I'm going to give you a couple of examples. Three models, book's going to be called Islands of order. See, where do I stand here? And the argument is that following exactly on what Brian was talking about, rather than a more realistic model is the one he showed us the second image of the sun. The sun not as an equilibrium system, but one that is In a kind of a low dimensional order, where there are lots of things going on, the same with the economy. So if you take, you're willing to accept the idea that the real world and the natural world has processes going on in there are islands of order, there are attractors, but generally they're relatively noisy. Then how do we understand them? So that's a good question. But I wanted to kind of chase ahead to the really interesting stuff. These phase transitions winter. They're interesting qualitative changes in behavior because we see that's what gets physicists excited about this. We see really interesting transformations. Does that actually help us understand anything in my world. So, when do the dynamics really change and I'm going to talk about two cases. One of them having to do with cooperation, and the second one having to do with language. So I'll start with cooperation. And I'll give you two physics models, which at first have nothing to do with cooperation. I'm not even sure if we talked about them yet, but these are two. This is right out of the textbook for nonlinear systems. So first of all, the most famous example is the sand pile model, Peter, I think you talked about sand pile, right? So you guys remember this, right? It's a experiment performed by toddlers, you drop sand on the beach and it turns into a sand pile. And then what happens? The interesting transition from our point of view here is at a certain point, the avalanches shift from being local phenomenon when little sand grain nudges the others and it starts to go to having the whole damn thing connected. So the frequency with which one more grain of sand will trigger an avalanche. The size of that avalanche is entirely predictable. You get a few big avalanches. More medium size and lots and lots of little ones. And once it's reached that point, which is called the critical point, it stays there. It stays at that transition point. So the punchline is you go from local dynamics to a globally organized system. And Peter did talk about, there are all sorts of things that look like they happen the same way for the same reason In the world, you just keep growing in the sand pile. So that's one example of a phase transition, the transition from local to global dynamics. Correlation,the behavior of the grains now suddenly correlates at all scales from local tail to larger scale, but it attenuates as you move out to the global scale. So that's a model. Okay, of a nonlinear change. There's another interesting one, which works differently which we've also talked about I'm pretty sure. In fact we have so it's called the Ising model, this is how you understand how magnets work, so you get something that's magnetizable right, get some little bits of metal which can have a spin, up spin or a down spin, at high temperatures, they are going to be randomly ordered. But as you lower the temperature in your magnet to be, then they begin to interact with their neighbors. And as they do so something changes, you go from local interactions, finally to global interactions. Now the critical point is the point at which that transition from little local spins interacting to the whole thing being connected occurs but it doesn't actually stop there. In the ising model, if you keep lowering the temperature, it becomes more and more magnetic. So it goes through a phase transition. But the phase transition is not the attractor. It's just a moment in the passage of the mag, the spins from very disordered to completely ordered, somewhere in the middle. There's this critical point it depends upon the temperature depends on the chemistry whatever you're dealing with, is a particular temperature in which that phase transition will occur. Okay, so big difference here is yes, you have a phase transition, but it is not the attractor for the system. Okay, so looking at that. Here we have high temperature, random spins. Here's the critical point where you see little local areas that are correlated. All ups here and downs there. Bigger ones you see a kind of strange looking distribution, take my word for it. Here we have a power law distribution of spins of this the patch size, if you like of things that are coordinate, and then down at the far end, you keep lowering the temperature and finally they all line up, okay? Critical point, at that critical point correlation of spins happens at all scales, critical points on an attractor. Okay, that has been useful in ecology in the last roughly even not even a decade, people have found this phenomenon and understanding the patch distribution and vegetation in savannas many kinds of ecosystems. So what happens is, as the system begins to be stressed a bit. You get a transition that looks like this in which from being completely covered, you get a patch distribution there both positive and negative feedbacks. Which take this thing to a point at which you begin to lose the largest patches and that is interpreted by the people are looking at this as a indication of stress. Effective suggested now it may be a nice way to look for proximity to extinction of ecosystem, because the past distribution is now no longer at the critical point, the largest patches begin to disappear. Lots of interesting basis as much as vegetation its muscles like clam like things on the beach. Lots of natural systems seems to work seem to work that way. So that's interesting already we have an example. But in each of the cases I've described to you so far, the transition is caused by an external force. Something changes, the temperature changes in the ecology or the rainfall changes or you change the temperature, the magnets, whatever, something exogenous is causing that movement. Adaptation plays no role. So could it? Is there another way in which adaptive process might lead to changes in correlation distances? So working with Professor Stephen Turner and luck you, I guess luck isn't here and several graduate students. We looked at this question on the Island of Bali, where I've had the pleasure working for many years looking at 1000 year old Balinese Rice Terraces, were in by 1000 years old. I mean, we have royal inscriptions that go back 1000 years that refer to them. So we know they've been around for a very long time, built by hand, with HOAs and things, this is an example of a physical example of large scale cooperation. because this had this, this is an achievement right? Imagine a lowland tropical forest converted to the landscape that you see they're all flooded, all those patties are flooded. They all have to be kept at the right elevation. Little stair step stairs pattern in couplets by now three villages and they've got just enough water flowing through it so that it's all flooded. The purpose of doing this is to remove the habitat for pests, they had big problems with rice, or excuse me with rats that year, so they flood everything, goodbye rats. Okay, all it takes is beautifully coordinated action by all those farmers. Okay, so I'm claiming that's physical evidence for large scale cooperation. So how did that happen, how did you know, was this ordered by the king or the oil engineer? Hey, you see the same thing here, you see, rice, which needs lots of water and you notice that kind of engineered landscape. I spent months actually in the Dutch archives trying to see was there some engineer in the 14th century in Holland, who decreed all this where are the plans? How was this all organized? It was clearly self organized, done by the farmers. So given that that's the case, how did that happen? How do you get this kind of pattern? Okay, well as I've just said flooding will control the pests. The farmers are not only conscious of this, it's their method for pest control. Create a flooded, flood the fields over a large enough area, you remove the habitat for the pests, populations go down. To do that you need to time things. And so here are the phases, the water changing as the farmer is using their calendars, using a sophisticated system for managing time based upon permutation cycles, wonderful interesting calendar. Anyway they time it, interlocking cycles of irrigation systems so that they can achieve both getting the water to the right place to grow the rice, but also if necessary creating a flooded area for a week or two long enough to remove the food for the pest and the bugs. All that takes cooperation. Okay, so now here, here's Bali. Here's a little piece of Bali. Let's look at it [COUGH] out here from the perspective of Google Earth, okay? So this is an experiment as you're going to learn in a minute. What I'm about to tell you, you can try on Bali or anywhere else you like. We provide you with the code to run. So here we are looking at Bali. These are villages, those are rice paddies. And you can see that there are different stages. The rice is little older here, it's greener here, this is different color. So we send this to a geographic information expert and he colors this picture according to the stage of the rice. Okay, so now we get a patch distribution. And we ask why this pattern, which doesn't look like much, right? Looks pretty random. Okay, but we build a model, because we're modelers right so we build a model to see if we can capture this phenomenon. Okay, here's the model. Super simple. Each of those colors is a farmer. Don is a farmer and the color indicates his irrigation schedule. So blue might mean plant in January and in August and yellow might mean plant in September I don't know, too much some random collection of timings. They have to make that decision before the year starts because they have to know where all the water is going to go, right. So they decide, each group decides what they're going to follow, what plan they're going to follow. In this case however we're just randomizing. So we randomize the irrigation schedules. And then we calculate how correlated they are. So that just means if I'm blue, how correlated am I with my neighbors, okay. I'm blue and he's yellow and he's green and he's yellow so the correlation is random basically. The distance is how far out does the correlation between this dot go. So if there's a big blue patch, then we'd have a correlation distance going out higher and further. And in this case, it's random. Okay, so here we have a random system, uncorrelated random dots. The result of planting according to that schedule will be lots of pests, because the rice will grow in different stages all over the place. And the little bugs can move anywhere they like, right? We're just, is the pest feeding recipe. So that's not so good. But we allow this thing to evolve. And what I mean is at the end of the year, a simulated year each little dot compares their harvest with their closest neighbors. And if anybody did better if the green pattern worked better for you, then I copy green or turned out that blue is better I copy Peters blue copy, blue I do. So we all make that decision, just the locally optimal irrigation scheme and then update it and try again. Within a few years, and by a few I mean like five or less actually, you get this pattern. Which of you think about it makes sense? Here are patches that have emerged. All of these farmers are planting at the same time. So then as a result, they're creating an area that's large enough to reduce the pest food. They're also kind of looks like they're kind of optimizing the distribution of water. Same amount of water is flowing through the system but now it's patchy. But it's not all blue or not all red. Everybody's getting their share. So fine, fine. But interestingly, the program has a mind of its own so it continues. We've got at this stage to the point where the correlation distance has increased, right? This is maybe 10, its from here to here, maybe uncorrelated with 10 neighbors the size of that patch, maybe 10. And they're all about that. Okay, so here we are with the correlation increasing a little, uniformly across the whole system. Here are pests. More rice growing. Everybody's happy, but it keeps changing and evolving. Now what happens here? Okay, here we have a very large red patch. It's too big, they don't need to be that big to control the pests. And this little patch is maybe too small. And yet, harvest yields have increased over the whole system. Any idea what happened? Phase transition, what happened here? That they've reached a global optimum. At this point, the whole path, the whole macro scale ecology here is controlling the pest and the water. The whole thing is controlling the pests in the water. And at this point, the simulation stops, everybody's happy. At this point is the transition many little interacting patches become one large patch and the harvest yields, the overall yields increased to a maximum. And the punchline to this story is, they then become Pareto optimal. So Pareto optimality. The level of economists and Game Theorists is the idea, it's a state in which agents are interacting and no one can do better without disadvantaging somebody else. Got it? So in other words, it's a situation in which resources are being used and nobody can have an improvement without causing a disadvantage to someone else. So it Pareto optimality or Pareto efficiency. Not only are they growing more rice, but everybody is growing more rice and they're growing the same more rice. Everybody's equalized in that sense. So the simulation stops, the farmers quit interacting. And our interpretation of this as well. Cooperation is easy if there's no disparity of benefits. If there's no, if you can't do better by changing then you may well not change, if cooperation leads to that happy outcome. Now, when this happens. Here's another way of looking at what's just occurred at the initial case. First at the early stage, right before the adaptation process has begun lots of small patches all over the place, but then as it evolves to the global optimum you get this distribution which is a power law, which you've seen a lot of probably seen two dozen power laws by now. Well, it's the power law distribution, indicating it's reached the critical point, indicating a transition from local interactions to a global scale interaction. And it happens that that creates both maximum yields and also Pareto optimality. Everybody does really well, okay? So, just looking at what we just saw, we go from random to many patches to one system. The Ising model, which describes the development of magnetism, looks much the same, which is how we stumbled into this idea, okay? Here's high temperature random spins in an Ising model Here they are at the critical point, right evolving towards this patch distribution. So, transition in both cases happens at the same point again, from local to global control. The Icing model the result is magnetism in the volume model, it's Pareto optimality Okay, question, should we believe this nice trick with a model? Does it actually mean anything? Well, before I get into the empirical data, let me just say, for this to work, unlike the magnets. If we imagine this actually happening in the real world the farmers would have to keep working at cooperation to maintain that distribution. Other words that would be sustained by a continuous adaptive process. If people started drifting away from the distribution, the optimal distribution, then they're going to be punished. So, if that's correct the ecological feedback dynamic is going to lead to maintaining the system at the critical point. The question is does that actually happen? So, lucky to my colleague from the physics department here, added noise to our model, because in the real world, not everybody perfectly follows the rules. So, we have just a little noise indicating some people who are not actually cooperating. As really happens in the world to see what does that do and here's what we see, here's the model results. Here's the expansion of the going to the critical point of the phase transition and here you see the size of the patches. So all this means is there are a few big patches and there are lots of little patches and here is the fit to power law model. Okay, so there's the model world, here's the real world. If I asked you if that was a beautifully organized example of a critical transition, I think you think I was. If you hadn't heard me talking until now you'd say what it looks pretty random to me. That in fact, if you calculate the frequency distribution of the patches, the blue ones, the yellow ones and ask, what is their distribution? How big are they? Here's the blue triangles of the model, and the red dots are reality. Five orders of magnitude, we don't see this in anthropology, it doesn't look like this. So, this looks like it might actually, there might be a real relationship. And in fact, an amazingly close relationship between the predictions of this very simple model and the actual view from google earth, okay? So, we fired up Google Earth and looked ,we thought we do this properly. So we didn't try to pick and choose, patches that look promising. We just look for areas that didn't have much cloud cover, so we could actually say, okay, here's the case, we can see and let's just draw boundaries around this. Send this to the geographic information guy, have him send back the patches and test them. So that's what we did, here's another case, and this is the fit of the patch distribution and then I began to think i've worked for a long time in Bali. I've been asking farmers survey questions for years, and one of the standard questions was, how good is your harvest? Now how does your harvest compared to the other guys in your subaki better, worse the same. And case after case until I stopped asking the question, they would say the same, if you ask, are you doing better than the people elsewhere in Bali? They'll say no, farmers never want to admit they're doing well. But if you ask them, how well are you doing compared to the other people in my particular in my neighborhood? They kind of can't claim other than they're doing equally well, because we also measure the harvests. And indeed, the harvests are uniform. They're all doing, they're all doing well, but more importantly, from the standpoint of cooperation, they're all doing equally well. I mentioned at the beginning these things have been there for centuries. We do not have a lot of examples of successful cooperative systems of resource management, at large scales that last for centuries. So, maybe this gives us a hint as to why that could evolve and then be maintained on the island of Bali. Here's another case, more Google Earth, I mean, even Stephen was impressed, right, this looks like physics, not like anthropology. Okay, I think, here's the overall thing I could keep showing you slides, but this is the average, okay? For 13 cases, we picked in some cases, different days, different years with the same patch and I won't belabor this any further, but I'm really happy with this graph. Okay, it looks like it worked, and now they talk about low hanging fruit. We just took two of the examples that are in chapters two and three of the basic text in nonlinear dynamics because the lace book. I think sample model, and we're just using that to look at this world and that didn't work. So, my message here be encouraged actually, maybe, we just look around a little we may find, we have hardly begun to ask where to look for application of physical models to the real world. It we already know that it works for things like the patch distribution of vegetation and it looks like can also work for these human systems. All we needed to add was adaptation, because in this case I mean what's different between this and Savanna. Nobody is forcing the savanna its internal, positive and negative feedbacks facilitation by vegetation. In this case the farmers are trying to grow rice, so, you need adaptation, right? You want to include adaptation in any model because they are actively manipulating the ecosystem to get what they want out of it. Okay, so that's cooperation, we gave it a name like two weeks ago. So, we decided we call this model adaptive, self organized criticality, so self organized criticality refers to things like the sand pile model. This is just adaptive, self organized criticality of the difference between this okay, so that's one difference between this and the sand pile. There is another important difference, here, the patch distributions have functional significance in the savanna model. One patch is much like, they only vary in size, but in this case, they're at different rice stages. The farmers are choosing when to plant and harvest so some are wetter than others and that's what drives it. Okay, so that's why it's hard to see that there's a dynamical process going on because what you see is a patchwork of colors, right? Patchwork of colors, those colors have functional significance. And so, the adaptive process tweaks allows the farmers from the bottom up to tweak and to manipulate those irrigation decisions until they hit an optimum. It just so happens that the Lord of nonlinear dynamics made that easy. Okay, Pareto optimality emerges exactly at the critical point, the code for the model is make available, you can fire it up if you like. It goes to their critical point, Bingo, it's done. Actually evolves that way just like this anti GMO, and that is except that, unlike the sand pile, it has to be sustained by the farmers. Okay, that's the model story, all they need to read are the signs from their own local neighborhood. There's nobody sitting on top designing the system as a whole, they're just local interactions. But they do interact group by group,they interact with each other. So I'm just going to explain that briefly. Here's our village. Here's our Water Temple. Here's our Subaks. Okay, but the water for us comes down through here and it's shared with this village over here. And how much guts to that we're, depends in part upon how much comes from up there. So we coordinate and what we do is we send out distinguished priests or two, to this village and then to that one. And say, okay, when are you guys going to plant and then we'll offset by a month, or something like that so that we can optimize the water use for everybody. You control the pests in the water. They do this constantly. If you go to Bali, you'll see water temples up and down the watersheds. What you will never see is people from this temple going to the next watershed over, there would be no point. Because this is the water temples are actually controlling their, temples are just places where people meet. But they provide a structure that enables the farmers from the bottom up to control the irrigation systems by simply going and talking, and coordinating with their neighbors. Just like the model you see, no global controller is required for that to happen. Okay, so each one manages its own terraces, but they also coordinate with the other subaks. Okay, so, A and B, and C coordinate, okay. Well hit a bell, okay so point is planning the same time controls the past, but uses all the water. If you try to write the equations to differential equations, you don't get all the water in the right place and manipulate all the manipulate solid. This is a problem, the case where we actually got real data included 173 Sue box, you can't solve it, it's too complicated. There's too much variation, so on the other hand, this bottom up system really works because all they have to do is adapt to local conditions. Okay, so that's how it works. There's one more point though, which is, I've given you a very straightforward, functional explanation about how it all works. But there's a little more to it. And this is the little more to it. So, there is a global attractor for the whole thing. All of these local groups are cooperating from one, from the top of the rivers down to the sea. So you have basically adaptation happening in several different watershed valleys. People are aware that this is going on. Right? And here's the goddess of the lake, who is believed to dwell in Bombata, this is the volcanic crater lake near the center of the island. Farmers this week are coming, roughly 250 villages are sending offerings to the Temple of the Goddess, culminates on the full moon. I'm going here this weekend, lucky me. Okay, so and what they're doing is bringing the harvest, bringing tokens of the things that grew in their fields. They then ask for the blessings of the gods that have to do with the fertility of fields and their children. And then the food that they bring to them, the rice, the things that grew in their fields, the temple people then cook and share with the other villages. So, my rice turns into your lunch the next day, this has gone on for as long as we know and it continues to go on today. So what's all that about? Well, this is the the ritual they call Pula, karate. It's all about celebrating the fertility that is created by the gods, but with a little help from the farmers, right? It's an obligation and a joy to participate in that, right? Far actually the Balinese performers compete for the invitation to perform in this ritual. This is how the temple used to look, we know it now exists on the rim of the crater of bachelor, but here you see it when the village and the temple were down by the lake. Here is there. There's the active Caldera. It's an active volcano. And here's a wall of lava. That arrived and then stopped just at the entrance to the temple,1906 I think something like that. In a lake and that was even the Dutch controller was there at the time, thought that was pretty miraculous, the walls just stop there at the temple. Okay, so anyway that happened later on. However in the 30s, the temple was covered with another volcanic eruption and they moved up to where they are today. Okay, the point of this, here they are today, okay making these offerings. So I've given you a functional explanation, but I also encourage you to think that there are consequences for this people. You know, if you're going to look for similar cases in the world, which I encourage you to do. Google Earth will enable you to calculate correlation distances in landscapes. We provide you with the code to do that, you can just move your look anywhere. We just started to do this and a few other countries looking at rice terrace and say, okay, here's an area that's an anthropogenic landscape. Meaning humans have affected it. So if I'm right, there's an adaptive process. If it is not commercial top down agriculture, but the people are managing it. Then my prediction is that there will be, you can calculate the correlation distances in that landscape. It may or may not be at the critical point. It's an open question. I'd love it. If any of you got interested in that. It's pretty straightforward. They don't mean their home, you have to. The only really tricky part is getting a GIS person to code the Geographic data. Once that's done, it's just a question of running the algorithm to find out what the correlation distances are. So I bet my prediction is that we're going to find lots of correlated landscapes out there in the world as a result of this adaptive process. Okay, so, there is a take home point to this, I think I'll just give this part of the lecture today. The story I'm talking about is intertwined with the story of the Green Revolution in Bali. Created by the government by the Asian Development Bank with noble intentions to feed the people, right, to increase the rice production. As I mentioned earlier when they launched this program of agricultural intensification. I told the farmers by all means continue your colorful rituals in the temples, but you guys need to plant as fast as possible we need to grow more rice get three crops of rice a year. Bonnie's now refer to that as the period of hunger. It caused chaos in the irrigation systems and explosions of pests. I'm quoting from the final evaluation report of the Asian Development Bank. When we first discovered how this worked, I wrote to the Asian Development Bank repeatedly and said, you guys are making a mistake. These water temples they have a functional role. And I got back two letters actually it was in teaching in California one address to the head of the anthropology department who happened to be me. And the other two me myself and it said, Please do not send any more letters criticising our agricultural policies in Bali, it's easy to criticise and damage a project. You're doing something dangerous and we were really at our wits enemy. We just thought they were making a mistake. Fortunately, they sent an evaluation team, including a trained high job hydrologist whom we happen to meet in Bali while they were doing their evaluation. And that guy was kind enough to go with us and observe, and he's now a great fan of the Water Temple system of Bali. In fact, they show our movie at the Asian Mellon bank, but it took some to make it possible to see this thing, took a kind of a shift in perception. I mean, it just looks like, if you look at the control mechanisms, what do you see? You see temples, and you see little guys with like cups of water and flower petals and irrigated, irrigated fields. The only really tangible evidence is the synchronization of rice cropping. You can see that if you're driving through Bali and you'll see areas where everything is planted at more or less the same stage. The water template work, if you see the rice at different stages Cooperation is broken down. You'll see that around the towns. You'll see that in places where the traditional system is under threat, mostly by us, but foreigners. Okay, anyway so that's the story. I think I got one more minute. Cambodia. Where else might this happen? Our next target is Camaro, this is aerial view of greater Angkor Wat. A few years ago, they use Lidar imagery and discovered that Angkor Wat was twice as large as they thought the largest pre industrial settlement and on the planet. Here we have huge irrigation tanks. And here we have this elaborate system of irrigation. So the archaeologists have been wondering for a long time how that worked. It looks a whole lot like Bali in the sense that there is also, they don't have a master Water Temple. But they have a master source of water this river, which flows over an image of Vishnu who is the god at the Water Temple in Bali, and the water is purified as it flows down. This was built by the way at the beginning of the Khmer civilization, down to the storage tanks. There we see the largest religious building in the world, here's what it looks like. I mean, it's an enormous system, and two orders of magnitude bigger than Bali. And they're in the middle of the lake, the storage device. Built by hand, I think it's like seven kilometers long, built by hand. We have this temple and who do we find there? But Vishnu, The male version of the deity of the goddess of the lake in Bali. Okay, in my last slide, okay. I couldn't resist because Jeffrey gave you a great talk about the dynamics of cities and a lot of people work in that area. But there's a city. There's a natural system. Things are changing in this world, we need to get better and smarter at understanding how our adaptive processes change the planet. So I think that's an enormous challenge. Not just cities. It's the rest of the world. Okay, I think that's it. Yeah, I'd have another whole talk on language which is a tale for another day. So thank you very much. [APPLAUSE]
