 Now let us look at some prescriptions for improving our thinking process. So far we have understood the various methods which we can use for solving problems and then we have also seen what is the meaning of creativity. It is an ability to look at the same thing as everyone else but think something different. So we have considered various examples to illustrate this definition. Now how do we apply this knowledge in practice and then try to improve our thinking? So here are some methods. Do mental exercises. We did a puzzle solving dividing a piece of paper, square piece of paper into five equal squares. Now like this there are many exercises which are available. Everyone can cultivate a hobby of solving such problems or exercises, puzzle solving. Even though we may not get solutions to the puzzles but the activity of solving, the struggle involved in solving puzzles, that struggle itself is very good to improve our thinking. So though we may not be able to solve the puzzles, if we attempt those puzzles it is quite possible, some other problem we will be able to solve easily if not the puzzle. Then another important practice that we must cultivate is maintaining a notebook of ideas and all our activities. So as you can see this is much more easily said than done. It is easy to say that you must maintain a notebook but few people maintain a notebook. Few people note the ideas when they occur to them. You know research has shown that when an idea occurs to the mind unless some methods are used to fix it or note it, it dies within a minute or a couple of minutes. That is the duration for which an idea stays in the mind. So you may think that when an idea strikes you that because it has struck your mind it is like your baby and you will always remember it, this is wrong. You will not remember it for very long. So it is good to make note of it and then go through the notes. Another very important thing look at the world in terms of analogies. Analogies are very powerful methods of generating new ideas and then learn different approaches to the same problem. We have seen that quotation that education is not about learning diverse subjects but it is about learning diverse ways to the same subject. So let us look at these four points in somewhat more detail. So I will give you two more examples of some exercises. You can find you know books which give problems like this. I am not expecting you to do these exercises now but these are assignments. So for example plant ten trees in five rows with four trees in each row. How will you arrange the trees? So that there are four in each row and there are five rows. Connect the nine dots by drawing just four lines and without lifting the pen from the paper. So nine dots are shown there you have to join them by just four lines. So you attempt this kind of problems your mind becomes flexible. Let us look at note keeping in some detail. So noting ideas as they occur helps you to remember them. Speeds of your thinking this is very interesting. This is a result of research in psychology. It has been found that when you note ideas when they occur to you it speeds up your thinking. Students are encouraged to take notes in the class rather than just sit and listen. Focuses attention on your subject, stimulates cross fertilization of ideas. This point is very important. So if you want to use one idea and another idea together to solve a problem and you think that these two ideas will be there somewhere in your mind. You know it is difficult but if you make note of various ideas and then you go over your notes then it is much more easy for you to cross fertilize ideas. If you do not record your ideas you will spend all your mental energy trying to resurrect old ones. So a lot of time is spent in trying to revive in your mind. You know some idea which would have struck you at some time when you are faced with a problem record ideas thematically. So you can come up with your own themes under which you can record your ideas. Review your notebooks when you face a problem even when you found a solution. So it is easy to understand why we should look at the notebook when you face a problem because you are looking for a solution. But why should we look at the notes of ideas when we found a solution. This is to reinforce some strategies of solving problems because they are much more suitable in our own area. So when you have got a solution you know how you have got the solution then you go over your notes of ideas and see how many more problems could be solved by the same approach. So if you find that many problems are getting solved by this technique then that technique is really very useful in your area. So this reinforcement takes place when you look at the notes even when you have found the solution. In fact Edison is said to have had this habit that he had hundreds of pages of notes of ideas and he would go over them most of the time even when he had faced a problem and even after he got a solution. Now what are the sources of ideas of course yourself others look for ideas in other fields as well not just your own this is important. So many times when I ask my students to attend seminars they say sir we attend the seminars but we do not understand anything. Okay suppose there is a seminar in suppose I am working in the area of Solis State Devices. Now there is some visitor who is giving a seminar on power electronics. The students feel what do I have to do in power electronics. Okay the point is it depends on what you are looking for. If you are looking for new ideas it is worth attending seminar in any area. Okay so long as you do not find an idea you can switch off fine but you should have sufficient interest to switch on just when a new idea is being discussed and you can make note of it. So you can get ideas from different sources and particularly you can generate ideas in your own field by looking at how people are operating in other fields. Now let us look at the topic of analogies. An analogy enables a look at a situation as an interrelated whole. What is the advantage of looking at things from an analogical point of view? Okay an analytical approach on the other hand dismembers a whole into parts and may destroy the attributes which may pertain to the phenomenon as a whole. So analytical approach of looking at things means you are separating the whole into parts and then try to understand the parts. We have discussed analysis what it means. As against this analogical approach is looking at everything together as a whole. We will discuss some examples of analogies to illustrate these points coming to the third point. Problems are solved and creative works are generated by transfer of existing ideas to new surroundings. So many inventions are nothing but ideas picked up from somewhere and then applied in a new situation either consciously or unconsciously. The active process leading to creativity is metaphorical in nature. This is another statement which has come out of research on creativity. Now let us look at examples of some great discoveries by analogy. Electromagnetic wave and matter wave. So how was the concept of matter wave proposed when Deep Role proposed the idea of matter waves. How did this idea strike him? So by the time he was working there was this concept of light as a wave as well as particle. So Maxwell's equations and so on they represent the wave nature of light. And then photoelectric effect experiments by Einstein showed that you can regard light as particles. So Lewis-Dubrolet thought that for light the wave nature is very evident in our day to day experience. But if you devise some special situations you can see the particle nature. The wave nature is easily seen for light but particle nature is seen only when you devise special situations. Then he thought for matter the particle nature is very evident. Why can't it be that there may be a wave nature for matter which you will see if you devise special conditions. So why can't this wave particle duality which applies to light apply to matter also. So it is this analogical approach of looking at things which gave him incentive for proposing the wave nature of matter. Another great discovery of the atomic structure. How did people think of suggesting that the atom involves a nucleus of one polarity and surrounding a nucleus you have electrons which are particles of opposite polarity moving about. In a circular fashion. Of course now you know that the orbit need not be circular and so on. I am talking about the primitive model. It can be made more sophisticated. But the first model on atomic structure how did the idea come about. So people had seen the solar system. So there is a sun and you have planets moving about. So some scientists thought that if this is the picture of the outer world where you have a central entity and then surrounding that you have other entities revolving. Why can't a similar structure apply something that applies at a macro level macro m a c r o macro level apply also at a micro level. Why can't this model apply at a micro level where there also you have a central entity and then other things revolving around it. So as a perfect analogy to this solar system the atomic structure was proposed. So you have a positively charged nucleus and then you have electrons revolving around it. And then based on this model they try to derive some facts and check whether these facts this theoretical derivations match with observations. And they found they indeed matched and that is how they decided that this particular model is quite good to explain the phenomena at the atomic scale. This is an excellent example of discoveries by analogy. One can give hundreds of examples of smaller discoveries or inventions where ideas have been taken from one area and then used to explain another situation. Let us look at some effective explanations by analogy. What is the motion of electrons in a crystal? How do electrons move in a crystal? Now instead of describing this in great many words, if you say that the motion of electrons in crystal is like dust particles in air. Everyone has seen dust particles. How they move about in air? Random motion, Brownian motion. And the electrons movement in crystal is exactly like that. When you explain by analogy it is very easy to understand the complete situation as it is. That is what we said is an analogical approach. It enables you to understand the complete situation as a whole. How do electrons flow in a crystal? So the flow of electrons in a crystal is like movement of ball in a viscous medium. So if you want to explain how electrons acquire an average constant velocity in response to an electric field when they move in a crystal. So the students have difficulty in understanding. Instead of going through the complete derivation which anyway one has to go through, mathematical derivation, if you first start with an analogy and say that if there is a ball which is falling in vacuum because of gravity it will go on accelerating. But if the same ball falls in a viscous medium, then after some time it will acquire a constant velocity because the friction opposites the gravitational force. Similarly if an electron is moving in vacuum you apply an electric field it will go on accelerating. But when it moves in a crystal, the other particles in the crystal, other electrons and so on and other particles they will act like friction to the motion of electron and therefore the electrons will ultimately acquire a constant velocity. Now take another example. The idea of energy quantization in quantum mechanics. If you want to explain, you consider the flow of water. Supposing I have water in a container and I am pouring it out into another container. Now how far can I reduce the flow? What is the smallest amount of water that I can transfer from the container to another one? In principle since water is liquid, the way we understand the liquid we can go on reducing this amount. But instead of water supposing you had sand and you are pouring out sand. At least you have to pour out one grain of sand at a time. You cannot pour out less than one grain of sand. So this is an example of quantization. You can have either one grain of sand or two grains of sand. You can't have one and a half grains of sand. Or three grains of sand and so on. So this is where your flow is quantized when you are transferring sand from one container to another. But if you are transferring water, then you can say it is a continuous variation in the amount. There are very interesting analogies used in philosophy to explain many important ideas. So once someone explained the essential difference between Eastern and Western civilization. So if you want to explain in very simple terms, he said you look at the concept of Mahavira in Eastern civilization and Superman in the Western civilization. It will give an idea of what is the difference in the way of looking at the world in the two cases. So idea of Superman is someone who has a weapon which can destroy anything, but who has a jacket which will not allow anyone else to destroy him. So he can do anything. He can conquer the world, but nobody can conquer him. Whereas you look at the concept of Mahavira. So Mahavira is a person who doesn't even have clothes on himself. Now why do you call him as a super human being? Mahavira, the word Mahavira means a superhuman because the person is said to be superhuman in the Eastern civilization if he has conquered his own mind. That is the definition of a superman here. It is not what you wear and how you destroy others. So this is how you can transfer very deep conceptual understandings and so on by help of analogies, something that you cannot do by analysis as effectively. Now let us look at different approaches to the same problem. We said one of the ways of improving our thinking is to learn different approaches to the same problem. So we have said instead of learning 10 theorems, you learn 10 ways of proving a theorem. So here is an example, calculation of pi. So they are the kind of things we should look for. We should be reading and we should be discussing as researchers if we want to improve our thinking. It is interesting to note so many different methods have been suggested for calculating pi. So some methods are listed here just as an example of how diverse methods can be used for doing the same thing. So let us look at a geometrical approach of estimating pi. So you take a circle. As you know, pi is the ratio of the circumference to the diameter. Now before I discuss various methods of calculating pi, let me tell in a few words why pi is important. Did we ever think about it? Why pi is such an important quantity? Why did people get interested in this ratio of circumference to diameter? So people observed for thousands of years that the circle has a very unique property that all circles look alike, whatever the size. So you draw a big circle, a small circle. All the circles are looking alike, which is not a property of other geometrical figures in general. All triangles do not look alike. All quadrilaterals do not look alike. So what is this uniqueness in the circle that makes all circles look alike? So when they looked at this issue in little more detail, they found it is aspect ratio of the circumference to diameter, which is constant for all circles. That is what is giving this feeling that these different circles, bigger or smaller, are all looking alike. So then therefore they got interested in looking at this ratio. What is this ratio, circumference to diameter? So once they realized that this is the circumference to diameter aspect ratio of this particular geometrical figure, that is of interest, then they started thinking of how to calculate. So one simple approach of calculating this can be you draw a circle, you inscribe a square. Now you say that approximately the perimeter of the circle is equal to the perimeter of the square. So supposing the square is of size side A, then its diagonal would be A into root 2. Now the diagonal of the square is the diameter of the circle. So I can say that circumference by diameter is approximately equal to perimeter of the square, which is 4 times A divided by the diameter, which is A into root 2 diagonal. So this gives you the value 2 into root 2. So this is an estimate of pi, 2 into root 2. Now once someone proposed this approach of inscribing a square, it immediately struck him that well instead of inscribing supposing you circumscribe a square. After all you can say that approximately the perimeter of the circle is perimeter of the circumscribe square. Now what is the value you will get? So in this case the diameter of the circle is equal to the side of the square. So perimeter of the circle is 4 times D and the diameter is D. So you get the value 4. And now you say that the value of pi should be greater than the value obtained from the inscribed square, but less than the value obtained from the circumscribe square. Because perimeter of this circle is more than that of this inscribed square, but less than that of the circumscribe square. So I can now write it as pi should be greater than 2 root 2, but less than 4. So one can then use an averaging approach. Why can't it be the average of the two quantities? 4 plus 2 root 2 by 2, which gives you the estimate as 2 plus root 2. Now you can see 2 plus root 2 is 2 plus 1.414, that is 3.414, very close to the value you get. This is a geometrical approach of estimating pi. So in fact the Greek mathematician who first estimated pi is supposed to have used this approach to get pi to a very precise value. He used a 72 sided polygon inside the circle. You inscribe a 72 sided polygon inside. Another one circumscribing the circle. So you say the value of pi obtained is the average of the value obtained from a 72 sided polygon that is circumscribing and the 72 sided polygon that is inscribing. You can get pi to several decimal places. Accurate to several decimal places. Second is geometrical approach, which helps you to get pi to very precise values, depending on how many sided polygon you choose. You can have a trigonometric approach of estimating pi. Now I want to mention that here our goal is not to discuss the calculation of pi. Our goal is to show how same thing can be done by different ways. That is what is our goal. So we are taking pi as an example. So this is a trigonometric infinite series. So Madhava proposed this series tan inverse x equal to x minus x cubed by 3 plus x power 5 by 5 and so on. We have discussed this series earlier in the context of problem solving. Now in this series if you put x is equal to 1 on both left hand side and right hand side, you get tan inverse x as tan inverse 1 left hand side. Right hand side you get 1 minus 1 by 3 plus 1 by 5 minus 1 by 7 and so on. So tan inverse 1 is pi by 4. So your pi value is equal to 4 times the right hand side infinite series. You can go on taking more and more terms and you will get pi to more and more precise value. The last method listed here, there are many other approaches. The last method listed here, Buffon's needle experiment is probably the most interesting of the methods of calculating pi. Now Buffon was supposed to be a rich man who had a lot of leisure because he never had to work to earn money. But he's supposed to have an intelligent also in addition to being rich. So the story behind this approach that he suggested is that once he was sitting on a floor, the floor had parallel lines equidistant, drawn on the floor. And he was sitting on a chair and smoking a cigar. And accidentally the cigar fell down on the floor. Obviously if the cigar falls down, it is possible that it can cross any one of the lines or there may be possibility that it will not cross if it falls, say, something like this. So when the cigar fell, it struck him. What is the probability that if a cigar of a particular length falls on the floor, which has parallel lines drawn like this, the cigar will cross any one of the lines? It just struck him that can we estimate the probability that the cigar will cross any one of the parallel lines? And then he did a mathematical derivation. And he found that a particular case when the length of the cigar is equal to the distance between the parallel lines, then he showed that the probability that the cigar will cross if it falls randomly on the floor is given by the probability is equal to 2 by pi. This is the formula he derived. So how do you get the probability in practice? How do you measure the probability in practice? So what you do is you do a number of times, trials. Or you can even, this is called Buffon's needle experiment. That is, instead of cigar, he replaced the word cigar by needle. Supposing you have a needle of a particular size, and you have a collection of large number of needles of the same size, and you just throw them up. And then you count the number of needles which are crossing the line divided by the total number of needles. That gives you a probability. So either you can throw one needle hundreds or thousands of times, or you can take thousands of needles and just throw them and see how many of them cross. That will give you the probability, the ratio. So from this ratio, you can get the value of pi. So this is a very interesting approach where from random events, you can calculate a quantity. Now in modern days, this approach has been used to estimate quantities simulation. What is the name given to this? It's called Monte Carlo simulation where you calculate quantities based on random numbers. So you see so many different approaches are there, geometrical approach, infinite series approach, trigonometric infinite series approach, statistical approach of calculating pi. So if you read this kind of material which discusses different ways of doing the same thing, it improves the creativity that we have. It improves our ability to come up with new ideas. So another example I would like to quote in this context is a book which discusses 100 different ways of proving Pythagoras theorem. There are 100 different ways of proving Pythagoras theorem. So as research scholars, these are the kind of things that we must spend time in reading, not only in taking more courses. I often found that research scholars are interested in taking more and more courses. Even the sincere ones and interested ones. Because they think by taking more courses, they can broaden their horizon. Nothing wrong in doing more courses. But you must understand that doing courses may not improve your creativity that much. It is reading these kind of things which is going to help you to generate new ideas and improve your creativity. So one assignment that we give when we do the course is you at least give 10 different proofs of Pythagoras theorem. This is assignment. Read up 10 different proofs of Pythagoras theorem. Nowadays the internet is a very good source of all this information. So you can do a search on the internet and find out 10 different ways of proving Pythagoras theorem. So you can do this assignment. Now some more prescriptions for improving thinking. You arrange and rearrange what you read or hear from different points of view. So as I mentioned in one of the earlier lectures, that is during the introduction. That is important to write up what you have done at frequent intervals. If you want to develop the writing ability. And after you have done this kind of thing several times, then if you take up writing your thesis, writing will be easier. Now when you write up your work, then you can write up and look at, you can write up the thing in different ways. We have also mentioned in this particular lecture earlier that note keeping or writing notes helps you to speed up your thinking. So if you write notes, if you write up whatever you are doing and you, at the time of writing you will think more and you will find out different ways of writing the same thing, different ways of looking at the same thing. So this is something that you must attempt. Then allow opportunities for cross fertilization of ideas so as to generate new problems. So what are the opportunities for cross fertilization? Note keeping we have already mentioned. In addition, interaction. So various forms of interaction like discussion, answering doubts. Someone has a doubt you actively participate in answering doubts. Teaching, it is a very good opportunity for research scholars to improve their thinking and their understanding and so on. If you have an opportunity to teach a subject. So you can take one or two classes in a course, teach a topic, explain, handle tutorial classes and so on. Then set aside time to read in other disciplines, keeping track of what others are doing that seems original. If possible work in areas outside of areas that we are currently learning about. If possible, you can do that. If you can cultivate friendship with someone of a different discipline. And then occasionally you can do some work with the other person. That is very useful. So now we can summarize what we have discussed so far. So as per psychology, creativity is an ability to see things differently than others. It is a skill that can be taught and developed through practice. The requirements for creativity are a strong motivation and an open mind, not high intelligence. Creativity can be nurtured by learning about different ways to a problem, visualizing the world in terms of analogies, doing mental exercises, and note keeping. These are some of the things that we have suggested for improving creativity. The hands over creative thinking, all those things that you have listed, they are fine in one way. Then what about the basic habits one has to inculcate? So that creative thinking. For example, there are people having creative thinking, but they use it negatively, not for constructive purpose. Really, though they call it as creative, but they use it for destruction instead of creation. So what are those traits or what are those habits essential for developing positive characteristics or positive creativity? Yes. Now, first thing is, one of the things that I discussed has to do with habit, note keeping. It is a habit that I've suggested, one must inculcate. Though it is not the kind of habit that you probably are talking about in this context. So broadly, I would say you are talking about ethics. So one of the topics is ethics that we are going to discuss, professional ethics, particularly for researchers, what it means. But maybe your question is much more broader than the kind of thing that I would have discussed under professional ethics for research scholars. For example, I have found it is very interesting. So many places I have done this course, people do not understand the meaning of plagiarism. Even our own students in IIT, BTEC students I have seen, do not know what is meaning of plagiarism. When they write their reports, they simply do cut and paste. And they are not aware that you should not do it. So those are some of the issues that I would be discussing. But your question is I think much more broader. So how do you develop positive traits in people? I think all of us know about it. It is the question of implementing in practice. Can you give me some examples that you have in mind? No, for example, one can upfuscate the issue by saying that first of all, what is positive and negative has to be first defined. And then you can say that what appears positive for one person may appear negative to the other. And one can go on like that, but that is not what we are looking for here. Can you just elaborate on what you want to say? Basically, any creative process, it takes place through integration. For example, one has the ability to put hard work and use his or her brain, along with some basic characteristics like one is pure, clean, honest, and positive attitude. Now if these things are put together, then there is going to be definitely a creative process which is beneficial for humanity. On the other side, the people work hard, rather they work more harder than the others. And they use brain, but they are impure, unclean, dishonest, and negative. Right. So naturally they go for again creation, but that is destructive in nature. Yes, now I will ask you one question. Why are you asking this question in the context of creativity? You're talking about good and evil. Let's put it like this. You're talking about good and evil. Yes, this is a very relevant thing. And it is important. But why are you asking it in the context of creativity? That is what I want to know. Maybe because creative people are influential and therefore you want to assure that there are good creative people and not evil creative people. That's not it. That is my point. Maybe that is what you mean. So creativity has to be finally put into the practice so that it should bring benefit to the humanity. Yes. Not otherwise. Yes. Now if you see motivation, this topic falls in the category of motivation to some extent. What motivates one to be creative? It is unfortunately a fact that a lot of developments in technology have occurred during the times of war. So destroying your enemy is a very strong motivation for creativity. It is unfortunate, but it is a fact. So this topic is actually much more deeper topic of human nature. What motivates people to do actions? I think this kind of discussion is very important, but I don't know whether we can do it in the context of this course. Because this is a discussion on human nature, human psychology. At least in Indian philosophy, all the saints have said that mostly man is motivated by so-called negative tendencies. If you see the motivation that are listed, that propels man to action, mostly negative and sometimes positive. So people are motivated by jealousy, envy, and all these other motivations. What is meaning of competition? Can you, let us have a discussion on this. People say that competition improves quality. What is the basic motivation in competition? So you are enhancing jealousy. So it is a unfortunate fact that there are negative tendencies which propel man. See, a lot of advertisement, you see creativity is there in advertisements on TV. What are the most of the advertisements appealing? What are they appealing? Which aspect of man are they appealing? This is an example of creativity. What is the motivation? So people are pumping in money, and of course there is, one cannot deny that there is creativity, the kind of things they come up with. But ultimately they are only appealing to the baser instincts because they know, and they think it works, and they know it works, they are doing it. Otherwise, so I think this is a much broader topic. We are discussing in the context of research. So yes, I mean one can say, should scientist develop an atom bomb? This is the kind of question that you are addressing. You want to be discussed. It comes in ethics, broadly it comes in ethics. So we are saying the same thing that negative motives are present which propel people into action. But it is not necessary only negative motive should be there. See, after all, example, example, the braille. What is the motivation of the person who developed the braille method of reading for blind people? It is a positive feeling, to help blind people. So there are examples of both types. Sir, I will ask, I mean there are competitions in which win-win situations are created. So that is fine. Like win-win those are those, if these kind of competitions are there, then they are not good. Yes. Also creativity is there. Yes. So my point was to give more emphasis on win-win situations kind of competition where creativity has to be there. So if there is a win-lose, then naturally jealousy is a dominant factor. And this kind of competition is a negative competition. Yeah, so what we are saying is you should try to develop creativity through cooperation rather than competition. There are many examples in the society. Like that they are creative peoples, but have a negative impact in the society. Like Harsad Mehta has done, he was very creative. Yes. He has done a negative impact. What is the use? Yeah, no, no, what I am saying, these questions are relevant, but I think they are moving away from the present topic that we have discussed. That is what? So if you have, we can discuss those, but right now if you have any comments or doubts about what we have discussed so far, other than the issue of motivation for creativity.