梅森·波特谈社区检测与数据拓扑

或者你可以使用其他你想要研究的方法，包括一些社区检测方法，并进行比较。

Or you can do some other method that you want to study, including some of these community detection methods and compare things.

最初对这100所学校的全面研究的一个贡献，就是提供了一个被他人用于其他用途的资源，无论是开发新方法还是其他方面。

One of the contributions of the initial study of going through all those 100 schools is to have something that people have used for other things, whether it's developing methods and so on.

此外，也有一些更偏向社会学的研究跟进并拓展了我们的工作。

And there's also been some more sociologically oriented studies that have followed up on what we did.

这就是基本的想法。

That's the sort of basic idea.

所以它的定位是一个应用性研究。

So it's meant to be an application.

我们内部开玩笑地称它为‘数据dump论文’，因为我们的方法是用大体的框架来比较不同事物的社区结构。

The actual we jokingly internally called it the data dump paper because it's like we developed this methodology and approach to think of, okay, let's in broad brush strokes compare the community structure across a few different things.

那是2011年的SAM综述论文。

That was the 2011 SAM review paper.

我们开发了这个宏观的框架。

We developed this broad thing.

就是说，我们有100所学校。

It's like, okay, but we have a 100 schools.

那就直接把它们全部比较一下，把我们做过的这些内容整理成数据dump。

Let's just compare all of them and take what we've done and do the data dump.

事实上，从我网页上下载的文件，名字就直接叫‘data dump’。

In fact, the file that one would download from my HTML file is actually literally called data dump.

PDF格式，因为这篇就是所谓的数据dump论文。

Pdf because this was the data dump paper.

不管怎样，我觉得这是一个不错的应用，我很享受这个过程。

Anyway, I think it was a nice application, I enjoyed it.

我至今仍在使用这个数据集，因为它是用相同流程生成的100个真实世界实例。

I continue to use this dataset because just having a 100 different instances of a real world thing that has been generated using the same process.

实际上还有一篇论文，虽然不能说是进一步的证据，但确实让这个观点更具体、更扎实了——它确实是由同一过程生成的100个实例。

There's actually a paper that really also gives, I guess, I wouldn't say further evidence, but strengthens the evidence, makes it more concrete that it really is a 100 instances of the same process.

所以这篇论文也涉及了我之前提到的一些人，但我本人并没有参与其中。

So this particular paper also involves some people I've mentioned before, so I'm not involved in this.

亚伦·克莱塞特、乔汉·乌甘德参与了这项研究，我一时想不起那些年轻研究者的名字了，这不太好，但我想其中一两位是亚伦以前的学生。

Aaron Clauset's on it, Johan Ugander, and I'm messing up and forgetting the junior folks, which is not good, but I think one of Aaron's former students or something, one or two of them.

他们研究的是，比如说，一所更大的学校，如果你把较小的学校按比例放大，它会不会就像那个更大的学校一样？

What they were looking at was whether, say, a larger version a larger school, if you took Is that somehow like the smaller one but having grown to a larger size?

对。

Right.

如果我把我的学校——规模为762人——让它增长，直到网络规模达到那个更大的学校，它们看起来真的像是来自同一个过程吗？

So if I took my school of size seven sixty two and let it grow until that network is of the larger one, do they actually look like they came from the same process?

他们的论文中对此有更多细节，但本质上答案是肯定的。

There's more detail on that than that in their paper, but essentially the answer is yes.

这确实是一个真实世界中的集合体，我特意使用“集合体”这个词，而不是来自合成模型——比如传统上我们所说的随机图模型——的集合体。

It really is an ensemble, and I'm using the word ensemble on purpose, from the real world instead of an ensemble from say a synthetic model, traditionally a what we call a random graph model.

因此，当你测试方法，或者想写一篇关于某种过程的论文时，比如疾病传播，当然也适用于信息传播或谣言传播，因为——好吧，你当然不希望传播谣言，但你确实会和你的Facebook好友交流。

So that makes it very useful when you're testing methods or when you want to put look, do it a paper which has some sort of process disease spread or of course, makes sense for, information spread or rumor spread because, well, you really would well, hopefully not spread rumors, but you really would communicate with your Facebook friends.

至少在某种程度上，这种网络具有真实性，是这类现象实际发生的网络类型。

It is at least at some level, there's a verisimilitude where it's the type of network on which this would occur.

对吧？

Right?

比如有些论文把疾病传播放在蛋白质相互作用网络上，你会想：好吧，数学上你确实可以这么做，但你有点脱离现实了，因为疾病传播并不是发生在蛋白质相互作用网络上的真实过程，尽管我可以把它数学化为一个网络，也可以数学上把这个过程施加上去。

Like papers where someone puts disease spread on a protein interaction network and you're like, Okay, well mathematically you can do that but you're suspending reality a bit because disease spread is not the type of process that occurs on a protein interaction network even though I can define it mathematically as a network, and I can mathematically put this process on it.

Facebook网络对于这类情况来说，感觉更真实一些。

The Facebook network feels a little bit more genuine for something like that.

我想你可能在谈到根据性别、班级年份对高中校友的同质性进行统计时已经触及这一点了，论文后面提到，高中在大型大学的社会组织中扮演的角色，比在小型机构中更重要，因为在小型机构中，来自同一高中的学生对通常较少。

So I think you may have already hit this point when you're talking about the tabulating assortativity based on gender made residents class year in high school and how these say later in the paper that high school plays a greater role in the social organization of large universities than it does at smaller institutions where there are typically fewer pairs of people from the same high school.

对。

Right.

这里有一个问题，和你刚才提到的另一个观点相关，我想看看这是否其实是一个问题：你说由于不同机构初期对Facebook的采用率不同，数据所代表的单一时点，可能有效地反映出在线社交网络形成的不同阶段。

There's this question for me that relates to another statement you've made here, and then I'll see if this is really all actually one question, where you say because of the different rates of initial Facebook adoption at different institutions, the single point in time represented by the data might usefully describe different stages in the formation of an online social network.

我正在思考我刚刚和艾莉森·戈普尼克关于探索与利用权衡的对话，或者更具体地说，关于儿童发展过程中行为模式的变化。

I'm thinking about the conversation I just had with Alison Gopnik about explore exploit trade offs or in, like, childhood development and how patterns of behavior change.

就像，我刚才想到，天啊。

Like, there was I've oh god.

我忘了是谁做的了。

I'm forgetting who did it.

我会在节目笔记里查一下，但这项工作出自杰夫·韦斯顿关于扩展和睡眠作用的研究，也就是为什么孩子需要睡得更多。

I'll look this up for the show notes, but the work that was on it was it came out of, I think, Jeff Weston on scaling and the role of sleep and, like, why it is that kids sleep so much more.

我想听听你的看法，一方面你说不要用疾病传播模型来研究蛋白质网络。

Curious what your thoughts are about because on the one hand, you're saying, like, don't use a disease spread model and protein networks.

嗯，

Well,

从数学上讲，你当然可以这么做。

math math mathematically, you can do it.

只是你稍微脱离了现实而已。

It's just a matter of you're suspending reality a little bit.

但数学家们经常脱离现实。

But mathematicians suspend reality all the time.

我肯定写过一篇论文，用过疾病传播模型在那种网络上的例子，但我真正想做的，是用数学方式描述疾病在不同结构网络上的传播机制。

I am sure that I have a paper in which I've used an example of a disease spread model on that, but what I'm really trying to do is to make a mathematical statement of how the disease spread works on a network with a different structure.

从数学上讲，我有权这么做。

Mathematically, I'm allowed to do it.

但当你开始思考这个例子时，你会觉得，嗯，这有点奇怪。

Just when you start thinking about the example, you're like, well, that's weird.

所以我想我真正想问的是，你认为这些发现能否推广，或者以某种方式与更广泛的网络增长理论联系起来，无论是社交网络还是生物系统？

So I guess I guess what I'm actually shooting for here is do you think that these findings generalize or, like, hook into in any way kind of a broader statement on the growth of networks, whether they be in social or biological systems?

是的。

Yeah.

我不确定。

So I'm not sure.

我要说的是，我提到的那篇由艾伦、约翰和他们的团队撰写的论文，实际上直接研究了Facebook网络的增长。

I will say that the paper that I mentioned by Aaron and Johan and company do actually that paper actually directly deals with the growth of of Facebook networks.

所以就你提到的更直接的问题而言，确实有一篇论文专门研究了这一点，并且在这些例子中似乎确实如此。

So in terms of the sort of more kind of immediate question, there is actually a paper that studied that explicitly, and that does appear to be the case for these examples.

至于更普遍的情况，我其实不太清楚，因为虽然我听说过你提到的一些研究，但我并不熟悉那些具体的论文。

In terms of more general, I don't really I don't really know because, I mean, I've heard of some of the works that you're mentioning, but I don't, like, I don't think I know those specific papers, for instance.

我想提一下同配性，因为我觉得这实际上是另一个问题。

One thing I wanna mention about assortativity because I actually think it's a bit of a different question.

你好像在说你不确定这是否是同一个问题。

Think you were saying you're not sure whether it was the same question or not.

同配性是一个具体的度量，某种同配性实际上是一种相关性的度量。

Assortativity is a specific measure and a certain measure of assortativity is actually a measure of a type of correlation.

即使我有一个很小的学校，我也可能有很高的相关性值，但同配性更多是通过本身拥有足够多的人数来影响结构的。

The idea is that even if I have a small school, I could have a very high value of that correlation, but that assortativity is impacting the structure more just by having enough people in the first place.

所以这不仅仅是测量那个问题。

So it's a matter of it's not just measuring that.

让我告诉你，我可以跟你讲讲这个计算的来源，以及论文中那些评论的由来。

So let me tell you, I can tell you a little bit about where that calculation came from and where those comments in the paper came from.

我不知道现在是否还这样，但以前感觉确实是这样的。

I don't know if this is still true, but it felt like this is true before.

你完全可以去批评一位社会学家。

You could you could kick a sociologist.

我不建议这样做。

I don't I don't recommend doing this.

你可以踢一位社会学家，他们会回应说：这是因为同质性。

You could kick a sociologist and they'll respond with, that's because of homophily.

这是因为同质性。

It's because of homophily.

那个评论的实际意思是：不，社区结构并不仅仅是同质性。

The actual point of that comment was that, no, in fact, community structure is not just homophily.

同质性是一个标量指标，旨在反映同质性的某种特征。

Assortativity is a scalar measure that is supposed to give some signature of homophily.

它并不是严格意义上的同质性，但它的目的就是如此。

It's not literally homophily, but that's what it's supposed to do.

关键是，这两种情况下同质性都可能很高，但社区结构及其影响会因人数不同而有所差异，以此区分这些中观结构并不仅仅是由同质性造成的。

The idea is that assortativity could be high in both cases, but the community structure and the effect on it would be different depending on the numbers trying to distinguish that these mesoscale structures are not just homophily.

所以，那个评论正是源于此。

So that's actually where that comment came from.

这仅仅是基于我说我有很高的相关性。

And that's just coming from saying I have a high correlation.

我有很高的相关性。

I have a high correlation.

我测量了一个相关性。

I measure a correlation.

这种相关性的测量及其对社区结构的影响，将取决于这类因素的数量。

And the measurement of that correlation and in terms of the impact on community structure is going to depend on how many of those things are there.

所以，社区结构的计算是一种不同的计算方式。

So the idea is that the community structure calculation is a different calculation.

它处于系统的不同尺度上，并不仅仅是同质性。

It is at a different scale of the system and it's not just homophily.

所以我认为这是另一个问题。

So I think that's a different issue.

不管怎样，这正是我们的想法，对吧？

Anyway, that's what we were thinking, right?

所以，我们当时写的就是这类内容。

So that was the type of thing that we were writing there.

我们是在回应那种‘这只是同质性’的说法，当时我看到太多次了。

Were reacting to the it's just homophily refrain that at the time I was seeing too many times.

我认为这和不同规模的网络在增长时发生的情况是不同的问题。

I think that's a different issue from what happens with networks of different sizes as they grow.

这更多是介观尺度上的某种现象，而不是另一种测量方式。

It was more something's in a mesoscale versus something is a different measurement.

是的。

Yeah.

因为我自己确实也陷入过你所批评的那种社会学家式的思维，读到这些时，我忍不住想：任何有过一定国际旅行经历的人都知道，同质性在敌对社交网络中占主导地位，因为你总会遇到这些……嗯，非常明显的例子。

Because I definitely I think I found myself going into the kick a sociologist kind of thinking that you're critiquing here, reading this and just wondering it strikes me anyone who's done any amount of, like, international travel knows that homophily dominates hostile social networks because you have these Well like, very Yeah.

但同质性实际上指的是互动。

But it's but homophily is referring though to interactions.

它指的是微观层面的东西。

It's referring to a microscale thing.

那么问题来了，介观尺度和微观尺度会受到什么影响？

Then there's the question is what is the impact on a mesoscale and a microscale?

这就是为什么我说它们并不是同一个问题。

That's why I'm saying I don't consider them to be the same question.

同质性非常重要，但并不是唯一在发生的事情。

So homophily is very important, but it's not the only thing going on.

我想听你进一步补充一点细微差别，因为我在你多篇论文以及你在圣塔菲研究所的演讲中都听到过，关于网络结构的许多思考往往假设模型中只存在成对互动。

So there's another piece of nuance I'd like to hear you add to this because I've heard you say in numerous papers as well as in the talk that you gave at SFI that, like, a lot of the thinking on network structure tends to assume pairwise interactions in the model.

因为这是最简单的方法。

Because that's the easiest thing to do.

对。

Right.

但如果你仔细观察现实，就会发现，嗯。

The reality is if you look at this, it's like, okay.

是的。

Yeah.

作为初步近似，比如某人是否接受你的好友请求之类的，但确实存在一些情况。

As a first pass approximation, whether somebody accept your friend request or whatever, but, like, there are Right.

这个问题涉及很多不同的方面。

There's so many different pieces to this.

我们这么做是因为我们知道如何做，而不是因为我们认为这就是终极解决方案。

So we do it because it's we do a lot of these things because we know how to do them, not because we necessarily think it's the be all and end all.

如果你要超越成对互动，或者要处理随时间变化的互动，或者要处理多种类型的互动、多种沟通渠道、多种关系类型，你最终会得到一个更复杂的数学表示。

And if you're gonna go beyond pairwise interactions or if you're gonna go to have interactions that change with time or if you're gonna go to have interactions that have maybe multiple types of interactions, multiple communication channels, multiple types of relationships, you're going to end up having a mathematical representation that's more complicated.

我花了很多时间研究其中各种情况，其他人也花了大量时间研究各种情况。

I've spent a lot of time studying various ones of those, and other people have spent a lot of time studying various ones of those.

这是一件非常有趣的事情，而且有充分的理由去做，因为正如我在演讲中常说的是，人们并不会真的拿着别人也拿着的棍子。

It's a very cool thing to do and there's good reason to do it because in the way that I probably phrase it in my talk, because I often phrase it that way, people are not walking around holding sticks that other people are holding.

即使说两个人是朋友，他们之间也存在一系列潜在的互动——电话、邮件、一起看电影、外出吃饭等等，这些你都看不到，却用一个矩阵中的数字来表示，说这两个人握着一根棍子，我们用数学模型来表示人们握着一根特殊的棍子，但这并不是我们实际看到的情形。

Even the notion of saying two people are friends, there is this latent set of interactions between them, phone calls and emails and going to the movie and going out to eat and whatnot, that you're not seeing and you are representing as a number in a matrix saying that these two people are holding and attached to a stick and we're and we're using a mathematical representation that says people holding a special ticket stick and that's that's not what we see.

对吧？

Right?

我们看到的是两个人一起吃晚饭之类的。

What we see is two people are having dinner together or whatever.

对吧？

Right?

好吧，希望你不会看到这些，因为你不应该去跟踪他们，但这些互动，我们 somehow 将这些互动表示为一个网络。

Well, hopefully, you don't see that because you shouldn't be stalking them, but interactions, and somehow we represent the interactions as as a network.

是的。

Yeah.

我经常很刻薄地做出这样的评论。

I'm very snarky and make comments like this all the time.

抱歉。

Apologies.

但无论如何，我们正在用一个数学对象来表示某些东西，即使我们包含了这些细微的非成对互动等等，它也远比现实简单。

But in in any event so we're representing something in a mathematical object that even when we include a bunch of these nuances, non pairwise interactions and so on, is a much simpler thing than reality.

这是对现实的极大简化，你总是需要担心：当你获得现实，然后从现实中获取数据——而这些数据本身已经做了一些简化，再将它们转化为你研究的数学对象时，你会意识到，好吧，如果我把它转化为一个数学对象，我可以说我可能对这个数学对象做出了精确的陈述，即使那样也存在近似，但我们就假设我确实这么做了。

It's a gross simplification of reality and you always have to worry that when you get reality and then you get data from reality, which is already making certain simplifications, and that you then turn it into a mathematical object that you study, you know, there's this thing of, okay, if I turn it into a mathematical object, I can say that potentially I am making a precise statement about the mathematical object, although even then there's approximations, but let's suppose that I'm doing that.

现在我对这个数学对象做出了一个精确的陈述，我想把这个陈述延伸出去，推断并说明一些关于现实世界的东西，尽管这个数学对象只是现实的简化。

Now I've made a precise statement about the mathematical object and I want to turn that statement and imply something and say something about the real world even though the mathematical object is a simplification of the real world.

你必须警惕，因为选择以某种方式表示事物时，会产生一些人为的假象。

You have to worry because there are artifactual things that occur by choosing to have represented something in a certain way.

而我们的期望是，你对这个数学对象所做出的任何结论，或许也能告诉你一些关于它所代表的更复杂事物的信息。

And the hope is that something that you then say about this object hopefully can tell you also something about the more complicated thing it's representing.

因此，当我们处理这种成对互动时，我们知道如何更有效地从数学上研究它们，所以我们花了很多时间在它们上面。

And so when you do something like these pairwise interactions, we know more about how to study them mathematically, so we spend a lot of time on them.

当我们试图推广时，比如多元互动，我在这里 conventionally 使用‘多元’来指代三个或以上的互动，有些人称之为高阶互动。

When we make efforts to generalize, so polyadic interactions and this I'm conventionally using polyadic to mean three plus, so some people call it higher order.

但单元、二元，然后是多元——即三个或以上——当你推广这些概念时，需要对不同的概念进行扩展。

But mono and then dyadic and then polyadic, so polyadic three plus, you need to generalize different concepts.

当你推广这些概念时，我们之前讨论过同质性或 assortativity 的概念。

And when you generalize those concepts so it's we talked about assortativity or ideas of homophily.

标准的同质性概念是一个成对互动的概念。

Assortativity standard type is a pairwise concept.

如果我要将这样的概念推广到多元交互，我会面临多种不同的推广方式，某些推广可能适用于某些问题，而其他推广则可能更适合其他问题。

If I'm going to take something like this and generalize it to polyadic interactions, I will have many different choices of how to generalize it, and some generalizations might be appropriate for some problems, and other generalizations might be appropriate for other problems.

我们需要开展科学研究。

And we need to work out science.

目前很多论文虽然不一定是直接讨论同质性，但在理论层面经常探讨：如果我们把某个概念以不同方式推广到更复杂的数学网络中，会有什么后果？

And this is where a lot of papers are currently not necessarily assortativity per se, but a lot of papers on the theory end are saying, well, if we take a certain idea and generalize it to networks that are more complicated mathematically in different ways, what are the consequences?

我们应该选择哪种方式呢？

Which way should we do it?

因此，目前有很多相关研究正在进行。

So there's a lot of work right now.

实现多元交互的一种方式是使用超图，并将各种方法应用到超图上。

One way of having polyadic interactions is with things called hypergraphs and taking various methods and putting them on hypergraphs.

我认为这在你提到的另一篇论文中有所涉及，把

I think that's on another of the papers that you pulled Putting

那实际上是一个重要的研究，关于超图上的有限置信度意见动力学模型，正是你去年夏天在圣塔菲研究所演讲的主题，我们一定会

That was actually a big that was the sub a bounded confidence model of opinion dynamics on hypergraphs was the subject of the talk you gave at SFI last summer, and we'll be sure to

链接到那个。

link to that.

是的。

Yes.

没错。

Exactly.

所以当你允许三个人在房间里互动，而不仅仅是成对互动时，你可以将意见模型应用其中，并以不同方式推广它。

So you can put an opinion model when you allow interactions with three people in a room, not just pairwise or whatnot, and you can generalize it in different ways.

因此，需要研究如何实现它，如何用数学方法研究这些模型，或者在超图上进行社区检测，而不仅仅是在普通图上，或在具有多体互动的疾病传播中。

And so working out how to do it and how to study those mathematically or doing community detection on hypergraphs, not just on graphs or disease spread where you have poly polypolytic interactions.

你需要弄清楚如何推广某些概念。

And you need to work out how you generalize certain concepts.

很多理论工作都集中在这一点上。

That's where a lot of the theory goes.

比如说，好吧，我有一个更复杂的数学对象。

Say, Okay, I have a more complicated mathematical object.

我想把我认为有用或有趣的研究内容拿出来，现在想在更复杂的数学对象上研究它们。

I want to take the things that I think are useful or interesting to study, and I now want to study them on a more complicated mathematical object.

我该怎么做呢？

How am I going to do that?

有多种方法可以做到这一点。

There's different ways of doing it.

即使在普通图或标准网络的成对情况下可能只有一种或两种方法，但在更复杂的情况下，通常会有更多种方法。

Even in cases where there might only be one or two ways of doing it in a pairwise situation on ordinary graph on standard network, there might be more ways, or usually are more ways.

我常举的一个例子虽然涉及一些流行术语，但其实所有东西都免不了用流行术语。

The example that I tend to like to give, although it involves buzzwords, but I will everything involves buzzwords.

就像《星际迷航》中某一集那样，所有东西都在引用其他东西，因此你必须找到一个基准。

It's like this episode of Star Trek where everything is in reference to something else and so somehow you have to find the baseline.

不是 turtles all the way down（乌龟叠乌龟），而是 communities all the way down（社区叠社区）。

Instead of being turtles all the way down, it's communities all the way down.

但有一种方法叫做奇异值分解。

But there's something called a singular value decomposition.

我不会费心解释它是什么，因为那只是另一个旁支话题。

I'm not going to bother explaining what it is because that's just another side point.

但每个矩阵都有一个奇异值分解。

But every matrix has a singular value decomposition.

你完全可以将一个矩阵分解为具有特定性质的其他矩阵的乘积。

You are guaranteed to take a matrix and to phrase it as a product of other matrices that have certain properties.

你总是可以这样做。

You are always allowed to do this.

好的。

Alright.

我可以将矩阵推广到更复杂的数学对象，特别是所谓的张量。

I can generalize matrices to a more complicated mathematical object, in particular something called a tensor.

你可以自己去查一下。

Again, you can look it up.

不是基努·里维斯主演的，至少目前还不是。

Not starring Keanu Reeves, at least not yet.

那部《矩阵》的续集本来应该叫《张量》。

That should have the sequel to the matrix should have been called the tensor.

但不管怎样，你可以对张量进行操作。

But, anyway, you can do a tensor.

对于张量，有多种奇异值分解的版本。

There are different versions of singular value decompositions for tensors.

然而，你无法保留矩阵版本的所有性质。

However, you cannot keep all the properties of the matrix version.

所以存在一些变体，比如假设你只能保留三个性质中的两个。

So there's a there are variants that keeps say, suppose you're allowed to keep two out of three properties.

好吧。

Alright.

我保留性质A和B，然后推广性质C。

I keep properties a and b and I generalize c.

不允许，我不能保留全部三个性质。

Not allowed I'm not allowed to keep all three properties.

我保留a和b，推广c。

I keep a and b, generalize c.

有不同的实现方式。

Different ways of doing it.

保留a和c，推广b，也有不同的实现方式。

Keep a and c, generalized b, different ways of doing it.

所以，好吧，这里发生的情况并不完全如此，但核心思想是我从图推广到超图。

And so, okay, that's not the precise thing that's going on here, but the idea is that I generalize from graphs to hypergraphs.

我失去了一些保证。

I lose some guarantees.

我必须改变某些东西。

I have to change certain things.

可能发生的状况更多了，它们在数学上具有不同的后果。

There's more possibilities of what can occur, and they have different consequences mathematically.

有些方法可能更适合某些应用，而有些则更适合其他应用。

Some might be more appropriate for some applications, and some might be more appropriate for others.

我们在这些理论论文上花费大量精力，主要是为了弄清楚不同的选择。

A lot of the effort that we spend time on in these theoretical papers is trying to figure out different choices.

我还不知道，我认为大多数人也不知道。

And I don't yet know, and I think most others don't either.

有些人可能声称他们知道，但我并不认为他们真的知道，哪些方法才是真正最好的。

I think they may some people may claim they know, but I don't think that they do, of which ways are actually the best ways to do that.

这实际上让我想到，我可能有点为难你了，但我还是想提一下，因为我们在最初讨论的综述文章中提到的一个例子非常有趣：在现实世界的情境中，社区检测具有切实的社会影响。

So that actually brings me to I might be putting you on the spot here, but I wanted to bring this up because it was a really interesting example in in the survey piece we we first discussed about real world settings in which community detection matter because they have palpable social consequences.

对吧？

Right?

你关于有界信任模型的研究以及你所做的报告，都强调了理解甚至缓解极化现象。

And you've actually the bounded confidence model piece and the talk that you gave emphasized understanding or perhaps even mitigating polarization.

论文开头有一张图，讲的是韦恩·扎卡里对空手道俱乐部的研究，展示了俱乐部内部的分裂过程，你可以在网络的可视化中清晰地看到，当中心无法维系、局势崩塌时，派系将如何划分。

There's this figure early on about research by Wayne Zachary on a karate club and the schism that happens in the karate club and how you can you can see in the visualization of that network exactly how the party lines, if you will, are gonna split when things when the center cannot hold, when things fall apart.

我不愿在此过多停留，但我只想强调一点：不仅在数据收集方式上存在伦理考量，你在做出这些具体选择时也同样面临伦理问题。

And not to, like, linger here, but I just wanna stress and then hear you speak to the fact that there are not simply ethical considerations in the way that this data is collected, but also in precisely the kind of choices that you're making.

因为如果人们试图用这些工具来预测社会结构中的分裂，那感觉就像突然间我正凝视着深渊，现实中决策者真的在运用这些东西。

Because if people are trying to use these tools to predict rifts in social organization, then it's like feel like suddenly I'm staring into an abyss here where, like, decision makers are actually running with this stuff in the real world.

是的。

Right.

情况只会变得更糟。

Well, it only gets worse from there.

关于空手道俱乐部的论文，或者原始的那篇，当然就是著名的空手道俱乐部数据集。

The Karate Club paper or the original one, this is The Karate Club, of course, is an infamous dataset.

我可以说是扎卡里空手道俱乐部的一员，因此这个数据集甚至有自己的维基百科页面。

So I am a member of the Zachary Karate Club, as it were, which so the dataset has its own Wikipedia page.

但即使在所谓的最简单社交网络中，这也不是一个庞大的网络。

But this even in the sort of, quote, simplest social network, and this is not a large network.

共有34个节点，即34个人，如果你仔细看原始论文，会注意到一个我称之为‘笔误’的错误——某个边是否存在并不明确，因为这是一个无向网络，但在邻接矩阵中，某个位置是1，而对应的转置位置却缺失了。

There are 34 nodes, 34 individuals, and if you actually look in the original paper, you'll notice that there is I'll use the word typo, but, like, error where it's not clear if a certain edge should be there or not because it's an undirected network, but then there's an adjacency matrix where there's a one in a certain entry and the corresponding transpose entry, it's not there.

问题是：这两个位置都应该是1，还是都应该是0？

The question is should they both be ones or should they both be zeros?

如果你只是说，而且再次忽略的是，那篇论文中有些版本在连接上还带有数值。

If you're just saying and, again, ignoring the there's some versions in the in that paper that have values on the connections as well.

但即使在最简单的情况下，你已经遇到了混乱，更不用说在数据中，更不用说我们现在研究的那些更复杂的东西了。

But so even in the simplest situations, you already have messiness let alone in the data, let alone in the stuff that we study now and more complicated things.

不过，那篇论文的关键在于，这种分裂其实是一种事后的回溯，对吧？

That paper though, the thing is the schism was really a retrodiction, right?

就像分裂发生时研究正在进行，扎卡里事后才观察到，并说：哦，好吧，也许我本可以根据谁和谁互动来预测到这一点，对吧？

Like it occurred while the study was occurring and so then Zachary looked at it afterwards and said, Oh, okay, maybe I could have anticipated this based on who was interacting with whom, right?

所以这项研究是在分裂发生之后进行的，而不是想象有人是一家公司的顾问，他们做了一项调查，而此时分裂尚未发生，他们请了一位报酬丰厚的顾问网络科学家来检测社群，现在我真的在幻想了。

So the study was occurring after the fact as opposed to imagine that somebody is a consultant for a company and they do a survey and so there has not been a schism yet, and they go to some consultant network scientist who's being paid a lot of money to detect communities, and now I'm really in fantasy land now.

对吧？

Right?

你靠检测社群就能发财。

It's like you're gonna get rich by detecting communities.

也许有人能做到，但并不是学者们在做这件事。

I suppose somebody could, but it's not the academics who are doing that.

无论如何，假设你是一名顾问，有人问你：好吧。

In any event, suppose you're some consultant and you're asked, alright.

我们做了一份关于谁和谁在一起的调查。

Well, we get some survey of who's hanging out with whom.

我需要担心是否存在分裂吗？

Do I have to worry about whether there is a rift?

我认为这样说很合理：确实有令人担忧的理由。

I think I think that's reasonable to say, well, there's cause for nervousness.

只要你的结果可能影响人类在现实中的行为，就存在令人担忧的理由。

Anytime your result might impact what a human actually does in real life, there's cause for nervousness.

对吧？

Right?

我认为还有更多更深层次的担忧。

I think there's much more there's much more nervousness than that.

对吧？

Right?

这就是为什么我说这仅仅是开始。

That's why I'm saying it's only the beginning.

比如，如果我开始识别出社群，而我的所有朋友恰好都是已知的恐怖分子，那么人们就会怀疑我也是恐怖分子。

Like, so for instance, if I start detecting communities and all of my friends somehow are known terrorists, then people are gonna suspect that I'm a terrorist.

这是一个随机的例子。

This is a random example.

我应该明确说明这一点。

I should make that very clear.

但人们会怀疑我是恐怖分子，不是因为我本身是已知的恐怖分子，而是因为我的所有朋友都是恐怖分子，他们都出现在同一个社群里。

But people are gonna suspect that I'm a known terrorist because I am or not that I'm a known one, but that I'm a terrorist because all my friends are terrorists who showed up in the same community.

于是，突然间，有人因为被分配到同一个社群，而被某种算法方法盯上。

So all of a sudden, you have somebody, say, being targeted because they were assigned to the same community and some algorithmic method.

对吧？

Right?

这比我仅仅担心公司内部会不会出现分裂更让我担忧，毕竟如果我们不希望公司分裂，也许确实该做点什么来防止分裂。

Like, that worries me a lot more than just purely wondering if there's gonna be a schism in a in a company, and maybe we should do something to prevent a schism in the company if we don't want a schism.

对吧？

Right?

比如，当推断结果开始针对个人时，这比公司内部出现分裂之类的问题更让我担忧。

Like, types of things where the result of an inference start targeting individuals concerns me a lot more than something at the level of a schism of a company.

原则上，你可以使用这些方法。

And you can use, in principle, these methods.

你可以这样想：假设我有一个由20个人组成的群体，他们都自称为红色，因此被标记为红色。

You can literally say, here's a suppose I get a suppose I get a community that has 20 people who all have a label and they're all colored red because they're self identified label that these people are red.

而这个群体中还有一个人没有说自己是红色，但我因为他的所有朋友都是红色，就推断他也是红色。

And there's one other person in the community who did not say that they're red, but now I think that they're red because all their friends are red.

而且他确实有可能是红色的，对吧？

And there is a reasonable chance that they are, right?

这些方法原则上确实可以做到这一点。

And that's something that these sorts of methods in principle can do.

你可以尝试对那些你还不了解的事情做出推断。

You can you try to make inferences about things you don't know yet.

对吧？

Right?

你有已知的标签。

You have labels that are known.

你有未知的标签。

You have labels that are unknown.

但你是如何使用这些标签的呢？尤其是在现实世界中使用，而不仅仅说‘这是一篇论文，颜色是红色’。

But then how are you using those labels, especially if you're using it in the real world and not just saying, well, here's a paper and it's red.

这是一个很大的问题。

That's a big concern.

这是一个非常严重的问题。

That's a very big concern.

所以，谢谢。

So in the thanks.

在我们剩下的时间里，我想特别提到你与米歇尔和埃莱尼·卡蒂福里在2023年1月发表在《今日物理》上的那篇文章，内容是关于数据的拓扑结构。

In the time that we have left, I wanna because did I specifically called out this piece just came out January 2023 in Physics Today that you wrote with Michelle and Eleni Katifori, and this is on the topology of data.

所以，让我们再次摆脱这些伦理困境。

So, again, we're gonna we're let's dig ourselves out of the ethical conundra.

所以我们现在处于2023年1月。

So we are now in we are now in January 2023.

我还应该说明，这是一篇解释性文章。

So this is an expository article, I should also say.

我告诉数学家们，《今日物理》就像是美国数学学会公告的物理版。

Physics Today is I tell mathematicians that this is the physics version of notices of the American Mathematical Society.

我知道这对这个播客帮助不大，但《今日物理》是月刊，实际上是一本杂志，而不是期刊。

I know that doesn't really help this podcast, but Physics Today is a monthly it's actually a magazine, not a journal.

你可以把它想象成给物理学家看的《科学美国人》，对吧？

So think of it like Scientific American but for physicists, right?

它可能比《科学美国人》稍微更专业一些，因为它假设读者具备广泛的物理学背景，但广泛的物理学背景并不意味着是物理教授，对吧？

So it's maybe a little bit more technical than Scientific American because it's assuming kind of a broad physics background, but broad physics background does not mean physics professor, Right?

所以你可以假设，大多数阅读《今日物理》的人，要么拥有物理学或相关领域的本科学历，这就是目标读者群体。

So you can assume that most of the people who get physics today are people who had either a physics or related undergraduate degree and that's the sort of audience.

对吧？

Right?

所以，任何谁

So anybody who What are

我们是在向我们的听众推广这本杂志。

we selling this magazine to our listening audience here.

我猜测

I suspect

哦，抱歉。

Oh, sorry.

是的。

Yeah.

其实我不是靠这个赚钱，我只是想说明一下，抱歉。

Well, that's not I'm actually I make no money from that, but I'm just trying to say what I'm trying to do sorry.

我总是忍不住陷入更深层次的细节中。

I have a tendency to go down into rabbit holes more than I should.

我该做什么

What I'm to do

可能是你把这说得相当吸引人了，好吧。

is is probably you're probably making it sound rather appealing to Okay.

嗯，

Well,

我们的文章就是为了这样的人群而写的，我只是想说明这一点。

our article so that I'm just saying that's who our article is written for.

所以这篇文章的定位应该是通俗易懂的，如果我们做得好的话，作为对比，这些社区和网络实际上也曾出现在数学家们的一个类似平台上，不管怎么说。

So it is meant to be an article that should be accessible, and if we did our job, so just as a contrast, this communities and networks actually appeared in an analogous venue for mathematicians for whatever it's worth.

总之，这篇文章发表于一月，篇幅必然很短，因为这是要求如此，而我们本来也想说说这篇文章到底讲了什么。

Anyway, so this came out in January and was necessarily short because it was that's what's required, and we we wanted to I guess I'll say what the article is.

有一个数学领域叫拓扑学，传统上的例子——我们论文里也用了这个例子来铺垫——就是拓扑学家分不清咖啡杯和甜甜圈的区别。

So there's a mathematical subject called topology, and the traditional example, and we do have this example in the paper to set the stage, is that a topologist cannot tell the difference between a coffee cup and a doughnut.

这就像一个常见的说法了。

This is like the standard trope.

我们想象的咖啡杯有一个把手，因此存在一个洞的概念，而甜甜圈也有一个洞的概念。

And we're thinking of a coffee cup that has a handle, so there's this notion of a hole, and a doughnut has a notion of a whole.

对吧？

Right?

你正在看一个甜甜圈。

You're viewing a doughnut.

我们不知道外面发生了什么，但这里有一个洞，而咖啡杯是一个整体，有一个洞。

We don't know what's going on the outside, but there's a hole, and the coffee cup is one piece and one whole.

甜甜圈也是一个整体，有一个洞。

And the doughnut is one piece and one whole.

现实物理世界有更多复杂性，比如甜甜圈的横截面是什么样子等等，但我们忽略这些因素。

Now physical reality has more complications than because of what a cross section of a donut looks like and so on, but we're ignoring stuff like that.

而数据本质上是离散的，对吧。

And then data is discrete, right, in its very nature.

对吧？

Right?

我们把它输入到计算机中。

We put it into a computer.

我们在对其进行离散化，于是你面前就出现了一堆点。

We're discretizing it, and you have a bunch of dots on a page.

所以现在你需要想象一堆分布在页面上的点。

So you're supposed to imagine now a bunch of dots on a page.

这在技术上被称为点云，你会问自己一个问题：我能否用这种视角来判断两个事物是否相同，比如它们是否具有相同数量的孔？

This is a technical name for this as a point cloud, and you ask yourself the question, can I use this lens of trying to say that two things are the same if they have, like, the same number of holes?

在数据上，我该如何实现这一点？

How do I do that on data?

有什么方法可以理解这一点？

What is there to make sense of that?

总的来说，这篇论文就是关于这个的，然后它特别使用了具有物理性质的示例。

That's broadly speaking what the paper is about, and then it specifically uses examples that have a physics nature.

我们选择了其中一些具体的例子。

We chose specific ones.

我们实际上在研究软物质物理等领域的内容，但那些具有物理性质的东西还包括宝可梦，不过宝可梦更多是在引言部分提到，并不属于真正的软物质。

Were really doing things from soft matter physics and so on, But stuff that has a physics nature and also Pokemon, that was more in the introduction, not really soft matter.

不过我想，胖丁大概是很柔软的。

Though I guess I imagine Jigglypuff as being fairly squishy.

我不确定这一点是否已被确认。

I don't know if that's been established.

但好吧。

But okay.

所以你有一个点云，我想谈谈如何观察这个点云的形状，也就是它的拓扑结构。

So you have a point cloud, and I wanna talk about how I can look at that shape of that point cloud, that topology of that point cloud.

因此，你可以想象自己在做这件事，这是一个非常视觉化的话题，如果不展示一些内容，很难讲清楚。

And so what you imagine doing, this is a very visual subject, it's hard to do this without showing you stuff.

但你可以去看论文，并想象自己在做这件事。

But you can look at the paper and you can imagine doing that.

我们来玩一个连点成画的游戏。

Let's take a connect the dots type game.

明白吗？

Okay?

所以你有一堆点。

So you have a bunch of dots.

现在，我不用线连接它们，而是想象眯起眼睛，让这些点变得稍微模糊一些。

Now instead of connecting them with lines, I'm going to imagine squinting and making these dots slightly blurrier.

所以，如果两个点足够接近，当我给每个点想象一个圆盘时，它们最终会重叠。

So two dots that are close enough together, if I imagine that I'm putting a disc around each dot, they eventually overlap.

于是我眯起眼睛，它们就重叠了。

So I squint and they overlap.

所以想象一下，我有足够的点来实现这一点。

So imagine that I have enough dots to do that.

人类非常擅长看着这些点，说：嘿，那是一个宝可梦。

Human beings are really good at looking at this dot, the set of dots and saying, hey, that's a Pokemon.

这不仅仅是一堆随机的点。

It's not just a random collection of dots.

那里确实存在某种形状。

There is some shape that's there.

但你希望有算法能做到这一点，让计算机也能做到，并且在你还不知道答案的情况下也能实现。

But you wanna get algorithms that do that, and you want computers to do that, and you wanna do that in cases where you don't already know the answer.

因为如果你只在已经知道答案的情况下才这么做，那你可以用更简单的方法。

Because if you only did this when you already know the answer, you could just do something simpler.

对吧？

Right?

所以你要构建的方法，即使在不知道答案的情况下也能做到这一点。

So you wanna build methods that can do this even when you don't know the answer.

因此，Jigglypuff的例子展示了我们正在逐渐把这些点变得越来越大。

So the Jigglypuff example is showing that we're gradually making these dots bigger and bigger.

首先，你会开始看到一些可识别的特征，比如Jigglypuff的眼睛。

And first, you start getting identifiable things like Jigglypuff's eyes.

所以，这是某种二维生物的眼睛，在这种情况下，因为它画在纸上。

So the eyes of some, well, two dimensional creature in this case because it's on a piece of paper.

然后你最终会形成这些点。

Then you eventually make the dots.

首先，特征会出现。

First, features appear.

你可以想象，我正在改变这些点的大小，特征就会首先出现。

You imagine I am varying the size of these dots and features first appear.

接着，点变得更大，眼睛逐渐填满，然后又消失了。

Then eventually the dots become larger and the eyes fill in and then they disappear.

你会根据这些点的大小来追踪特征何时出现（即被‘诞生’），以及特征何时消失。

You track as a function of the size of these dots when do features appear, they are called to be born, and when do features or disappear?

它们被称为‘消亡’。

They're called to die.

我知道你看不到我的空气引号，但无论如何，你可以想象此刻正伴随着口头的空气引号。

I know you can't see my air quotes, but, anyway, you can imagine verbal air quotes are occurring right now.

因此，这给你提供了一个特征的持续时间。

And so this gives you a length of a feature.

人们使用的术语是持久性。

The term that people use is persistence.

对吧？

Right?

所以这是在使用一个英语术语。

So it's using an English term.

这实际上是数学术语成为精确版本的少数情况之一。

It's actually one of the times where the mathematical term is a precise version.

它提供了正确的直觉。

It gives the right intuition.

你有这些用于测量持久性的算法工具。

You have these algorithmic tools that measure persistence.

对于固定的点大小，我可以使用拓扑学思想。

For a fixed dot size, I can use topological ideas.

我固定点的大小，然后可以使用拓扑学思想。

I fix the dot size and I can use topological ideas.

在处理数据的形状和拓扑时，你希望关注那些在一系列连续的点尺寸或你可能变化的尺寸范围内持续存在的特征。

What you try to do for the shape of data, for the topology of data, is you want to look at features that are there for a large set of contiguous dot sizes or contiguous sizes that you might be varying.

点尺寸是你可能变化的一个因素，但如果你研究的是其他东西，这时这篇说明性论文中关于‘哀悼部分’的内容就派上用场了——你可能变化的是别的东西。

A dot size is one thing you could vary, but if I'm studying something else, this is when the mourn parts of this expository paper come in, it might be something else that you're varying.

理想情况下，这应该受到你系统物理特性的启发，比如本文的情况，但也可能受到某种领域知识的启发。

It might be ideally something that is informed by well, in the case of this article, the physics of your system, but it could be informed by some domain knowledge of some type.

对吧？

Right?

因此，你以一种受领域知识启发的方式进行这种数学构建。

So you do this mathematical construction in a way that is informed by domain knowledge.

我和我的合作者也在这方面发表过若干研究论文。

And there are various research papers that I and my co authors have also done on this.

这就是我们采取的视角，我们已经做了大量工作，比如处理各种类型的地理空间数据。

That's the perspective that we've taken to try to put so we've done a bunch of stuff with, like, different types of geospatial data, for instance.

我想在这里稍作停顿，因为今天早上我刚参加了一个关于人工智能与理解的对话，参与者是我们SFI行动网络的几位成员。

I'd like to hairpin out here for just a moment because I just sat in on a conversation with several of our people for the SFI Action Network this morning on AI and understanding.

我们的一位研究员阿尔谢尼·莫斯克德维奇指出，他认为大型语言模型的未来将是经过精心挑选的定向数据集，而不是这种大规模的抓取方式。

And one of our fellows, Arseny Moskdevichev, made the point that he believes that the future of large language models is gonna be carefully curated targeted datasets rather than this enormous, like, mass capture approach.

这一点很好。

And that Okay.

如果我们真的想与这些类似ChatGPT的系统协同工作，那么我们接下来要做的，听起来就像你所说的那样，我想确认一下你的观点。

That if we really want to work symbiotically with these chat GPT style systems that we're going to start doing is sounds like this is what you're saying, and I just wanted to check this on you.

你确实需要引入一种筛选方法。

You do need to bring in a curatorial approach.

作为人类，你正在为数据的筛选提供领域专业知识，对吧。

You as the human being are lending domain specific knowledge Right.

这些系统实际上正在处理的数据。

To the curation of the data that these systems are actually

正在处理。

chewing through.

对。

Right.

所以我认为这两者之间是有重叠的。

So I don't I think there is overlap between that.

我不确定它们是否完全相同。

I don't know if they're exactly the same.

我没看到那场对话，但我认为‘筛选’这个词至少是一个还算恰当的用词。

I didn't see the conversation, but I guess curation's not that's I think that's at least reasonably a reasonably apt word to use.

本质上来说，你知道，人们在研究中做的各种事情都可能让我吐槽。

It's basically like I you know, there's various things that people do in the research that can go make me rant.

但拓扑工具在数学上具有一种抽象性。

But so the topological tools mathematically have a certain element of abstraction.

而在过去几年里，人们正在让这些工具的软件变得越来越易用。

And right now, in the past few years, they're in the process of people making more and more accessible software and so on.

我刚才提到，我们希望特征更长一些，因为那些我们认为更有用，但这取决于你调节的参数。

I was mentioning that, okay, we want features that are longer because those are the ones that we think are useful, but that depends on the knob that you're tuning.

我们所考虑的这个参数，比如点的大小，必须是一个合适的调节项，因为如果选错了，你只是简单地说‘更长的特征更好’，那就会有大量现成的方法和代码，有人可能会说：‘我就用这个包，它说这个特征更长，那这就是我的算法输出，这些就是正确的特征。’

This was the size of the dot as we're thinking of a knob that we're tuning, needs to be an appropriate knob because if it's not, if you just say, oh, a longer feature is better, you've got bunch methods that are out there and code that's available and somebody says, well, I'm just going to use this package and this thing said that this feature is longer and now here's the output of my algorithm and I'm going say these are the features that are right.

这就像是，好吧，让事情更易用确实很棒，我非常支持这一点，但随之而来的也有相反的风险：人们不会明智地使用它，只是简单地认为‘越长越好’，于是我就把这东西丢进机器里，然后直接拿输出结果当答案。

It's just like, okay, it's great to make things more accessible and I'm strongly in favor of that, but then there's also the reverse risk that goes through it and the people don't use it intelligently and are just like, oh, longer is better and so therefore I'm just going to say that I'm going to put this in the machine and I'm to just, here's the output of my thing.

比如波特写了篇论文说‘越长越好’，因此这就对了。

Well, Porter wrote this paper and said that longer is better and so therefore this is right.

但其实并不是这样。

And it's like, well, no.

当然，这种事情在其他领域也发生过，对吧？

And of course, this has happened with other things too, right?

这在社区检测和其他各种工具上确实都发生过：当一些远离开发过程、缺乏对潜在问题深入思考的人使用这些工具时，他们会说：‘我可以直接信任这个在线发布的、易于使用的工具的输出结果，只要把它套用在我最喜欢的數據集上就行，根本不用去思考我研究的问题本身。’我认为这绝对是个问题——我希望工具能易用，也希望人们使用它们，但我更希望人们能明智地使用，认真思考自己研究的问题，确保得出的结果是合理的。

It happens certainly has happened with community detection, happened with all these other tools where by the time somebody who is removed from a lot of the development and thinking about what can go wrong is using it, they're saying, well, I can just trust the output of this thing that has been put online that's easy for me to use without putting it on whatever my favorite dataset is, without actually thinking about the problem I'm studying, and I think that's definitely the I want tools to be accessible and I want them to use it, but I want people to try to use it intelligently and that you think about the problem you're studying, make sure that the answer makes sense.

而解决问题的方法绝不是让工具变得难以使用，或者阻止人们使用，因为我觉得这也是个错误，关键在于领域知识非常重要。

And there's just the answer is not to make tools hard to use and for people not to use them because I think that's a mistake as well, but just when Domain knowledge matters a lot.

领域知识真的非常重要，而且常常存在一种危险：认为‘现在有个工具用起来很简单’。

It really matters a lot, and and there's often a danger of saying, well, here's now a tool that's easy to use.

于是就盲目地把它应用到所有事情上。

Let's apply it to everything indiscriminately.

这确实是我们在科学传播中每天都会遇到的一个基本问题。

That's certainly a kind of a base issue that we run up against on a daily basis in science communication.

对吧？

Right?

数学形式化的精确性与语言类比的易懂性之间存在矛盾。

There's the the specificity of a mathematical formalization versus the accessibility of a verbal analogy.

而且人们不喜欢，人类就是不喜欢，他们就是想知道，答案是肯定还是否定？

Well, and people don't like humans humans just don't like they they it's like they wanna know, is the answer yes or no?

嗯，也许是吧。

It's like, well, maybe.

像我这样理解这些问题的人，会欣赏其中的细微差别。

Like, I and someone who understands the issues is going to appreciate the nuance.

但如果你解释得太多细节，整体图景就会被淹没。

But if you come if you explain too much of the nuance, then the big picture gets lost.

但如果你忽视了，就会有人问：为什么你们还没治好癌症？

But if you ignore the it's like, oh, why haven't you cured cancer already?

嗯，就是这样，抱歉。

Well, it's like, well, sorry.

哦，你的理论变了。

It's like, oh, your theory changed.

这些科学家到底在干什么？

What the hell are these scientists doing?

其实，我们一开始就没打算用绝对的术语来告诉你这些。

It's like, well, we were never trying to tell you things in absolute terms in the first place.

我理解科学传播有多难。

I appreciate how hard scientific communication is.

我总是想表达细节，这就是为什么我的论文里有这么多括号注释。

I always want to speak in nuances, and I don't like to this is why my papers have so many parenthetical comments.

就连对科学家来说，我也不想假装这些细节并不存在。

It's just like, well, even for scientists, I don't want to pretend that the nuances are not there.

但如果加得太多，就会影响阅读的流畅性。

And then if you put in enough of them, there's a cost to how easy things are to read sometimes.

因此，即使在与专家交流时，也存在一种平衡，当你与其他人群交流时更是如此。

And so there's a balance even when you're talking to to an audience of experts, there's really a balance when you're talking to others.

所以，我的意思是，我非常喜欢这些工具，喜欢研究它们，我认为这正是科学的意义所在。

So I mean, it's I love these tools, I love working on them, and I think science means that.

好的。

Okay.

我不是科学传播者，但偶尔也参与过一些文章的撰写，我也很喜欢这种工作。

I'm not a science communicator, but I've occasionally dabbled in some of these articles and I love that too.

但当人们希望我抛开所有细微差别来说话时，我真的——我在一开始就说过了，我讨厌把问题掩盖起来。

But it's just like when people want me to say something without a nuance, I really and I told this to at the beginning, I hate things being put under the rug.

我真的很反感这样做，因为那样的话，别人就会说，哦，你可以做x。

I really I just there's a fundamental dislike that I have of doing that because then someone's like, oh, you can do x.

然后过一段时间，你发现其中一个细微差别其实非常重要，结果发现并不是x。

And then suddenly later, you figure out something where one of those nuances turned out to really be important, and you it's not x.

而是变成了x'。

It's now x prime.

他们就会说：你怎么敢？

And they're like, how dare you?

为什么现在变成了 x'？

How come it's now x prime?

其实，从绝对意义上讲，它从来就不是 x。

It's like, well, it was never x in absolute terms in the first place.

所以我认为，这为我们提供了一个机会，可以重新回到数据拓扑的明确讨论，因为是的。

So this, I think, actually gives us an affordance to double back into this the explicit discussion of the topology of data because Yeah.

还有你的其他工作，我们甚至还没谈到，但我稍后会链接一篇相关文章。

And also your other work, we didn't even get to this, but I will link to a piece.

你曾与丹尼·巴斯特共同参与了一个大团队的研究，对吧？

You were on a big team that Danny Bassett coauthoring Right.

《学习过程中人脑网络的动态重组》。

The dynamic reconfiguration of human brain networks during learning.

这里还有另一个关于时空尺度和层次组织的绝佳例子。

And here's, like, another here's another great example of spatiotemporal scales and hierarchical organization.

这是真实的数据，而且是大脑数据，所以非常复杂。

It's real data, and it's brain data, so it's really complicated.

对。

Right.

但我觉得，也许这里并不是适合讨论这个问题的地方。

It's like though we think about maybe this is not the place to live this.

但从集体学习的角度来看，作为一种过程的输出，需要在专家和非专家之间进行沟通，而这并不是单维的。

But in in terms of, like, collective learning as a an output of process in which things have to be communicated between experts and nonexperts, and that's not a one dimensional thing.

对吧？

Right?

我们上一期和保罗·斯马尔迪诺以及阮团队讨论过，专家识别是一个高度多维的问题，因为专家遍布于越来越多的领域，而这个问题确实如此。

We talked about that in the last episode with Paul Smaldino and team Nguyen talking about expert identification is highly dimensional problem with, like, experts in this proliferating number of myriad of domains and question of yeah.

总之，我想说的是，我看到这些关于理论的问题，比如有人用过Adobe Illustrator或其他矢量绘图程序，就会思考Jigglypuff每个点周围圆盘的宽度问题。

So at any rate, what I'm getting at here is that I see these theoretical questions about somebody's used Adobe Illustrator or some kind of other vector illustration program that this question of how wide the disc around each dot of Jigglypuff.

我对于这类考量的后果有一种直觉，特别是当你尝试给这个东西填充颜色的时候。

It's gonna gonna there I have an intuition around the consequences of these kinds of considerations based on if you try to put, like, a color fill into this thing.

如果它是一个小点，那么颜色就会从你概念上视为一个物体的区域中渗出。

And if it's a tiny dot, then the color bleeds out of this thing that you conceptually consider an object.

对。

Right.

所以无论如何，作为应用数学家，我们在这里要说明的是，理论与实践之间存在联系，以及在何种层次上适合作出解析和研究。

So at any rate, there's I guess, what we're laying this is in as an applied mathematician, there is this connection between, again, theory and practice and the levels at which it is appropriate to resolve and investigate something.

这具有重大影响。

And this has big implications.

你提到使用俞和冯的方法来研究城市中的街道网络、雪花和蜘蛛网。

So you talk about using Yu and Feng, use this stuff to study street networks in cities, snowflakes, spider webs.

特别提到杰夫·韦斯特和路易斯·贝坦库尔，他们研究过血管网络的拓扑结构，对。

Call out call out to Jeff West and Luis Betancourt who've looked at vascular network topologies and Right.

所以是城市研究。

So urban research.

是的。

Yeah.

有很多人已经做过这项工作，实际上我们自己没做，但其他人已经用这些工具研究过不同形式的血管网络。

There there's a number of people who've done there's actually we haven't done this, but there's other people who've used these tools for vascular networks of different forms.

已经有不少相关研究了。

There's a bunch there's been a there's been a bunch of work on that.

所以实际上，是的。

So actually yeah.

我这篇论文的合著者埃莱尼·卡蒂福里，以及她的一些研究论文——虽然我没有参与这些论文——就是使用这些想法研究血管网络的人之一。

So my co author on this paper, Eleni Katifori, and some of her research papers, and I'm not I'm not involved in these papers, is one of the people who's used these ideas for vascular networks.

是的。

Yeah.

所以这与杰夫和路易斯等人所采用的方法不同。

So it's a different approach from what people like like Jeff and Luis have done.

对吧？

Right?

也就是说，这是不同的工具，研究的问题也不一样。

Like, it's different it's a different set of tools and different they're asking different questions.

这些系统在某种程度上有相似性，但它们对系统提出的问题却截然不同。

Somehow the systems have similarity, but they're asking really different questions about the system.

是的。

Yeah.

你能再稍微澄清一下吗？

So could you clarify that just a bit?

因为，没错，我只是想把这个问题想清楚。

Because, yeah, I just I wanna get my head straight on this.

对。

Right.

所以，从拓扑学的角度来看，人们可能会提出这样的问题：首先，好吧。

So the type of questions that one might do for this from the sort of topological lens is, okay, you first say, okay.

我有一个数据集，我可以直接问：它里面有没有空洞之类的？

I have a dataset, and I can just ask, do I have holes in it and so on?

然后你会想：在这个特定的应用背景下，‘空洞’到底意味着什么？

Then you say, well, what does a hole even mean in the context of this particular application?

当我们研究街道网络时，这是一篇论文中的一个例子，该论文包含了一系列示例。

When we were doing the street networks, this was an example in a paper that was a sort of set of examples.

这是另一篇论文，我们之前已经发表过一篇理论性论文，但由于应用数学的出版速度比物理学慢，那篇前期论文的实际发表日期反而更晚。

This is another one of those papers where we had a prior theory paper, although because applied math publishing is slower than physics publishing, the prior paper actually has a later publication date.

但不管怎样，有一篇论文介绍了相关方法，然后我们想，既然我们已经投入精力去实现这些方法，

But anyway, there was a paper that has methods and then we're like, well, we spent effort trying to do these methods.

不如再写一篇面向不同读者群体的论文，包含其他多种应用，包括街道和蜘蛛网。

Let's also have a paper that we write for a different audience that has a bunch of other applications, including the streets and the spider webs.

其中，街道应用是最重要的一项，在这篇论文中，街道应用是由Michelle Feng和我共同完成的，也是最核心的部分。

The street application was the most serious one and after this is Michelle Feng and me, the street application was the most serious one in that particular paper.

我们当时关注的并不是一个点逐渐变大，

What we were looking at was we did not have a dot getting bigger.

而是以一种不同于那种方式来定义我们的参数和调整对象。

We actually defined our parameter, our thing that we tune in a different way than that.

我还没有解释过我们是如何定义这个参数的具体方式。

There was a particular way that I have not explained in how we defined it.

这样做的目的是要说明：如果我取城市街道网络的一小部分，我得到的是像洛杉矶那样网格化且单调的结构，还是更有趣的结构？

And what this is meant to do is to say locally, if I take a small part of the street network of a city, am I getting something that looks grid like and boring like LA, or am I getting something more interesting?

洛杉矶是这个数据集中最单调的例子之一，因为它的街道结构非常规整。

And LA is one of the most boring examples in that dataset because it's a street structure.

还是我得到的是像伦敦或欧洲大陆城市那样的结构，它们有死胡同和其他各种复杂特征？

Or am I getting something like London or a city in Continental Europe that has dead ends and other various things?

比如，我认为我们在论文中展示过一张图片，是巴塞罗那之类的城市，那里有各种不同的街道布局。

Like, one of the ones that I think we show a picture of in the paper is, like, Barcelona or something that has a bunch of different things go going on.

因此，我们关注的是这类局部结构。

And so it's getting at a local structure of things along those lines.

还有其他人尝试用不同的方法研究局部结构。

So There's other people who've tried to get at local structures with different methods.

我之前提到过的马克·巴托洛梅就是其中一位研究者。

Mark Bartholomew, who I've mentioned before, is one of the people who's done that.

事实上，在我们的论文中，由于他们研究的是一个相似的科学问题，只是采用了不同的数学方法，我们甚至在一个小节中直接与他们的论文进行了对比。

In fact, in our paper, we even because they were really looking at a similar question scientifically but just a different mathematical approach, we even have a direct comparison in a sort of subsection where we actually compare to one of their papers.

而路易斯和杰夫所做的则更偏向宏观层面。

Whereas what Luis and Jeff are doing is much more at the macro scale.

他们在探讨某些现象如何随规模变化。

They're asking questions about how certain phenomena might say scale with size.

对吧？

Right?

因此，即使系统是来自城市的街道网络，我们所提出的科学问题却处于不同的尺度，且是完全不同的问题。

So even though the system may be a street network from a city, the question that we're asking scientifically is at a different scale and a really very different question about it.

所以，两者之间的重叠之处仅仅在于，好吧。

So where there is overlap is really just, okay.

我们在探讨一个城市的问题。

We're asking a question about a city.

但除此之外，我们所提出的问题就完全不同了。

But then beyond that, everything else is just really different, the questions that we're asking.

是的。

Yeah.

我想我之所以这么想，是因为特别关注了路易莎关于城市结构中网络干预的研究，比如在巴西贫民窟等地实际增加血管网络之类的举措。

I guess I'm just I was thinking specifically to Luisa's work on network interventions in city structure where they're actually adding vascularization into, like, Brazilian favelas and that kind of a thing.

对。

Right.

对。

Right.

因此，这正是可以用这种方法来研究的问题，比如你可以问：这样做会带来什么影响？

So that would be something that one could look at with this approach where you could ask, does doing that okay.

我们还没有讨论过如何实际测量拓扑摘要的各种方法。

So there there are various ways that we have not discussed of how you would actually, like, measure the topological summary.

比如，有一些特定的统计指标是你需要关注的。

So, like, there's certain types of summary statistics of certain things that you would look at.

因此，今天我们把它当作一个黑箱来处理。

And so we're doing this as a black box for the purpose of today.

你可以探讨这些拓扑摘要统计量如何因干预而发生变化。

You could ask how those summary statistics, those summary topological statistics, change based on intervention.

而且即使使用我们自己的代码，你也可以做到这一点。

And using even using actually our code, you could do that.

对吧？

Right?

你可以提出这个问题，去研究这个问题。

Like, you you could ask this question and look at this question.

我们还没有做过。

We have not done that.

如果你做了，你可能会问，这个拓扑摘要是否能提示某种干预措施？

And then if you did that, you would say, well, you could ask, is the topological summary something that might suggest an intervention?

对吧？

Right?

因此，人们可以设想这种做法，即这些测量结果是否有助于实现这一点。

So one could imagine that type of approach asking if these measurements can help with that.

这不是我们做过的事情。

It's not something we've done.

或者在另一个血管网络中，对吧？

Or in another vascular network, right?

街道其实并不是血管网络，但你可以想象一下，你讨论的是营养物质的流动之类的，对吧？

Streets are not really a vascular network, but imagine you're talking about the flow of nutrients or something, right?

在真菌数据上的实验中，我知道这些方法至少有一些变体已经被用于真菌数据了，牛津的马克·弗里克来自他实验室的数据，实际上，我曾与马克·弗里克和李相勋合写过一篇论文，其中发布了这些数据；而在另一篇论文中，丹尼·巴斯特、埃莱尼·卡蒂福里以及一些其他研究者也使用了这些数据并结合了拓扑方法，但涉及不同的论文和合作者。

With experiments on fungal data, and I know that these approaches, at least some variants of them have been used for fungal data, so Mark Fricker from Oxford is data from his lab is stuff that actually, there is data that I was it was released along with a paper that I wrote with Mark Fricker and Sanghoon Lee that in a different paper, Danny Bassett and Eleni Katifori and some various others actually use that data with topological methods, but there's different papers and collaborators involved.

因此，你可以想象，这些真菌实验中，你实际上可以控制实验室的设置，可以设想不同的拓扑摘要能反映出良好的状态，或者某种你可以测量的状况。

And so one could imagine, so these fungal ones, you actually have experimental control of how you set up the lab, and you can imagine different topological summaries being indicative of good situations or of something that you would somehow measure.

我不知道对真菌来说什么是‘良好的状态’，但不管怎样。

I don't know what good situations means for a fungus, but anyway.

但你可以想象先这么做，然后进行干预，从而达到那种状态。

But you could imagine doing that and then doing an intervention that would get you there.

这并不是我见过的一篇论文。

This is not a paper I've seen.

对吧？

Right?

我没见过有人做过这样的事，但我至少能想象这是一个有人会去探索的项目，这是一种可能性。

Like, I've not seen someone do that, but I can at least imagine this as a project that somebody would explore, and it's a possibility.

在试图整合所有这些内容时，我想问你一个可能听起来有点疯狂的问题。

In in there's like, trying to synthesize all of this, and I in so doing, I wanna ask you what is honestly probably kinda an insane question here.

好的。

Okay.

因为这在我看来，并不能仅仅通过拓扑分析来解决。

Because this is not this does not strike me as something that you can get at solely through the application of kind of a topological analysis.

但在这个过程中，你提到洛杉矶有着非常单调的网格状结构，而伦敦则有着错综复杂、很多死胡同的结构。

But in in so doing, you mentioned LA has this really boring grid like structure, and London has this weird convoluted lots of dead ends kind of thing.

这篇文章的最后一页，你谈到你发现研究受精神活性物质影响的蜘蛛所织的网的拓扑结构特别有趣。

And last page of this article, you talk about how you found it particularly amusing to examine the topological structure of spider webs built by spiders under the influence of psychotropic substances.

我应该说明一下这个想法的来源，也许。

I should say where this came from, maybe.

我不知道。

I don't know.

所以，这也是另一篇研究论文中的一个例子，我们决定在讨论这篇流行论文时加入了一点相关内容。

So that was also an example in this other research paper, we decided to include a little bit of it in the discussion of this popular paper.

所以，这个例子原本是为了有趣而设计的。

So it was an example that was meant to be fun.

所以这个想法背后有一段很长的科学故事。

So this idea so there's a couple there's a long story behind this in terms of science.

有一个人叫彼得·维特，他多年前就做过这项研究，后来NASA确实发表过一篇一页纸的论文，内容是他们让蜘蛛服用药物，然后观察它们织出的不同网。

There's this guy, Peter Witt, who is somebody who did this years ago, and there was actually subsequently, there was a one page paper by NASA where they what NASA did is they sent they had spiders and they gave them some drugs and they're like, okay, what are the different webs?

但他们没有说明原因。

And they don't say why.

这项研究在网上可以找到。

Online for this research.

是的。

Yeah.

网上有一段视频。

There's a video online.

有一段半严肃的视频，开头是真实的研究，然后就跑偏了。

There's a semi serious video that starts out with a real study and then goes off on there.

所以这些图片中的一些被传播开来，我记得看到一些图片时就想，这太酷了。

And so there's these some of these pictures got circulated and I remember just seeing some of the pictures and I'm like, that would be cool.

我们可以从拓扑学的角度来做这个。

We could do this topologically.

于是我去找我当时的学生米歇尔，对她说：嘿。

And I go to my then PhD student, Michelle, and I'm like, hey.

这太令人兴奋了。

This is exciting.

顺便说一句，你有个很棒的博士生。

You have a good PhD student, by the way.

嘿。

Hey.

你有没有兴趣把这些拓扑方法用在受药物影响的蜘蛛所织的网上面？

Do you wanna take these topological methods and do this on the spider webs of spiders produced by drugs?

他们说，好的。

And they said, yes.

所以我觉得，这真是个好迹象，说明你有个很棒的学生，他们真的觉得去尝试这个主意不错。

And so I'm like, that's a really good that's a sign that you have a really good student that that they actually think that's a good idea to go and do that.

于是我们决定这么做，顺便说一下，咖啡因蜘蛛和安眠药蜘蛛织的网是最值得关注的两个，所以我来喝口咖啡。

And so we decided to do that, and by the way, the caffeine spider is the the web of the caffeinated spider and the web of the sleeping pill spider are the two to really worry about, so I'm gonna sip coffee.

干杯。

Cheers.

是的。

Yeah.

不过，我们觉得这很有趣，因为它是个有趣的例子。

So the idea though, we were amused by it because it was a fun example on it.

我们喜欢在论文中加入一些有趣的例子，而且我们当时做的是方法类论文，只是想通过一个应用来给你个概念。

We like to include some fun examples in the paper and since we were doing a methods since we were doing a paper that just said, here's application one to give you an idea.

再举第二个应用，让你有个概念。

Here's application two to give you an idea.

这是第三个应用。

Here's application three.

在这篇论文中加入一个有趣的例子是很合适的。

It's a nice paper in which to include a sort of fun a sort of fun application as part of it.

大家都喜欢咖啡因蜘蛛。

Everyone likes Caffeine Spider.

人们觉得这个例子很有趣，所以我很高兴我们做了这个。

It's people get a kick out of the example, so I'm glad we did it.

这正是我想问你的问题，我觉得这正是复杂系统科学一直在追求的风车——它所测试的桥梁。

Well, so this is the question that I had for you, which is it strikes me that this is the kind of windmill that the questing of complex systems science is always going after the bridge that it's testing.

我们真的能跨过这座桥吗？

Can we actually walk across this?

这里的类比真的成立吗？

Is there actually an analogy here that holds?

LSD蜘蛛让我联想到洛杉矶或威奇托式的拓扑结构，而咖啡因蜘蛛则让我想到一种类似伦敦的拓扑结构。

The LSD spider strikes me as like a Los Angeles or Wichita style topology, and the caffeine spider strikes me as a kind of like London topology.