a half-life based on how long it takes for papers to receive half the citations they used to receive. Of course, some papers are no longer cited precisely because they are so influential. No one is citing Newton's Principia even though we still use a lot of his ideas. But by and large, the citation rate of papers is a good proxy for the half-life of knowledge.
What scientific fields decay the slowest—or the fastest—and what drives that difference?
Well it depends, because these rates tend to change over time. For example, when medicine transitioned from an art to a science, its half-life was much more rapid than it is now. That said, medicine still has a very short half-life; in fact it is one of the areas where knowledge changes the fastest. One of the slowest is mathematics, because when you prove something in mathematics it is pretty much a settled matter unless someone finds an error in one of your proofs.
One thing we have seen is that the social sciences have a much faster rate of decay than the physical sciences, because in the social sciences there is a lot more "noise" at the experimental level. For instance, in physics, if you want to understand the arc of a parabola, you shoot a cannon 100 times and see where the cannonballs land. And when you do that, you are likely to find a really nice cluster around a single location. But if you are making measurements that have to do with people, things are a lot messier, because people respond to a lot of different things, and that means the effect sizes are going to be smaller.
What is a "fact phase transition" and how does it make events like the first Moon landing predictable?
First, here is what I mean by a phase transition. An example in the natural world is when water goes from liquid to ice when it freezes. For most people that is pretty unremarkable. But it is actually really interesting when you look at it from a physics perspective. A continuous change—in this case, a change in temperature—is accompanied by a step-change is other properties: water going from being a liquid to a crystal. This is a good way to think of rapid changes in knowledge.
Some of these happen rapidly, but underneath there are these gradual changes. For example, with the moon landing was a pretty big change in human knowledge and human accomplishment. For all of human history, no one had ever set foot on the moon, and then one day in 1969 people had. But if you look carefully you will see that the moon landing was completely predictable. Look at the fastest speeds enabled by technology, for instance, and it turns out that they follow a regular curve. In the 1950s the American air force graphed this out and determined that if transportation speeds continued rising at the rate they were going, humans should be able to get into orbit, and then eventually land on the Moon, within a set number of years. And, sure enough, right on schedule, Sputnik happened, and a decade later humans landed on the moon. That was a fact phase transition, an abrupt change with slow incremental processes hiding beneath the surface.
One theoretical fact phase transition that you describe is "actuarial escape velocity", a concept borrowed from medical science.
Actuarial escape velocity is the idea that at some point average human lifetime will grow by more than a year each year. Right now the rate is only a fraction of a year (thanks to changes in medical science and hygiene) a year. If it exceeds one year per year, people will effectively live for ever, without having to solve the immortality problem. The reason I bring it up in my book is to illustrate that small changes in science can actually bring about big changes in other areas of knowledge, or elsewhere in the world.
For example, if an astronomer finds another planet outside solar system, unless it has certain properties, it will just be another piece of data. It is not going to alter the structure of people's ideas about planets. But if he discovers a planet that can harbour life, that is a game-changer. And actuarial escape velocity is similar, in the sense that these incremental changes in medical science and hygiene can eventually create a huge change in how we live our lives.
In your book, you make a convincing case that scientific breakthroughs are becoming more difficult to achieve with time. One gets the sense that the low-hanging fruit of empiricism have been picked. But you also argue that science as a human activity is growing, and getting better. How is that?
In some fields science is getting harder, but I would not say that science as a whole is becoming more difficult. We are still adding new scientists every year, but the rate of growth has slowed and science is increasingly being done by large teams. But there are many areas where we thought there is nothing left to explore, only for someone to come along and say that there is something there, after all.
In mathematics there was an extreme case of this in the 1990s, when two high-school students figured out a new way to prove one of Euclid's theorems, something that had not been done in a thousand years. So even though basic geometric proofs are not the frontier of mathematics, there are still things you can do. And even where things slow down in science, often that slowing forces scientists to be cleverer, both in finding ways to create new knowledge but also in finding new ways to combine disciplines. Plus nowadays new technology is a real driving force; the new computational tools have created the potential for a scientific revolution.
Reading your book it is difficult not to think about consilience, the term that Edward Wilson uses to describe an idealised unity of all scientific knowledge. Do you think scientometrics can get us to something like consilience faster than if science were merely left to its own devices?
There is a great deal of power in the idea of consilience, and in synthesising ideas. When it comes to understanding the march of knowledge, scientometrics can be very helpful. I don't think it is necessarily going to help us realise the complete synthesis of all knowledge, but if we have a better sense of how we know what we know, and how what we know changes, that will force a reckoning in how we think about how knowledge as a whole is organised. If you create a networked view of different scientific fields, you quickly realize how connected they are. There are surprisingly few steps from thinking about abstract mathematics to thinking about models of how population size changes in an ecosystem. As science grows and becomes more and more complicated, having people that can exist in these liminal spaces is going to be increasingly important.
It seems that one of your purposes in writing this book is to call attention to the human habit of becoming accustomed to whatever state of affairs is true when a situation is initially examined. By showing how knowledge about the world shifts systematically, you seem to be suggesting a renewed vigilance against growing complacency about knowledge of the world.
That is certainly one of my arguments. I want to show people how knowledge changes. But at the same time I want to say, now that you know how knowledge changes, you have to be on guard, so you are not shocked when your children coming home to tell you that dinosaurs have feathers. You have to look things up more often and recognise that most of the stuff you learned when you were younger is not at the cutting edge. We are coming a lot closer to a true understanding of the world; we know a lot more about the universe than we did even just a few decades ago. It is not the case that just because knowledge is constantly being overturned we do not know anything. But too often, we fail to acknowledge change.
Some fields are starting to recognise this. Medicine, for example, has got really good at encouraging its practitioners to stay current. A lot of medical students are taught that everything they learn is going to be obsolete soon after they graduate. There is even a website called "up to date" that constantly updates medical textbooks. In that sense we could all stand to learn from medicine; we constantly have to make an effort to explore the world anew—even if that means just looking at Wikipedia more often. And I am not just talking about dinosaurs and outer space. You see this same phenomenon with knowledge about nutrition or childcare—the stuff that has to do with how we live our lives.
Samuel Arbesman, a mathematician at Harvard, calls this "The Half-life of Facts", the title of his new book. In it he explains that this churn of knowledge is like radioactive decay: you cannot predict which individual fact is going to succumb to it, but you can know how long it takes for half the facts in a discipline to become obsolete.
Put simply, scientometrics is the science of science. It grew out of bibliometrics, the science of books and research papers. In bibliometrics the unit of measurement is a research paper, which are easy to study because you can quantify different aspects of it: who the authors are, who has co-authored papers with those authors, how often a paper is cited, by whom, and so on.
You can use these same methods with citations in newer papers. There, you look to see how long papers are cited in a field and then derive a half-life based on how long it takes for papers to receive half the citations they used to receive.
专访：萨缪尔 阿布斯曼
笔者在上小学时知道了太阳系有九大行星。当时人们还没有找到太阳系之外的任何行星。现在，天文学家已经找到超过800颗围绕其它恒星公转的行星（此外可能是行星的“候选”天体数量更是上千），而同时冥王星却已被降级为一颗“矮行星”。即使粗略检视其他领域你也会发现类似的情况。
哈佛大学数学家萨缪尔·阿布斯曼（Samuel Arbesman）给这种现象取名叫“知识的半衰期”，并写了一本以此为题的书。在书中他解释说知识的新旧交替如同放射性衰变，你无法预知某项特定知识是否会受这种衰变效果影响而被淘汰，但你能够找出某一领域的知识在多久之后会有一半被淘汰。这种对科学的定量分析被称之为科学计量学。我们和阿布斯曼博士就知识如何随时间改变、以及这对人们使用信息的方式有何影响进行了一次专访。
什么是科学计量学？
简单来说，科学计量学就是研究科学的科学。这是从研究书籍和论文的科学——文献计量学中引申出来的。文献计量学使用的测量单位是论文。论文是比较容易研究的课题，因为你可以量化论文的各种特点：作者是谁、谁曾经和该论文的作者合作发表过论文、该论文被引用的频率、被谁引用等等。
图书馆员是最早进行这类研究的人士之一。20世纪70年代人们发现身边的科学知识增长速度非常快，但当时论文还没有数字化，图书馆的规模和资源都有限。因此图书馆员必须处理该让什么书上架这一问题。换句话说，他们必须计算哪些领域的知识更新速度非常快，哪些书籍和论文会在未来变得无关紧要。
但文献计量学只是科学计量学的一个子领域。要量化科学有各种方式：你可以测量某个特定领域内新发现的数量，元素周期表内元素的数量等等。大体来说，科学计量学研究的是如何量化并理解科学成果产生的方式。
这包括科学的社会面以及科学和技术之间的关系。我们使用的工具的能力和我们能发现的成果之间有密切的相互依赖关系。对于科学发现来说技术是至关重要的。研究科学的科学致力于研究所有这些不同的方面。我的书讨论的是世界上的知识——我们所知的事物——如何增长、如何改变。
知识有半衰期是什么意思？
我说知识有半衰期是为了用放射性现象的比喻来描述知识的变化。就放射性现象来说，你如果给我一个铀原子，我可以告诉你它最终会衰变。一旦衰变发生，它会分解为特定的产物，并释放一定的能量。但是我不可能告诉你它什么时候会衰变。可能再过半秒它就衰变了，也可能要等几万亿年。
但是如果你给我的不是一个原子，而是大量原子，情况就不同了。当你有一大块铀时，你可以绘出衰变曲线。你可以确定这些铀中有一半原子会在44.7亿年的时间里衰变。你不知道具体哪一半会衰变，但你可以确定总体的衰变率。对于科学、以及更广义的知识来说也是一样。虽然我无法预测会出现什么样的新发现，或是有哪些知识会被推翻，知识随时间增长并变化的规律是有迹可循的。
例如，在研究肝炎和肝硬化的医学方面，研究者对过多久这些领域内的一半知识会被推翻进行了研究。他们将50年前的一批论文交给一个专家评审团，判断其中哪些的结果如今已被推翻，或是已经不再重要。他们将结果绘成一副图表，并在图中看到非常清楚平滑的衰变曲线。你可以用该图预测每过45年，该领域的知识都会有一半变得过时。
把同一方法用在最近论文的引用上，你可以研究某一领域内的论文在多长时间内会被别的论文引用，然后你可以根据论文发表后多少时间内其引用次数会减少到其最初引用次数的一半来推算出半衰期。当然，有的论文不再被引用恰恰是因为它们影响力极大。现在没人会在论文内注出对牛顿《原理》的引用，但我们还在继续使用很多他的思想。但除了这些特例，基本上论文引用率还是很适合代表知识半衰期的。
哪些科学领域的“衰变”最慢？哪些最快？它们之间为什么会有这样的差异？
这是没有标准答案的，因为衰变率本身会随时间推移而改变。例如，当医学最早从一门艺术变成一门科学时，其半衰期比现在要迅速多了。尽管如此，医学仍然是半衰期非常短的一门科学，实际上它是知识变化最快的领域之一。知识变化最慢的领域之一是数学，因为在数学里一旦证明某一定理很多时候结果就等于是敲定了，除非有人发现你证明过程中的错误其一般不会被推翻。
我们观察到的一个现象就是社会科学的衰变率比自然科学要快得多，因为社会科学在实验水平上存在的“噪音”要大得多。例如，在物理学里，如果你想要研究抛物线轨迹，你可以发射大炮100次，看看炮弹会落在哪里。你会发现炮弹大多非常漂亮地集中在某个点周围。但是如果你测量的对象是人，那问题就多了，因为人对大量不同的外界事物会有反应，换句话说，效应大小会小得多。
什么是“知识相变”？它如何让第一次登月这样的事件变得可预知？
首先，我解释一下相变这个概念。自然界的一个例子就是水凝固时从液态变为固态。对大多数人来说这一现象平淡无奇，但是从物理学的角度来看你会发现这其实是一个很有趣的现象。某一属性的连续转变（在这个例子里是温度改变）会伴随着其它属性质的飞跃：水从液态变为晶体固态了。这可以用来帮助我们思考知识的迅速改变。
有些改变是迅速发生的，但在突变之下隐藏有上文所说的渐变。例如，登月对于人类知识和成就来说是一个巨大的飞跃。在人类历史上，从未有人踏足过月亮表面，1969年的某一天某人突然就做到了。但如果仔细分析，你会发现登月完全是可预见的。例如，你如果看看依靠科技所能达到的最高移动时速，它基本上沿着一条正常曲线一路升高。20世纪50年代时，美国空军把该数据绘成曲线图，发现如果移动速度照这个趋势继续升高，那么人类会在若干年内进入绕地轨道，并最终登陆月球。事实和他们预测的一样，斯普特尼克准时登空。之后又过了十年，人类就登上了月球。这就是一个知识相变，受到隐藏在表面之下渐变的过程推动而发生的突变。
你提到的一个理论上的知识相变：“死亡逃逸速度”，这是来自医学的一个概念。
死亡逃逸速度是指最终人类寿命每年会增加超过一年这一观点。现在人类寿命每年增长的程度（多亏了医学和卫生）还只是一年的一小部分。如果这个增加速度达到每年增长超过一年，那人们实际上可以不需要解决不死问题，就能实现永生。我在书中提到这一点是为了描述科学中的细微变化可以在其它知识领域、或世界其它地方产生巨大的实际改变。
例如，如果天文学家发现太阳系外的一颗行星，除非它有某些特殊性质，不然这仅仅是多一份数据。发现新的行星不会改变人类对行星的理解。但如果天文学家发现的行星上有生命，那就完全不同了。死亡逃逸速度也是如此，医学和卫生领域内的渐进改变最终可以导致我们生活方式的巨大改变。
在你的书中，你令人信服地论证了随着时间推移会越来越难做出科学上的突破。读者会了解到易摘的经验主义果实都已被采光了。但你也论证了科学作为一项人类活动正在增长，而且蒸蒸日上。这怎么说？
在某些领域科学研究确实越来越艰难，但我不认为科学研究整体正在变得更为艰难。我们每年都有新的科学家加入研究队伍，但科学研究的增长率确实在放缓，而越来越多的研究要依赖大型团队。但是有很多领域我们原以为没什么可以探索了，不料却有人在该领域仍然发现新的事物。
在数学里就有一个很极端的例子发生在20世纪90年代，当时两位高中生发现了一种新的方式来证明欧几里德的一条定理，从一千年前起就已没人找出过欧几里德定理的新证明方法了。因此虽然基础几何学如今已不是数学的前沿，还是有新发现等待人们去发掘。即使科学发现的速度放缓了，这种放缓现象常常会让科学家变得更聪明，因为它迫使科学家设法创造新知识并寻找新方式来综合各个领域。此外如今新技术是真正的推动力，新的计算工具酝酿着新的科学革命。
你的书很容易让人联想到“知识融通”，爱德华·威尔逊（Edward Wilson）用这个词来形容所有科学知识的理想化统一。你认为和任科学自己发展相比，科学计量学的出现可以让我们比更快达到这一境界吗？
“知识融通”以及综合思想是非常强大的概念。在理解知识的累积增进时，科学计量学可以帮助很大。我不认为科学计量学一定会对实现知识的完全综合有所贡献，但是如果我们能更好理解我们是如何掌握现有知识的，以及我们拥有的知识是如何随时间推移改变的，这将会迫使我们思考知识整体是如何组织的。如果你将不同的科学领域之间的联系看成一个网络，你会立刻意识到不同领域的相互联接非常发达。从思考抽象的数学问题到思考生态系统内的种群数量变化模型之间其实只需要没几个过渡步骤，这是很让人惊奇的。随着科学逐渐进步，变得越来越复杂，能够身处这样的模糊临界领域思考问题的人将来会变得越来越重要。
你写这本书的其中一个目的好像是为了让人们注意到自己的一个习惯：即人类会逐渐把最早研究某一事物时得到的观察视为理所当然。你的书告诉人们知识是如何系统化地改变，其中似乎蕴涵让人们重新自省，防止在对知识的认识上过于傲慢的意思？
当然，这是我的论点之一。我希望让人们看见知识是如何改变的。但是同时我也想指出一旦你知道知识是会改变的，你必须要常常警醒，这样才不会在你的孩子放学回家告诉你恐龙有羽毛时大吃一惊。你必须经常查阅资料，意识到自己年轻时学到的很多知识并不是最先进的。我们已经大幅接近对世界的真实理解了，我们对宇宙的认识比仅仅几十年前已经多得多了。知识在不停得更新并不意味着我们无知。但是很多时候，我们确实没有意识到这种改变。
某些领域开始意识到这一点。例如，医学在鼓励从业者时时保持学习最新知识这一点上做得很好。很多医学院学生会被告知他们所学的一切在毕业后不久就会过时。甚至有一个名叫“最新信息”的网站在不停地更新医学教科书。在一定程度上各个领域都可以学习医学，我们必须不停地努力来重新探索世界，就算这仅仅体现在更频繁地查维基百科也好。而且我所讲的不仅只是关于恐龙和外太空。你在营养和育儿这些和我们生活息息相关的领域也会看到同样的知识更新现象。
IN PRIMARY school Babbage learned that there were nine planets in the solar system. None were known to exist outside it.笔者在上小学时知道了太阳系有九大行星。当时人们还没有找到它们之外的任何行星。
评论：for reader’s benefit: exist outside it = exist outside the solar system.
哈佛大学数学家萨缪尔?阿布斯曼（Samuel Arbesman）给这种现象取名叫“知识的半衰期”，并写了一本以此为题的书。在书中他解释说知识的新旧交替如同放射性衰变，你无法预知某项特定知识是否会被淘汰，但你能够找出某一领域的知识在多久之后会有一半被淘汰
评论：for reader’s benefit: succumb to it = succumb to this churn of knowledge.
简单来说，科学计量学就是研究科学的科学。这是从研究书籍和论文的科学——文献计量学中引申出来的。文献计量学使用的测量单位是论文。论文是比较容易研究的课题，因为你可以量化论文的各种特点：作者是谁、谁曾经和该论文的作者合作发表过论文、该论文被引用的频率、被谁引用等等。
评论：which are easy to study 显然不对， 或不好， 应当是 which (=a research paper) is easy to study
把同一方法用在最近论文的引用上，你可以研究某一领域内的论文在多长时间内会被别的论文引用，然后你可以根据论文发表后多少时间内其引用次数达到一般引用次数的一半来推算出半衰期。
评论：把同一方法用在最近论文所引用的论文上，你可以研究某一领域内的论文在多长时间内会被别的论文引用，然后你可以根据论文发表后多少时间内其引用次数减少到当初引用（used to）次数的一半来推算出半衰期。
