[MUSIC] Welcome back to the third lesson on the examples of alternative approach based on complexity to develop qualitative analysis of the metabolic pattern of sociological system. Here, we will illustrate the Sudoku effect. We'll explain later on why, what we mean with it, and that make possible 200 impredicativity. Impredicativity is a bad word in qualitative analysis. Nobody wants to deal with it because, as a matter of fact, the differential equation, you cannot describe a system which there is an internal loop. This is the chicken egg paradox. You need to have a chicken to have an egg and you need to have an egg to have a chicken. And so, this is something that totally destroy our way of describing things based on. We will use an example of metabolic analysis. The metabolic pattern of letters in a society, the letter that you exchanged through mail. So let's imagine we have 1,000 people. As we saw already before that we can transform 1,000 people in 8.76 million hours of human activity per year. Because we are measuring the metabolism of social ecological system in terms of how much human activity is found in the system and how much energy, what are food, letters, whatever is metabolize per hour that we have in this system that this amount of human activity is metabolize 24,000 letters per year. This is implied that the angle here is a 2/letters/person/month. Then out of this human activity we can calculate what fraction of it goes into the paid work sector. This would be the sector where human activity's on work they are paid. And they are organized by institution. Then, of course, starting with 1,000 people and 50% of dependency ratio only 50% work. Those that work only 2,000 hours per year. So we will have 1 million hours of work available in this society. Of course, not all these workers male, estimated that only three mailmen would be getting a salary for delivering mail. That is a remarkable amount, it's 0.6%. This is a poor theoretical example. So read that. The numbers matter. And let's imagine in these mailmen will work 2,000 hours per year is implied that we would allow, this society would have 6,000 hours of work to deliver 24,000 letters per year. This provide a first constraint that basically the throughput of hours that may deliver per hour. So labor, here, is compatible as capable of matching the demand of mail to be delivered expressed by the society. We can see there is a relation if the society is metabolizing 0.03 letter per hour. And the people here are only a very small amount. Use only a very small amount of the human activity available, they will have to deliver 4 letters per hour, which is an amplification of the metabolic rate when considering the pace of consumption and the relative labor of 1,400 times. Why it is important to have this type of relation? In this way, individually, what are the factors of fund and flow, a fund flow ratio? They are affecting the possibility overly this little poly part, the society consuming that amount of latter in this specialized part of the compartment. The main sector to deliver the letter. Why this is an negative loop, because we can adjust all the factors of this loop. Let's imagine we have more letter to be delivered, rather than 24,000, let's say 30,000. Then, of course, since the population is the same, you could Increase the workforce for instance by using the age of retirement. Or you could increase the number of mailmen over the workforce by eliminating then these people working in museums. A certain amount of educational support is cool. And that increases the mailmen. Or you could increase the workload of the mailmen working in overtime, only along working 2,600 hours like 2,000. Or we could add more technology or better computerized system to deliver more hours per hour. So, in this case, we are changing the distribution, the amount of fund human activity here. We can change the flow fund per the productivity of the job, or we can simply say, you cannot write all these letters. Let's imagine then if a lot of the population began aging, as a matter of fact in Italy and Japan we have 60% here. We will have less and probably we can no longer afford to write all these letters. Or we have to do something else. What is the point here? This system is in a way expressing a set of relations. They are determined, there is not everyday goals, but at the same time, there is not a clear relation of constraint, and this has to do with the Sudoku concept. And because impredicative loop analysis make possible to handle the ambiguity over the definition what is the dependent, independent variables. That is something that a conventional reduction analysis cannot do. You can make models of how eggs make chicken or how chickens make eggs but you cannot make a model of the two together. So why does this have to do with Sudoku? Because I don't know if you know the name of Sudoku. You have numbers. You have a set of constraints, for instance, the number of a column must be numbers from 1 to 9, the number on a row has to be 1 to 9, and numbers in a square must be 1 to 9. These set of constrains imply that as soon as I start putting numbers into the system, the system build up mutually for measure about what order number you can put or not put. And then, let's imagine that these would be what we have been seeing before and analysis of the metabolic pattern of society across different scales, then would see as soon as we put the a constraint of economic viability, constraint of biophysical viability, constraints of desirability. We can't establish a relation among the value of the number that we have in the metabolic part. It should be not as decimated as we are. Playing a Sudoku in which there are no numbers at all. This is what's called in jargon supercritical Sudoku. Supercritical means that there is not enough mutual information to define all the numbers in the grid. So basically, as soon as I put the number, this number is the defining constraint for a lot of other sets. Here, you can no longer put 6 in this column. You can no longer put 6 in this row, you can no longer put 6 in this square. In theoretical ecology, this is called the Survival of the First, when you are the first species colonizing and you inhabit it, they really impose constraints on the others. This would be a bottom up. And for those that are familiar with complexity of the theory that bottom up so that the cassation is coming from bottom, the lower levels are affecting upper levels. The reverse, if you are looking at a subcritical Sudoku. In this case, the mutual information is so strong that basically you can only put numbers in that specific location. There is no option anymore to put a number at will. So you are in the situation and shape out. So can to the relation between number, the blue number and the grey number. If you're looking at the Sudoku, in reality let's imagine that you don't see the grey number and you see also the blue number. The one that we saw in the beginning. In reality the grey numbers are already written in the Sudoku, the Sudoku is subcritical, the one that we play on the newspaper. The second number in the grid are already determining all the other numbers, it's simply that we cannot read it, but they are there. So the question is, are the blue numbers determining the position of the grey numbers? Or are the grey numbers determining the position of the blue numbers? Because if you are looking at the critical Sudoku out of time, the two numbers define each other. What happened that in reality, the Sudoku can be seen as a set of constraints that generate mutual information depending on the numbers that you put into it. But this depends on the order. So the position between blue and grey number out of time is impredicative. You can either put the blue and you get a grey. Or you get a grey, you get a blue. But, if you start with an empty grid and you start putting a number in the grid, then the one that written in the beginning when the Sudoku is still super critical, they are independent variables, and they all became dependent variable, and this is simply due to pan dependency. It's an extremely common situation in in the public system.