Yn hyn mae'n mynd i gyd yn ddweud y cyflogol yma o'ch cyflogol, ac yn y gweithio dechrau ynghylch, mae'n amser. Mae'r cyflogol yn fwy o'ch ddweud ar eich eich ddweud. Ond oedd yn ddweud yma i'r tespwynt, a'r ddweud yn yr eich tespwynt, yn angen i'r ddweud, yn eich ddweud. On dyna ei ddweud i'n ddweud. A dyna'r cyflogol yma, yna mae'n ddweud yma i'r ddweud? Byddai ar y ddweud cyntaf llwyddiadol cyflogol? ond byddwn i'n gweld hynny'n ddyn nhw'n meddwl? Onw'n ddyn nhw'n meddwl. A dyna'r ffordd y ffordd yn cyffredinol y ddechrau o'r amlion maen nhw'n meddwl. Y ddechrau ymgyrch, o'r ddyn nhw'n meddwl, sy'n meddwl y cyffredinol. Mae'r ddyn nhw'n meddwl ysbryd yn lleol am ddyn nhw'n meddwl ac yn ddyn nhw'n meddwl mae'n meddwl yma'n meddwl. Ond yma, yma'r ddyn nhw'n meddwl yma'r ddyn nhw, mae'r cydwyddoedd y gallu cyfnodol efallai yn cael ei gael. If you want his project of his whole being, then I would want anything that diminishes, anything that becomes an obstacle, anything that detracts from this will begin then to acquire the face of what we don't want to call evil. Or something wrong or whatever type of thing. ac ydy'r cyfnod ydy'r cyfnod y cwynhau hyfyddon o'r cyfnod, mae'n gwertho'n gwybod sydd y cyfnod yw'r cyffredin yn llwyddoedd, yn llwyddoedd, yn llwyddoedd, yn llwyddoedd. Ac ydych chi'n cyfnod, mae'n cyfnod yw'r cyfnod yw'r cyfnod yw'r cyfnod, yn eich cyfrannu, yn ystod y bydd o'r dwy i'ch gael, a yn ystod y byddwyr hyn yn cael ei wneud gallu ei wneud gyda'r ddigonfod o'r gwahod, o'r gwahod, o'r gwahod ychydig yn y cyffredin gyda'r bod hynny'n hanes? Llynyddu i ddigonfod o'r ffordd. Yn ychydig o'r aelod, mae'n ddigonfod yw'n ddigonfod, eraill yna'n gwybod, mae'r ffordd wedi gweld ddigonfod, mae'n gweld ddigonfod y cyffredin gyda cyllidau efoolishyn. Mae chi'n gweld o'r fath o'r cyffredin ac yw'r cyffredin hwnnw, y llyfr, y llyfr, y tyfnod, y tawch, ac so ond, mae chi'n gweld o'r fath o'r cyffredin hwnnw, y bwysig yn ohol yn gyfnod y rhan. Mae gweithio ddim yn ei ffaith bod i'r cyffredin hwnnw sy'n cyffredin hwnnw bydd y cyffredin hwnnw o'r rhan o'r llyfr o'r cyffredin hwnnw, wiell y cyntaf, ychydigwch y cerdyn nhw ddwy αυτid y cyflawn i'r cyflawn a dwy'r cyd-pwynt o'r dweud. O'r cyd-dylchedd o'r gyflawn i ymwilio i'r fwrdd ein ysgol o'r cyflawn o'r parodydd, o'r hubauолодd ddisא�ckl, os yna ym mwyaf, os os os os os os os... Fydde cenedlaethau o'r cyngor fawr o'n cyfrifiadau o'r cyfrifiadau. Yna'r wybodaeth ei hun i gyfan ar gyfer ysgrifennu, gan rhai yn dromu. That's where I'm hoping we'll get away in this marvelous company with this huge metaphysical question of my existence, the evil. If we get to the definition of what evil is, and those who commit acts that would define as evil, I move them away from the status of human beings. I reduce my recognition of what is acceptable as membership of the human community. But then how do you define those acts of evil? You can't take that position unless you say this is evil and therefore establish the difference between good and evil, correct? That's why I say it can be codified. We can't say any human being who does this to another being has already put himself or herself out of that community of homo sapiens. You know that that is basically what has underlined some of the worst regimes in history as well, what you're arguing, that you are subhuman. We mustn't go this theological way because they are in trouble. Some of us are non-believers. But then what is this? You say if they do this then they have removed themselves. So then how do you treat them? We can list them. Kidnapping, torture, rape, et cetera, et cetera, et cetera, et cetera. Why is it not possible to list it? Because it's the problems with the et cetera's, right? I don't think anybody here. Acceptance, oh yeah, we can propose it. The et cetera's. Oh et cetera, yes. So nobody I think here has a problem with rape, torture, imprisonment. I have a huge problem. We've got all the time in the world to do it. The amount of time which is used for instance for peacekeeping, peace enforcement, et cetera, et cetera, can simultaneously be used for making this list. And then proposing it for acceptance. Today you have religious extremists who believe that not merely non-believers, but luqwam believers should be put to the sword and practice it all the time. I think generally the major part of the world believes that this is pernicious, that this is wrongful thinking, it's disrespect for the other people, their thinking processes, their grasp of phenomena, et cetera, et cetera.  I think on that, and that's the issue of volition that I keep talking about, on that I think generally the world disagreed. And then those who insist on flouting that protocol, which the majority, just like the Universal Declaration of Human Rights, this took ages, we know it began, those professors who came with the warriors to fashion something out of the rubble of World War II, it took some time. And so we shouldn't imagine that everything is definitive, but it is possible to define the new human being. But that doesn't begin to address the real issue, and yes, we would all agree that killing, murdering, raping is bad. But dignity, it dies by a thousand cuts, it dies by all sorts of actions which are in your et cetera lists. And that's where the issue is. And you said the human being is a relational being, like Aristotle said, a political. I completely agree, but relational is two, but it's more than two. It's a society, and so when one talks about dignity, one talks about the dignity of a society, what kind of principle organizes a society? If one tries to answer the question just focusing on one individual, is that person killing or not killing? In a way, that's the easy issue. But ethics is about the uneasy issues. I think I find myself in the same position as when I'm asked, especially about my country and the continent, are you a pessimist or an optimist? And I say, neither. And I think of it the point where I look at issues of good and evil, and I say, all right, I know in me what defines a member of humanity. And what is acceptable in my definition of humanity is what seems to be the equivalent of good. What is not acceptable goes in the direction of evil. And if you want to be a member of my human community, please come on this side.


I'm Salvatore Bobonis and today's lecture is Sociologizing the Technological Frontier, the next generation of growth in China and the world. In this lecture, I'll examine the concept of the technological frontier in economic growth theory and how countries can move towards it. Let me start this story with exogenous growth theory in economics. Exogenous growth theory was the dominant theory of economic growth in the immediate post-war era. Exogenous growth theory implies that all countries will tend to converge to rich country income levels because poor countries will adopt technologies from rich countries and thus grow towards rich country levels of productivity and thus rich country levels of output. In fact, poor countries should grow to rich country levels very fast because not only can they adopt rich country technology but also investments should flow from rich countries to poor countries. But once a country reaches a technological frontier, its growth is limited by the advance of technology. They have to innovate to grow. Thus you get people saying that intellectual freedom and creativity are crucial for growth. Intellectual property must be protected. Countries have to promote the leading edge in order to develop. But is that really true? And if so, where is the technological frontier? I mean if we go to the United States and on a map I ask you to point where on this map is the technological frontier? Is the whole country at the highest possible level of technology? Most people would point to Silicon Valley and say no, no, Silicon Valley is the technological frontier. Of course it's the home, Google, Facebook, Cisco, Intel, HP, Apple are all in the Bay area around San Francisco. So clearly this must be the part of the United States and part of the whole world that is literally at the technological frontier. But of course Silicon Valley is also a major center of homelessness in the United States. Are these people at the technological frontier? It seems obvious to me that there's plenty of room for growth even in Silicon Valley. Plenty of room to move more people up toward the technological frontier. Most economists treat the U.S. as a single economy with a single frontier but clearly this is a problem. I mean there are parts of the United States where gross state product is in the 60 to $70,000 range per capita places like Delaware and Connecticut and there are parts of the United States where it's more like $35,000 per capita in the deep south. It should be obvious from just a look at the map of the United States that even the United States could be much richer if the U.S. could bring poor states up to the level of productivity of the rich states or not put to fine a point on it to bring the red states of the deep south and midwest up to the level of productivity of the blue states of the northeast and the west coast. But even if the U.S. is the technological frontier which is something we can really debate there's another problem for exogenous growth theory and that's that over the long term other countries are simply not converging to U.S. income levels. This graph shows the disparity in countries' income levels over the last 200 years and as you can see the disparity it's technically measured by a standard deviation of log GDP per capita but it's just a measure of disparity between countries. That disparity was rising, rising, rising, rising until around 2000 or 2005 when it finally started declining. For most of the economic history of the world since the Industrial Revolution countries have not been converging to the technological leaders. The technological leaders have been pulling away from the rest of the world. Exogenous growth theory just doesn't fit this pattern at least not until 2005. Even that convergence that's occurred since 2005 is highly suspect due to problems with the restatement of economic statistics especially in sub-Saharan Africa. But because of the lack of convergence economists came up with a refined theory, endogenous growth theory. The idea that growth happens because of factors within the country. The fundamental insight of endogenous growth theory was that countries would be converging to the technological frontier if it weren't for factors inside the country that held them back. In other words there was conditional convergence towards the technological frontier. Countries only converged if they had the right conditions. That is if they had the right levels of education, labor force participation, labor market regulation, et cetera, et cetera, everything about the country. If they got the society right the economy would follow. What the question still remains, what would they converge to? Economists usually say they would converge to the United States but they would converge to the United States if they had societies as good as the United States. What if they had even better societies? Could they converge to the level of California? Could they converge to the level of the Bay Area? Could they converge to the level of the Google campus? If you got your society working truly well could you converge to the very, very top pinnacle of the world? Well I suggest not. I think most countries are actually converging to Mexico. If you think about Silicon Valley, Silicon Valley is a mix of rich and poor. The United States as a whole is a mix of rich and poor. The world as a whole is a mix of rich and poor. High technology doesn't mean that every single person lives at high technology. It means that the society or in the world's case the whole planet lives at high technology. And while high technology may be enabling for many individuals as a society or as a whole social system of the world, high technology may make it possible for someone to live in extreme comfort in a developed country while other people work under extremely terrible conditions in a developing country producing for that person. The garment workers in Dhaka, Bangladesh are enabled by high technology to serve my clothing needs in Sydney, Australia. So the use of technology actually enables the disparities that exist in the world. Mexico is a great example. Mexico is a typical mix of rich and poor. It has the typical, I would say the equilibrium policy mix in the world. It doesn't have the best policies in the world. We can't expect everyone to have the best policies. It has a typical mix of policies. Mexico's level of about $10,000 GDP per capita is roughly speaking the market outcome you get if you just let the market go wild. If you just let people do what they're going to do, if you just let people be as corrupt as people usually are, if you just let the world go, if not wild, at least, feral, what you get is Mexico or Brazil or Russia or China. You get GDP per capita of about $10,000 per year. In other words, Mexico represents the average state of the world. Conditional convergence in the contemporary world economy does not necessarily mean convergence to the top. Why should we think that the world will converge to the U.S., or to California, or better yet, to Silicon Valley? There will be convergence. In fact, conditional convergence and endogenous growth theory shows that there is conditional convergence, but it's not convergence to America. It's overall convergence, convergence up towards Mexico for poor countries and conversion down towards Mexico for rich countries. The only thing stopping rich countries from converging down to Mexico is that they shield themselves from the global market, from the forces that would result in downward convergence in an economy at complete equilibrium. Like Mexico, most middle-income countries are in the same boat, a mix of rag pickers and superfancy skyscrapers. This is pretty typical. Many people in Shanghai's Pudong district are clearly at the technological frontier, but garbage pickers on the outskirts of the city are not at the technological frontier. The point is that the country as a whole utilizes advanced technology in order to maintain and reproduce this massive social disparity. China is the golden example of conditional convergence toward the world mean, because China has been converging to the global mean since 1979. The United States and European countries may have especially good policies that shield them against downward convergence and keep their people at high incomes, while before 1979, China had especially bad policies, terrible central planning that kept its people down well below the global mean. To see that, all you have to do is compare China with Russia. Russia had basically decent central planning under communism, and as a result had a above-average level of income throughout the communist period. China had terrible central planning, Chairman Mao sending people out to yell at birds to keep them away from the crops as a means of pest control. Locusts go away as a way of getting rid of the insects. This kind of central planning obviously produced terrible outcomes. As China has opened itself, it has become like other countries, that is its government has been captured by economic elites or vice versa, it has high levels of market inequality, it has a meager welfare state, relatively low tax levels, it has selective rule of law, it has a repressive government, all these things are fairly typical. They're typical of Mexico, they're typical of Brazil, and they've become typical of China. And as that's happened, its income has converged. China is still poorer than Brazil and Mexico by most counts. China's convergence with Brazil, well I had previously projected 2018, this is a graph from an article I published several years ago, with Brazil's collapse in the last two years, China has passed Brazil, probably passed Brazil this year in 2016. The question is not, will China converge with Brazil and Mexico? The question is what happens when it does. And since 2010, I have been repeatedly predicting that when China reaches Brazil and Mexico's level of income, China will cease growing rapidly and settle in to the long-term trajectory of Brazil and Mexico. In contemporary terms, that means settle in to a GDP per capita of $10,000 or $11,000 per year. That's why I see the current slowdown in China as a secular slowdown, not just a temporary slowdown in growth that's going to return to double digits, but an inevitable slowing down to a two or three percent rate of annual growth. And frankly, I think that China's private sector economy didn't grow any more than two percent in 2015, and I think the total economy won't grow any more than three percent in 2016, except through massive government deficit spending. India is much poorer. It has a much longer way to go. If you're going to bet on a country to grow for the next 20 years, bet on India. It may not have the best managed economy in the world, but it has a lot of headroom to grow until it reaches biddle income status. Examples of upward mobility beyond the global mean are extremely hard to find. I mean, they're the four Asian tigers, but we might call them the four Asian tiger cubs. Hong Kong and Singapore are statistical tigers only. They're cities that are statistically separated from their natural hinterlands. Hong Kong having a statistical wall between it and Guangdong province. Singapore having a statistical and sovereign wall between it and Malaysia and Indonesia, despite the fact that two million people work in Singaporean factories in Indonesia. Millions more work in Singaporean businesses in Johor Bahru in Malaysia. Taiwan's a questionable case for many reasons, not a fully sovereign country. It's a refugee island full of people who moved from the mainland, highly skilled, educated people who moved from the mainland to the island of Taiwan after 1948. Korea is maybe not really a tiger. It's not as rich as the other tiger economies. Again, it depends which statistical series you use. Also, Korea is, again, a shorn of its natural hinterland in North Korea. So 20 million people who should be included in Korean statistics aren't. There's really only one clear example of a country that grew from middle to high income status. It did so after World War II. By 1940, Japan had risen to middle income status. The US imposed a new society on Japan. When Japan got an American-style society, Japan got American-style levels of income. Statistical regression to the mean implies that without an extraordinarily good society, without major efforts in the part of countries to prevent convergence down, and without an extraordinarily bad society, without terrible mismanagement that prevents convergence up, countries would achieve a mix of technologies, a mix of income levels. They would end up somewhere like this photo from the Dominican Republic. It's a nice Saturday out in the Dominican Republic. The boy there sold me a kite, sold my wife and me a kite. And then he said, oh, and for an extra dollar, I'll fly your kite for you. And so we hired him to fly our kite for us. You can see he's holding a string. That's our kite that he sold us, that he's flying for us, a great little entrepreneur. Countries like this are a mix, you know, half and half of super poor like we would find in India, super rich like we would find in parts of the United States.  You end up right back here. Is this really occurring?  So Shanghai and Beijing, but also the eastern hinterland, the eastern provinces that are in the hinterland of Shanghai and Beijing are the slowest growing areas of today. The fastest growing areas of China are the very poor areas in the West. In America, we have this kind of internal division that the economy continues to grow, but ordinary Americans are converging down towards middle income levels of income. The average American, so 50 percent and below in the American income distribution have had no increase in salary for the last 40 years. Now that's unprecedented. For 100 years, American incomes, this red line, median income, rose, rose, rose, rose, rose. But since 1972, it's just been flat, 40 years of flat. Well, flat income effectively means convergence down as other countries catch up with ordinary American workers. And in fact, they say that some factories are moving back from China and Mexico to the United States because wages are rising. In China and Mexico, they haven't risen in 40 years in the U.S., and so U.S. workers are once again becoming competitive with Chinese and Mexican workers for low-end manufacturing. But what does this mean for China? It means that the secret to economic development is not to bring up the top. I mean, the top of the top, the Fudan universities of China, are already at or close to the technological frontier. Highly educated people are already highly productive in China. The challenge is to bring up the productivity of the bottom. The challenge is to make poor people rich. Making rich people richer won't substantially grow an economy like China's. But making a billion poor people middle income, that will have a substantial effect. If you think about it, a fancy new laboratory that doubles the productivity of a few thousand engineers has no impact on China's economy. But measures that double productivity in the retail sector, well, that has a massive impact on Chinese GDP per capita because so many people work in the retail sector. The policy implications are that we should get rid of this idea that countries move from factor-driven economies, more raw materials to investment-driven economies, with more investment and finally to innovation-driven economies. There's no such thing as an innovation-driven economy. Innovation drives the technological frontier forward, but it doesn't drive economies forward. Because in every economy, even in Silicon Valley's economy, most people are nowhere near the technological frontier. Instead what we need are human-driven economies. What we need are high levels of government investment to drive productivity forward. That means education, healthcare, housing, transit. A lot of it is physical infrastructure that's needed because even things like housing and transit increase people's productivity by allowing them to take advantage of opportunities in the economy that they previously couldn't reach. Simply moving a rural worker from an isolated village to the suburbs of a big city dramatically increases that worker's potential productivity and, thus, in the end, GDP per capita. Raising the technological level of the bottom 80% yields much more growth than raising the technological level of the top 20%, and it's much easier to do. The goal of economic growth is not to push the technological frontier. The technological frontier is moving forward anyway, and any increase in the technological frontier is rapidly externalized to everybody. Once something new is invented somewhere in the world, it's available for the whole world to use. It's not pushing the technological frontier that develops a country. It's bringing the country's population up towards that frontier that leads to economic growth. Since 1979, China has done more than any country to build its human infrastructure. I mean, it's done a fantastic job expanding schools, public health, mass transit, but simply being best in class among poor countries is not enough to make China a rich country. To grow beyond the global mean, countries like China or anyone else have to grow their societies beyond the global mean. They have to provide public goods at a level that is above equilibrium. They have to provide public goods at a level that would not be provided in the ordinary course of human events. Now, China has a plan to do that. In the next five-year plan, and looking forward to 2030, to the 100th anniversary of the Communist Party and beyond, China has a fantastic program of public investment planned, high-quality schooling for all, improvements in environment and food safety. What it needs, though, is an expansion in the fiscal capacity of the state to make these things happen. China has the right policy goals, what China lacks is the money to pay for them. My policy recommendation for China is to raise taxes that may sound counterintuitive, but China should be financing the policies, the fantastic policies that it has already laid out in its 13th five-year plan and beyond. The real threat to Chinese growth and the reason China is likely to stagnate at its current level is not for lack of ambition or lack of knowledge of what to do. The real obstacle is that they're not going to be able to pay for it with their current fiscal structure. Thank you for listening. You can find out more about me at salvaturbabonus.com, where you can also sign up for my monthly newsletter on global affairs.


I'll come back to 105. So we're done all the content for the midterm. Yay, we're a week ahead of other people. So good, I guess that's good. So today we'll be doing some more practice, we'll be solving a larger program. And then next week we can do all midterm review so we get a lot of practice and we can all do very, very good on the midterm. So we'll have like three lectures to go through it. So again, use the discord, post questions, go through the old exams, look at them, the old midterms. Let me know if there's anything in particular you want me to pay special attention to. Otherwise we'll just go through them in reverse chronological order and we will figure it out from there. But we can breathe a sigh of relief now. So as a detour, let's try and write a bigger program. So there is this thing called the gold box conjecture and some very, very smarter than me person, like 200 over 280 years ago, apparently just came up with this and he just said for every even integer greater than two, this it is the sum of two prime numbers. And this is still to this day unproven. It seems to be true. People have tested it up to very, very, very large numbers that it is true, but no one can actually prove that it is indeed true. But today we'll write a program to see if it actually holds and actually be able to go ahead and test this conjecture that has not been proven. So we are starting from absolute scratch. So nothing here, there's just an empty main, returns exit success, doesn't do anything. So this is a very daunting position to be into because well, I don't know where to start. So given this problem, anyone want to tell me where I should start? What is the first thing I should think about if I want to write a program that will go ahead and test this for us? Yeah, yeah, maybe how to find a prime number. I also should probably be concerned about getting some input from the user. Maybe I want to verify that it's, I can actually get the input. What about in terms of solving the problem? Well, I should probably, the easiest thing to do is just not even worry about how to program this in C. Just think about how I would solve it if I was on paper because basically programming is the art of explaining all of the steps to solve the problem to a very, very stupid machine. So computers, really dumb, you have to guide them through solving all of this. So if I were, sometimes it's nice just to write it out by hand, so if I were to do this by hand, how would I prove this conjecture is true. So just so we have it, let us just write. So every even integer greater than two is, all right. So given that conjecture, if I just give you an old, just some number, so let's say an even number greater than two. So let's say I give you the number, I don't know, 44. How would you come up with proving that this is true or at least that it hold, not prove because then you'd be smarter than 300 years collectively of humans, but showing me that 444, this conjecture does hold. Yeah, yeah, so 44, it isn't, so it is an even number. It is greater than two, so this is a valid input. So after I have the number 44, how should I see if this conjecture does hold or not? So for this one is not a prime number. So try three, so I try three, how do I try three? Okay, so the other number is like 44 minus three, so 41. So I could try that and then see if they are both prime numbers. So how do you come up with three? Why wouldn't I be able to use two? So I will counter that, so that's a good thought of like, okay, well, if I start with two, then if I minus the other number, well, it'll be even and that will not be a prime number. What about if my input is simply four? Yeah, so you're being a bit too clever already. So always good just to start with the first prime number. So maybe I should check that or maybe that's not two, but in this case, yeah, if I did two plus 42, that's not it, so I could just cross it off the list. Thanks, go to the next one, three plus 41, oh, they both happen to be prime. But what would I do if this was not actually the sum of two primes? What would be my next step if for some reason that was not true? Yes, yeah, so I could try five, which is the next prime number. So when we're solving this and we have to explain it or like write it in C, any of the terms we use that like, we take the number and we get another number certainly sounds like a function. If we can give a name to an input and an output, probably gives us an idea of something we should write. So you said, if that wasn't true, I should go to the next prime number and then subtract it. So I probably need a function called next prime, which would probably take an integer and return an integer. All right, so that's good. We're already breaking the problem up into steps. What other function would be useful? So what did I say? So I took 40, so like I would take three, then figure out, okay, whoops, the other number is 42. What did I ask about 42? If it was prime, right? So maybe I need a function called bool is prime. And then other than that, this is good enough to get me going. I can kind of see it. So I can ask for some number. So let's say I was asked to use it for some input and all I get is a single integer. So might be nice to just write your function like this because I don't need any, whoops, and this needs an int, sorry. So don't need any input to the function. I'll just ask the user to input a number and make sure it holds true. And well, I don't have to deal with pointers because I'm just returning a single value, so I should probably just use a function. So with that, that seems to be enough to get going. So let us turn to C. So first function we should probably write is the user input one, user input, whoops. So we're returning an int and we don't need any arguments. So if I want the user to input a number so I can test it, I should probably tell them what they have to input, right? So let's say enter a integer greater than two and it's an even integer.  So it's a percent D format specifier. Oh, okay, right, I need to give it a variable. So let's just call it input. I'll just initialize it to zero just to be safe. In this case, it doesn't matter. And then scan F, so now through that pointer, it goes ahead and sets that value for me. That matches the user input and then I just return that input. And in the main, I'll use it. So I'll just say num equals user input. All right, is that a good user input function? Looks good, all right, let's see it.  So if I go ahead and run this, enter an even number greater than two. Sure thing, hmm, should probably do a bit, something a bit better than that. How would we do something a bit better than this? Yeah, yeah, okay. So maybe have a while loop that the user, that doesn't let the user input something that's not greater than two. So while the input is what? So while the input is what? Less than or equal to two? So while the input is less than or equal to two, maybe I, maybe I cost the user a little bit. All right, maybe I do something like that. And maybe if you want to be clever, the more times the user gets it wrong, the meaner you get. So that could be an extension to our program.  So let's see, we enter one, we get hey jerk, enter a number greater than two. We say two, tells us we're a jerk again. Okay, three. Was that an even number? All right, what else do I have to put on here? Yeah, or if it's odd, odd equals zero. Like that, maybe, okay. So looking at that, so that should continue asking the user if they enter something that is less than or equal to two or it's not an even number, right? Either one of those that fails, so this should do the trick. So let's say I enter a one, okay? I enter zero, okay? No, enter a two. No, okay, three, five. Seems to not let me enter an even number and then some number greater than two that is even 10. So that seems to be good for our user input. Any thoughts about that or does that seem good now? Seems relatively decent. All right, so what is, or the other one? So maybe we want to just write all the function prototypes we thought of up here. So we had this one, we had next prime, and then we had is prime, bool is prime. And then we used a bool, so we need this. And let's move this to the end just for argument's sake. Which one should we write next? If it's prime? All right, so let's write bool is prime. We'll just be clever and call it an x. So how do we know if a number is prime or not? Yeah, so if it's prime, it's only divisible by one and itself, right? So if it's divisible by any number between two and less than itself, then it is not a prime number. So what would that look like? So what should I write here if I have to write it in C? First I could check if the number is even, yes? So if the number is even, then it is not prime. Oh, I had a question also in the discord if I enter a or nothing or a large number, we're assuming that user inputs at least an integer for this course because like I said before, scanf's hard to use, so it doesn't actually do good. So this starts us off so like this, if the number is divisible by two, then it's not a prime number, unless it is two. Hmm, and if I kept going with this, in general it's like up to how big the number is, right? So I would have to be like, well, if the number is divisible by three, then it's not prime. If the number is divisible by, well, four maybe, then it's not prime, although I could skip that one because it's not prime. Yeah, this looks like loop territory, right? Every time through I'm going up by one and for the sake of this course, like sure, if I don't really have, well actually, I would have to check if it's divisible by four, but we have this pesky situation where I shouldn't do this for the number two because the rule is you're prime if you can't divide by like more than one and yourself, right? So two is itself, so that doesn't count. So probably there's like a bound what number I should go up to here, right? So I shouldn't go up to myself and I should also start at two. So if I should start at two and this number, so this is like X divided by something, right? All right, if I want to give the something a good name, if you do like number divided by something, what's the end something actually called? Anyone remember their math, the divisor? Yeah, we'll call it the divisor. All right, so yeah, we can do a loop divisor so we can start it at two maybe. So we start at two, doing it by one, pretty useless. So we can let the divisor go up till less than X because that's our input. So if my input is let's say two, it wouldn't try and divide it by two, it would stop before that and guess what, it wouldn't even try anything. So we would do plus, plus divisor and then we can kind of move this in. So instead of checking if X is divisible by just some number, we can do if it's divisible by the divisor and then here we have a few choices of what to do. So if we find that it is not like if this is divisible, so it's a factor and we know for sure if we go inside this if statement, we know for sure that it is not a prime number. So two strategies here, maybe I just have a Boolean that I keep track if it's prime or not and then I set it equal to false but usually the good thing to do in functions is if you already know the output of it, you can do a return and it will just immediately end that function and it wouldn't even try bothering trying to divide anything else. So I can just immediately return false and then functions done, wouldn't have to try anything. I know it is not a prime number. All right, anything else with this function? So I return true at the end. So if the thing is prime, then it, yeah, so I have to return true if it is prime. So how do I know it's prime here? Yeah, so X can just be any integer. So we're just assuming it can be anything right now because we're writing just as function, just as a little helper function because we know we'd need to ask, hey, is some number prime or not? Yeah, yeah, exactly. So if I go through this entire for loop and I never go into this if statement, so it never returns anything and eventually I've tested literally every single divisor and it's not divisible. So at the end of this for loop, we know for sure that, well, it wasn't divisible by anything that was two or less than itself. So it must only be divisible by one in itself. So we can just immediately return true and we're all good. So just to test it, yeah. So we do have to return true in this case because if you just leave it out and you compile it, C will say something like non void function does not return a value in all control pass, which basically just means it's possible for this function that returns a value to end without you calling return. And for the purposes of this course, there is usually it returns zero. So usually the default value it returns is a zero, which is not what we want. We want to say if it makes it to the end, it's true. So, but that's a new error. I don't think we have seen that one yet. Well, it's a warning. So it still compiles. The compiler will do something, but it would have been a complete pain to debug.  How about four? Okay, I can enter that. So maybe we test in our program. Let's just see what the result is of just making sure that it is prime work. So we can do is prime two. Let's make sure that we can say that two is an even number or a prime number. So it doesn't matter what input I give it, and it says, yep, it's prime. So that's good. Maybe when they test it, we don't care about the user input.  So one is technically not prime.  So maybe we have to fix that because that's kind of a bit of an edge case where I even think they considered one as a prime number before, but then they've changed their minds. I don't know, math people are weird. So we can just make sure that if x equals one, we can just special case that. We'll just say it's not prime. And that's fine. And we'll assume that this works for integers one or greater. So we won't bother to deal with negative values because it has slightly weirder rules. And yeah, we just won't bother, won't test it, and doesn't really matter because our input are going to be always positive. So don't have to deal with negatives. All right. So now we got some user input and a prime function. So how did we say, oh wait, we need another function. We need next prime. Okay, so we need next prime. All right, how do I go about next prime? So my x is just going to be some integer that I assume is prime and I should give you the next prime number. Yeah, so I could probably use next or is prime. So how would I use this prime? So we can think of it in little steps, yeah. Yeah, well, we can just check, right?  So if it works, it works. So for next prime, what we could do is just take the number, add one to it and see if it's prime. If it's prime, great. If it's not prime, do it again. Okay, we try it, we increment it again and it's prime, great. If it's not, we do it again. So if I was to translate what I just said into code, how would we do that? Yep. Yeah, a loop, what kind of a loop? For loop. So if we do a for loop, we have to know where to start. So where would I start with a for loop? So we're assuming X is just some random number we get. We, all we can assume is that it's probably prime. In I equals X? Or like that, we start with X. I guess we can. So remember we should use for loops when we like know how many times we do something. So in this particular problem, do we know how many times we're gonna say, oh, this one's not prime. This one's not prime. No, so for loop, what's our other option? While loop. So there's also like a do while and a while. So in this case, well, let's think about each time we need to go through it, we just said we increment X, right? Yeah. Oh, so we're going back to the for loop, so you want a for loop. All right, so if we want a for loop in I, so what's it start at? X plus one. Okay, and the condition you want is just that X. So you want I is not prime, which is like. Not. Uh-huh, and then how far do I go up? Plus I? So you don't want me to write anything here? Cause this is like normally where I do like plus plus. Okay, so that. All right. So if I do this, then how do I know when it stopped? And what's the next prime number in this case? So X, so X we didn't actually change. So, and like if I do, you might be thinking, I can kind of see where you're going here. Like at the end of that for loop, I is a prime number, right? So I can do return I, get a red line, error. Can you fix that? Yeah, so the I is only in scope between these brackets, other than that, we can't access it. In this case, yeah, if we want to, we could just do in I over here and then get rid of this. So now I is in scope even after that. So I create I immediately and it is in scope for the duration of the function. So I could do something like that. So that seems like that's a good solution. Let's see. So let's just, we can test it by printing a few results. So let's say the next prime of some number equals some number. So let's say next prime of three. All right, so what is the next prime of three? Do we actually know the result of or what that should be? Five, right? So let's see if we get a five. Oops, I did not comment, yeah, five, so it seems to work. So the only slight comment I would have to this is like a for loop with nothing in it. It's a bit strange. So it like just converting it to it's loop equivalent might be a bit, might be a bit cleaner. And we could also like, we get a copy of X. So we can just modify that. We don't actually have to create another variable. We can just change X if we want. So we could do something like plus plus X and then check if that's prime. So we always do that. So if we always have to do an operation no matter what, we can do a do while loop. So we could just like do plus plus X while not, while I can't type, not is prime X. And then we can return X. But mean the same thing. Oh, I can get rid of this. So mean the same thing. Some people pride themselves in using as little variables as possible, but means the same thing, last one, perfectly acceptable. But some people might find this a bit easier to read. Again, some things are up to taste. Usually people don't like when for loops have nothing in them. But like we saw, a for loop is basically just a fancy while loop. All right, so now we're looking pretty decent. So how would we test this now? So remember when we, so this we probably have to go back and when we did by hand, right, we started with two and then we took that and we subtracted whatever the number was and then checked if the result of our subtraction was a, was prime and then if it was prime, then we're good, we're done. So we can do the same thing here. So let's go back. So we can pick a first number. Two was our first number because that's the first prime and our second, well, that would be num minus the first. And then I could go ahead and just iterate on this a few times. I don't know when I have to stop asking about when a prime number is, but we can just kind of see. So we can write the body first of like what we have to do every single repetition. So all we have to do is check is like if the second, whoops, sorry, if is prime second, then we're done. And then if that's not true, then we have to, you know, go through it over and over again. And kind of seems like we're also doing another boolean and it's kind of messy if we have to like just finish this loop or break out of it. So that might tell us that, oh, we should probably just write another function. So like boole, conjecture holds for some x. So let's start writing that. So we'll just take our input and or our solution and put it there. So maybe we have here if conjecture holds num and then if it's false, we can just say else. If it doesn't hold, then we win like millions of dollars, we broke math, cool. All right, so I called this num. All right, so if the second number is prime, right, we can just say the conjecture does hold, we can return true. Otherwise, well, what we just do is the first number, when we did this just goes to the next prime, right? So if I were to say that, I update first to be the next prime of first, right? Something like that. So if the input, if my first is two, then I get a three out of it. If it's a three, then I get a five, then five is seven, and then after seven is 11, oh no, that's like my limit. And then here I would have to go ahead and recalculate second. So second is equal to num minus first. All right, and then kind of like looking for primes, we should probably figure out when we should stop this. So if we do this, let's say we have to go on and on and on. So we get up to like, say we get up to the number 22, and then we do like 22 plus 22. So if we get up to that, there's no use going to the next prime number because, well, I would have already done it on this side. So I can stop as soon as these numbers are like equal to each other, or there at least this number should always be smaller than this number, otherwise I'm going the other order. So I can just say that while first is less than or equal to second, then I do all this. And then if I go through that and I run out of numbers, then I know that this whole thing is false and we broke math. So that same reasonable, yep, yep. So equals two is included in this case. So the first case that we would probably want to check is make sure this works for four because four holds because it's two plus two, right? So let's go ahead and run that. So four holds. All right, and then we can try it with, let's say, let's try it with 45. Oh, I can't do that, right? Jerk, all right, 46 holds. We can do, I don't know, 60 holds. Seems to hold. And then last thing to do, maybe I just super-functionize this whole thing and be like, okay, well, this kind of looks like a logical thing where I'm just outputting information about the conjecture. So maybe I just do avoid conjecture output. Wow, why can't I type? Put put is not a thing. So maybe I make this a function, maybe I have it overkill where I just move it in and then conjecture output of num. All right, so now my main looks like super simple, right? Take the input, give it an output. One of our goals to make our main, like make our functions just do one thing and then whenever we read the code, it becomes a lot easier to read, right? I can kind of understand, okay, I take a number and then I give an output. Can't really get much simpler than that. So 44 holds. All right, let us make this better. So looking at this program, if I just give you like some giant number, so say I give you that and say it holds, wouldn't be more interesting if I like said what numbers that was true? All right, so if we wanted to make this program better and say what numbers did this actually apply for? Like what numbers did I find that are both prime that sum together to give the original number? How would I do that? So the function where I figured it out was this conjecture holds one, right? So I already figured out the first and second, but this function already gives a value that I'm using as part of my logic and I kind of want to like output three things, right? I kind of want to output whether it holds or not and then what the first number is and what the second number is. So how would I do that? I want to like return three things.  It's like scan F, right? Scan F can use multiple values. If you need to give multiple outputs, then you have to use pointers. So we can say, okay, well, we need to use pointers. So we can say a pointer to int called first, pointer to int called second, and then these are the things that I'm going to change so the user can get that as input. So we have to change a few things around. So my argument for that becomes this and then here. Okay, well, I should probably, I need to create variables here so that I can essentially get their inputs or let this function, this conjecture holds function actually update the values for me. So maybe I just do int first equals zero and second equals zero. I'll just initialize them to something just so I feel better about myself. And now this looks like scan F where I have to give it the pointer to that integer. So I'll give it the pointer to first and the pointer to second. So luckily for us, the compiler helps us out a bit here because while we declared them before because we needed two integers, but now we're being supplied two integers that we get to update. So we can get rid of the declaration but here we do need to set them. So how would I change this to, so if I just delete the int, is that all I need to do? So first is a pointer, right? So if I say first equals to two, what does that mean? So that means first, like a pointer is just an address, right? So I say first is address two. Is that likely to be good? Probably not. So what do I need to do to actually update the value that first points to? Yeah, yeah, I have to dereference it first and dereference it, all I have to do is put a star.  So if you see that little yellow underline or compiler warnings when you compile, well, then you should just get rid of it. So turns out before when I wrote this, each time I used first and second, they were integers, now they're pointers. So anytime I see first and second, I should just dereference it first because I'm still just using integer values if I dereference it, well, it's still an integer value. So I'll just go ahead and change all of them, which is fun. So I'll just put an ampersand in front of all of them and including these ones, whoops, and including this one. All right, and now all my compiler warnings went away. So now if I compile it, no warnings, thankfully I didn't miss them all. Hopefully C would give me some help. If I missed one, but in this case, it doesn't look like I did. So now if I wanted to print off the two values that function set, what do I do in this print statement? So I can just say the numbers are d and d. So what's the first number called? Is it first, is it star first, is it ampersand first? Just first, right? So that was the actual integer. I gave this function the address of that integer and it just constantly updated the value. And while whenever it returned, first was a prime number and also second was a prime number. So here I can just simply say first and second. So now, whoops. So now my program looks a bit more interesting. So yeah, cool. And because I wrote this one way, too, I can actually test it a lot of time. So now let's say I wanted to just test it a whole bunch of times and I wanted to see, hey, does this hold for the numbers up to, I don't know, 10,000 or something like that? That turns out to be easy because I can just do like four in x, I don't know. So the first valid number was an even number greater than two, right? So it was four. See, I go all the way up to x equals, or x is less than a thousand, sure. And then, well, I could do plus plus x here but that's not part of the conjecture because it's every even number. So I could just do x plus equals two instead. So each time through instead of incrementing it by one, I increment it by two. So I just go to the next even number. And here, I can just go ahead and say, print off the conjecture output and then I don't need any user input. So I can just test numbers up to, and let's say including a thousand. So if I run that, boom, I can look through it. Maybe I want to also print off and hear what my original number is. It holds for d and that would be called x. So maybe I do that so I can actually verify it. So it holds for a thousand, numbers are three and 997. I can scroll all the way up and see that seems like we haven't broken math and it has figured it out. There's some weird patterns that math people probably love explaining. Ooh, there's a cool one, it goes up to 31, wow. Let's see, we can go all the way up. We didn't see, we broke anything, oops. And it makes it easy, right? We wrote it in a function, testing it up to like thousands was easy. If I want to test more numbers, I can just increase that number until, my computer takes too long to actually do it. All right, whoo, that was a whirlwind. All right, any questions about that? All right, cool, we developed a whole program together that's probably bigger than your next lab and we did it in an hour. And I didn't actually really do that much except type and I typoed most things. So you can do it faster, maybe. Yeah, and then again, so ask on Discord if there's any particular midterm questions you want me to go over. We'll be doing midterm practice all next week so we can all do super well in the midterm. All right, so just remember, pulling for you, we're all in this together.


beautiful snowfall here in Toronto and I'm thinking about a comment from a viewer on one of my other videos who says he's feeling depressed, that he is so physically unattractive that he will always be alone and unwanted. And this comment was deleted before I was able to reply. But I hope that if this commenter is watching that he may, I may be able to reply this way. I think this is, this is a common enough sentiment. First thing that I would reply is that this is not such a rare and unique thing. This feeling of not being good enough. The feeling that no matter what I will not be appreciated. In my younger days I sometimes felt that sense of being completely socially isolated and unwanted. And I think there's no way to completely make it go away, you know, just as nothing. It can't be dismissed. First of all it should be accepted as a feeling that this is real and not simply dismiss it and, you know, say you shouldn't feel that way because, fair enough, a feeling like that is a feeling. And we cannot dismiss the desire to be loved and wanted and appreciated by other people. That's always going to be something that is important. So there is no way to make that go away. But I think that part of that feeling, part of it relates to this more general question of what is my value? What am I worth? And how do I judge that? How do I know or decide what is my value? What makes me good or bad or what makes me worth anything? And it's so easy to apply this judgment that we have, this sort of judgment of other people to turn it on ourselves. This idea that if nobody else likes me then clearly I am unlikeable and therefore I will follow this opinion that I believe others have. So others say no to me and therefore I will say no to myself. And it's natural to look at things this way sort of automatically because when we're young, when we're children, we are at the mercy of others almost entirely and we learn from others how to behave towards ourselves. We learn from others what our significance is, what we mean. And we depend on others to accept us and to judge us to be good. That's the default state. When you're a baby you're in the world and everything is dependent on other people. And we simply passively submit to the will of other people. As we grow up into adults we have to learn to do certain things ourselves and we have to take care of ourselves. We don't have people changing diapers or feeding us with a spoon every day. We have to learn how to take care of ourselves. But there isn't anything automatic that says automatically the way we feel about ourselves is fundamentally changed. We can grow up and we can do adult things but still inside be crying out like a child. But as adults there's nothing that automatically makes us cut ourselves off from the judgment of others and choose to judge ourselves first. The idea that our own opinion matters, that I can have an opinion about myself that is separate from what other people judge about me. There's nothing that automatically takes things in that direction. That seems to be a matter of choice.   This is an extreme case. Now in that case would it be fair to say that you have no value because everybody dislikes you? Can that really be enough? And if everybody in the world loves you, everybody in the world admires you, does that mean automatically that you are good and what if it changes? If everybody goes, if everybody loves you and therefore you're good and then suddenly everybody hates you and now you're not good, can it really be dependent on others?  It's a matter of what is your standard for value? What matters? How do you define yourself and your own worth? If it is based on others' opinions, it will never be reliable because others' opinions can always change but your own opinion of yourself that is something that is much closer to your control. Now it can't automatically change because it's so imprinted from years of habit but it can change over time and it has for me as well. My opinion of myself has improved as I care less about imagining what other people think about me and instead ask myself, do I like myself? And at first I answer the question, it's mixed. I like some things about myself and I don't like some other things. So that led to me then taking steps to improve myself to the point where I can say overall I like myself. It's a long journey. It takes a long time to overcome the habits of judging myself according to some standard of whether other people like me or not. But it is possible and not only is it possible but I believe that it is the best way to live. The less I care about others' opinions of me, the happier I am. The important thing that I like to remind myself is am I living according to what I believe to be good? If no, then it's time to make adjustments. It doesn't take away the desire to be appreciated, loved, wanted. All those things are still there but it doesn't have to be the center. It doesn't have to be the core principle. I believe that if we can make ourselves the judge of ourselves, choose what we want to be and take steps to become that person, the person that we admire, the person that we like, become that for ourselves, do good, add value to the world, become something good. That is something that we can control. That is something that is free to choose. It's not dependent on what anybody else thinks. It seems like the more bold that a person becomes, the more they will divide people into the people that love them or hate them. If we don't do anything, then it's essentially indifference. So when I feel that feeling of not having value, that's when I have to ask myself, how am I judging my value? How do I determine it? And then how do I make it better?


Hello and welcome to this new segment of CD and MOSBIR Spectroscopy for Chemistry. My name is Arnab Dutta and I am an Associate Professor in the Department of Chemistry at IIT Bombay. So, in the previous segment, we are discussing about MOSBIR spectroscopy. Today, we will revisit the basic and fundamentals of MOSBIR spectroscopy and then jump into different applications of MOSBIR spectroscopy that is happening all around us and we will discuss how MOSBIR spectroscopy is aiding us to understand the conditions, the oxidation state and this MOSBIR spectroscopy is going to help us to understand the oxidation state, spin state and the molecular structure of different complexes. So, let us start. So, we know in MOSBIR spectroscopy, this is actually a spectroscopy where we change the ground state of a nucleus. So, it is a nuclear state we are talking about and then we excite it to the its particular excited state. Now, as we are changing the nuclear state, the energy are very high for this particular transition. So, we need transition in the gamma ray region which is very energy dense and this particular energy we actually develop by using another set where excited state actually relax back to the ground state and this is coming from a source. So, the source is already present in the excited state which is relaxing to the ground state and in the meantime it is leaving the gamma ray which is being captured by my sample and the sample goes to the excited state and if there is a resonance then we will see a band over there. So, now when we are doing this experiment what do we expect that will be the unit of percentage of transmittance which we can also use as an absorbance unit if it is needed and over there there is a energy axis and if I am talking about the transmittance. So, first there will be all the things will be transparent because the gamma is not accepting at all but when this resonating condition is stuck I should get a line over here and typically the line is a little bit broad one and you get a signal like that. So, let me just redraw a little bit. So, we get a signal like that and that says us we are absorbing them but over here the systems of MOSBAR spectroscopy a little bit different than the other spectroscopy that we discussed like optical spectroscopy or NMR or EPR. Why because over here this gamma ray when it is coming out it is a huge amount of energy. So, that is why what happens this source and the sample get some momentum shift during this. So, when the gamma is coming out this is actually shifted on the back side because it is leaving the energy whereas on the ground state of the nuclear state of the sample when it is accepting the gamma ray it actually also move back a little bit because of this momentum. So, that is why unless this momentum energy is concluded and properly associated with this overall energy change it is very tough to get the resonance condition. So, that is why what happens the actual source is actually make a static system similar goes to the sample and this particular condition when I am putting in a static condition. So, how I am actually putting it in a static condition I am putting it in a form of a solid matrix or in a lattice condition and by that I ensure the momentum based recoil is not happening so it is coming to have a recoil less condition and at that particular condition I can expect that there is a very better chance or a very good chance to have a resonance over there. And on that top of that we also make this full system static for sample whereas the source we put it on a wheel which can be movable on either direction because what happens that over here we are using a source which is actually going to develop for an example I am taking an example of iron 57 that I am generating and my sample is also iron 57 and we have discussed earlier in detail why not all the possible isotopes cannot be MOSBAR active only a few of them are MOSBAR active and iron 57 is one of the most prominent one. So, over here let us say my source and sample both are iron 57 but their energy of this particular ground state and excited state of the nuclear state is going to vary depending on what is there around it and that is why we are doing MOSBAR spectroscopy so that we can see the effect of surrounding environment on the nucleus which will be reflected in the MOSBAR spectra. Now over here because the surrounding environment is not the same there will be slight difference and that is why the source and sample even if we put them static the resonating condition may differ because they are not actually experiencing the same environment. So, this slight difference I can cover with the help of momentum because previously momentum was actually ensuring that I am not getting resonating condition. Now momentum I am actually using strategically so that I can ensure that resonating condition is being achieved and for that we actually move this source either on the towards the sample or backwards to the sample and using Doppler effect to the system so that I can generate a good resonating condition. So, that is why in the actual MOSBAR spectra the unit of energy is giving by velocity and I am moving at millimeter per second speed so not a high speed only slight speed to ensure that we are seeing a resonating condition and that is how the MOSBAR spectroscopy look like and over there it depends on like when we actually going to match and by that particular velocity I can define the different conditions of the particular iron as an example of MOSBAR active isotope. Now over here we want to ensure one more thing when we talking about this particular system to be static and we are talking about some recoil less energy that we are talking about so when something is recoiling what are the different things it is going to happen one thing is going to happen the translation energy that means the molecule or the sample is moving either forward or backward depending on whether it is getting an gamma ray photon or leaving a gamma ray photon. But over here making this source and sample static I am getting that translation energy totally out but there is one more system the vibration one. So, this recoil can happen also the vibration through this particular molecule molecule is there with all these bonds and bond angles and it can vibrate and this vibration energy can also contain energy which is coming from a momentum based energy transfer and this particular energy of vibration it can be written in the form of n h cross i where n can be different value 0 1 2 3 depending on the different conditions of its particular vibration state and this is quantized and over there I wanted to always be at n equal to 0 then this system can be actually recoil less system.  Now over here this particular expression I draw this is actually showing a different vibrational state what is that is actually going to experience for vibration and over here this is actually nothing but an expression of a phonon based system which is connected to the temperature. So, as we hit that a system we see that it is actually going to be at high temperature it is actually vibrating more it is actually going to higher energy of phonons and over here we wanted to go to at lower energy of phonons as possible if it is possible phonon energy is close to 0 then we will be achieving this absolute recoil less system. So, that is why temperature plays a huge role during MOSBAR spectroscopy and we are going to get a better resolved signature in MOSBAR spectroscopy if I go to a lower temperature system. So, that is actually going to happen when you are doing the MOSBAR spectroscopy. So, over here we have established why temperature is a huge factor and how we are going to look into a MOSBAR spectra on the y axis is percentage of transmittance varies from 100 to 0 and on the x axis it is velocity at one point it will be 0 then it is the positive direction then it is the negative direction and this is the speed by which I am moving my source either towards that means the positive or far away that is the negative from the sample and we are creating a Doppler effect to ensure that we are having a resonating condition. Now, when you are talking about a perfect matching of a system there are two important factor comes say in MOSBAR spectra percentage of transmittance is there, velocity is there and we first get a signature signal and where I am getting the maximum we call them it is the delta which is isomer shift. Now, what is an isomer shift? So, during the transition as you are discussing and let us say I am talking about a 57 iron. So, over here the ground state is i equal to half system whereas excited state is i equal to 3 by 2 system. So, this is the transition I am trying to achieve over here. So, first I am going to get it from a excited source which is going to leave this gamma ray and which will be absorbed by my sample and go to this excited is still the same i equal to 3 by 2 and ground state is i equal to half system and over here it is actually coming down from here. So, this is actually happening now over here when you are talking about this the source and this is the absorber or sample is going to have subtle difference on its energy of this particular nuclei. So, how nuclei energy is getting affected by the electron density and we have discussed earlier there is a possibility finite possibility that the s electron density can reside in the nuclei. So, it can bridge the nucleus and can stay there. So, that is why that is why the s electron density we are worried about now in iron if you take a look into it it can have 1s electron, it can have 2s electron, it can have 3s electron. So, this electrons can be there when you are talking about a valence shell and among them this 3s electron density we are more worried about because 1 and 2s are the core electrons. So, they will be minimally affected by the other valence electrons whereas, the 3s electrons will be very much affected in the valence shell by the valence d orbitals electrons and over there one particular factor that comes in it is the shielding effect. So, it is nothing but a competition between s and d electron in the 3 shell that means the 3d and 3s electron who is going to capture the attention of the nuclei and over there 3s electron has a finite possibility that it can reside inside the nuclei and that is going to be controlling what will be happening on the energy of this ground state and excited state of this iron over here. Now, if I want to look a little bit look into much closely and try to find an equation. So, this isomer shift can be explained in the following delta is equal to 4 by 5 pi z is square r square delta r by r and then psi 0 square of the absorb from the absorber minus psi 0 square of the source over here absorber and source that means that iron centers we are talking about and psi 0 square means s electron density. So, this psi 0 square over here minus s electron density and over here this 4 pi by 5 z z is the atomic number of the iron we are talking about e is the electronic charge r is that nuclear radiate the atomic radiate of the system. On the other hand the dr by r it is a very important aspect over here what is delta r by r. So, delta r by r especially delta r is the difference of the nuclei when it is in the excited state minus when it is from the ground state and for iron system 57 iron this value of delta r is actually negative why because the excited state radius is actually lower than the ground state radius and when you talk about this excited state ground state I am talking about the nuclear spin value of half for the ground state nuclear spin value of 3 half for the excited state. So, talking about the nuclear states and over there a nuclear state at 3 by 2 is actually smaller it shrinks down when it is go to the excited state compared to the ground state I equal to half and that is why this delta r value is going to be a negative one. And then we talk about this electronic difference the s electron density difference and as we discussed we can see the absorber and the source is not going to have all the time the s electron density present in the system same and why it is different because it depends on the s electron density and s electron density on the other hand depend on the d electron density and that is going to vary from compound to compound and that is going to reflect in this particular value of psi 0 square absorber. And then I am going to take a particular source if I subtract that I am going to get a particular delta value. So, even if I take the same system as a sample and source only then I am going to get a 0 value or by some other features I am going to get a similar amount of s electron density in the nuclear I am going to achieve the same thing. So, that is what is actually happening over here and over there we have to remember this delta r value to be negative and what is the consequence of that that we are going to follow right now. So, over here I am taking examples of iron 3 plus and iron 2 plus and over here I am trying to rationalize how we can explain what would be the trend of the isomer shift which will be positive which will be negative. So, let us go through that first we find how much d electrons you have. So, iron plus 3 is a 3d 5 system and plus 2 is a 3d 6 system. Then the next question we found if these are the 3d 5 and 3d 6 electrons what about the shielding effect the shielding effect on s electron the 3s electron. Now, 3d 5 versus 3d 6 more the d electron more is the shielding. So, comparatively this is actually having low shielding effect this is actually going to have high shielding effect but over here I am saying it is comparative comparatively iron 2 plus has high shielding effect and iron 3 plus has low shielding effect and if that is the case then what is going to happen on psi 0 square value on the absorber lower is the shielding effect that means s electron has more chance to go into the nuclear and more chance to go into the nuclear that means more chance to find it over there. So, the psi 0 square which is actually the electron density inside the nucleus is going to be having a high value compared to the 3d 6 system and again it is a comparative system right. Now, we already know this full expression we had for the delta value I am writing it over one more time over here with a lot of constants and all those things. So, let me try that one more time 4 by 5 pi z is square r square into delta r by r into psi 0 square of the absorber minus psi 0 square of the sample or the source. So, that is the full expression and over here these are all constant delta r by r depends on the delta r value which we found negative delta is nothing again the difference of the radii of the nucleus in the excited and the ground state and that is why what will be the delta value trend it is a high value multiplied with a negative number. So, it will be on the negative side whereas this one is a low value multiplied the negative side. So, it will be on the positive side again comparatively and over here I want to mention this negative does not mean it has to be negative number it is a comparatively negative for an example it value might be 1 unit whereas r and 2 plus will be 2 units. So, we can say 1 unit is actually on the negative side compared to 2. So, that is what we mean by negative side similarly this positive side does not mean that it has to be have a absolute positive value it can be minus 0.1 and this minus 0.1 is sitting positive compared to minus 1. So, you can say yes is on the positive side we are not talking about the absolute value but actually the trend of the system. So, over here you can see iron plus 3 will be on the negative side iron 2 plus will be on the positive side and this is going to happen if I talk about the iron oxidation state and taking all the other factors remaining constant only difference is the iron oxidation states as we go from low to high oxidation state the delta value what is going to happen you can say on the negative side for the high oxidation state. So, that means delta value is going to negative side from the positive side. So, lower is the oxidation state it will be on the positive side higher is the oxidation state it will be on the negative side again it is not absolute negative or positive it is a relative negative or positive. So, with that now we will take some examples but before that one more particular factor remain over here and that is the quadrupolar splitting. So, this quadrupolar splitting factor what it says that typically we expected that this transmittance and this is the velocity and again this velocity it is reduced velocity but it is actually representing the energy axis. So, any particular spectroscopy it has two axis one is the absorbance or transmittance which says like how much system you have and an energy axis which says that exactly what do you have. So, over here starting from 0 to 100 we expect that we will get a signature signal like this but in certain times this signature actually split it up like this and why it is happening so this is actually happening. So, this is where is the delta value is isomer shift but this signal is split it and why does it split that is because split and why does it split because over here when you are talking about the excited state and ground state we talk about ground state is half and excited is 3 by 2. Now if there is a quadrupolar moment a quadrupole moment exist in the molecule that means it is not equal to 0 then this states will split up the half will remain because there is no other possibility the plus minus half will stay together whereas this excited state will split up plus minus half and plus minus 3 by 2 because excited is 3 by 2 it can split up in 3 half and half and 3 half and half are not the same system they have different distribution of the charge density and which is going to interact with the quadrupole moment quadrupole moment and non zero quadrupole moment can distinguish them so that way they are going to split up and that is why instead of one signature I am going to get two and they will be equally splitted that is why if I average it out I will say where it should be so that is the isomer shift and over here I am going to see a difference between them and that difference is known as quadrupolar splitting. I want to mention over here this quadrupolar splitting defense whether your molecule have a electrical field gradient or not which sometimes it is written as EFG so it has to be non zero fellow and when I can expect an electrical field gradient for two different systems first you can see that during the lattice contribution the lattice contribution is nothing but the coordination geometry. If your coordination geometry is symmetric you do not have an electric field gradient because everything is quite symmetric but if that is asymmetric then your electric field gradient is non zero so you will see a splitted most perspective scope. So what do I mean by coordination geometry is affecting the electric field gradient so now example you have a perfect octagonal geometry around a metal all of them are equally bound with a ligand and that ligands are remaining all same so that means electron density is well distributed all around the octagonal geometry and that is not going to create any electric field gradient but if you remove one of this particular ligand and change that to another one so then what will happen you would now disrupt the overall symmetry of the charge distribution and there you create an electric field gradient and that will showcase in the lattice contribution. And the next one is the valence contribution which is the same thing electronic distribution of the metal how it is going to be symmetric for example if you have a T2G3 EG0 system we will call it as a symmetric system and my EFG will be equal to 0 but now if you say T2G2 EG1 and that becomes asymmetric or EFG is not equal to 0 at that condition it will showcase the quadruple splitting whereas in the first case because it is symmetric it is not going to show up. So that is the other point of valence and lattice contribution which I have also discussed in the earlier class in details. So that is the backup of all the different topics that we are going to cover in the next applications. So this is actually a setup where we revisited our thought process and the important parameters that we are going to use in the upcoming segments when you are talking about the applications of MOSBUS spectroscopy. So again going back the important factors are isomer shift quadruple splitting and how they can tell me about the oxidation states, spin state and about the coordination geometry around the molecular complex. So with that we would like to conclude this segment over here. Thank you, thank you very much.