Okay. Good afternoon. Welcome to the Urban Transformations lecture series at Purdue. I know a lot of you may not be on campus. So welcome we have a distinguished speaker it's my honor to introduce him. I'm Andrea Rinaldo, Professor at EPFL in Lausanne, Switzerland, as well as Professor at Padua University in Padua, Italy. So I'm wearing a t-shirt that has a logo Padua logo if Andrea hasn't appreciated that. I have one. So, in honor of you. Here you go Andrea. Oh, lovely. Yes. Yes. So I've had the pleasure of working with and knowing Andrea for a long time. He's a world renowned authority on many subjects, and his degree, we are proud to say PhD degree is from civil engineering. 1983. Since then he's gone on to fame, including many honors, or list just three here is a member of the National Academy of Science as well as National Academy of Engineering. And he is honored this year as the recipient of the distinguished engineering alone at Purdue. We had a virtual ceremony recently. And he's also honored as the first cohort of Neil Armstrong distinguished visiting professor in civil engineering. And so he's visited Purdue several times, given couple talks in the past, but he's agreed to give a special talk constructed only for this lecture series. And Andrea, we are recording this and will be only available for consumption on request from Purdue colleagues. And with that, the floor is yours somewhere. Yes. And I just set my alarm to make sure that I don't get carried away because of things I, I like quite a bit and well, thank you so much. It's a great pleasure to have the pleasure in the non to lecture to my fellow Purdue students. I'm a boiler maker, as you heard, and probably so. And I'm glad that to Satish to duration to buy up or making this possible. It's a pleasure to talk to you about. I give you my five cents about a few issues that are in fact stimulated by the discussion we had with duration satish. Maybe a couple of weeks ago. So, can you see my screen first of all. Yes. So that's after some mumbling that's that's the title that I chose for you it's called reflected in water means that it's taken from it's a it's a what if you wanted to tribute to Sandra Postel just got the stock of water prize. It's beautifully well about the global water resources issues and reflected in water means that it's reflected in something we can actually see for what I'm a hydrologist. What I do for a living I study eco hydrology that is water controls on living communities by all time general. And I tried to sell you although I'm certainly not an expert in urban transformations or regional resilience. I tend to believe that some of the things that we see actually from the water patterns have to do with development have to do with resilience and have to do with inequality something I care very much for like your teachers. So, the main I can anticipate the main lines of lines of thought that my talk will follow is that, while the impact of improved agriculture, it's all of urban transformations for instance it perceived immediately and directly by economic indicators like gross domestic products and the likes of a of a whatever region whatever appropriate scale you might devise economist work from that for a long time. The, the social and economic costs incurred with the with the ecosystem services you lose in many a case not all but in many cases is typically largely unnoticed it doesn't have a balance sheet. So very idea that I want to, to make specific examples of course in the course of things. And while contemporary economics in fact considers the proper manner to account for the, for the cost of, for instance, loss of workforce of any kind. Certainly you can actually devise fairly well we are development economics so it is called is fairly my fairly developed discipline any rules in fact whether covertly or, or overtly our, our lives. In material factors pitch in and a tour assessment of the values where natural capital you lose by certain things that certainly includes urban transformations and certainly have to do with regional resilience. And so I'll be I'll be somewhat insisting on on some of these concepts in what comes about. And the picture you see here, I know it just you see that, well, I put on the upper right corner that that the remainder of the screen of a zoom thing in there you see in here is Sir Patha das Gupta from Cambridge University, good friend of mine, and major movement shaker in environmental economics in fact one of the founders of the discipline. And if you look at if you Google him up, you'll see that they he's re very recently has been frontline news because of a so called Das Gupta report on the economics of biodiversity. It's a, it's a very long and elaborate book but it's I only read because I'm waiting. I mean good quality time like Easter vacation for instance 20th only, but I read the executive summary and it's absolutely breathtaking super, super interesting and Well, what is his thesis as as you've seen here report as something from his beautiful the development of nature and the nature of development there was the title of the long article for political weekly political science weekly that he published a few years back not remain What he contains is that an economy gross domestic product or whatever measure you want to have of a well being of a wealth of nations could be made to grow and it's related societal indicators made by can be made to improve for a while by mining natural capital. What is natural capital is that is the ensemble of ecosystem services the nature provides for free in fact and we tend to devalue precisely for the reason. That is, the loss of natural capital because you decimating forests damaging soils, destroying ecosystem services like in particular case I'll be showing you has to do with water. And this is taken from a picture I took in Burkina Faso where did some fieldwork for studying waterborne disease and the lady simply crossing the spillway operating spillway of an affair and federal stream in a sub Saharan nearly tropical nearly equatorial effect climate which are hanging there and I'll talk about the development in this case embodied by the by a small dam and the answering irrigation structure and and those ecosystem services could be as I was hinting at renewable resources or using biodiversity whose price you can certainly not immediately use but they pathos thesis is that there is no excuse for not using what we have learned recently to assess the true costs and benefits that include the loss of natural capital and make specific example and what and to rethink something very, very clearly worded in the presentation of your beautiful urban transformations classes series of lecture, that is, how to rethink distributed justice for a large share of the basis of environmental thinking could be made quantitative. And the ability is in fact is that precisely hinging over fact that it's many a case is too vague to lightweight the kind of predictions that economists are allowed to make. In terms of in of, for instance, ecosystem services it's one of the liabilities of ecology that's why engineers and boiler makers can help because we are inherently quantitative. Why can't I progress. Okay, here it is. And let me make an example which is a trivial example from a beautiful paper which I recommend for all of you to read, because it's written by a famous mathematician in a contemporary physics in 2005. It's a very obscure journal, and he has lovely like 5000 citations because the pieces written beautifully well and explains the mathematics of complexity in a straightforward manner. So what you see here, it's a one of those calculations you can do by opening any archive in any particular place of the world that is, you have essentially an archive of the size of the cities ranked by population in any particular case in the case in the United States in a particular year. And what you have in there, you simply do you're at you calculate in its trivial. You said for instance the population and then of course you have to define what he's a city. And what is the city of course it's your urban transformation and suppose the city is something which is bigger than say and people gather together right, the smallest city in fact they're making fun of what is the smallest city population for, or something but let's avoid for the sake of argument, the definition of what is a city suppose it's a reasonably large human gathering with some admin structure behind it. Okay. So what you do essentially here, you count the, the, you have a population of each size, and you set a threshold for instance 10,000 people then 100,000 that a million and 10,000, and you count the relative proportion of the cities you have in your whatever geographic area you are dividing relative proportion that is the number of cities larger than or smaller than it's a complement of that a certain value divided by the total number of cities you have in your archive. And you got a curve like the one you see on the left. Okay. So you have like in this case 20, 200,000 or 400,000 it's a particular sample of the United States. What the new man asks you is to have something which can do with any of those tools can do it on your phone if you want, but he's put it in the log log plot. And I'm afraid I don't have to tell a boiler maker what the log log plot is right and something like what you're seeing here appears. It's something in which what plots is a straight line in the log log plot. Obviously if you take a logarithm of the P of X, of course, in this case of probability, the probability density function if you want or I'll show you in a minute probability of exceedance is what I showed here. So it is no trick. The two things are completely related. And suppose the underlying random variable that you want to define that is the size of a city at a certain point in time. Why it's interesting because you want to monitor urban transformations right. So the X is the size of a city and the probability density of X is simply something of this kind. Right. So that is the shape I want to test what I do in a product in the log log product and I have the log P is equal to log of C minus alpha by the log of X by mathematical properties you know from high school, certainly from boiler makers have been exposed to that for a fair amount of times. I have been attending very serious theoretical physics conferences especially the in the early in the beginning of a century when this was a very hot debate. And you've been people discussing what is a straight line in log log plot what fits as a straight line in log log which is not immediate. It doesn't take a very sophisticated statistical analyst to see that this very much looks like a power law that is a structure of this kind. And the slope of this curve is exactly this value alpha which is quite interesting in fact because for instance half has to be larger than one. And for this distribution to be normalizable you have to have a mixed mean, but that's interesting because we said you cannot have a city of size zero. You cannot have a city right to have a minimum value for sure. And I have to be a larger than one, the empirical value observe better larger than two because there are consequences but I'm not talking about the mathematics of power laws anymore. And so it's essentially I'm asking you to count relative proportions you can do an Excel sheet and plot them in the log log plot, any kind. The, the size of the cities in Indiana it does already something of that kind, but you take the Midwest, when you take the US you have those data electronically you see that this is remarkable. In fact, the slope of this curve is remarkably close this alphas close larger than or near to, which is what is called zip law that is something which in the, in the history of quantitative urbanism plays a role in the size of a city was what it was devised for. And then why power laws matter. Well, the idea is that power laws I won't do the math but is essentially is a distribution scale invariant. It is, is a distribution that whatever scale you look at, or however you decide to course grain, for instance, if you want to average, if you take the value of what you observe within Indiana, the distribution had within Indiana, or in the Midwest, or in the US should be the same. That is a true probability distribution that follows these algebraic law in here. And why this is important because scaling variance is a signature or something which is fundamental in this theory of dynamic systems, because it sees is the signature of something which is essentially inevitable. What it means in essentially maybe something can do anything about it. I mean you perturb the system as you then please, and the system will go back to initial state. And this is particularly interesting. I, the conferences I was mentioning in which people have been discussing for a very long time, what is a straight line and log log plot what fits a straight line in a log log plot. It was when pair back my friend, the inventor of the SOC, so I can actually here was roaming conferences all over the world to explain this thing. The idea of statistical inevitability is something which is very important because if the outcomes of an open dissipative system with a huge number of degrees of freedom is the same regardless of initial conditions regardless of tuning or parameters, a goddess that tunes the parameter of the thousands of tens of thousands or million of parameters that define the urban transformation that means there is something which is quite interesting other than completely chaotic the system goes in the exact opposite system. Power laws are telling you that. And, well, what's interesting because in fact that clarifies briefly and it's a technicality but the fact that if you want to study the probability distribution that is a sample. You have to do a thing which is called the beanie that is to calculate how many you have in a certain area. You essentially stated bin and say how many guys fall within that area and divide by the size of the integral. So what looks smooth in a log in a linear plot looks rough in a log linear plot when you have oscillations that tell you, okay, look, there's something quite interesting about the situations in the system because when you have, for instance, how many cities you have a size, like, whatever, but this is a particular sample taken from a synthetic sample is not the city, but how many cities you have around 10 minutes have only one. It's an issue of positive of data, which is generated and exacerbated by the size of your sample. So the idea is that you can always do that and change the sample into something like a logarithmic beanie, or better than anything you simply take the percentages. You can take the size of a system with value larger than X plots beautiful well, like a straight line in this case. And what happens is that the slope of these guys related to this one by one, for instance, the PDF, the p of x has an exponent alpha the other hand exponent alpha minus one. For example, I want to show you it's it's something I worked on for many times where it's a particular narrow and idiosyncratic. The view of course it reflects the five cents I know what I'm saying is that my, I never claimed my reflections are not idiosyncratic they are certainly, and they are my, these are my path to my idiosyncratic reflections on resilience inequalities and the river network something can extract objectively manipulate over orders of magnitude simply based on digital terrain maps, which you can buy by green grocers nowadays and free on a scale of 30 by 30 meters worldwide. You can extract beautiful shapes that are generated by the system. So essentially in there the master variable is essentially at any point through the various directions which is gravity rule, which is fairly easy to extract. And if you take for any size within the, the, the, your catchment you can calculate the total contributing area is a number of nodes you have connected on your back. And this is a random variable and which has a certain, a certain features don't look at the, and the recycled slides in which I was talking about more serious mathematics that is involved with it. And see what happens. That's also an interesting feature which is part of a scaling and that fails many observers, even important ones and that has important has to do with what I'm trying to tell you today. Suppose this is the largest size of a very large catchment. Okay. And this is a probability of exceedance of area is your close your eyes, you point your finger at the map. And this is the value calculated there you have a total contributing area because you have a tree in there and the number of nodes connected. It's a quantity which is capable and it's unique. You treat this as a random variable and you study the probability of exceedance of a certain value small a as you're seeing here. Now what happens is that you do have this effect that is, it's a power law with a well known coefficient, we explain how nature works in the sense, but that dies off as soon as you approach the largest size of area. Now, why this is interesting because if you chose, if you chose a smaller some, okay, you will still have that much of it has enough data. So for the power law, but falls off relatively soon because you can't have areas or statistics of them. So you have to start off larger than the maximum and you lie yourself to expose so there is a sample effect. There is the finiteness of the sample effect and this is called the finite size effect, which as I've been trying to show will have a small role and it hasn't a major role in science because the guy who developed it through the research approach got an overpricing will in physics, Dr Wilson in fact, and, but it's very important even for modest engineering purposes. So we learned that's where we come from we learned how to extract from digital terrain maps for these look this a leader or lighter, if you prefer a flight in which you get elevations very precise filter vegetation over size over, nowadays, and you can actually extract those landforms and wonder. For instance, I'm tempted to see that there is an interplate of name of the built and financial environment in this case, although it's not totally obvious to me, but certain beauty pictures in, and the idea that the only way you can actually start thinking of attributing values, for instance, cultural services to the ecosystem ecosystem services that can be cultural services that beauty, for instance, pleasure and the likes seems to be within reach. Well, power laws are almost everywhere. Many of them and many processes tend to show this particular behavior. And these are called Pareto distributions because in some cases you have a tail, which is an algebraic tail that is put straight in a log log plot, and it can be big and can be very large but these cutoff effects in fact can be reasonably well considered within a framework that can be a cutoff in which you have the minimum size cutoff over maximum size cutoff. For instance, one example I adore, and this the other one population of the city is the one we have seen that is called the zip law, and the richness is something talking about inequality net worth in us dollars, the distribution of richness in a sense, which tends to be a power law, a framework of inequality because I have very few guys that super rich, and a hell of a lot of guys, the largest proportion that, in fact, have not. So the difference within have nots and haves as you jargon, you typically say, is one in which that tends to be broader. It's very interesting and I would take, in fact, the two hour lecture on these. That is, if you take the Koran or you take the Bible or if you take mobidic, which was done for first time inside the frequency of words, what is absolutely phenomenal is that the slope of the frequency of the use of words in different languages, different aims, etc. is exactly the same, regardless of the type of book you're reading. So what this is telling us is that Chomsky is right, that he is probably grammar and language is a reflection of the way we built in in our brain. But anyways, that's not what I wanted to tell you that it's relevant to another issue more directly I could chat about that for a good two hours anyways. So, this is taken from a work in which I had a part because I suggested the, the, the scaling analysis that we carried out the guy is an urban scientist and urbanist that there was a design at the time he got his PhD and then moved on somewhere with the fact that he was working with a company in Switzerland, Emmanuel Estrano, and what he took on was the study of of the global road network, which is a very large database required a very, it's big data, big, big, big data, actually. And what the guy was capable of doing by proper layering of something which is probably, you know, 100 times better than I do. It's, it's the idea on how in fact you would be attributing area to urban areas, cropland areas or same is so-called natural areas the colors you see in there, red, blue or whatever. And any fight, what are links that are parts what is the length of the road, you take junctions and junctions will be defined properly of course I'm not giving you detail but that's absolutely ordinary. And you defy link length that is the road length is the size in between two consecutive junctions notes on the system. Okay, something of this kind so they get the fraction of total road length, for instance, and you see the course you can't have roads, bigger than say something like 100 kilometers right this is 10 kilometers and this is a 1000 kilometers or something. But certainly what you can say is that the footprint of of ongoing urbanization is immediately shown in something we can remotely acquire them exactly manipulate, like in this case, the road length structure, which is this is data is no manipulation that what you can say that in reality by manipulating by using those scaling arguments you see that is, you look at the structure and you can do some tricks for instance studying what happens to be the distribution is very different, much shorter, the one in which you have urban areas in fact and it's typically the case, right. So urbanization has a footprint as a clear footprint in the shorter length of the links because you have to serve way more nodes, essentially, and yet for something as you're seeing here, in which you can have those distributions collapse. Perhaps telling you look footprints are evident and yet, there's something of the features that call for inevitability that pitch in at a certain point. And you can do that in particular if you study for instance the rural roads of India, hotbed for urban transformations of course, because it's of a base that you had in there well what's about developing world is something quite interesting if you think of my friend Jonathan Ledgard, master of contemporary thought, this is professor at PFL for a couple of years and chief and economy chief correspondent of the economist from Africa, said in a famously delivered beautiful talk that for instance you think that within the next 15 years he said last year, 800 million Africans will live in cities that do not exist yet in 15 years, one five. The idea is that is very new way of calculating footprints for instance, and, and those properties you can use some of those beautiful properties of power laws if our laws will tend to become. Then, if you course grain the distribution, the distribution should be untouched because the distribution looks like whatever the scale you look at. That's something which you can test physical so in a sense, you can actually do GIS to the geographic information systems, and a bit of an idea what we believe that should be in fact the footprint of the urban transformation should do the trick for us. That's also an interesting plot suppose that now the richness as we have seen empirically obeys a power law distribution, so few rich guys and many poor guys and inequalities tend to be exacerbated in fact with the with the pandemics ongoing of course because they protected social classes and not very many indeed I mean I belong to one which is protected in fact so that's not why I should be particularly happy. What happens is that so this is a vision of the quantity and as empirically known I showed you before. So you can see that you can calculate the fraction of the population, for instance, and that's the trick that does it for you. You want to know what is the fraction of population which supports half of the other wealth and half of them and the fraction of the population. If you calculate the value of the wealth you calculated this value one half, and if you do the carry out the calculation defined the variation of this, this you see is actually from one half to to the total is refraction of a relative wealth equal w this value here, and you call P the fraction of the population that is one which don't put the P here. And the exact result is that the value is P of alpha minus two divided by alpha minus one P raised to it's an exact result pretty easy to derive. What happens is that now figure that the distribution of wealth has a typically is a power law distribution that very closely approximates 2.1. It is larger than two, just larger than two. Why this is particularly worrisome, because that means that to the 20% of the richest population owns 80% more than 80% of the wealth. So the inequality is majestic. Meaning the upper the richest 20% of the population embedded in a distribution we have the feature of statistical inevitability. It will happen almost no matter what you do that will concentrate inequalities in a in a spasmodic manner, which introduces me to another thing which this is again back to my friend. And it is then isn't that perhaps because we don't calculate wealth properly. Well, no economy can be made to prosper forever by mining natural capital the example that I show you here is a transformation of an of a mangrove swamp into something which be drained and convert to say that's example I typically take because that's the case here.  And the account of depreciation for natural capital means that in the GDP of that area was immediately see I mean immediately in a year or two, the benefits of employment of commerce or whatever you name it okay. And then you will see the costs of ecosystem services you have lost, there were issued by nature freely in terms of fiber production these and fish nursery area flood protections you name it carbon sequestration and the likes, even on a grand scale. Why am I suggesting that and why this touches the issue of reducing the qualities which is central in your in your considerations because it's a call the curse of a could snets curves, what are they. The first snets was an expat Nobel Prize for economic was a Harvard professor, in which he plotted these variously quoted, in fact, curves, in which essentially, you have a per capita income, or proxy by proxy for economic development. You have certain outgrowls like pollution on one side on social quality. What could snets used to say is that in pre industrial societies in transition you have these inequalities increasing only to have it beyond a certain establishment point, the richer the society, the lower the level of social inequality. And the same happens for pollution at a certain point, a developed society. I mean, first, there was a famous Latin say that at first, you have to survive and then you can start being philosophizing about matters of this kind. So we were under the spell of a could snets curve in which we said, Well, let's start on bother. Let's get richer. And then things will mend themselves automatically. Thomas Piketty in this beautiful book. Well, beautiful is a strange word for a book which is like 800 pages. At first 30 are totally exciting and then is boring like hell because it's an empirical book et cetera who nevertheless had enjoyed planetary success is called capital in the 21st century. It took head on the could snets curve and demonstrated that the reason why could snets had that empirical here he produced the empirical evidence that the could says basis consideration song, but they were post Second World War recovery, thereby not representing what happens now. And it is far from true that richer means today means a more equal richer society is sports and supports and forces less inequality, even empirically, and my faculty basis. That's something we have to remember. That we have to be fair, we have to price for planet, but the price tag on what we see in the system we have to. It's kind of considered no unclassy certain circles in Europe. There's something fishy about the leading the price tag on a thing it's not stylish right, but in reality to say it's priceless means worth nothing in the economic terms. And the key why we've been slow in realizing that you see for instance is how can you, can you put a price tag on on beauty. This is my lagoon of Venice my hometown, and my, my birthplace actually I've been living outside the city for many, for many months, and we have the symbol of the science of a coexistence of anthropocritic is a built environment in this case, fishermen's nets, and the science of the self organized system of, in this case is the title network of the next one where this cost a concept of ties. And this is an example that my friend, Suresh Satish, my friends are bored to see but something I care for I took a picture in Bangladesh when I was doing fieldwork on on cholera on the save the ecology of the, of the water controlled on the cholera pathogen. And what happens if that this guy was actually trying to show me that it can be the water, the mighty waters of the Magna River that causes infections. Well, by the way, I keep I keep going I assume that my, my, I still have six minutes and 16 seconds before the 40th minute. So, this guy was showing that it can't be water the Magna is a mighty river, etc. The only thing is that this guy was drinking the water like 200 meters downstream of the largest Dariel disease hospital in the world in that in Matlab, believe it or not, near to DACA Bangladesh, where in fact the pathogen evolved originally in the system. Now, why I was disturbed by that it's a cover of my recent book I'll show you at the end of the, of a discussion to see my, my, my punchline is that can we predict whether the guy will catch cholera or not. Very complicated. Why, because you catch cholera if you if you drink a dose of bacteria, if you ingest a dose of bacteria that depends on your body weight essentially, but depends on the number. And the probability of being capable of predicting the point wise concentration of a of pathogens here, given that you don't even know the boundary condition upstream, you don't know uncertainties and things run so huge, but in reality, you see that are the weakness of our predictions is a permanent liability to put price tag serious price tags. And an example particularly important sorry for the, I forgot the label in Italian here is a debilitating disease called schistosomiasis, something which is generated by a cycle in which a pathogen survives in the bowel in the urinary tract of a person then he excreted with fishes or depending on the type of bug if you want. It's excreted in certain form, which is called the schistosomia aponecum or mansoni or hematobia depending on what happens, etc. That has to affect the intermediate host, which is a fresh water snail of a bulliness genius, etc. that hatches this particular path that is called sir carrier, and if you put your hands in the water, you catch the disease can be clear by getting the anti parasite project one 10, but it doesn't give you any immunity, so you can get it as many times as you go next to the water, and you see that this is a learning impairing and disability a strong disability thing and what happens is this is happening so where the incidence of that disease became gigantic, this is a picture I took right after the first big storm, the water courses are ephemeral, and where they built something like 1500 small dams financed by the World Bank by generating huge networks of irrigation structures and the result that the incidence of the disease went sky high. So what what was disturbing is that the meta analysis of the relation between schistosomiasis and water resources development shows that there is can be any possible doubt, the fostering a better agriculture through the extension of agricultural networks, in fact, very large and very developed 1500 dams, I mean, no big thing, is certainly showing up in the GDP or Burkina Faso, but certainly the cost of the incidence of a disabled years of workforce of a poverty reinforcing effects of the disease, it's not seen by it, and with that ecosystem services in the natural capital that goes after that. So just running around what I'm saying is that with these considerations I'm showing three giants of the field Ignacio Rodriguez from Texas in a university. Ilka Hanski the late Ilka Hanski the ecologist and Marino Gatto, my colleague and friend the theoretical ecology started building on that and started thinking whether we could, how far we could stretch this concept by using the Steve Hubble's gigantic step forward to the unified neutral theory of biodiversity and biogeography which I won't be able to discuss today. Long story short to make the idea that you can actually calculate and that's the urban transformations that you can take into account, for instance, by changing for instance, by removing some of the small dams artificially in Mexico if you care, you can calculate the mean distance from any human settlement to the water, and with it the probability that of the incident of the disease, in effect, the random reward of small dams gets an increase in this measure this measure is the prevalence of a disease from zero to one, the pockets in which you have prevalence one in a certain age group. And this is a basis to which you can calculate what happens. I'm pretty sure that this will soon bloom out of proportion. The idea is that then you can study disease and what about disease in particular in this case. So, what I'm showing you is just other field work I delighted in doing field work in this case in Haiti at the peak of the 2010 outbreak, which is the, you know, it's a symbol of our responsibilities because Haiti, the poorest country in the world, struck by an earthquake that killed 300,000 in 2010, was in fact seeded, it was cholera free for like 200 years, and the disease was seeded by UN peacekeeping troops coming from Nepal, which is a shame. And it's not the story I'll tell you about, and only to introduce the last thing and you have a super expert on the subject and professors who could surely satishize a real expert. What happens is this lady that was approaching this guy here, and even at the height of the color epidemics in the car for suburb of Port-au-Prince, again, the most dilapidated market in the poorest country in the world. What happens is that this lady has shown an Nokia 1900, the phone, with a proof of concept and got one of those cabbages to take away.  Here it is, I'm only five minutes short. Yep, and I'll be concluding very rapidly within five minutes. And so you had no police in this case, no roads because no road infrastructure remained at the earthquake. And still Nokia had inroads in there, and the ownership of the phone, for instance, as no social layering or social connotation we thought. It's very short, you can show where people moves by tracking their phones and this how in fact you can model cumulative cases from data and model, of course, I won't bore you with that. But what I'm saying is that, in particular, this is important to say, well, you could actually had you heard perhaps about gravity model, radiation models and the like. Well, try to go to Senegal, like with the flabby finger my student did. What you see here is the number of people tracked by the phone calls old phones in fact you needed to make a call to be able to end to be relatively roughly related. New generation of phones in fact have a GPS embedded so you have effect on can have very large numbers if commercial reasons don't prevent it to know where people go. And even here, in the actual movement of a population have peaks, what are the peaks is a religious pilgrimages. This is a grandma gal the tuba one year, and the next year, and these are all the things of religious ceremonies. What is interesting so this is the population during the grandma gal the tuba concentrating the place where they sing. It's one of those very respectable events, etc. And of course, if you have a concentration like 100 times more than the normal population, which you're seeing here, you expect that you can have sanitary problems, etc. And this is the map of where the disease was spread throughout the system. Also because in fact, whom mobility, this is how it operates in Senegal. And this is how we simulate the system. A long story short for showing you that that's instead something completely different, but relevant because if there is one thing that's changing our lives and the future of cities in terms of as advertising your beautiful leaflet for your class is 19. This is I'm sorry for them. I forgot to change the label. It's in Italian. This is how, in fact, the epidemics spread in Italy in the early phases of the thing and there's nothing like a mixed system in there. What happens in my region, the Veneto region close to the place where Suresh got his beautiful shirt that is porting up vis-à-vis events and what you're seeing here, this is spotting things, etc. These are the daily new cases in a place and the cumulative patterns, etc. This is how in fact you can have these things simulated. And you can generate systems in which in fact, even in this case by the same token by tracking mobility of the people by tracking phones, in fact, vital, vital, vital ingredients of a spread of infections. You can actually make computed and simulated values of a system. And that's my last slide and that what I'm saying is that we, I mean, we published a book, in fact, November 2020, which contains not the urban part of it, but they reflected the water part. That's what I'm saying. So I'm asking, will future large-scale water resources plan be capable of making compelling arguments for including the reduction of the loss of biodiversity across the river basin? Or could the structure of the river network be a template for the spreading of waterborne disease? Can it be seen as a template for urban transformations, as we have seen in some cases indeed? For instance, the method would be suggesting the main directions of a population migration, something which is very important in coupling the system. I'm coming to my conclusions. I'm leading to you to respect the five minutes of the other blah blah. But what I'm saying is that what I care very much for, is why this is a very important for the issues of your class. A fair distribution of water is a major societal and economic goal. Something which would involve discounting the environment and completely rethinking social equality. Thank you. Thank you, Andrea. I hope it's probably close to what you wanted. Thank you very much. We will take some questions from the audience if there are any. Unmute yourself please and ask a question. And then mute yourself so Andrea has a chance to respond. Are they able to unmute themselves, Gaia? You should be, yes. So yeah, go ahead. Thank you. Dr. Rinaldo, yeah. Good to see you, lovely. Good to see you. I'm in the same continent. So first of all, thank you so much. You are in Leipzig, right? In Magdeburg. Whatever. Yeah, close enough. I actually, my question is not, I think it's not a question. I want to, I am curious to listen your perspective to expand my thought as well. So, as we know, a lot of like scale invariance in a diverse systems in urban or natural landscapes, and how we can, and also from, let's say ecosystem or ecological world, they are more diversity are acknowledged as more worthy. So I see like there are two terms, like there is a similarity which manifested as like a scaling in the mean. And the other point is like scaling inviability. So how we can like harmonize these two opposite term to make, let's say more ecosystem, better and more sustainable and like more resilient, like, yeah, as a researcher, so a kind of perspective or some like philosophy needs to be embedded. Yeah. I take very good question actually and then I give you my five cents I'm not pretending that I'm particularly enlightened in this but what I'm saying is that look, when in science we go hierarchical right. So we take the simplest possible model and see whether what he's telling you, and from where you move on to make it things is a progressively more realistic respect to what happens in the system. In the case for instance of pure power laws, which has been the frontier, then Pareto at the beginning of the 20th century, started the Italian economies to working in Lausanne, by the way, started saying okay now it can't be and you have to have some sort of a, they, the distribution of Pareto distribution has a tail, which is a power law, but and then you have something else a finite size effect if you want to all the things in which they can progressively tell you how you could see whether those sites and those pieces of the power laws, mind you they have to be on a reasonable range size to be meaningful because everything looks straight for a little bit on the log not plot know. But there are tools to stay just to establish whether you can actually make the statistical claim that the sample belongs to the distribution. But there are certain symptoms, which are the quote, beautifully Benoit Mandelbrot, whom I remember an honor, no matter what, called the syndrome of infinite variance. For instance, the scale of variability you will be talking about. Suppose, so you take a sample. Okay. And of course they take daily rainfall. Okay, measured in Padua, they started in 1690. And they've been operating ever since one of the longest time, time series. Okay. And you said, Okay, let's take the weekly variability that you have in daily variations, so you're talking at scaling of the fluctuations. Okay, I'm not making very particular sophisticated math. Think of that. Okay, so you have one week, and you calculate the standard deviation in that week. Okay. But then how many weeks you have in like 300 years, a hell of a lot 300 times 52. So I think so a thing, etc. So it's a large sample. So you take the average of that. That's the mean fluctuations you have for a signal when it lasts for for a week. Now take a month. Okay. And so you calculate the variability over the month. Right. And then, and then you take the average over the 300 times 12 months you have in the time series I'm making 300 years to make it simple but it's more less 300 years. Right. Next, and I'm getting to what you know it's called the Hearst effect. You look how whether there is an effect you simply plot the average of a fluctuation against the duration that is seven days, 30 days a year, 20 years, 50 years 100 years 300 years which have only one value, one value but it's a huge number of points right. And so that's what Mandelbrot beautifully said, and it's a property of a power line that's absolutely trivial calculation that the high school student can do. Now, if you had that this grows without bounds. That's what Mandelbrot called the syndrome of infinite variance that is, you by manipulating elementary manner the beauty of those signatures of inevitability, it's easy to calculate. If there is the fact that is with a size grows the range you explore, then the system is telling you something I'm trying to get to a state in which regardless of initial condition of my dynamic process, regarding all the parameters you have, regarding or whatever you want to have you're going to have the same result. If a self the critical self organization, which is the essence of why, but what we look around, rather than having a system in which nothing is fixed, etc. With a number of degrees of freedom you have a phenomenon like for instance the distribution of a statistical feature of a, of a ribbon network or distribution of wealth, or a stupid example. Why on earth, the grammar, the book textbook of grammar in your original language and and Melville's Moby Dick should have the same distribution of our frequency of words. Isn't that because it's inevitable. And this is easy to measure the beauty of power laws and those scaling analysis in pinpointing the features that make a phenomenon inevitable, as opposed to controllable in some manner. And also the ones that allow us if you look at for instance, and that the scaling analysis was technologically very about scientifically was very easy, but technologically very evolved because if you take the global road network, the technical capabilities to manage those files is gigantic. So it's big big data. Right. So if you look at the city where the city, you see that was the actual roads. So you have indicators of or although it ever transformations and possibly where you had it for, and possibly whether the society will be facing will be a one in which you have had less inequalities. I'm afraid not but that's, at least you know it. Right. I don't want to measure those values. I don't believe, neither in communism nor in capitalism, as was famously said in the beautiful book about patterns in nature. So those kind of network structure kind of an in between, neither nor. Sorry, I took. But what I'm saying, yes, but what I'm saying, I always sorry and I always would like to take, take a simple statistics you make it a hierarchy is that simple, any complicated needed. But in many a case, those even a log log plot of a priority of exceedence that I didn't frequency on observing does wonders in telling you what happened. I see. Thank you so. Like, like on what he cried Terry, like what combination of different kind of the power low plots like whether fluctuation scaling or some scaling from the mean. But it says, study the scaling of fluctuations with a size of sample. Because you can have and I recommend, if you take a look at the beauty that the new one paper, you, you just new contemporary physics 2005 or whatever is like a 40 page thing, etc. It starts from elementary concepts and it's done beautifully well I recommend it even to undergraduate students, because it takes a mental method to get to very deep concept, etc. It's been wonderfully well, because in a finite sample in a system, for instance, a power law with say a coefficient in between two and three, the mean diverges right. So what happens is that in why is that any finite sample has a finite mean, but syndrome is that if you take larger and larger samples, you will see how these diverges and that's an estimate. Okay, thank you so much. Thank you so much good to see you. Stefano also. Hey, Stefano, hey, that's family. Again, hi. Good to see you. I go to see you. I thanks for the talk I wanted to ask you something about connected also to what you mentioned now this inevitability, inevitability. So my question is this the system that has this scaling properties has some from my point of view drawbacks. For example, you mentioned that they show infinite variance and this is a problem because, for example, it's difficult to, I don't know, estimate what is the behavior. I'm thinking about, for example, the results for river networks in terms of floods. So, once we know that also the, like the anthropogenic system like cities, they tend to have this, this same, we tend to build the same pattern. Can we build in a way that we don't build this pattern to avoid the drawbacks of these structures. I mean, do you think something like that would be possible. I have to have two things to note. The first is that, of course, infinite variance or infinite mean applied in the infinite sample size is a property of the population of a disability distribution. Any finite sample, which is anything you could see from data has a finite mean period. The idea then is taking sub samples of different sizes and whether they as as you make your sub sample bigger, whether they diverge. That's the syndrome. This is telling you the system is standing to go to there. So the theory of dynamic system which is interesting is the following. What is chaos is a system in which a minute perturbation of initial conditions can lead to completely different outcomes right. The butterflies batting their wings in in daily generating the hurricane in New York City or something or whatever Lawrence transformation. It's an infinite sensitivity to conditions that through the kind of non linearity. Okay, that's that's interesting concept. Why then, every single river networks in the world in there are not generating area, regardless of vegetation climate exposure lethology, you name it whatever has the same statistical features. The problem of I'm talking about the networks that happens in a, in a number of why distribution I made the example I find most compelling it. Why the frequency distribution of words words defined even in an in an electronic text is easy, whatever is separated by, by, by a space. The frequency of word for later the in English, which appears many a time I said to the idiosyncratic that happens only once or whatever, something like that you have a distribution. Why all books you can possibly analyze with a few exceptions well understood like, by the way, yeah. I'm not saying for instance, because of a sketchiness of a language of a, of a low income Manchester suburbs that was a subject of the thing, etc. Or the distribution of a text messages that young guys send themselves, they are abbreviated simplified, they're not a fine to the, to the others, but in any book, regardless of the language regardless of the age regardless of the subject of the book, you have the same distribution. Does he mean that there is a goddess that adjust the many that the thousands of thoughts that the guy who writes the book. Actually, to make a distribution look like that, or is it more reasonable to assume that this is inevitable. I think the second is absolutely obvious to me, and that's self organized and self organized critical because it's a power law. So the realization means that regardless of the minute difference because had majestic different in which conditions, majestic differences regardless of the values of the parameter of a dynamic process, whatever you have it, you're going to have the same outcome, not perfectly diverse for my new differences, but the same outcome for widely different conditions dynamic and initial. And the signature of SOC of self organized criticality is the emergence of that scale invariance, meaning something which you course grain at different scales and the distribution of the power law is the only distribution which is invariant is the same. It is over averaging of the different sizes. So we have tools for not for evaluating and if you talk to a statistician they always kind of whatever statistical testing, of course, etc. But symptoms of symptoms symptoms is not the disease. I mean, as was famously said, I mean, you can't define pornography, right, but you have to say for the symptoms you know what you're talking about turbulence is the same. It's the same for turbulence attack. And it's the same for many phenomena. Simple measures, simple tricks to as Sweden was asking, if you make scaling for instance, or what happens to it once you average over different windows of different sizes, whether it is divergent with a number of size is the signature of that feature. Once you had those those footprints, then you know that something of the same kind is happening. So in a sense, you have a way in early symptom or whether you'll be leading to something. And in terms of inequalities where the distribution of richness tense. I mean, irresistibly towards the power law and towards the power law in which 80% of the wealth is in the hands of a 20% of the region fraction 20% of the population, which is very chest. And this is disturbing in my view. A proper distribution distribution of policy in fact is something we should be a main, etc. And once you know, you can perhaps find some corrections. Hopefully, that's my sense. I mean, I'm just touching so many things and that's good to see you. Where are you. If you have questions around line Mark Miller wants to ask you. Hey, hey, look at that. Good to see you. Some of you know people from. Hopefully, hopefully not for long, I shouldn't say that right. So I really love your talk as usual and I was particularly intrigued by the connection that you pointed out between the power law exponents and inequality. And it never occurred to me but it's, you know, it makes sense thinking about it. And I apologize in advance if my question is simply sitting my brain is a bit fried after listening to you for an hour. And this since you know parallel behavior is a signature of self organized criticality, and the value of the exponent is a description of inequality. Do you have any thought on how on the relation that this suggests between inequality and resilience like, does it mean that the system that is more unequal defined as a parallel is also more or less resilient. That's a very deep question actually. All I'm saying is that well now, if you were capable of finding a very well defined uniquely defined exponent, then it would be a measure of resilience. I'm afraid that noisy data and the size of data that are required to make a really small thing etc, typically, you won't have. So it's in principle answers. Yes. But I think that a clean cut distinction with especially resilience which is a higher level concept. So complicated that it could be kind of impeded by the features of a data but certainly I mean you're great. I said that so the kind of size of data I can characterize of course they have to be homogeneous or sure enough I mean that's not exaggerating what we're not it's not. Of course I am exaggerating of course, but it's the sense of direction if you were capable for having homogeneous homogeneous in terms of the statistical properties features, and you're going to have big data indeed. And then the answer is yes, you can. Yes, so which direction does it even go because it's an intuitive to me whether a more ecosystem or more ecosystem is more and more. The exponent itself. It's a good indicator of resilience and good indicator of the inequalities as you've seen in the 80 training room for instance, you have to be right and you can't normalize a distribution if you're not it has to be larger than one for sure. But then you have you know from the. Then you have in the infinite size limit, you have diverging second moment or third moment the set of it depend on the, on the on the value of coefficient so it has to be strong decay that is to from two to three you're going to have infinite variance and finite mean, an infinite sample. If you go from three to four and the likes etc. But the idea is that once you face real data. Then many factors pitch in and what I'm advocating for is the so called finite size effects which are inevitable. And then the road networks, which I, I told them and well as trying to be the same, the same funny things I'll be telling you tonight. I told them in a, in a, at like 10 p.m. with this graduate student, a man well as trying I was passing by, I was saying you should do this etc. And then as a result, I mean six months afterwards, the guy, I mean diverting the sizable part of his thesis which was actually in GIS with Francois Gaulet. But. So the technical capabilities and that's a message especially for the producer of for engineers this is a great opportunity for engineers. Why, because we need to be technologically study. We need to. And that's what I want to say I mean I've been, I've been working of my mind. It's amazing. We published a paper on COVID-19 spread in Italy in PNAS in less than a year ago. It came out at the end of it. It has 500 citations by now, cause the size of a problem.  Well, what I'm saying is that I'm keep telling you that the few times have been interviewed I said, look, what is absolutely clear to me. It's not a problem for doctors, it's not a problem for epidemiologists, not a problem for virologists. It's a problem for engineers, whether you like or not, because you have to trace like satish does so wonderfully well, where the hell people go.   And which is embedded in the wonderful work, for instance, that satish is doing that is human mobility network. It's when the infection goes I mean it doesn't take a, it's not my doggy, right. And it's for us. It's a good opportunity for us. It's not for virologists or medical doctors, etc. You have the doctors, etc. You have the doctor may have no idea how an infection spread. Of course, you know how the infection operates on you but that's not predicting large scale patterns of infections. I'm not very popular with the fact that you made this in here. I'm afraid. I apologize, I have to end the formal part of this seminar where about 10 minutes over the. I'm so sorry. Thank you. Everybody will log in to listen to me today. If you want to log off, we'll end the formal part of the lecture, and few of us will stay on to carry forward the conversation with them. So thank you very much.