 Welcome, you know, when we had this discussion about living and non-living examples, I noticed that several of my audience were very uncomfortable and I would like them to express themselves now. So, let me now request Pratik Fegre to express his thoughts on what we have discussed about the examples. Sir, I do not quite understand how the human body is so linear, like I have a feeling that it should not be very linear even in the region where it seems to be linear, I feel it is just monotonic and not linear, could you just expound on that? Very good Pratik, I am very happy that you raised this point. In fact, in a way, I gave a provocative example there because I was hoping that our listeners, our audience all over the world would react in the way you have, that the human example is a rather poor example of linearity. If at all one would like to insist upon linearity, it is almost in a negligibly small region as far as human behavior goes with nutrition and the equivalent energy output. I gave that example because I wanted to provoke a lot of people to realize that, yes, monotonic and linear are different, you are right. So, something could be monotonically increasing but not linear and to an extent the example that I gave about the work output and the nutrition is a monotonically increasing relationship again within certain bounds but not linear in the true sense, I agree with you. So I am glad that you responded to the provocation and I am sure many others in our bigger audience all over the world will but now let me give you a better example. So now let me take the example of a bank account again within a certain range of currency operation. So, let us say I have an account operated by a number of people jointly operated by several people and the account with the savings bank account. So, it earns interest depending on what you deposit into the account. So, let us say there are people A, B and C who operate this account. Person A deposits 100 units of currency into the account at a certain point in time and then he observes what interest is earned let us say after some period, let us say one year. Now person B independently in a separate experiment operates the account, deposits let us say 200 units of currency into that account and observes the interest that is earned at the end of the year. So, let the interest in the first case be I1 and the interest in the second case be I2. Now in a third experiment A and B both decide to deposit 100 and 200 units of currency at the same time at that same point in the beginning of the year and they together observe the interest earned at the end of the year. You expect that the interest would be the sum of the interest I1 and I2 clearly an example of linearity. Now where would of course here this is an example of additivity a part of linearity how would homogeneity come in suppose A deposited 100 units of currency at the beginning of the year and observe the interest that is earned at the end of the year. In another experiment A deposits 200 units of currency and then observes the interest you would expect the interest to be twice. So a real life example of a system created by human beings whether it is linearity to a wide extent you know for a large range of currency of course you have this linear behavior additive and homogenous. Of course what could make it non-linear is some kind of saturation of interest you know there could be a cap after a point there may be a decision by the government that you cannot pay more than this amount of interest that kind of a thing would create non-linearities good. So now Pratik you also told me that you had an example to give let me invite you now to give the example that you have in mind. So my example relates to a printer so say we have a printer which prints sheets and say it prints one page per second and so in my case the input will be the number of quests for pages I give it per second so I tell it print say two pages per second so that is my input the number of pages per second I need it to print and the output will be the number of pages it actually get prints out and gives it to me. So in this case as the printer just can print one page per second and not more than that so until I give it less than one page per second that is on an average say one page per two seconds or something like that the output will match my input rate and hence the system is a linear system actually it's an identity system till the input rate hits the maximum threshold of one page per second. However once I hit the one page per second rate and go beyond that say two page per second or three pages per second in that case as the printer won't be able to handle the load the request will be queued and the output will just be constant at one page per second so then and that region outside one page per second the system is not linear and the printer will saturate if you increase the input rate to even higher values the printer might also crash as a result it's not exactly a linear like it's linear in some portion of the input and non-linear outside so that is one example I feel is a good example. Very nice very good so here you have an example where there is an identity relationship up to a point and then there is a saturation that's very often the case with systems. Now for all our audience in different parts of the world we have intentionally just given you some indicative examples and in a sense left them incomplete because we want you to respond and not necessarily respond with praise you could respond with criticism this example is bad this example is not accurate this example is only partially correct we want you to do that that's why this discussion this is not meant to be an exposition of everything that is correct in a discussion we want you to respond and we would like to look at what you respond and then work with you to understand what you are learning from this course and to try and add value in addition to what you are routinely learning as a part of the of the sessions that are being created you know the formal sessions of the course so the discussion sessions and repeating are provocative they are meant to be that way and let me keep them that way let me begin with some provocative discussion here provocative in the sense that they should inside thinking and a response from you not provocative in any other sense is that right so with that we look forward to your responses thank you.