 So, let us get further on today's class on causal loop diagram. We introduced very basic concepts on systems thinking and system dynamics and characterize that in this course we are going to be looking at the dynamic behavior of systems, looking at causal loop modeling and then stock and flow diagrams to understand accumulations and thinking endogenously. These are the four concepts we discussed as basics for system dynamics modeling. Hence, the underlying theme will be to look at things that evolve over time that is a dynamic behavior. We will we will be starting with the first pillars of that which is the causal loop modeling. So, let me introduce you to that, so causal loop diagram. So, basic idea here is the causal loop diagram is nothing but a visual representation of the cause and effect relationship between various elements of system forming feedback loops that is how it is at least written on the board. The purpose of this CLD is threefold. One is to conceptualize the problem, understand what it is about and communicate with others. That is the first and last point. The key idea is to capture the hypothesis about the causes of dynamics. Understand what are the variables in the system, see how they are linked with each other and through that visual representation see how we can explain how the system is evolving over time. So, that is the entire idea of this developing this causal loop diagram. In that sense it is slightly different concept because this is one of the first course we are looking at the actual modeling of a any system, how do you identify the variables, how do you identify the links and once you establish those relations then we can later study how to come up with the equations underlying the system. So, first is just to identify relationships between the various variables within a system. CLDs are causal loop diagrams, CLDs in short nothing but consists of variables connected by causal links or arrows, it is not very difficult to visualize, we just have an x which is affecting y or x influences y as we read it. The variable at the end of the arrow or the x is independent variable and y is a different variable, it is nothing, it is kind of straightforward there and the arrows show the direction of causation. So, we can illustrate this very simple examples. So, for example, you can identify variables such as say births and population or deaths and population here we can say birth influences population, deaths also influences population we could. So, we want to read it as births influence the population, deaths also influence the population here and we can construct many such examples like production affects inventory, sales also affects the inventory. To elaborate on that causal link we can associate it with the link polarity, we use a symbol plus or minus, plus indicates it is a strengthening and minus indicates it is a opposing or S can stand for same direction go for the opposite direction. So, let me go back with that idea to the same examples, here what we want to do is we want to visually represent how the births affects the population as more births happen the population increases. So, as more births happen population is also going to increase, so it is in the same direction we indicated by a symbol plus against the causal link, by the plus here on the causal link. Again deaths as more deaths happen the population falls down as more deaths happen population falls down. So, as deaths increases the population falls down. So, that we can indicate by a minus sign against the head of the arrow, so this gives us an idea that as deaths increases the population falls down or births increases the population increases. So, we just see simple concepts we can establish a nice causal map of various problems that we can look at. So, we can go back to the example noise more production happens the inventory on hand should increase correct. So, that we can indicate it by a plus and as sales happen an inventory decreases. So, sales increases my inventory is going to decrease, so I am going to put a minus sign against sales and inventory, this is a very simple example on plus and minus. So, we can as more population occurs more births occur, yeah we can do that, so you can put an to indicate that we can close the loop by adding this population at birth and have a plus sign here. So, we can reconstruct the similar thing will happen with deaths also. So, we can extend this idea simply here let us write it births population deaths as more births happen the population increases it is the same direction let us use a symbol plus as more population is there more births will also occur. So, direction is still the same, so we will put a plus as more population is there we can expect more deaths to be there right, the share the share the number of deaths this population increases the deaths can increase and as more deaths are there the population is supposed to come down more people die or more what are the population of whatever community or species you are looking at that population has to come down as more births happen population comes down you can indicate it by a minus sign right here. So, what we have just drawn is a it is not just the causal link we have even moved ahead and drawn a causal loop as you can see it we have drawn our first simple feedback causal loop here and there is loop here. If you look at the loop on the left side here as births increase population is going to increase as population increases births further increases etcetera it keeps on going to increase in fact, it will increase exponentially. So, this entire loop is what we called as a reinforcing loop well if you look at population and deaths as population increase more deaths happen and more deaths happen population decreases at some point it is it can reach some sort of a equilibrium can be expected there. So, this loop is called as a balancing loop we have done two types of loops one which we can expect an ever increasing behavior influence of births on the population and as population increase deaths can increase which kind of limits the growth of the population. So, that loop is called as a balancing loop examples are to work suppose we have two variables just say x affecting y we can have various kind of relationships just to put a numerical sense of things because you are used to that. Suppose we take the first case say x of x y and the relation you give as x is equal to y equal to 2 times x very simple example suppose in this case both the value of x is 1 y is 2 as x increases as x increases here from 1 to 2 y is also going to increase to 4 as this goes to 3 this goes to 6 etcetera. But as y comes down say x comes down say from 1 it comes to 0.5 this is going to come to 1 as this comes to 0.25 this comes to 0.5 etcetera still that is a decrease. So, you can take this as a reference point. So, initially it started with x as 1 and y take the value of 2. So, as x increased from 1 to 2 and beyond y will also continues to increase from its reference point of 2. If x falls below from 1 y also falls below 2. So, the direction of movement is the same. So, direction of movement is the same that is the case we indicate this link with a plus sign. Let us take different colors, but let us do x by 2 again let us take the same reference point. So, when x is 1 y is going to be 0.5. So, next increases to 2 y will take a value 1 x is 4 y is going to take value 2. So, as x increases y continues to increase again this is a reference point. Let us see as x falls down. So, instead of 1 it becomes 0.5. So, y will be 0.25. So, as x falls y also continues to fall. So, we are just it is still multiplying by constant. If you are multiplying by 2 you are multiplying 0.5 still multiplying by constant the direction of movement is the same. So, you continue to represent it by a plus sign x influence y to positive direction. So, these kinds of things can lead to some tricky behaviors that is why I explained it. So, let us take up the third case say x influences y. Let us take y in this case equal to 1 over x. Let us again take the same reference point as 1 y is 1 that is the same reference point. So, as x increases 2 y becomes 0.5 x goes to 3 y becomes 0.33 x becomes 4 y becomes 0.25. So, here you can clearly see as x is increasing y is decreasing. Now, let us see what happens in opposite direction as x becomes 0.5 y becomes 2 and so on you can expand the case. This we make it understand. So, here it was related to movement. So, to indicate this kind of relation as x increases y increases. So, then we do a plus sign or x decreases y decreases it is a plus sign same direction. Other option where x increases y decreases or x decreases y increases it is an opposite direction or opposing we indicate it by a minus sign. This is a very simple artifact of us using the thumbs it is a simple trick, but if your thumbs are in the same direction that means a positive link. So, x increases y increases or x decreases y decreases then this plus sign x decreases y increases opposite direction then it is a minus sign. So, here plus and minus are just symbolic it is nothing to do with addition or subtraction it is just symbolic to indicate the direction of causation. So, that is a simple idea. Just to go over what we did we found a formal definition if all other things being equal a change in causal variable generates a change in the same direction and affected variable relative to its prior value that is a formal definition of it, but if you want to get a feel of it it just says that if x increases then y increases above what would have otherwise been but if x decreases then y decreases below what it would have otherwise been. So, that is what it simply means as a plus sign. So, in this course we will be using this symbol plus, but there are some books and papers which use the symbol s instead of plus, but that is very few most general convention our days is just use a symbol plus or minus if all things being equal a change in causal variable generates a change in opposite direction of the affected variable relative to its prior value that is as x increases y decreases below what it otherwise have been then we use a negative sign or a minus.