Transcription
In this video, we're going to try to make some mathematical models of the rise and fall of countries. We'll base this off the work of Peter Turchin, who's written a number of books on the subject, both looking at historical trends and applying them to try predicting the trajectories of countries like the United States. You can tell by these titles, he isn't the most optimistic about the near future.
One of the things that sets Turchin apart is that he explicitly writes out the formulas and data he's basing his predictions off of. So, we're going to try diving into those equations to better understand both his theories as well as other complex dynamics. We're going to be looking at the simplest version of the models he suggests from his book, Historical Dynamics, both because it lets us model everything in its totality, whereas more complicated models will have a number of variables that are not really quantifiable in the same way, and because, as you'll see, the math and visualizations are going to get complicated enough just with these simple models.
So, starting with the most basic concept. A big part of understanding the models we're going to be talking about here lies in having an intuitive understanding of the difference between linear and exponential growth. Linear growth, like we have on the left here, means we have a constant change over time. In this case, we have 100 balls being added to this pile every second. But in exponential growth, like we have on the right here, the rate of change increases over time. Here, I have the balls splitting every second or so, which means that as the number of balls increase, there'll be more balls that are splitting, and therefore the number of new balls added each second is going to increase over time. The practical result of this is that while exponential growth might start slower because it's building over time, by the end, it explodes way faster than linear growth.
Now, when you're trying to mathematically model real-life systems, there's a number of different techniques you can use. For example, you might know that the equation for linear growth looks something like this, and the equation for exponential growth looks something like this. But in this video, what we're going to be interested in is less the full value of some variable at a specific time, and more the dynamics of how things are changing. Given where we are now in history, what's likely to happen in the next x years? And for that kind of reasoning, it's more helpful to look at what are called differential equations. Differential equations output the rate of change. And so, linear growth will look like this: It's just a constant number. It's always a hundred new population every second. Whereas exponential growth will look like this: the rate of change is dependent on the current population. And I think this is a much more intuitive way of understanding the dynamics of what's going on here. In our example, it's really obvious that below a hundred population, the exponential growth is going to be slower. But above a hundred population, it's going to be faster. And I think that kind of intuition is a lot harder to get from the normal equations.
So, in this video, you're going to see a lot of differential equations, but we're also going to be using what's called agent-based modeling. And that's what you saw with the balls there. The idea here is that instead of just manipulating numbers, you can actually make a simulation of the thing you're trying to model in real life. It's kind of like making a little mock-up video game of the thing you're trying to analyze. Here, I'm not directly tracking the population numbers at all. I'm just having each green ball independently decide when it reproduces, and then measuring how often that happens. As computers have gotten better and better, this is becoming an increasingly common way of modeling complicated systems. And hopefully, I can show in this video that sometimes you can understand a situation better by seeing the agent-based model as opposed to looking at differential equations or normal equations.
So, we're going to start by trying to model a country's population. And that broadly works according to exponential growth. But in real life, you can't just exponentially grow forever. You'll eventually hit some limit on space or resources or whatever that'll slow down growth and eventually stop it. So, for our agent-based model, we're going to start with the same green balls to represent population that we used earlier. But now, we're also going to have this big field of orange cubes that represent resources. The pops will have to consume resources both to survive and to reproduce. Each pop will first grab up to five resources, place one at its home location it started at, and then the rest in a surplus zone. We'll then create a new green pop for every four resources in this surplus zone, and then send everyone back to do it all again. As I speed this up, you'll see that the population keeps growing larger and larger, and the amount of resources they're collecting keeps getting bigger and bigger too. But eventually, we'll reach this point when the pops can grab all the resources that are available. Now, the population is still going to be growing, but each individual pop is collecting less resources than they could, so the growth is going to start slowing down. Eventually, we'll reach a saturation point where there's only enough resources for each pop to get what they need to survive, and there's no leftover resources left to reproduce.
In biology, this model of exponential growth but with diminishing returns is called logistic growth. And if you go and look up the equation for logistic growth, you get something that looks like this. Which, at least to me, is not really intuitive and easy to understand what it's doing. But on the other hand, if you look up the equations for the differential equations for logistic growth, you can find stuff like this, which to me is way more intuitive. Here, N is the population size, r is the rate of change, and k is the carrying capacity, which in our case is the maximum amount of resources that can be grabbed. If you remember, our differential equation for exponential growth was just r times N. That is the base rate of change multiplied by the number of population that currently exists. So, the only addition that logistic growth is making is this element, which you can pretty obviously see when N is 0 or close to 0, this is around 1. And when N is about the same as k, this ends up being 0. So, the rate of change for low population numbers is going to be about the same as exponential growth, but as N approaches k, the rate of change is going to drop down to 0.
When logistic growth is applied to human population, it sometimes gets called Malthusian growth, after the author Thomas Malthus, who wrote a book about this in 1798. To directly quote his words: "Population when unchecked increases in a geometrical ratio and subsistence for man in an arithmetical ratio." Now, this was written over 200 years ago, so the language being used is a little different. For example, in my dialect of English, the adjective version of 'arithmetic' is 'arithmetic', not 'arithmetical', but he's basically talking about the same thing we were. By geometrical, he's talking about exponential growth, and by arithmetical, he's talking about linear growth, or at least close enough concepts. So, he gives the example that the United States doubles its population every 25 years, which is, interestingly enough, a stat he got from Benjamin Franklin, but that's a whole other tangent. He expects that as of 1800, when he's writing this, the US could maybe double the amount of food they're producing in the next 25 years to match that. But quoting him again here: "In the next 25 years, it is impossible to suppose that the produce could be quadrupled. It would be contrary to all our knowledge of the quantities of the land." So, he thinks the amount of food produced in the US could maybe be doubled what it is in 1800, but certainly not quadrupled that. No amount of better farming or land management could get over that. And, uh, I don't know if you've been paying attention, but let me just pull up this Wikipedia page about agriculture in the US. Um, from 1997 to 2014, we doubled the amount of food we produced. His ideas of the theoretical limits are so far below what they actually were. And that's because he didn't really fully comprehend the effects of things like the industrial revolution. The US didn't quite double its population every 25 years like he said the utmost limit could be, but our population now is like 70 times bigger than when he was alive. And in general, there's like 8 times as many people on the planet now.
And I think that's important to bring up here because a lot of times, modeling future situations like this, you're going to be wrong. But that doesn't mean the underlying logic is incorrect. People today generally agree with the ideas that Malthus put forward, but it turns out that real life was a lot more complicated. There were other things he wasn't taking into account when he gave his upper limits of human growth, both like technologically, but also socially. Like, if you look at birth rates today, lots of countries are making more food than ever, but have their birth rates going down. The decisions of individual people is a lot more complicated than just food in, babies out.
Now, despite Malthusian growth being not accurate to how population works anymore, it's still the basis of the structural demographic theory that Turchin is arguing applies to today. But it's applied in a kind of more metaphorical sense. The idea is that while populations aren't quite following this, there are other processes that are analogous that are still following a model of exponential growth with diminishing returns. For example, things like supply versus demand curves, where initially you're going to get increasing returns on your investment, but eventually you're going to saturate a market and get lower returns. We'll talk more about that later, but we're going to keep going with the basic pre-industrial version, as that's just simpler to model for now.
So, as our next step to get a little more realistic than the basic Malthusian model, we're going to add a concept of a state that takes in some resources as taxation and then uses those to increase the total amount of resources available. The idea is this is analogous to something like state-funded infrastructure or civil administration that make it more efficient for people to get the resources. So, our agent-based model is going to start with some of the same mechanics. We have pops that grab resources from this big field, place one at their starting location that they used to eat, and then place the rest of what they gathered in a surplus zone. But now we have a couple new mechanics. Some percentage of the surplus resources collected is going to go to the state as taxation, here represented by this smaller box with the dotted line, which is 20 percent of the surplus. The state also has expenses, which is this box here. In my example here, we're having the state need 0.2 resources for every member of the population. If the state made more money in taxation than it needs to expense, then it can store the rest in this box here. And finally, we have the state increase the supply of resources. So, the bigger this box of state resources is, the bigger this box over here is, and this is bonus resources that are created by the state. I realize that's a number of things to introduce at once, but the main thing is that this box is the state's income, and this box is the state's expenses. So, as long as the income box is bigger than the expense box, the state is making money, and the total supply of resources is going up. But if the expense box is bigger, then the state is losing money every cycle, and therefore the supply of resources is going to go down.
Now, at this point, I'm going to speed up the simulation to see what happens, but I want you to try predicting what you think the trajectory of the population size and the state size is going to be as this runs. Keeping in mind that the state expenses are based on the population size, and the state income is based on the amount of surplus resources. Okay, let's look at some graphs to talk about what happened there. So, population over time of our first Malthusian simulation looks like this. It starts out slow, speeds up, and then slows down again. It starts out slow, speeds up, and then slows down again. It starts out slow, speeds up, and then slows down again. It starts out slow, speeds up, and then slows down again. As it reaches the saturation point of 2500. If we compare that to our new model with state taxes, we'll see that growth starts slower. And that's because a percent of the surplus is going to the state, and so less is going to just growing the population. But because the state is then growing the maximum amount of resources, the population goes above what it was in our old model. Population growth starts slowing down as we reach this higher point. But instead of just leveling out there, it crashes way back down to that base level we had before. Interestingly, if we look at the state resources compared to the population, we see that they kind of change at different rates, with the state resources starting to slow down and eventually dip before the population crashes. The reason for this lag is that state resources are dependent on the surplus the population gathers, and therefore indirectly on the rate of change of the population. The state resources then feed back into the rate of change of the population, which causes it to snowball even faster in its decline.
Now, like with Malthus, I think this is still too simplistic to draw conclusions about real life from, but the concepts here show up in a lot of areas. There's this phrase that "Things change slowly and then all at once." This was originally used by Hemingway to talk about a character going bankrupt, but was also used by John Green to talk about a character falling in love, and was used by Atrioc to talk about the AI bubble, amongst other things. That's an interesting collection of people to reference. But anyways, you can see all of these have this kind of idea of some kind of exponential combined with linear things. Bankruptcy obviously makes a lot of sense to what we're talking about. You can look at falling in love as having exponential relations, like I find someone more attractive if they find me attractive. That's some exponential growth right there. And then there's some linear things, like the amount of time we spend together. For economic bubbles, if you look at a graph of the stock of Cisco during the dot-com bubble, it looks pretty suspiciously similar to the graph we had here of population. You can even use roughly the same logic, where investment acts like population, where it's going to exponentially grow initially, the more money you have, the faster you can grow, kind of thing. And then there's an asymptotic limit to how much that can grow in isolation. But then we can add something like 'hype', which is similar to state finances. It makes sense that the hype around a stock would go up if the stock is increasing fast, which is the same as our population having a large surplus. And it also makes sense that the hype would go down if the total value of the stock is high. People are more worried that it's overvalued, which is again like the exact same mechanism as we were modeling with population. You obviously can't actually model the entirety of a market with two variables, but just to emphasize that this type of thinking is very important in a lot of situations other than the one we're talking about here.
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Alright, so now I want to try getting a little more insight into our state financial model by looking at the differential equations that model it. I'm going to show the actual equations I'm using here, but if you're just watching this video casually, don't really worry about it. We're going to get to some interesting properties afterwards. I'm just including this for the type of person who wants to pause and try implementing it themselves. We can start with our population growth equation from before, and now instead of the carrying capacity being a fixed value, we're going to change that into something that's dependent on the state. Here's an equation that gives diminishing returns as the state resources increase, and then we want to add a second differential equation for how the state finances work. This whole chunk of the population growth equation is the amount of surplus that a population gets, so we can just plop that into the state resources and multiply it by taxation rate to get the state revenue. And then we take the amount of population and multiply it by some value to get state expenses. Again, we use 20% for both of these values in our agent-based model.
Once we have our two differential equations, we can graph them in what's called a phase space, where we put our population on a y-axis and our state finances on the x-axis. Now, we can place a dot somewhere on this graph and evaluate our differential equation at that point to get a vector that dot should move along. Here, we can see our dot is at the equilibrium point for our population, and so if we raise the population any higher, it'll just fall back down. Our state finances are at zero because when we're at the equilibrium point or higher, all the food is being consumed just to maintain the population. If we raise the state funds any higher, then we start the cycle of state funds going up, population going up, and then eventually crashing. You can see we get different arcs of different sizes depending on how much state finances we have. We can also lower the population below that point, and if we lower it far enough... that'll also start the cycle. Because once the population is low enough, then each member of the population will have a larger chunk of resources, and there'll be enough that state taxes can come in, get some funds for the state, and start the cycle that way. I find it interesting that in this model, the state finance is nearly always zero, which in real life would be a little more complicated because, like, a lot of states can print money, so conceptually a state could have no money but still pay for things at the cost of creating inflation. But again, this is intentionally a much simpler model than anything going on in real life.
Another neat thing we can do in this phase space is put dots at multiple points and then run them all together to help understand the overall movement pattern of the entire system instead of just one run. And an interesting thing to note here is that in phase space, these lines can never cross. That's because in phase space, a point is a set of values that then give the vector of how they change. So, for a line to cross, that would mean at the same point, it would have to give two different values for how it's gonna change. And this is significant because it means for this kind of arcing behavior where the population goes up but then goes down later, that's only possible to do if you have multiple variables. If you're just modeling the population number, you can't get this kind of behavior. Our population model here always ends up at the same equilibrium point, no matter what you do. But there are some systems of differential equations that can have stable loops. A famous example is this predator-prey model. Here, there's a number of different stable loops depending on where your initial condition was, but you'll see again, none of them ever intersect.
And actually, quick programming tangent while we're here. So, the simplest way to implement differential equations on a computer is called Euler's method, where you take the rate of change you get from your differential equation and then just multiply that by the amount of time it takes your computer to run that. So, if you're running at like 60 frames per second, that's like 60 milliseconds. But the problem with that is that sometimes you can overshoot curves. So, like for these predator and prey equations, if I increase how fast we're running the simulation, then my estimate overshoots the curve and it gradually spirals out. If you notice earlier in the video, there were some distortion patterns with where resources were being placed, that's kind of similar. It's based on the computer's approximation of some stuff. In pure math world, this isn't a problem because in theory, you'd be running this infinite times per second, but unfortunately, computers aren't quite that fast yet, so we're gonna have to use one of a bunch of algorithms to have a better approximation. I'm using one called RK4, where you take four different estimates and then do a weighted average of them to try to get more stable. It's a whole thing, but anyways, if you're trying to do this on your own, know that that's a component of this.
From here, we can look at the final component of Turchin's structural demographic theory, which is to split the population into two distinct populations: one for the commoners and one for the elites. In the pre-industrial society, the idea here is that instead of the state directly taxing people, there's like peasants who are doing the actual farming and mining and production of resources, and then there's like nobility or some upper class that is directly getting resources from them, and then the state is just taxing those rich nobility types. This is again an aspect you have to abstract a bit to apply to modern societies, so you can do something like look at the ratio between the elites and commoners as an analog for like wealth distribution or something like that, but for now, we're just going to play it straight and have these be like actual populations.
Implementing that in our agent-based model, we now have these purple balls which act as the elites. These are similar to the normal populations, but they grab their resources from the normal population surplus, deposit one at their starting location, and then put their surplus in an elite surplus location. This is way up here because we need room for when things expand. The state works the same as before, but now the expenses are based on the elite population numbers, and its revenue is based on the elite surplus. With all that in mind, we'll run it again and see what happens. So, overall, this model has very similar dynamics to both of our previous ones. If you just look at the population of the elites, it's very similar to our last model, where they grow and then hit some point and then collapse after that. And if you look at the behavior of the general population, it's very similar to our first model. This all happens faster now because we have the elites siphoning off some amount of resources to feed themselves, but it's overall generally the same dynamic. This fact that sometimes you can add a bunch of new mechanics and still get the same general behavior is part of why it's good to keep your models as simple as possible.
Another thing worth noting here is that when you get more complicated models like this, the amount of parameters we have that control how things work keeps going up and up. So, like in this model, we added a parameter for how many resources it takes for a new elite pop to be created. And looking at this run and seeing that the elites gradually took over the entire supply of resources, I want to try making the elite growth rate go down, so I increase this value to 15 instead of 4. We're going to try to fast forward through this run a little bit to save time, but the interesting thing here is with just that small modification, it went from, oh, always plateauing and collapsing to infinitely growing all three variables. When the elites grow slow enough, then that means that when they get bigger, the state gets bigger, so then the supply gets bigger, and then the population rises to that supply. Turns out that the only reason that wasn't happening before is that the elite population was growing faster than the normal population, so the elites gradually took all the available supplies. I honestly don't know how YouTube's bit rate is going to make this look, but from my perspective, this is some cool, like, abstract algorithm art type stuff, which is fun to look at, but obviously not very realistic in the infinite growth of resources in all aspects. It's also a crazy testament to modern computers that I'm getting like 15 FPS despite the tens of thousands of things moving and happening every second. I'm going to post the source code to this. This is like me trying to learn Unity ECS, if you know what that is, but I don't know. It's crazy.
Anyways, we're going to now switch over to the differential equations because it's a little easier to make changes quickly in that. I don't have to code a bunch of new logic and state machine type things for that to happen. Here's the literal equations that Turchin uses, which are a little different in a couple ways from our simulation. It's like the max carrying capacity does have an upper limit, and there's like diminishing return on state resources. He also has what I think a little less intuitive way of how the elites get resources, where he just has at a certain number of elites, they get a fixed percentage of the resources, and then at a certain number of elites, they get half of the resources. So, like, say at 100 elites, they're always going to get 50% of the resources of the population, even if the commoners have a million or 10 million population, 100 elites will still get half of it. Which again, is probably abstracting some level of bureaucracy or whatever, but just to know that's a little different from what I did in the agent-based model.
Despite those differences, when we go to our phase space, which is *3D* now, we can see that we get basically the same behavior as before, where population goes up, which leads to the elite population to go up, which leads to the state to go up, but eventually this starts getting reversed when state funds arc down, which leads to a reverse of all the other trends until everything collapses to a situation where there's no state. Turchin does this by changing the equations a little bit, so instead of worrying about like carrying capacity and things like that, he simplifies it down and just adds this component of elite extinction, where if there's no state, the elite will die off really quick, and if there's a state, that reduces the rate of elite extinction. This could in theory be modeling a lot of things. You could consider something like a legal system, where what the state's main job is is resolving conflicts between wealthy people so they don't fight as much. In a more nihilistic sense, you could say that the state defends the interests of the elite, and without the state, the elite will get overrun by the commoners or something like that. It could potentially mean a lot of things, but from a pure math perspective, what this does is drop elite numbers quicker once the state goes broke, which then gives room for the commoner population to generate a tax base to get the elites to have a tax base, so then the state can restart and loop the whole thing once again. And you can see that with those modified equations, we do in fact see a cyclical loop in our 3D space.
One of the cool things about this set of equations is that it creates a limit cycle. So, we saw that even in 2D, you can have these stable loops, and the predator-prey example had infinite number of these different stable loops, but our stable loop in 3D doesn't quite work like that. If I pull any of the variables off the loop, it just gradually settles back down to that same loop. It's topologically analogous to a shape like this, where you have a stable loop, and then everything inside that loop is going to gradually radiate out towards it, and anything outside will gradually spin in towards it. If I put a variety of starting conditions in our phase space, we see they all arc and gradually will form back towards this stable loop. So, like I said, that's called a limit cycle, and it's really important in things like engineering, where you want some behavior to be guaranteed to settle back into. But in our context of analyzing history, I think it works really well. The idea is that there's this general rise and fall of things that you can predict, but you're not always going to know it for sure. If there's some slight variation to all these numbers, it can get back on track. The loop might be slightly smaller or slightly larger, but it'll eventually stabilize back to the same thing. And we can show that by adding some random jiggle to one of our variables and see that we get these kind of intermediately sized loops, which I think look pretty cool.
The general pattern we can see from this that then Turchin expounds a lot on in his books is that we start in a position here where all three values are really low, and then the commoner population starts rising exponentially, which after a delay will cause the elite population and the state finances to also increase. But eventually, because those are increasing, the tax burden on the commoners is going to go up, whether directly through the state or indirectly through the elites grabbing more and more of the commoner surplus. This will eventually cause the commoner population to slow down and then start sharply declining, which will lead to the elites being able to take less resources from themselves and then the state to be able to take less resources from those elites. This period where there are too many elites but not enough for resources for them to grab is called elite overproduction by Turchin, and is a big thing he tries to track over history, whether through things like actual conflict between elites or things like how competitive is it to get high-level government positions or university professorships or things like that. This large amount of elites fighting over a smaller and smaller pie is going to put a lot of pressure on the state, which, as we established in this model, is responsible for somehow alleviating this pressure. Eventually, the state is going to go bankrupt, which causes the elite population to go down. Again, either through either through fighting each other and wiping each other out, or through a lack of viable positions that they can fill. Eventually, the state collapse leads to a collapse in elite numbers, which leads to less repression on the common population, which leads them to start increasing their numbers again, resetting the whole cycle. And that's at a very high level what Turchin argues is these 'secular cycles' in history. He does a bunch of analysis and proposes how long this whole cycle takes, quote unquote, "by default," but as we saw, because it's a limit cycle, the idea is that if any of these variables change because of like war or famine or something not in this model, it'll stabilize back to it. The whole cycle will still happen, but it might be shorter or longer than the default length.
Now, I really made this video because I just think it's cool how closely the math can track this overall more narrative description of how things are happening. Whether or not any of this is accurate is very much not a thing I'm super qualified in. Even at a really high level, you can pretty easily consider ways in which different societies should work differently than this. Like, how are the resources going from normal people to elites to the state feels like a thing that's going to be different from country to country. If you kind of go in a Marxian direction, you have different like modes of production, which would tie into that. And also, this division between commoners and elites, to me, feels like somewhat arbitrary. Like, it makes the math work, but like, I don't see any reason you should split it into two groups specifically. Conceptually, you can do stuff like split this up by regions of space. I could apply it to this world model that I've been building in other videos, or you could break it up into more like social classes or time periods or things like that. But as you increase the number of variables like this, eventually you're going to stop being able to analyze it in the same way. Because as we increase the social classes from 1 to 2 to 10 to a million to an infinite number of divisions, then at that point, you're not dealing with, quote-unquote, ordinary differential equations, which is what all of the math we've been doing has been. And now you're dealing with partial differential equations, which is a whole related but other field of math. And a lot of the ways we've been talking about to analyze this stuff, like phase space, doesn't work on partial differential equations. This is getting more into stuff like simulating liquids and other big fields of data, and is actually more complicated than that, because unlike liquids, we have a bunch of these funky non-linearities and exponential growths. So, you can't use a lot of the tools that exist for analyzing other partial differential equations.
There's also just a bunch of variables/parameters in the math that we're just kind of making up. Like, you saw how arbitrarily I changed it from four resources to a pop to 15. I kind of just messed around with numbers until things looked good. And so reasonably, in Turchin's books, he spends a lot of time trying to justify what numbers he's picking for these kind of things and how he's arriving at those numbers. If what I'm doing feels arbitrary, you should just read his words and not the summary you're getting from me.
An interesting note about this kind of thing is talking about how can we tell what the quote-unquote proper number of variables we need to model something is. So, like, we saw with the initial elite model, we had adding another dimension didn't really make the simulation more complicated, but there are properties that can only exist in certain dimensions. Like, we talked about, you can't curve back on yourself in one dimension. There's also a whole part of chaos theory, which is this idea that you can't have a chaotic system unless you have at least three variables. The YouTuber Not David has a cool video about this, where you can use something called shadow manifolds to just look at one variable and see how it's changing, and use that to determine the minimum number of dimensions that the underlying system has to have. And doing the research for this video actually made me understand that more, because he has a whole comment about how it doesn't work if the lines ever cross, and he's talking about how in phase space, lines can't cross, and I didn't realize that was what was going on in that video, but anyways, it's a good video, you should check it out.
This video's book recommendation is Nonlinear Dynamics and Chaos by Steven Srogatz, which is literally a math textbook, but for me, was a pretty entertaining read still. Srogatz does a great job at giving a lot of interesting examples and saying stuff like, "Oh, here's the math, and that's pretty unintuitive, so let's look at a diagram instead," which at least I found a lot more helpful than when I learned about this stuff in a university course. If you're the type of person who learns better from lectures than from reading through a book, you can check out Dr. Shane Ross's full online course that goes through this book on YouTube. I'll link that in the video description here.
If you're surprised that this YouTube channel, which started with me talking about anime, is now just me lecturing about calculus, I'm also surprised, so here we are. This whole video actually started as a footnote in the script to the last world-building video, where I just had one line in the outline that said, "Oh, it's interesting that structural demographic theory is a limit cycle," and that was it. And, you know, that's turned into this 35-minute long video or whatever, but genuinely, the channel is called Fractal Philosophy, out of that idea. Philosophy being the love of knowledge, and fractals being something that the more you zoom in, the more detailed they get. So, the idea being, you learn a thing, and then you learn some new questions that are interesting, and then you look into those, and that causes new questions, etc., etc. And actually, this is like the two-year anniversary of this YouTube channel, so let me know if you've been watching since earlier. I genuinely would be interested to know if, like, people came for the anime stuff or the video game videos and are still interested in this stuff. Like, obviously, I'm interested in all these things, but I'm not sure how much audience retention there is, or if there's a big split between people who watch my technical videos and my less technical video essay kind of videos. I don't know, let me know. I'd be genuinely interested.
The next video on this channel is similarly a result of me rabbit-holing from one line on a previous video, so it's going to be about the connection between stories and games, and I think that'll be interesting. Next technical video is going to be about a variant of rock-paper-scissors that I'm super excited about, but like, I'm not sure how much I can convince other people that it's interesting, but like, I find it so cool. So, I'm excited about that video. And then there's another AI video in the works that's a little more talking about like art and philosophy. There's a poll to decide whether to do that one or the game video first, and the poll was very unhelpful, so thanks guys. But the real deciding factor is I wanted to reference a line that's in the new Chainsaw Man movie, and that movie's currently only in theaters, so I can't really do that successfully until it's streaming or on blu-ray or something. Also, there's currently no shortage of video essays on AI, so I figure spending a couple months thinking about it and letting those ideas marinate a bit is probably beneficial.
But yeah, thanks for being around. Year one of this channel was basically me talking to myself, and year two has been really exciting. We're always learning new stuff. Obviously, we're trying video sponsorships this video. This is also a much more technical video than I normally do, so we'll see if I'm able to convey ideas like that well or not. Also, like, what I'm doing now. This is a new thing. Is this weird? Should this be a separate video? This is more vloggy style? Should this be on a separate channel? I don't know. We're trying things out. Anyways, thanks for watching this far into the video. Thanks to the patrons for helping fund this stuff. I'll be back with more stuff next year.