 Okay, good morning everyone. Welcome to the fifth lecture in our course and this is a special lecture because here we start the real stuff in a sense so we well not to say that everything we did was imaginary but this is what two-thirds of the course is going to be about. It's systems dynamics and then nonlinear dynamics and chaos but more or less this is like encompass the same thing. So before we start this are there any questions about anything that we did before? Anything regarding administrative things as well? I have a few announcements to make but before that let's let's hear some questions. You can ask me if something comes up. But basically the quizzes everybody passed the quiz so the first four lectures should have conveyed the proper message. There are interesting results from the survey and I would ask all of you to really complete it. We'll discuss it next time. I will not discuss any results right now because I don't want to bias some of you but let me just tell you that I've read your comments and some of the suggestions are going to be incorporated as of now. So even though I can't say what it is it's going to be is going to happen. All right a quick recap of what we did so far. You know this but I'm going to repeat it in every lecture. Finding solutions that's what we looked at in the beginning including first of all before we find the solution we need to have defined the problem so including defining your problem defining your objectives and then we look to the problem-solving cycle. After this implementing solutions project management mostly critical path method quality control stuff like that and now we start with controlling solutions. This is the last part of the course and the goal I mean what does controlling solution mean. The goal of this is we take the system as a given. I'll talk about this later but we take the system as a given and we want we want to understand why it works the way it works and for this we're going to analyze it analytically if we can and if we can't simulate it. Very important is modeling the role of modeling in in system dynamics. I'll talk at length about modeling but the purpose why why do we need modeling is well we want to not just to explain what the most important parameters for the operation of the system are but we also want to be able to predict hopefully something and these are not the types of predictions that you read in the news for example financial crisis is going to end next year point full point or full stock. I mean nobody can make these predictions to people make them but that's another story. The predictions we're going to make are about so-called critical behavior of the system so when would this system if we've modeled it correctly when would it suddenly change its behavior from stability to instability or from instability to stability and with modeling we can also identify what are the key parameters which leads to this sudden change which lead from a crisis to to stability so this is what controlling solutions mean. There is a slight confusion sometimes because people say well quality control is some kind of controlling some form of control so what's the difference between implementation can't we control the system during implementation after all we're building it up so we should probably know how it's going to work. This is a more or less valid point but for complex systems that's difficult to do. If you build complex systems yes you can exercise some kind of quality control but it's very hard almost impossible to control the overall operation of the system so for us we draw the line implementing solutions means building it block by block your system and that's all controlling solutions mean given your system so the system is given how does it behave. Okay and as I mentioned the role of control parameters is very important we need to identify key parameters which lead or do not lead to some expected behavior so now hopefully you know that solutions and systems sometimes don't behave as we expect them to do and the reason for most real-world problems is very simple. Complexity is built in into the system that's just how it is. We cannot get rid of complexity we cannot kind of discuss it away we cannot simplify it it's there so we have to learn how to manage it and in this course so far we saw four types yes four types of four mechanisms for generating complexity and these are the four mechanisms first of all positive feedback loops positive feedback loops generate instability okay which means it puts limits to your predictability if the system becomes unstable you basically cannot predict how it's going to behave for all time and an example is the undiscovered rework from the systems dynamics model last week which basically says that well after quality control we get some work that needs to be rechecked no matter how you call it undiscovered rework or whatever this work that needs to be rechecked and redone goes to the work to be done stock variable so basically it increases it and there is a positive feedback loop more work to be done causes more red undiscovered rework due to quality problems which in turn increases the work to be done but this was just one one of the positive feedback loops there are others you probably remember them so this is one mechanism positive feedbacks second mechanism are the small changes or the small either changes or random deviations however you'd like to look at them with the US Navy case these were small changes they were not that random from the US Navy perspective they were quite random from the from the shipbuilder shipbuilders perspective so these small changes through positive feedbacks get amplified to enormous proportions sometimes this is another source of complexity negative feedback loops are something good they bring stability but unfortunately in most real-life situations every negative feedback loop is associated with a corresponding positive feedback loop and often we're not aware of the positive feedback loop so always think how your measures affect your organization or your system in ways that you don't normally expect these are the positive feedback loops that you need to try to identify and last lecture at the end I couldn't finish it completely we addressed the most important figures in the self study it's the role of concurrency or time-boundedness what this means is even though we can parallelize project phases or we can parallelize activities within within a project phase there are still some time boundaries that we need to respect some things simply need to be done after other things have finished just how it is we cannot really start designing a product before we have some form of product concept so this sequencing in a sense leads to changes in the downstream so changes in the in subsequent stages to propagate back to back upstream for instance if there is a quality problem downstream this thing may propagate through positive feedbacks again may propagate all the way up and in fact if you if you've already seen the so-called bullwhip effect in in the supply chains you will going to see it in the next lectures and try to model it but it's exactly what happens there you have a very small change downstream to the customer so the demand fluctuates very little and then this whole this fluctuations they propagate all the way up to the manufacturer of raw materials and then they see huge inventory fluctuations there and I'm pretty sure you're going to see this in other courses as well namely management information systems if some of you are taking it from a different perspective here we try to model it but this is the idea due to this kind of time constraints that we have changes propagate and get amplified so these are the sorts of complex that we saw now we start with systems dynamics and what is systems dynamics system dynamics is the following we take the system as a given somebody gives us the system we don't try to build it up there is a difference because next semester there is another course thought by this chair which is called collective dynamics of firms and there we actually build systems but here the system is given airport society whatever and we consider the structural view remember in the first self-study we had a structural and we had a functional view of the system we consider the structural view which means what is the system made of what are its elements and we focus on its behavior with on the behavior within the system meaning mostly feedback loops within the system because these are the most important ones so system and environment also are given for us and then we focus on what is the system made of and how do different elements in the system interrelate with each other via not just via direct links but also via positive feedbacks and here this this is taken from the Wikipedia page on systems dynamics the figure is correct it's kind of it's nice also but I wouldn't recommend reading the this informational system dynamics from Wikipedia because it seems to be a very special case of what system dynamics is it seems to be what some guy did in his in his project at work so this is what I mean you don't need to read it but if in case you read it don't don't read too much into it just so for now don't try to understand what all these elements are so what is this and that just try to get an idea of how a systems dynamic system dynamics model looks like it looks like this I'll explain this in during the rest of the lecture but also also now a little bit so what are the systems elements that's very important system dynamics the systems dynamics perspective considers elements as typical elements or in other words representative agents which is what macroeconomics does all the time so we don't have different individuals different firms different countries different suppliers we have the typical individual or the average individual in fact that's exactly what it is it's mathematically the average individual when people have let's say market survey from 1000 people then they would average over some some parameter and then they would say this is what the average person or representative agent wants and that's an important thing because if you know this you will know what to expect from a systems dynamics model you cannot expect that the system dynamics model is going to tell you why your particular company doesn't work the way you want it to work okay it's a representative agent we'll get back to that later yes so if you have representative for typical agents normally your system would have just a few elements a few of course is relative in that sense few means relative to the other perspective which is actually considering every individual agent or every individual element as its own entity and there is this different perspective on on modeling as well I'll talk about this but for now just remember this typical agents and we don't have a lot of them in the system and we're interested in the macro dynamics of the whole system we're not interested in the problems of the typical firm we're interested let's say in the output of the system that the firm is embedded in for instance this could be an economy of a country so we're interested in let's say the output of the economy GDP for instance but what does it mean we're interested in macro dynamics it means two things first we want to understand when you apply an input to your system what is the output that you get back okay and for this we need to understand what is what are the key control parameters yes so the relevant parameters so we don't want to just look at the system as a black box which is fed something and then we get something on the outside we want to understand how this input is transformed to an output this is also important and why do we want to do this well not only would we understand how the system works but we also understand how different how different elements interrelate among each other which is going to help us to make predictions all right this was the systems that systems dynamics perspective now let's look at that picture I hope you can see it on your slides so here we have actually I cannot see it there I have to look here yes so here we have product adoption a model for product adoption it's not important to understand the details I'm just going to give you a flavor the details are going to come later on we have product adoption we have potential adopters we have actual adopters who've already adopted the product we have new adopters they and we have some kind of probabilities for an adopter big for a potential doctor becoming a non-adopter becoming an adopter and we have feedback cycles this is a word of mouth-effect saturation we'll understand all these components later on I'm not going to focus too much on them but an example for systems dynamics model it's actually this is taken from a textbook economics textbook so all the standard economic texts use systems dynamics models so this is the economy of a country all right and in fact this is the starting point for economics I would say I mean this equation here but anyway so what are the constituent elements in our country well people said we have firms typical firms of course not individual firms we have the firms we have the households and we have the government and all the other things that you can think of for example the geographical location of the country you may think that this influences the economy and that's true you may think that the financial situation in your neighbors influences your own economy and that's probably true you can think of many things which are not in this three simple boxes what you do in this case you simply take all these other things and you put them in in something which here is called overseas that simply in this is outside of your system right it simply means you don't care about them why why don't you care well we're gonna see later on but in short you don't care because your model is going to become so complicated so complex that then you're not going to be able to tell what is the influence of every individual parameter if you have thousands of parameters you can reproduce any result you want but then which is the parameter which produce this result you can't say because you have so many interdependences that it's just impossible to account for so here we have the firms firms pay taxes get subsidized from the government especially with the subsidized part I think you all know that especially visa banks so they get subsidized households they offer their work for for the firms they get income but they also consume their products so they give some money back to the firms and they also pay taxes to the government and what what are we interested in we're not interested in the well-being of the households or the firms we're interested in the systems be on we're interested on a macro parameter of the system and in this case that's a GDP or the output the total amount of good and services goods and services and you know that this is simply the sum of consumption plus investment from plus government expenditure and neck net exports and this is the basic equation so this is a systems dynamics model we already know this probably most of you already know this so in that sense we're not going to learn something incredibly new with this kind of modeling things that we're going to do which reminds me that now the self-studies are going to be completely different from what they used to be up to now up to now we had discussions and we had kind of a hand waving but now we're going to have models it's getting a bit technical that reminds me of some people want more technical things so it's going to be like this the self-studies are going to be a lot of modeling and yeah there is still not the right model but you see that so this is the systems dynamics perspective there is a different perspective which I just hinted a couple slides before and that is the so-called complex systems perspective what is a complex system I mean that's there is no single definition but in general every time you have a system which consists of very many elements incredibly many elements and they're so interconnected that you also have very many interconnections then you can call this a complex system because it's very hard actually to analyze all the interdependencies that happen within that system so many connections so many elements as an example the brain comprises of huge amount of neurons and interconnections between these neurons and when you have so many elements it's difficult to predict what the brain would produce as macro properties of the system it's difficult to predict by studying how two neurons interact or five neurons interact even if you know how they do which people do of course it's difficult to predict why consciousness for example emerges when you combine so many of them right and that's why in general of course that's not a very technical and correct definition there is no correct definition what a complex system is if you have many elements with many connections that's a complex system well it's a candidate let me believe this way there are other examples ants ants are probably the prototypical example of a complex system why because with ants there is no centralized decision-making there is no yeah the queen but the queen it doesn't actually make decisions it just breeds so yeah but there's no centralized policy or decision making as to how to search for food for example or how to search for a new home the ants self-organize entirely via local interactions so an ant would probably communicate with just a few of it of the ants in its vicinity via user pheromones and stuff like that and I would like to show you a simulation of ants just to give you a flavor what this whole self-organization self-organization means so unfortunately now it's completed so yeah there is there is a in your notes I believe yes in your notes you have the link to that simulation unfortunately it's kind of slow so what you see here well maybe I'll take the chance take the time to explain what you see what you see here is ants the blue things are ants they start from the middle and here with red you see food okay so ants these guys they need to search for the food and a yellow ant is an ant which has found food and tries to get back to the nest or leave some trail so that other ants can can detect what it's found but yeah so this is a very simple model ants can only move I don't remember the details but they can only move randomly they don't remember where the home was so they can't get to it they just have a very limited memory of what they did and then if we wait long enough you're going to see that the ants and basically there are a lot a lot more ants here in the in in the in their nest they don't all come out at the same time obviously so what you see is if we wait long enough see more and more ants find food unfortunately there is no centralized place where they can call and say well we have found food tell everybody else they just leave local trails like local pheromones so that if another ant finds it then it knows okay there is food nearby and what you would see is amazingly the ants will find eventually the most the most efficient way of going here getting the food from the top and getting the food from the bottom and if remember what we saw there was this kind of a line and I hope we can see that now first we're going to see yeah well every time it's different obviously because it's random but yeah they will have to find it eventually and yeah if you remember we saw so we can already see this kind of path which emerges here so all these ants self-organized into creating a stable path this is entirely via local interactions and then eventually this path would also go to the to the top so we're not going to wait for that but this is the other perspective the complex systems perspective and this is in fact what the research of the chair is about it's the complex systems perspective not the system dynamics but both are valid of course alright and then of course this perspective it focuses on how did these ants self-organized via local interactions into a system which exhibits let's say the most efficient path finding for food and the focus is on on the this link between the micro interactions and the macro behavior that's the focus of that of that perspective but again we want to understand how the system work you know the question is entirely the same how does the system work and we just go from here we study these different interactions we go to here we try to explain what the important parameters are and so this is what the actually research is about in the chair but we stick with system dynamics and in fact this perspective is thought next semester in collective dynamics of firms where we try to explain how the behavior of a lot of firms emerges from individual interactions between firms and competitors yes systems dynamics so the question is what is the difference basically remember in systems dynamics we look from the top we look from we take the bird's eyes perspective and we look on the system on a given since the system is given for us we look at it from a very coarse grain perspective we don't care about individual ants we care about the average ant what would the average ant do and then we can only embed this average ant in a system which doesn't have other ants right then it wouldn't be the average one so we can only embed the average ants let's say into a system which has a government there although I would be very curious what that system might be but that yeah that's the difference in the complex systems perspective it's just a name complex systems perspective I call it bottom-up perspective because we start from the bottom yeah so we start we study we don't define what the system is in this bottom-up approach we build it entirely by modeling how this guy communicates and interacts with this guy and then we just have thousands of these guys we let them interact and we see what happens basically that's what it is in the system dynamics we don't care about the individual interactions we care about the coarse-grained elements and it's top-down right because you you take the system is a given and you start you start drilling down in a sense all right so before we go into the formal modeling let's introduce a few easy notations we have links so each element is linked to another element that's very simple element a causes an effect on element B it's a unidirectional effect obviously because B doesn't influence a back there is the feedback a influences B B for influences a and there's an indirect influence or indirect indirect cause that's that is a influences B B influences C and then indirectly although C may not know it a influences C as well so these are the links or the can how we model the connections but of course they might they must have not might have but they must have polarities so each link must be positive or negative if X in that case it's X if X causes a positive change in Y meaning every time X increases Y increases as well we have a positive link polarity vice-versa negative link plural polarity and we can write this in this mathematical form so Y and X are linked with some nonlinear function F and F has a control parameter this is these are the parameters we're interested in in fact by changing this parameter we change how the X and Y are linked and we completely change the system behavior so for example in a supply chain the control parameter may be if you define it like this it may be the average delay that you have in two sequences of on your production line but it's entirely up to you how you define it right so if you have a nonlinear function F which links X and Y then obviously the rate of change of Y so the increase in Y caused by an increase in X is given by the first derivative of the function if that derivative is positive then we have then we have positive link polarity if it's negative we have a negative link polarity that's very simple now an important thing is causality most of you have at some point of your lives some of you all the time you have encountered mathematical equations but what at least what I didn't do before I looked into this slide I wasn't reading the equation from right to left at least not consciously what does it mean well imagine we have yeah so what this means is that the thing on the right actually is the is the cause and this right here so the thing on the right is the cause and it has an effect on your on your thing on the left so the causality goes from right to left in a mathematical equation for example here we have the rate of change of X with time imagine we're interested in this rate of change of X what is it caused by well it may be caused by a deterministic force F X squared for instance plus a stochastic influence all right it's very simple but this is how causality flows in mathematical equations and then example here is the second law of motion the Newton's second law of motion we have the force is equal to m times a something which everybody knows for instance if we take the friction force and we substitute it here right this is the acceleration of course and the acceleration is the rate of change of speed so the rate of change of speed or the acceleration is equal to f divided by m if you take the friction force you get this thing divided by m m cancels out and you just get minus gamma times v where gamma is the friction coefficient and here you see cause and an effect the speed has a has an effect on the acceleration and there is this kind of feedback between the two right or in this case it's a balancing feedback because there is a minus here and most people don't look in equations in terms of feedback loops but it's exactly what it is if we increase v here the acceleration decreases and vice versa so the system is driven towards a stable state and without even solving it you can say that the system is driven towards a stable state yes yes that's only true for differential equations that is true all right so without even solving it we can say there is a stable state there is a balancing state because we have a negative feedback loop and if you solve it you see that actually it's zero so this thing eventually dies down all right why was it important or not important but I mentioned that there is a nonlinear relationship between x and y between two elements in your system well that's important because if you look in this figure you have the cause the right hand side and you have the effect so sometimes and often you drive some input into your system and you don't get any effect you don't get you don't get any result but that's not because the two things are not related so sometimes when you study you don't get anything out of it and you study more you don't get anything out of it but eventually right you may you may be here this is a very unfortunate nonlinear relationship especially if you want an effect but eventually at this point of time something happens and you have a sudden shift and you have a huge effect right kind of a threshold behavior your quiz is an example of this if you get less than 50% there is a fail right and suddenly you get slightly more than 50% and there's a huge change it's a pass right so that's that's important to know because this may also be stability and suddenly we have a crisis so what what is the control parameter what is the cost this is what want to identify and this is the point most important that we want to identify the point when the critical behavior emerges the system suddenly changes its qualitative state and for this the mathematical terms are face transitions and bifurcations you don't need to know what they mean right now they're all going to be to be introduced okay another important thing which I would really like to stress out especially given my opinion that it's violated blindly in real life in popular media and even some kind of academics violate this correlation does not imply causality probably from some economics courses you know that already especially if you take courses in development economics they're this they try to make this point very clear what does it mean if two variables are correlated for instance here we have and that's that that's actually an empirical fact I don't know which country and which time but I remember that this this was an empirical fact ice cream sales are positively correlated with murder rate okay so when ice cream sales increase murder rate also increases so does this mean that that people who buy ice cream become murderers or does it mean that when you commit the murder you feel like eating an ice cream and then you go and buy an ice cream obviously in this very simple case it's ridiculous right you would say no there must be something else going on there must be a third variable or third factor which influences these two at the same time and so it happens it's the average temperature right when when it's hot you tend to eat more ice more ice cream and apparently something that I don't understand quite a lot when it's hot you also tend to get nervous I guess right but this is the correct way how you model these things and I said it's violated blindly maybe yes yes I didn't understand that the average temperature oh yes yes yes that's true so there is no proof that that yeah you're right average temperature may influence ice cream sales and something else may influence murder rates at the same time that's true indeed but why why is it valid well I've noticed that a lot of think about it especially if you think in the in the field of development economics you see a country with a high GPA is likely to have very educated people so the two things are correlated so what is it is it the fact that the country invests in education and gets back educated people which in turn increases GDP is that the causation which means that the policy should be investing education you would get higher GDP or is it the other way around is it that countries which were rich in the first place they were able to invest in education or is it that the third factor influences GDP and and education at the same time or maybe fourth factor influences the education so you see depending on how you look at the causality different policies may emerge and sometimes when it comes to sensitive topics like let's say immigration people tend quickly to jump into making the causal link given just correlation and if you somehow try to look for this in newspapers or in media even experts you would quickly see that people without justifying why they make the causal link but please be aware that causality the correlation does not imply causality you'd really need to work hard to prove causality and there is no accepted way how to prove causality but that's a different topic all right yes exactly the common thing what is the common thing I'm not sure you can you can if you can define a question like this well because it's very tempting to think that they're the same it's very tempting to do this but and in our models we need to win a lot of times I would say but when you create a model if you're not aware that correlation is different from causality then you can create the wrong model you can think that you can create a model which which is like that right which would be completely wrong you can reproduce probably you can reproduce whatever behavior you want with this model but it would be wrong yes yes that is true the way you prove you try to prove causality is you basically try to isolate let's say you try to isolate these things and then you try to vary the one that you think is the cause and you see if you get some effect another way is to look into time into how the things the two factors are related in time if one always comes before the second one the world and it's likely that it may be the cause but often we don't have this strict and convenient time ordering of events or factors yes but this is this is in general how you how you go about causality proving causality you try to isolate everything and you vary the cause what you think is the cause and see if you get an effect but then again keep in mind this okay you already saw this light in general what what this what this light tells you is that x and y may be related by some function f nonlinear function f but a completely different nonlinear function y g in this case may link y and x and see here we have this kind of a balancing well it's not yet a balancing feedback let me just finish with this light if the positive feedback is stronger than the sorry it's not a feedback but if the this polarity of that link is stronger than the negative one here then you have a positive feedback right because the net difference is positive otherwise you have a negative feedback yes and with this I believe we are ready to start with some models but this is going to be after the break let's go on let's start with our first model and see what's wrong with it or what's missing this is a model which tries to explain how population dynamics work in a country for instance the population growth rate and something like this although with a little bit more more elements is in fact used when people try to predict or to explain where a country is going given its current birth given its yeah birth rate and death rate so what we have here is the following we have what we're interested in the variable of interest that is the population we have a birth rate and we have a death rate now you can complicate things a little bit more and you can say well the death rate obviously depends somehow on the average lifetime you can also say death rate depends on many other things epidemics and wars come again yeah exactly wars and stuff like that we don't care about this because the model is going to become too complicated we'll see that later but it's going to become too complicated in for us to understand how varying this affects everything else because as you said everything else that needs to be held constant would now be much much bigger if we include all these other things and it's hard to to hold many things constant at the same time but there's two merit merit to this model all right so how it works death rate obviously if we increase the death rate the population decreases in on the other hand if we increase the population for some reason endogenous maybe or let's say exogenous the population if we increase the population the death rate increases as well provided it's constant obviously now you may argue well what if we increase the population by better health care then the death rate would also decrease that's true but this is not the point here so the population increases death rate everything else held constant so there is a balancing feedback or negative feedback loop in this diagram it's taken from a book actually this Sturman book it's a very nice book it gives a lot of real-life examples and their corresponding models how people have been trying to model these situations so it's a thick book it's available well I shouldn't say that you should buy it yes so yeah there is the balancing feedback on the other hand we have birth rate as well and the birth rate depends on a fractional birth rate this so the real birth rate that you're thinking about like percentage so 2% more people every year it's this one and the birth rate in that model is just the real the sheer number of people which were born the number so 2% out of 10,000 would be what is it 200 no one well something so birth rate if we increase the birth rate obviously we increase the population if we increase the population we increase the birth rate there is the positive feedback or the reinforcing in this diagram reinforcing feedback and you see there is a balance between this these two feedbacks not only there is a balance but every positive feedback here is associated with a negative feedback what we talked before so depending on the strength of these feedbacks is it no it's not given here depending on the strength of these feedbacks the population either explodes so if the if this feedback is stronger than this one eventually the population will explode if you grow by 2% every year forever that's equivalent to explosion or this is why the system is unstable in that sense it goes it explodes or this brings balance here if this feedback is stronger the system would go into a stable balanced state it's unfortunate that this stable state means total death for everyone because this would be zero right if more people die than they're born but it's nevertheless a stable state what we want however is neither of those we don't want complete explosion we don't want complete death we want some form of dynamic equilibrium meaning we need to be constantly playing with these two feedback loops and adjust the result according to what we want maybe we want growth of the population like most European countries would like so we somehow trying to increase the positive feedback loop in some other countries they may like to slow things down a bit they increase the negative feedback loop so we constantly play with these things and we change the equilibrium and that's why this is this what what is meant by dynamic equilibrium it's a stationary non-equilibrium it's in technical in the technical sense it's not an equilibrium because we constantly change it and this is somehow illustrated by this one by this graph the positive feedback this is the positive feedback would would move you away from an equilibrium state and and mind you equilibrium state is not always stable this is a very unstable equilibrium state because slow slow small pushes to the left or to the right would completely move you away that's the road of positive feedback but if you imagine now we take that ball and we put it right here like that there is a negative feedback which goes together with every positive feedback and the negative feedback would move the system towards a post equilibrium state but what is wrong with this model except of course for all the things that we didn't include which we could have but we didn't meaning wars epidemics stuff like that what is what is wrong with it what is missing conceptually yes come again migrants what is missing I didn't get it immigrants yes that goes into the direction of things we didn't include but conceptually what is missing is the goal of the negative feedback loop every negative feedback loop should have a goal in that case is what is the desired population that we want to achieve that we want to have otherwise how can you balance the two feedback loops if you don't know what you want to achieve so the goal of the negative feedback loop is missing and this is the example here imagine we have now a different setting we have product quality and we have quality improvement programs very simple Mickey Mouse model if the product quality goes down that supposedly we need to increase our quality improvement programs so we need to increase their number or their duration or whatever if we do that product quality would go up if the product quality goes up we decrease them so there's this balancing or negative feedback loop here but what is missing is the goal what is the goal of the negative of this feedback loop well the goal is obviously the desired product quality what quality do we desire now this is the a better model because the decision whether to be concerned or not whether to push forward these quality improvement programs represented by this quality shortfall now depends not just on the absolute change in your product quality but it depends on the relative change of the product quality with respect to what you want what your goals are so in all the models that you do and that you will do always try to have the goal what is the goal of the negative feedback loop and then that's a much better model because you can really you can influence things in an educated manner so you you change the strength of the feedback loop for a purpose you don't just change it randomly let's go with another example now more complete example we have the following we have the following attributes or following elements in your system product well imagine want to model some kind of product adoption or want to model yeah product adoption is good we have product attractiveness we have quality all the things that we think influence product attractiveness quality price delays in delivery and functionality you may think of more it's perfectly valid first what do we do when we build a model we identify our elements remember going back to the structural perspective of systems dynamics we need to identify what elements are in our system so what and then we define the we have the elements we need to identify the link polarities or the positive or negative or correlation in other words what is the correlation of the causality in that case it's causality actually so what do you think happens what should be the polarity between quality and product attractiveness meaning these are the causes and this is the effect so we increase our product quality what happens to the product attractiveness in your opinion yes it increases so there is a plus here price decreases delivery delay decreases functionality obviously increases when you increase the price your product quality your product attractiveness decreases because decreases so there is a minus well it's not valid for all products obviously some products even though they're expensive all it takes is a nice keynote speech all right so yeah next thing we've identified the the link polarities we need to identify and that's the the tricky part we need to identify the feedback loops and remember every negative feedback loop has a positive feedback loop so let's start with the negative feedback loops this is an example of what you can think of we have the same old things product attractiveness depends on quality price delivery delays and functionality but now we've expanded the model a little bit because product attractiveness is also related to demand so for instance if product attractiveness increases for some reason then obviously the demand for this product would increase I mean that that makes sense if the demand for that product increases you would feel more production pressure to produce more of this right your production your manufacturing plants would feel more pressure to produce more however so there's a plus when your production pressure increases you may not be able to satisfy all the demand in most cases so if you if you're not able to satisfy all the demand the price would quickly go up because normally what happens the demand is much more elastic than your capability to manufacture things so you have huge search of people wanting this product right now this week but in general you can't satisfy all of them so you would feel more pressure to produce more but it generally it won't be enough so you have kind of a scarcity for this product temporal scarcity which would drive the price up if the price goes up we we know product attractiveness goes down if that goes down everything else goes down so there's a huge balancing feedback loop here this big one be one or negative feedback loop but there is another one as product pressure is increased you may sacrifice some quality checks some quality programs may get swept under the carpet so your quality is likely to go down which if your quality goes down your product attractiveness goes down as well and there it goes again negative feedback loop B2 and so on and so forth I mean that it's pretty self-explanatory if you if you have production pressure to produce more of this you will obviously be limited in the amount of other things that you can do in terms of innovation in terms of launching new products and so on so if that decreases the functionality of of your product would also decrease you would not be able to incorporate innovations in your product because you say yeah I couldn't hear you sorry good point good point so the question is do all these influences or links weight the same that doesn't have to be the case and you can change that but not in in this diagram there's no way that in these diagrams you can you can you can you can have this in your model when when you build the model in with the software that I'm going to show you in a second you can do this of course because this is think of it as the front end you still have to specify in the back end what exactly this relationship is is it linear is it nonlinear and then that's where you specify the weights but in yes for instance how can you be how can you be sure about anything the quantitative aspect to the modeling is I'll get back to this when we go to the modeling slide the quantitative aspect to modeling is slightly different from what you think that is true but let me get back to this when the slide comes alright so yeah there is this other feedback loop and of course there is I mean this is taken straight from the book and I believe yes you in your notes you have all the feedback loops explained so all this this is all fine the system is stable but then you start thinking well what are the positive feedback loops and this is just an example what the positive feedback loops may be or the reinforcing product attractiveness increases demand for that product increases as well your economies of scale also increase right when you produce more you would have better economies of scale of course up to some point but in general you will have your economies of scale increase you would be able to learn more about your product as you produce more of it the quality increases product attractiveness increases correspondingly and so on there is this process improvement positive feedback loop it's important to realize that these two feet this one and this one they are kind of transposed on each other they exist at the same time it's not like first you go like this this would explode and then you go with the negative feedback no they exist at the same time they constantly balance each other out all the feedback loops what is this okay so in general yeah but let me let me first explain one more the big one let's say this one so your economies of scale increase due to higher demand and obviously your delivery delay goes down because you have a lot more products that you can deliver now provided of course everything else is held constant meaning your supply chain works the way it worked before your delivery delay goes down product attractiveness product attractiveness goes goes up since you can deliver so fast and then there is a positive feedback loop reinforcing feedback loop here as well so what you may have noticed is that positive feedback loops they always have an even number of minuses right so to in a sense in a very intuitive way two minuses cancel cancel out to produce a plus they don't cancel out but you multiply them they cause them they make a plus so everything else is a plus so if you have a loop with only an odd number of minuses that's a negative feedback loop otherwise it's a positive feedback loop yes which number oh which loop this one but that's all come again where which loop tell me the number you mean this one no but this is not a loop I mean this is a loop I mean see how this is I mean a loop is really a loop like all the things are connected I mean okay so now this light what is modeling and that's an important slide I would like to spend a few minutes on this light probably more than than I should but I really want to explain this light well there are two types of models one is the so-called lifelike model or let's say realistic model where we you really want to quantify the exact behavior of your system and that's the quantification that you have in mind you really want to predict what the temperature is going to be tomorrow okay you really want to predict for instance at what temperature what critical temperature superconductivity occurs in a material you have to incorporate as many details as possible in these models all right so think of a flight simulator you I mean flight simulators really need to be realistic to the last kind of drag force okay so or think of weather forecast you don't want to know well the cloud density affects the weather by increasing the temperature for instance no you want to know the temperature is it going to rain and certain times of the year it's easy to predict the rain but in general you want a very precise very precise model so what you do you put this in a computer that's why weather forecast people they need super computers for their models think of games computer games who plays computer games nice very nice but so you know your computer games all the developers they always try to produce the most realistic models of humans facial expressions water flowing in a river it has to be hundred percent correct to convince you that this is real but in the same case of flights in the same sense flight simulator is the same thing so real life models we want exact behavior to predict exact behavior quantity in a quantitative way so the result is yes the model is correct it predicts properly the temperature or no this flight simulator is not correct pilots always crash afterwards something like this it is yes I'll get back to this but it is good to learn yeah it is good learn the flight simulator is good to learn how to fly you know exactly if you steer a little bit to the left what happens you you have the exact same forces acting in your flight simulator as they would act in your plane when you're in a plane but it is difficult to learn how a plane works when you're in a flight simulator meaning you know when you press a button what is the result you know exactly what the result is but you don't know why really I'll get back to this the second the second type of models that we're going to be using in this course and that basically we're going to be using all the time also in next semester in in this other course are the so-called kiss models keep it stupid and simple or simple and stupid what was it simple and stupid those for viewing software those of you in software engineering you may have heard this kiss principle the kiss models are completely different from the previous type there are minimalistic models we only we're only interested in what causes a given behavior what are the necessary the bare bones of parameters needed to reproduce a given behavior and I would like actually to give you an example here because I think it's an example always drives the point much better let's think about we observe a social system and we see that people cooperate and you want to understand why do people cooperate and it's actually the topic of my PJ thesis so it's an easy example for me to come up with so why do people cooperate come again yes that's an empirical fact unfortunately otherwise it will be very easy but let me let me continue so why do people cooperate then you say okay people have emotions they have feelings they have neighbors they have friends they they have work they have some cultural dependency you try to put all this into a model into the model of your people the average person you let the your society grow and you get cooperation did you really understand why people cooperate no you have thousands of factors which may have been the cause you still don't know why people cooperate so what you do you start with a very minimalistic approach you say okay people are selfish let's assume that people are selfish that's the only cognitive ability that the people in my model have they're selfish you let your model run and you see that selfish behavior does not produce any cooperation which makes sense therefore you compare this with the empirical facts meaning people do cooperate your model produces different results nobody cooperates so it's wrong it needs something more selfishness is either wrong or is not enough so you go to a psychologist and you ask a psychologist well what could be this extra ingredient and a psychologist tells you well it's an empirical fact that people care about fairness there have been a lot of studies and people do care about fairness so you say okay my people are selfish but in addition they care about fairness and depending on how strong these two feelings are you get cooperation and then you can then you can say okay probably people's sense of fairness promotes and causes cooperation but now imagine I didn't go to talk to a psychologist imagine I went to talk to an economist and an economist tells me oh well principle number one or two I don't know is in economics is people respond to incentives all right so I decide to punish the people who don't cooperate in my model so people are selfish but in addition they're punished if they don't cooperate and then again I get cooperation of course they would cooperate if they're punished then I will say well punishment causes cooperation now imagine what kind of society I would build if I just stopped there so you see there is both of them are probably true also punishment and the sense of fairness are probably true at the same time but the point of these models are that we're interested in the key parameters the bare bone of factors that are required to produce a given behavior and we can only do this if we start from the bottom and we start slowly adding things to the model slowly adding meat to the model unless we get the behavior otherwise there is no way to tell which factor was the important one and that is what is meant here by good to learn what is important to get a certain phenomenon all right yes and we can only get a given in we can only get an insight into the problem for instance the two different cases that I described to you sense of fairness and punishment they're probably both true and they are just as these two uh pictures are correct right this is kind of an x-ray and this is some kind of what is it ultrasound in fact I don't know what this is um probably some of you know maybe there's a baby inside is it I have never seen one I mean I I don't know okay where is the baby actually this one this this is a head how can you say that this is a head this one wow okay so but the point the point was this is correct and this is correct but it gives you a different perspective right this shows you the bones this obviously doesn't show you bones this doesn't show you soft tissue this shows you soft tissue right so my model with with punishing people gives me an insight the other model with sense of fairness also give me an insight they're probably both wrong as as it says here I mean all models are kind of wrong because you only get the different perspective from a very complex beast if you imagine you only get a different like spotlight from the perspective that you're interested in and what perspective you're interested in actually depends on your customer what they're interested in or if you're into research it means what you as a person are interested in are you interested in coming up with policies for punishing people more effectively so that they cooperate more or are you interested in coming up with policies which reward those who who cooperate so addressing their sense of fairness so these are the models this is the modeling approach that we take and in that sense we're not trying let's stay here we're not trying to come up with the value the quantitative value for selfishness that destroys cooperation for instance it would mean nothing it would be just a parameter alpha for instance and the value maybe 2.5 what does it mean nothing it means nothing but the insight that we got is is what we're interested in does this somehow address your quantitative question from before what do you mean you want to study something new that you don't know how can you study something if you don't know it exists yes oh I think you're going into the direction of this type of models if you want to have a model for an airplane it has to be correct it has to be very accurate even in a quantitative sense weight and and what is good what you can do you can do two things if you want to if you want to answer the question how many pieces of of this thing should I produce to maximize my profits this of course would depend on what your customers want and on your estimation of what your customers want but if you want to answer this precise question is it one million is it two million then you need these type of models if you want to answer the question what is it that makes my customers buy this thing is it the shape is it is it the weight what is it then you're not interested in what the perfect weight is is it five grams or ten grams you only need to know that it's the weight so this is the insight that you got you see all right let's let's let's try to talk about this after the lecture all right good so it's important to make this difference here because then your expectations would change you shouldn't expect that the parameters that you get mean anything in real life for instance product attractiveness of 2.3 you get the product attractiveness of 2.3 what does it mean it means nothing obviously but what is important is are the insights you got from what influences product product attractiveness and are there any critical points where product attractiveness simply jumps and changes completely or qualitative changes critical behaviors in in product attractiveness it will become clearer when after you do the self-study but I hope it's it's not as vague as as probably it was in the beginning let's repeat what we know so far I repeat this because again there were some comments why don't we have sample solutions why don't we have exercises and probably there would be comments why don't we have exercises for the exam why don't we have sample solutions for the models the answer is there is no sample solution existing it's impossible to say this is the right model as you saw before what what is it is it this one or this one it depends on your perspective that's why there are no sample solutions as far as for exercise for the exam goes we don't need those everything is in the slides it's not like you have to calculate uh balance sheets or stuff like that and that's why the importance of you of people as problem solvers is important and that's why we needed project management we needed problem solving cycle because it's not just a question of engineering to crank up a few equations and put it in a computer you really need to know what you're solving why you're solving it what your goals are otherwise everything else doesn't make sense doesn't connect to the larger perspective and this is what the engineer of the future should be able to do as was mentioned in the in the first in the first lecture so an engineer of the future should not only know differential equations and modeling but also why we need these models what problems we're solving and what problems we cannot solve um yes as as we talked about models allow for quantitative verification of prediction if you want this if you want to know this is the temperature tomorrow uh you have this kind of models but if you want to just highlight mechanisms that are important to reproduce certain behavior then you do something else you go with minimalistic models yes so this is what we're interested in what is the mechanisms and if you start playing just a little bit with the models with just come up with the with the situation that you want to model and think of what may influence it and then talk to a few friends of yours probably all of you would come up with different things the point is you can reproduce any result you want i mean it's a fact you can take a model you can you can put there thousands of of factors that influence human behavior for instance you can reproduce anything but do you really understand what caused the behavior no because there are thousands of these of these factors so that's what we want to understand um how do we we have complex systems right so we have a the systems we want to study are complex how do we model them first we start from the bare bones the simplest thing possible the way i explained with cooperation you start with just one thing very simple you see does this thing produce the behavior i want no then we need something more what is it well i don't know it depends on your perspective you add more and more until you get the behavior so this is the principle of successive refinement you start with a coarse-grained picture and you constantly refine and then keep in mind sometimes systems certain systems just cannot do what you want them to do they're not i mean this is what what is meant by respect visibility they just cannot do what you want them to do and you have to accept this the self dynamics of the system so if you have a system running by itself without any influence from the outside how does it work oh god i need to speed up all right so this this is not so important no i've already i've already talked about this we need to identify the system elements the challenge of course is initial conditions how do we jump start the system that's a challenge but we're going to see that yeah that that's definitely not not so important we're going to use vensim in your self study the self study for today there are instructions how to install vensim so this is how vensim looks like these are alternative to vensim you can read them if you want alternatives to vensim doesn't matter introduction and so on yeah i mean these are not so this is very confusing this means delete it's not the pacman so it's not something good it's it you know i mean i got really confused i would i would delete my system elements all the time but it's it's it's not the pacman let's go to your model in the self study it's the rabbit fox population it's a very prototypical example of a population dynamics model uh yes let me ask this one we have the two populations one feeds on the second one and the second one somehow is constantly regrown and you can think of humans feeding on natural resources right and the implicit assumption of most people is that natural resources are limitless all right so yeah we have either the the consumer as predators and the raw materials let's say oil as the rabbits or the prey let's look at these two populations separately prey and and predator this is the rabbit this is the prey there is the rabbit population here there is a birth rate for the rabbit the number of births the absolute number of births and the absolute number of deaths okay and of course the deaths and the births depend on the birth rate and and the average lifetime that's fine you can put this oh i'm sorry for this the rate of change of the rabbit population so this is x the rate of change with time of the rabbit population is the difference between what is born and what dies at any given point of time so if you solve this r here r is the difference between birth rate and death rate so if r is positive if you get more births than deaths this thing explodes exponentially if it's negative so this is the positive feedback right if it's negative we have a negative feedback which is zero if it's not something important okay thank you uh all right so explosion death let's look at the foxes uh what is that no that's the rabbit populations right so you might say this is not realistic this is a minimalistic model but it's not realistic because rabbits don't explode uh i mean rabbit pop rabbit population doesn't explode so you say we need something more in our model we need carrying capacity a given piece of land can only support so many rabbits so you you include the carrying capacity which obviously produces the effect of overcrowding so when rabbits or people start to overcrow yeah i know i mean this is quite negative so this increases the death rate so the more rabbits you have the more overcrowded they would get and the more deaths you will have so with this you get the saturation okay the rabbit population now saturates to the carrying capacity okay sorry of course it's scaled by the by the net birth rate r m is the carrying capacity so these are very simple differential equations the rate of change in the rabbit population depends on the birth minus the carrying capacity and you can already see that this would produce saturation because the square term would kick in and would limit the growth as sx grows fox foxes the difference between fox and rabbits are the foxes need rabbits to live one minute rabbits are reproduced by some eternal machine or something they always come up but the foxes need rabbits here the fox food availability these are the rabbits by the way this is in vensim and this is the model you have to play with for yourself study so in vensim if you click on any of these variables you can see an explanation of what the variable does and what it means fox food availability how many rabbits are there for for the foxes to eat you see this is the typical the average fox representative fox again fox deaths for fox births we have an initial condition here the average fox life everything is the same as before with the difference of fox food availability we get these dynamics if you couple now the two populations together which is the model you have to play with in yourself study you get basically two couple differential equations you can solve them via analytically or with vensim right so you see this is the rabbits the rabbits eventually lead to to more consumption by by the foxes and this is the dynamics the different dynamical regimes that you can get these are the foxes rabbits you can get them oscillating more or less it kind of regularly this is these are also oscillations for instance have a look here the rabbit population reaches a maximum at time step 10 at time step 10 the fox population also reaches a maximum there are so many rabbits foxes eat them suddenly the rabbits decline because they're all eaten by the foxes and the foxes decline but now look the rabbits the rabbit population recovers much faster much faster than the fox populations so it takes some time for the foxes to find the rabbits and eat them right so you have these different periods you have you see these are different regimes and in your self study yes that's the end in your self study you need to play with all these parameters here and reproduce these regimes and more and the self study is about explaining how the different how the different factors here influence the dynamics thank you