Transcription
All right, here's a game for you. Go to Wikipedia and click on the random page button. Then, from that page, click on the first link. And then, just keep repeating that, always hitting the first link. What do you think is going to happen? Will we wander aimlessly around Wikipedia forever, or will we eventually hit a dead end?
Well, neither. Because actually, roughly 97% of Wikipedia pages lead to philosophy. And I had a lot of questions about this, like, what's so special about philosophy? Or why should we stop at philosophy? Or is this something that's specific to the first link, or will it work with any link that we choose? You see, despite the fact that the philosophy game has been around for a long time, it even has its own Wikipedia article, which, yes, does also lead to philosophy. I've never seen an in-depth analysis of it. So, in today's desperate attempt to get my own Wikipedia article written about me, masquerading as an educational video, we're going to take a look at the structure of Wikipedia and figure out why almost every Wikipedia page leads to philosophy.
With a giant asterisk: the problem with making a video about Wikipedia is that Wikipedia changes a lot. And since I originally recorded that intro months ago, someone broke the philosophy game, and then unbroke it, and then broke it again. Let's just say making this video was a wild ride. But I think it's really cool how it broke, and how it could have been even worse. So, first, let's take a look at the philosophy game as it was when it was working. And then we'll go into how it broke. Of course, things may look different when this video goes up, but the approaches we'll use will stay the same. If anything, I guess it's fitting that a video about Wikipedia is changing as it gets made. Feel free to assume that was intentional.
Okay, so there are, in fact, several types of Wikipedia link games. For example, how many links does it take you to get from, say, banana to Neptune, the planet? It took me seven. But that's not what we're talking about today. The philosophy game is, on the surface, really simple. Like I said at the start, we go to a random page and keep hitting the first link over and over. We'll keep doing that until we hit philosophy, hit a loop, hit a dead end, or exceed over a hundred jumps. So, that last one never actually occurred for me. We'll collect the articles and keep track of how they're linked together in order to make our network.
But how we actually implement that was a bit of a pain. Because telling a computer what the first link is is a bit trickier than it first appears. After all, the first link is not this, but rather it's one of these icons. Obviously, though, these aren't really in the spirit of the game, so we'll ignore them. Next, we'll also ignore International Phonetic Alphabet pages and citations. These aren't true Wikipedia articles; they have slightly different URL addresses, so we'll ignore those as well. Lastly, and most importantly, I want to introduce the language exclusion rule. But don't worry, we'll also compare without this rule. It goes like this: the first link on many Wikipedia pages is just the language of the name of the article, specifically these ones in parentheses. The language exclusion rule is to disregard these.
Hear me out for a second. "Plastic Love" is a famous city pop song from 1984 by Japanese artist Mariya Takeuchi. Without the language exclusion rule, "Plastic Love" goes to Japanese. But with language exclusion, "Plastic Love" links to Mariya Takeuchi, which links to City Pop, which then links to Japanese pop music, and so on and so on. The first link path is now representing more what "Plastic Love" is, rather than what country it happens to be from. But more importantly, I think it also gives us better insight into how we, as humans, write definitions for things, which is, to me, the most interesting aspect of all of this.
And we've got enough to start tackling the question that started this all off: do all Wikipedia articles lead to philosophy? Coding everything we talked about just now was not easy. But after some hair-pulling, a lot of coffee, and moving to Germany for unrelated reasons, here are the 5,000 articles that I found for the Wikipedia first link network. And here's the star of the show: the Philosophy article, right in the middle of this big chunk of nodes and arrows. This giant component represents all the articles that I found that have a path to philosophy. Percentage-wise, it contains 97.3% of all nodes in the network, which agrees quite well with other estimates I've seen online. So, no, not all articles lead to philosophy, but the vast majority do.
Let's take a second to appreciate some of them. [Music] "Orange Juice" (the best juice) arrives to philosophy in 13 steps, while "Orange Juice" (the best band) arrives to philosophy in nine. "Apple Juice," being further from the light of God, appropriately takes a longer 15 steps to reach philosophy. The game Celeste takes 14 jumps, and it might fill you with determination to learn that Undertale takes 15. Both the Calgary Flames and Edmonton Oilers take 16 clicks each, which, I guess, I should just be happy that the Flames can tie the Oilers in something at least. And finally, Philosophy arrives to Philosophy in... wait, what? Uh, maybe let's put that one aside for a second.
And we could keep going. Trust me, I did. Though maybe it's easier if we instead summarize it as a graph. The x-axis shows the number of steps it took to get to philosophy, while the y-axis shows the number of pages I found that took that many steps. As you can see, the number of articles with a given distance from philosophy is bell-shaped, with an average of around 14 [Music] steps.
The physical structure of the network is also kind of interesting. I found 10 articles which link to philosophy. We can think of these 10 as roads to philosophy. If we color the different parts of the network according to which of the 10 roads they arrive on, we'll find that the vast majority of the network belongs to only one of three paths. 53% of articles, representing mostly science and countries, arrive to philosophy by way of Analytic Philosophy. 25% of articles arrive by Awareness; these articles are mostly about institutions, whether they be political or academic, though interestingly, all of mathematics is here as well. Lastly, Philosophy of Logic, which accounts for 15%, had a lot of articles focusing on, well, logic, but it also has a focus on languages. So, effectively speaking, 93% of the Wikipedia first link network can actually be thought of as three giant lobes joined together by philosophy.
But what about those articles that don't lead to philosophy? Well, I found two articles with no links at all, ending the run. Honestly, though, I'm just going to ignore these. Given how rare they are and the fact that Wikipedia actively discourages pages with no links, they feel more like mistakes to me. Much more likely are clusters that end in loops. For example, if you somehow reach the page "Node (networking)," you'll never get to philosophy because it links to "Telecommunications network," which then links back to "Node (networking)." Similarly, "Mathematical optimization" and "Discrete optimization" make a loop, and so do "Information technology" and "Information and communication technology," which, yes, apparently those are two separate pages. The very largest loop I could find was the single cycle of three, the one on screen right now. Everything else was a cycle of two.
But I think the fact that some pages don't reach philosophy raises an important question: should they? Like, it seems somewhat arbitrary to me that they don't. As an example that's not really related but speaks to what I mean: Dog, Cow, and Chicken all link to Domestication, but Cat links to Domestication of vertebrates, a different, though weirdly similar, article. Why don't they all link to the same page? I don't know. And what's more, have you ever seen what a cat can do with its body? Cats don't have bones. This is clearly a mistake.
Now, I have to admit, I did do a bit of a lie. I set that the largest loop I could find was the one with three articles, and that is true if we're only talking about these small islands that don't connect to philosophy. There is actually one more loop hidden in the main body of the network, and it's a big one. A full 11 nodes, or 16 nodes if we don't use language exclusion. And that's the loop containing Philosophy. Yeah, that's right. Following the first link path from Philosophy and hopping across 10 other nodes leads you back to Philosophy. Which, I mean, the fact that there is a loop isn't that surprising. A good Wikipedia article should have at least one link, and so we should be able to keep clicking forever. But because the network is finite, the only way that's possible is if articles repeat, hence a loop.
But at the same time, doesn't a loop make the philosophy part of the philosophy game kind of arbitrary? Why is it not the Three-dimensional space game or the Geometry game, both of which are also in that loop? What makes philosophy so special? It turns out that the answer to that is a bit tricky. One of the most common ways of identifying important or special nodes in a network is just to see which ones have the most connections. Network researchers often call this degree centrality, where degree just means the number of connections, and centrality is another word for importance. Personally, though, I like to call it the popularity centrality. Essentially, the more popular you are, the more important you are. Maybe don't read too deeply into that one.
In my network, Philosophy connected to 10 other nodes, though of course, these were just the ones I found. But relative to the rest of the network, 10 isn't that high. Seven other nodes, including Mathematics, also have 10 connections, and 18 have a higher number of connections. Association football is the most popular at 51, and my favorite, coming in in fourth place, is the article Moth with 17 incoming connections. Yeah, Moth had more connections than Philosophy, and it's not called The Moth Game. Though maybe it should be.
Now, that being said, even though Philosophy is not the most popular article in the network, it is the most popular within the big loop, which is a good first step to motivating that it's not arbitrarily chosen. But it's also clear that popularity is not the be-all and end-all. Luckily for me, instead, it could be that Philosophy is important because of how it's positioned in the network. Structurally speaking, we already saw that we can kind of view the first link network as three big lobes connected together by Philosophy. But can we make that a bit more formal? Well, yeah, but bear with me for a second.
The corpus callosum is a thick bundle of neurons that connect to a bunch of things, but it's mainly famous because it's the bridge between the left and right hemispheres or lobes of your brain. So, by virtue of being a bridge, it's important. When network neuroscientists want to measure the, uh, bridgeness of a neuron in a network, they measure something called betweenness. So let's use that for our network as well. Unlike degree centrality, which assigns importance based off popularity, betweenness centrality quantifies the importance of a node in a network by measuring the number of shortest paths to pass through it. Applying that to our network and resizing the nodes so that they reflect their scores, we'll find that Philosophy is the node with the highest betweenness, not just in the big loop, but in the whole network.
So, Philosophy really is acting as the bridge between all these different concepts. Which brings us back to the big question: given that Philosophy is in a loop, isn't it kind of arbitrary how important is Philosophy, actually? Well, it's certainly special. It's got a relatively high number of connections. I maybe downplayed it a bit when first talking about it, but top 20th place out of 5,000 is pretty good. On top of that, Philosophy has the highest betweenness centrality in the whole network. No other member of the big loop has both of those features. Of course, the fact that Philosophy is in a loop to begin with means that you can never miss it, and you're also most likely to enter that loop on Philosophy as well. So, I think for those reasons, yeah, Philosophy is important. And even though it's in a loop, it's not arbitrarily chosen. It makes sense to call the Philosophy game the Philosophy game. A nice and easy conclusion. Congratulations.
Except, except none of that is true anymore, because someone broke the Philosophy game. So what exactly happened? Remember how we found that Wikipedia can be thought of as three big lobes connected by Philosophy, and how the page for Awareness connected 25% of the network to Philosophy? Well, someone redirected Awareness to instead point to Psychology. Links get redirected all the time, so that's not a problem in and of itself. The issue is that Psychology is within that 25%, meaning that whoever did this made a new loop, and in doing so, cut off a quarter of the network from Philosophy.
But it gets worse. Even though 75% of articles still lead to Philosophy, there's no compelling reason to stop there. It's become completely arbitrary. It's just another of the 97% of nodes that now lead to Awareness. The Awareness Game, if you will. All things considered, this attack, if you will, wasn't so bad. This is because Awareness was also a member of the big loop, meaning that even though Awareness no longer pointed to Philosophy, there was still a path back to it. So, 97% of Wikipedia pages still led to something. I'll leave it to the philosophers among us to debate whether that something should be Awareness or Philosophy, though I suspect they might be a bit biased. But regardless, the overall shape of the network is largely unaffected.
It could have been much worse, though. If someone decided to redirect Analytic Philosophy to somewhere else, not only could they have cut off 50% of the network from Philosophy, but because Analytic Philosophy wasn't part of the big loop, they would have actually split the network into two completely separate halves with no path from one half of the network to the other. The structure of the network would completely change, and arguably, there wouldn't be a star of the show. Analytic Philosophy was actually redirected since I originally recorded that section, but the reason it didn't break the Philosophy game is because it wasn't redirected back into its own lobe like Awareness was. It was sent to one of the smaller ones.
And this idea of attacking the weak points of a network to ruin my YouTube video is probably one of the most important and applicable parts of network research. Using essentially the approaches we took in this very video, we can identify the weak points of a network to either attack or defend it. To be clear, I'm using the word "attack" in a general way. A targeted attack on a city's electrical grid is obviously a really bad thing, but a targeted attack on a metabolic network of a cancer cell is a really good thing. Attacks also don't have to be targeted. A tree knocking out a power line is a random attack, as is an attack from neurodegenerative diseases like Alzheimer's on brain networks, though that's obviously a bit more complicated. Targeted or not, by knowing the structure of the network, we can predict and prepare for how these attacks will affect a city or a patient and help to defend against it before it even happens.
Which begs the question: was the attack on the Awareness article random or targeted? Well, if we go into the article history for the Awareness page, we'll find some juicy drama. On April 5th, 2024, someone made a change, logging the following: "Changed order of Psychology and Philosophy so it doesn't break the rule that every first link brings to Philosophy." Now, I know Awareness did first link to Philosophy when I started gathering data in early 2024, so presumably someone had changed it at some point, and this person changed it back. I think it's worth pointing out that one day prior, I posted a short short preview of this very video to my Patreon subscribers. Obviously, that can't have been a coincidence. So, thank you to my amazing and patient subscribers.
Anyway, on May 22nd, 2024, someone undid that change and wrote, "See talk page for why Psychology is first." Now, I'm not very familiar with this backend part of Wikipedia, so I couldn't find whatever they were referring to on that talk page. Regardless, all of this has me convinced that this was, in fact, a targeted attack meant to ruin my video and make me look like a fool. But the jokes on them, I'm already capable of doing that all by myself.
Anyway, let's go back to the Awareness page for a second. Notice that even though Philosophy isn't first, it is second. Which gave me an idea, and it's something I haven't really seen anyone talk about at all. What happens to the Philosophy game if we don't use the first link? Well, we've done it before, so let's do it again. Go to a random Wikipedia page, click the second link this time. Repeat until we hit a loop, then start again. Rewatch all of Neon Genesis Evangelion while the code runs. Okay, it's done. Generate the second link network. Realize there's a bug in the code that affected the first link network as well, and go back and regenerate that network. Reanalyze and question why you do this to yourself. Repeat the previous steps, and finally, here it is: the second link network.
But why stop there? Why not the third link network? Why not the fifth link network? Why not the 100th? Okay, well, maybe not that one. And here they are: the second, third, and fifth link networks. As you can see, unlike the original first link network, these are much more fragmented. The importance of Philosophy is also heavily diminished. The probability to even reach it is 2% for the second link network, 1% for the third, and my program never even found Philosophy for the fifth link network.
What's more interesting, though, is how the network is changing shape. Part of this is because it's becoming increasingly likely that we'll run into a page that doesn't have enough links to continue the walk, which is why I stopped at five. That that explains the fragmenting, but not why the connected components of the network are changing shape and becoming kind of stringy. What we're seeing is, I think, our collective agreement on how we discuss concepts. Early links tried to contextualize a topic within a broader concept, while later links reflect individual properties of that topic. "Neon Genesis Evangelion" and "Gorden Legon" are both animations produced by Studio Ghibli about giant robots and making friends. Given their similarities, it's not a surprise their first couple of links are also very similar, whereas the later links reflect more of their individualities. In other words, for larger link numbers, the chance that two articles point to the same thing decreases. Instead, they just continue like a string.
You can really see this effect if we choose links completely randomly. The network just looks like it dissolved in some soup. Hopefully, you can see how the second, third, and fifth link networks are kind of trending towards that. The main difference being that anytime you reach a page with fewer than five links, the fifth link walk stops, while a random walk can continue with just one link. And it's this trend that's interesting to me. If the structure of the second link network was already very stringy, it would suggest that there's no collective agreement in how we describe articles beyond the first link. But that's not what happens. While greatly diminished, the second and third link networks still show some residual agreement, and from there, gradually trend towards the random network. We're essentially seeing the functional decay of our collective agreement on how we write definitions for things.
Wasn't this supposed to be a math video or something, though? Actually, I think that's what's really amazing about this. We're using math and we're analyzing the structure of an abstract network to learn something about how we communicate and connect the world around us in our mind. Wikipedia is this uncoordinated mess that tries to encapsulate everything that we know about our universe, and in doing so, sometimes reflects a bit of who we are, if you know where to look. Looking into Wikipedia is kind of like looking into the night sky. Staring into either for too long makes me start to think, where's my place in all this? And that's when I realized maybe I don't need a Wikipedia page about me. Maybe the connections I was looking for were already all around me.
I guess what I'm trying to say is, it's a great big and amazing universe, but you're what makes it mean something, especially if you're signed up to my Patreon. [Music]