 So, I now move on to the next topic namely productive thinking. So, in this session or rather sessions because I am going to continue tomorrow also with the same topic, how can I develop my thinking to generate ideas? This is one of the questions that we would like to discuss, answers to this question. And then in how many different ways tabular, graphical or other, can I present the data? So, we would like to answer these questions in the course of next few sessions. Now, I have used the term productive thinking. So, let me define what I mean by productive. Many times a good definition for ideas and concepts is obtained when we say what the idea means and what the opposite of the idea means and or what it does not mean. So, for instance let us first define what would reproductive thinking mean which is the kind of thinking we do most often. Reproductive thinking, a thinking is said to be reproductive when it is based on similar problems encountered in the past or thought to solve. Most of our examination questions involve only reproductive thinking. So, you teach some matter in the class, then solve a few problems, give a few assignments which are modified problems in some form which you solve and then give further modifications of these ideas as problems in the examination. So, most of this is reproductive thinking. As against this a thinking is said to be productive when it generates as many alternative approaches as possible. So, one can say that one's thinking is productive if the thinking process leads to different ways different alternative ways of doing a particular thing. So, different ways of doing a particular thing, different alternative approaches for doing a particular thing is normally a mark of productive thinking. Research is all about productive thinking which is also called higher order thinking and it consists of critical thinking and creativity. So, I am throwing some words which are commonly used in the context of research and good thinking and then we will define these words and explain with some examples. The idea here is that if you want to develop your thinking to generate ideas you must know what is meant by good thinking, right. So, let us start a discussion with two words intelligence and creativity and let us try to see the circle differences between them. Now of course, it all depends on how you define intelligence and how you define creativity. One could define intelligence in such a way that it includes creativity, right. So, I realize that such confusion is possible but I am using the words intelligence and creativity in a very conventional sense as understood by most average people. So, let me illustrate this concept with example. Now, all of us have known about what are called IQ test, intelligent quotient. So, you measure intelligent quotient of people. I am aware that in psychology a lot of research is going on intelligence quotient whether intelligence can be measured and whether there is a reliable way of measuring intelligence and so on. So, we shall leave all those questions or confusions aside and let us assume that there is a way of measuring the intelligence. And one such attempt was made to measure an intelligence of large number of people using a particular test that a psychologist had defined. Now, the same test was administered to a large number of people. Now, here is a result of such a test in the for two people one person the name is Marilyn Woth Savant. This person got a score of 228 in the test regarded as the highest ever on that particular intelligence test. And there are many different intelligence IQ test designed by many different psychologists we are talking about a particular test. Now, another person Richard Feynman all of us will know this name because Richard Feynman was a well known physicist. This physicist received only a score of 122 which is less than many run of the mill physicists this means many other physicists also received the same score were not so well known as this Richard Feynman. Now, if you go by this course then Richard Feynman is a less intelligent person than Marilyn Woth Savant. If you assume the intelligence quotient test to be testing the intelligence under this assumption. Now, people also saw that what was their practical contribution in their life what is the contribution? Marilyn Woth Savant was merely a question and answer columnist for parade magazine. Though the intelligence quotient was very high the contribution was next to nothing as there are so many columnists for questions and answers you know in newspapers in magazines you have that section question and answer. So, you ask questions and the columnist answers them on the other hand Richard Feynman is a Nobel Prize winner and recognized as the last American genius. So, this shows that intelligence alone cannot decide what would be your contribution and how well you are known for your work. So, what is it that people are known for they are known for the creativity when we talk about contributions of people we are really talking about their creativity. So, Richard Feynman is a much more creative person than Marilyn Woth Savant though Richard Feynman scored less on an intelligence test, but we know that in terms of their creative output Richard Feynman was far ahead of Marilyn Woth Savant. So, we must distinguish between these two words intelligence and creativity let us do that in little bit more detail. So, intelligence and creativity are not the same things intelligence in a domain means the ability to function at a high level in that domain, but creativity involves asking new questions and altering the domain. So, this is the important thing is a person able to ask new significant questions this is what decides whether the person will be creative. Ability to function at a high level in a domain what does it mean? It means one example of that could be that students who are able to solve even a tough question paper. So, some matter is taught and questions are set which are relatively tough and still the student is able to solve them then we can say that the student is able to perform at a high level in the domain that does not necessarily mean the student has the ability to ask new questions and alter the domain. Altering the domain normally follows when you are able to ask questions. Now, what is the meaning of altering the domain? Let us take an invention like the incandescent lamp it change the way lighting happened in the world. So, Edison came up with the incandescent lamp and that change the world this is what is meant by altering the domain. So, all significant contributions generally alter the domain. Electrical engineering for instance 50 years back involved teaching some ideas today 50 years later electrical engineering is significantly different right. You talk about to VLSI technology very large scale integration micro electronics nano electronics is the new topic that is being discussed and so on. So, this is what is meant by altering the domain. So, new ideas emerge on the scene and change the world internet has changed the world right. So, this is how domain has been altered. Now, all such alterations of the domain on a large scale happen when there are people who ask new questions. So, asking new questions is the quality of a creative person not just scoring high marks in a tough question paper. So, one can be highly intelligent but rigid non-creative or lacking in the kind of single minded passion drives creators. Now, let us take some detailed example what kind of questions alter the domain? Here is one example right. So, all of you like to know how do you choose a problem for research? How do you know whether the research problem that you choose will make impact? Will it really matter? Will it change the world? So, let us take what you should do is you should read biographies of scientists and you should read the history of various ideas how technologies have developed and so on. This kind of reading is very important for a research scholar because this gives guidelines on choosing a right problem and choosing a strategy for attacking the problem and so on right. So, I am going to discuss one such here. A scientist questioned the following hypothesis regarding cause of obesity. So, this was the hypothesis right that is written there. Now, let me give a brief background to this particular problem that we are going to discuss. In the west there are a large number of people who are overweight. In India probably you will find many people who are underweight but in the west the problem is other way around there are many people almost 50 percent people are overweight. So, a lot of research has been happening on why what is the cause of this obesity? Now, one hypothesis that was believed by many scientists was that overweight people overeat because their level of hunger is higher than that of average weight people. So, this is an observation actually is not a hypothesis. This higher level of hunger is responsible for their overweight. Now, this connection between a higher level of hunger and the overweight is the hypothesis. So, we do observe that overweight people eat a lot but question is why do they overeat? So, the hypothesis said that it just so happens that these people have a higher level of hunger and that is why they overeat and that is why they are overweight. Now, some scientist said he does not believe this hypothesis really right. There could be reasons why a person overeats which are not internal to the person. Hunger is for example, internal to the person right. So, hungry I feel hungry so hunger is within me. So, I feel more hungry for some maybe genetic reasons maybe other reasons and that is why I am overweight. So, this scientist said I do not believe this. So, let me really establish can there be causes external to the person which can cause overweight or overeating. So, this is the now questioning of the hypothesis now just questioning is not sufficient. So, what do you do next? So, you come up with some sort of an experiment to check whether your questioning is on the right track. So, this is an interesting experiment that the scientist suggested and actually carried out. Now, there are many details to this experiment I am giving some sort of a summary in a very abridged form because we are trying to discuss an idea right. So, those who are interested in more details of this can always look up the source and this is a well known research work in the area of obesity. Now, what the scientist did and this is what will tell you what is good research many of you want to know. So, what how do you decide whether research is good? We give some criteria like truth, a newness, sound technique, sound reasoning and so on. So, setting up an experiment to prove or disprove a hypothesis is one aspect of good research right setting up a good experiment that conclusively proves or disproves the hypothesis. So, design of experiments so that can be your contribution right other people might have suggested some experiments, but you are suggesting a much more improved experiment that more conclusively establishes a particular hypothesis or disproves the hypothesis. So, here a very simple experiment this scientist did. So, what he did was he took two groups of hundred people. Now, each group of hundred people there were fifty overweight people and fifty people who were average weight. There are lot of things in design of experiments that should be taken care of. In fact, this is a very good example where people can learn how to design good experiments. For instance, the fifty average weight people in both groups should be of the same approximate average their weight should be very close to each other right. So, two groups should be more or less equivalent, epivalent how to choose this is a question that can be discussed in experimental skills right. Now, we will assume that you know you have chosen two groups which are equivalent. Now, each group was given sandwiches to eat. So, group A was given one sandwich each person in group B each person was given three sandwiches and both the groups were told that they need not eat everything that is given to them and on the other hand if whatever is given to them is not sufficient right they can go to a room that was located about hundred meters away from this place where the sandwiches were kept and they can get the sandwiches from there and eat if the sandwiches that were given to them were not sufficient. Now, we will let us assume that all these people were had not eaten for a certain amount of time and it was the care was taken to see that there was some sort of you know equivalence in the amount of time they have not eaten before this experiment right. There are many things that have to be taken care of I am not going into those details. Now, what was the result? The result was very interesting it was found that in group A where each student was sorry each person was given one sandwich to eat on average the overweight people ate only that sandwich none of them asked for more or went and fetched any more sandwiches. On the other hand average weight people they ate two sandwiches meaning they went out and fetched one more sandwich because they felt that one sandwich was not sufficient. Now the design of the size of the sandwich is an important issue here right the sandwich was designed in such a way that it will not fill it will not be sufficient for the level of hunger that an average person has okay. Now in group B interestingly all the overweight people ate all the three sandwiches on average all the three sandwiches were eaten by the overweight people. On the other hand average people left behind a sandwich they did not eat because they felt you know the three sandwiches were too much they ate only two sandwiches. So the result is that summarized average number of sandwiches eaten by an average weight person in both groups A and B was two whereas an overweight person in group A which was given only one sandwiches ate only one sandwich and an overweight person in group B which was given three sandwiches ate all the three sandwiches. Now this is something very interesting so based on this experiment it was clear that the eating habits of an overweight person is are influenced by external factors. In this case for example availability of food so if you make a lot of food available right the tendency of an overweight person is to eat more because there is some lack of internal control on the amount of food that an overweight person eats. On the other hand average weight people their constitution body constitution internal constitution is such or maybe psychological constitution is such that there is a control and if less food is available they make effort to eat sufficient amount get more food that will be sufficient for them. On the other hand if more food is available even then they eat only the required amount of a certain amount of food that is required. Now this experiment did change the direction in which the research on obesity proceeded okay it in fact showed that external factors are very important in deciding eating habits of people other than internal factors. So it is for this reason that there is a lot of opposition from medical experts to fast food joints and making food readily available they feel it is not healthy because there will be always a lot of people in society who have a tendency to overeat if more food is made available and they will spoil their health. So we summarize our observation over eating habit of overweight people is governed by an external factor namely availability of food rather than an internal factor namely hunger okay. So now this is how you question an hypothesis and then you think of an experiment or a setup which will advance your point right you have a thesis and then you defend your thesis you defend your hypothesis by with the help of an experiment and the results and you design the experiment properly. So design of experiments is also an important area of research. So this gives an idea of how through questions you alter the domain or you come up with new ideas. So questioning is very important not merely ability to answer difficult questions your mind should be able to raise good questions. Now here is an assignment for you read up the article the following article which highlights the elements of productive thinking. Now here is an article from nature right it is a very interesting exercise a very interesting piece of research done by school students guided by a school teacher. Now that is what is nice about it so school children 8th and 9th grade children who have collected the data and did the experiment about bees some of their habits. So if you read up the article you will know more about it. So you read this article to understand elements of good research and good experiments how to design experiments and how to prove or disprove a hypothesis this is readily available on internet okay. Now all articles of nature are not available to everyone but this particular work gained lot of publicity and so it has been made readily available on internet. Now when we are discussing about productive thinking people may get a doubt is it a gift or a skill in other words is thinking ability in bond or can it be developed. Answer to this question is very crucial because if you believe that thinking ability is mostly in bond then there is not much point in education to have a course or have a discussion on how to develop it because it is in bond there is not much you can do about it. On the other hand if it is a skill so what is a skill skill is something that you can develop by practice. So if it is something that can be developed by practice then it is worth discussing how to develop it what is meaning of good thinking and so on. So fortunately research in psychology shows that a significant part of good thinking is a skill that is developed by the individual there is an element of gift no doubt but there is a significant element of skill and this is the positive aspect of the research that has come out on creativity. Now here are some quotations Peter Medaver a Nobel Prize winner he is not a person who has done research on psychology but then we are just taking his quotations because he is a good thinker what does he feel creativity is beyond that creativity is beyond analysis is a romantic illusion we must out draw now the next two statements are conclusions of scientific research on creativity by psychology. So one research for example makes the following conclusion creativity is a skill which can be developed by practice conscious application is needed not the vagaries of inspiration in order to achieve a creative output. Another conclusion creativity is a matter of organizing one's basic skills not regretting that one was not born with a quick or logical mind. So next time you come across someone who thinks better than you please do not jump to the conclusion that that person was in born or gifted with a better thinking ability it is quite possible that that person has developed the thinking okay they spend time and spend time in the right way to develop the thinking right. So if you spend some time on developing your thinking you can also be a good thinker. So we are going to discuss how to develop but there are some prerequisites right for developing thinking so what is crucial for creativity what is crucial for asking good new questions the motivation this is the most important point you must be motivated unless you are motivated you will not do this. So here is a conclusion of another psychologist on high quality work. So he studied a large number of cases who contributed significantly to various aspects various subjects and studied their biographies and so on and observed a few in his own life lifespan and then put down the conclusion of a study as follows okay motivation is recognized as a crucial factor in the development of talent and application of creativity. The importance of intrinsic motivation in driving an individual to practice and work hard to master a specific domain is undisputed Cox that is the name of the psychologist who studied in 1926 in a study of 301 geniuses wrote high but not the highest intelligence combined with the greatest degrees of persistence will achieve great eminence greater eminence than the highest degree of intelligence with somewhat less persistence. Now please read the sentence carefully right this is how conclusions of research work have to be made conclusion is normally a very crisp statement of the main finding of the work. So you might have done lot of work running into several pages and so on but you must conclude it very crisply in the course of one or a few sentences right. So we will discuss this point more when we come to this is writing there is a difference between summary and conclusion many times students are not clear about the difference between summary and conclusion right. So they think both are equivalent this is not true summary can be detailed much more detailed than a conclusion conclusion is a very crisp point. Sometimes you can have a situation where you have done lot of work and you can make a summary but you do not have any significant conclusion out of it it can happen. So let me read the sentence again high but not the highest intelligence combined with the greatest degree of persistence will achieve greater eminence than the highest degree of intelligence with somewhat less persistence. So the difference between the genius and the not so well known famous people is not so much in their intelligence level it is in their persistence level. So it is a persistence that distinguishes great people from the average ones. Professor Sukath may also mention this point that a person should be persistent and not just intelligent. So this is the same point being made by this scientist. So therefore what is the meaning of this that we must focus on motivation if you want to do research you must be well motivated. Now what is meaning of well motivated I have listed many of the motivations in an earlier slide for doing work say service to society, intellectual satisfaction, satisfaction in tackling a challenging or a difficult problem then I said some people do research because they want to earn money they want to get promotion and so on. So this motivation for research for earning money a little bit or more money right and then getting a promotion these are not sufficiently strong motivation for doing great work. So normally I have even given you another quotation of a famous mathematician that you must have some sort of a taste for intellectual work. Now a question will arise how do I develop a taste for intellectual work? Yes as you start delving into this topic more and more you are getting into psychology and this topic is really a very difficult topic to deal with but one important thing we must know. So like infection right how do you get infected with diseases? So sometimes some of the diseases you get infected because you are close to other people who are infected with the same disease right. Similarly this is true of motivation also if you are among people who are well motivated then some of that motivation will rub off on you this is what something works in practice therefore it is important to cultivate such a company right of well motivated people so if you are working with a guide who is well motivated then you will also develop lot of motivation for good research. So this is one way of developing motivation to be in the right company there are other ways also you can read biographies of scientists who have done great work and so on these are some of the ways of developing motivation if you do not have it already but this motivation you must develop and then only take up research there is no point in just getting into research or joining a PhD degree because you do not have anything else to do you will not be able to do good work right. Now let us get more specific about good thinking how to develop it and so on what are the different ways you can represent data right those are some of the questions that we said we will answer now as a preview to the discussion that is coming this is an important let me put an idea in the form of a statement of Aurobindo who is a well known educationist often we hear statements like our education is not you know good enough for developing creative thinking and we are not turning out people who can solve problems and so on now the question is but what is wrong with the education now here is one opinion of a great thinker Aurobindo he says that if you want to develop creativity then you must recognize that the quotation says education is not about learning diverse subjects but about learning diverse ways to the same subject recall in the beginning of this part of lecture I mentioned to you what is meaning of productive thinking it is the ability to think about alternate ways of doing the same thing now very interestingly Aurobindo seems to say the same thing here in a different way that we normally think that if you learn large number of different subjects then we will develop our thinking then we will develop our creative thinking no doubt we will get lot of information we will be well informed if you learn diverse subjects but that is not being well informed is not the same thing as asking new questions developing creative output. So if you if you focus on learning diverse ways to the same subject this is important then you develop creative thinking then you develop research potential okay let me illustrate with an example let us say we are teaching some theorems to students in a course like mathematics we can teach 10 different theorems or alternately we could teach may be 2 or 3 theorems but each theorem we discuss different ways of proving the theorem take an example like Pythagoras theorem for instance a person has written a book titled 100 different proofs of Pythagoras theorem now it is this kind of book which may not be prescribed as a text in any course that a person must read to develop creative thinking. So research scholar should be reading these kind of books in addition to text books related to their own courses so often research scholars feel that doing by doing more courses they will be able to prepare well for doing good research this is not entirely true in fact this is a very prevalent misconception so by doing more courses you become well informed and you do get prepared to some extent for doing research but that does not necessarily develop your thinking that can generate new ideas so you can get new ideas you can make your mind more flexible by reading the books like this that I mentioned 100 different proofs of Pythagoras theorem there can be many other reading material that can be prescribed but all this essentially tries to tell you how the same thing can be done in different ways and that is what will develop productive thinking ability. So in fact this is an assignment for you please find out 5 different ways of proving Pythagoras theorem I have chosen Pythagoras theorem because it is relatively a simple theorem that all of us understand that if you take a right angle triangle hypotenuse square is equal to sum of the squares of the remaining 2 legs of the triangle ok. So because I have a diverse audience not all of whom may be very mathematically inclined I have chosen this particular example you can other proofs are available on the internet now it is internet has almost anything that you want ok but you must learn to use it properly you can use it for developing research skills this is one example so do an internet search and find out 5 different proofs of Pythagoras theorem.