Welcome to Free Thoughts from Libertarianism.org and the Cato Institute. I'm Aaron Ross Powell, editor of Libertarianism.org and a research fellow here at the Cato Institute. And I'm Trevor Burrus, a research fellow at the Cato Institute Center for Constitutional Studies. Our guest today is Dan Ikinson, director of Cato's Herbert A. Stiefel Center for Trade Policy Studies. Free traders often tell us that trade is good because it creates wealth. And we can see how like manufacturing creates wealth. We had things and they turned into better stuff, right, and people were employed in this. But how does trade create wealth? Well, trade by expanding the size of the market enables people to specialize, to focus on a division of labor that was unattainable before trade was available to increase the size of the market. The economies of scale that enable producers to continue to produce more and achieve a reduced cost of production, unit cost of production, enables countries, individuals, companies to exchange what they can produce more efficiently for things that they're less efficient at producing. So there's this idea of comparative advantage which was kind of fleshed out by David Ricardo. So the classical economists started talking about exchange and trying to demonstrate how we can benefit by trade.  So this means Portugal is better at producing wine than England and also better at producing cloth than England? Correct. But because Portugal was relatively better at producing wine than cloth and England was relatively better at producing cloth than wine, it would make sense for them each to focus on what they could produce more efficiently, maximize production and exchange their surpluses. So that is how you create wealth. That is how you expand the size of the market. Now, at the time that Ricardo was writing and also, of course, Adam Smith was really interested in the wealth of nations and trade, there was a really different theories of what we've called mercantilism type of theories of how governments and nations just interact. What is mercantilism? What was the kind of trade theories that they were doing back then? So mercantilism was commercial theory at the time. The businesses at the time thought that it made sense to obtain a trade surplus, to export more than you import because by doing that, you obtain specie from your trading partners.  And Adam Smith pointed out that that is not how you create wealth among nations, that there was a better formula for maximizing the wealth of countries. And that was to specialize and take advantage of this division of labor and exchange. And really, there were attempts to address the mercantilist arguments during the 16th and 17th centuries. It sort of fell short, but he really did a very good job of it. And there were challenges to his notion that free trade was the way to go to maximize the wealth of nations. Challenges from the classical economists over time, ideas of infant industries, actually protecting infant industries might be a good idea that came from John Stuart Mill, that you could actually use tariffs effectively to improve the terms of trade. But none of these objections have really stuck. So theoretically, I mean, the case for free trade, I think, was won with the wealth of nations in 1776. That said, when trade policy seems not to really heed those facts, it seems to be the gospel of trade policy around the world really remains mercantilism. That is one of the things that strikes me as weird about the way that we talk about trade and the policies and the way that politicians address it because this issue of specialization is good. I mean, we all recognize that in our day-to-day lives, right? Like, we all kind of recognize that the person who tries to do everything, like you fix your own car and you grow your own vegetables and I mean… Make your own toaster from scratch by smelting the metal down.  Those are the kinds of people who are poorer, right? And we all recognize that… They would survive the zombie apocalypse, though. But the richer people are the ones who are really good at one thing and get paid a lot to do it and then they buy the other things they need and we all get that. There's very few people who would argue the contrary except for maybe some people in Brooklyn right now. In Portland. Yeah, in the Unibon radius. But when you make those exact same arguments… And we do the same thing about states in the U.S. No one's like it's bad that California seems to specialize in high-tech industries. They ought to also specialize in everything else. We don't make those arguments but suddenly when you're talking about national borders, people seem to forget this. Yes. No, I think that's right. I mean, what's prudent on behalf of family should be prudent in the pursuit of a great kingdom or however that quote goes. What happens is we recognize on a daily basis that we specialize. You guys come to work, focus on what you're good at. I come to work, focus what I'm okay at. And I get paid for that. And so in exchange I'm trading with the rest of the economy for the things, the necessities that I need as well as the luxuries. What happens, I think, is there is this perception when it comes to national boundaries that the rules no longer apply. Aaron, you mentioned over… People don't think you should have trade barriers between states and the Constitution forbids it. But when it comes to trading at an international level, this mentality of us versus them really takes hold. And the thought is, you know, exports are our national points. Imports are the foreign team's points. The goal of trade is to achieve a surplus. We have a trade deficit in the United States. That means that we're losing a trade. And often we're losing a trade because the foreigners are cheating. So that's a very mercantilist expression of purpose of trade. It's very misguided. The purpose of trade is to expand the wealth of nations. And we know that, but we're inconsistent, I think, as a country. And we fall prey to those trying to steer policy toward their benefit. And that's why protectionism persists in the United States. That's why we have so-called free trade agreements that really aren't about free trade. They're about managed trade. And we can get into whether or not I think these are good or bad. It depends. But I just think that there is this tribal mentality that takes hold when we're talking about trade at the international level. Now you mentioned the surplus and the deficits, and that's probably the single most common watchword phrase that comes up in free trade. And oh, we have a trade deficit. Oh, we have a trade surplus. Can you a little bit more – what exactly those are? And whether or not one of them is good and one of them is bad or sometimes they're good and sometimes they're bad, or should we always try and you have surpluses or what's the right way to look at that problem? Yeah. It's an accounting identity. I don't think it matters at all. There has been a lot of debate in the United States in particular recently about whether our trade deficit is dragging down growth, whether it's sustainable in the long run. We have had a trade deficit for 40 straight years. And what that means is that the value of our imports exceeds the value of our exports. So we are buying more goods and services from foreigners than we are selling to goods and services to foreigners. But that comprises the trade account. Slightly broader manifestation of that is the current account. That includes remittances sent back and forth and profits on investments. You mean remittances like immigrants sending things back to their families in Mexico or things like that? Exactly. So we have a deficit, but we have a capital account surplus. So when we buy more goods and services from foreigners than they buy from us, they are investing more in the United States than we or Americans are investing abroad. And as a result, there's no leakage. Protectionists, those that express profound concern about the deficit point it out that this trade deficits impede job creation and slow economic growth. But the fact is that those dollars come back to the United States in the form of direct investment in factories, equity investment, purchases of U.S. government debt, which is probably the least efficient form of foreign investment in the United States. But it does undergird economic activity. It does support jobs. So it doesn't matter to me whether we run a trade deficit. So I think entirely too much is made of it. It shouldn't be an objective of trade, but you'll hear both sides in the current trade policy debate. When I mean both sides, I mean the pro-trade agreement side, the business community, the anti-trade agreement side, the labor and environmental community, citing the trade statistics as evidence that we should or should not pursue these new trade agreements. And it's really mindless. You said that trade creates jobs, but it also, I mean, it clearly does destroy a lot of jobs, right? Like there used to be more manufacturing of certain types in the United States. We constantly, you know, shipping jobs overseas, outsourcing. Is that something we should be concerned about? Is that, I mean, does that cut against the glories of free trade that it's putting all these people out of work? Or to add on to that too, it would have to be the case that, I mean, there are specific people. We're talking about jobs and the big abstract, but there have to be specific people who lose from free trade. Well, trade is a factor in the churn of our economy. Yes, there is this creative destruction that is going on. So we are creating jobs and obsoleting jobs at the same time. I don't think trade theory speaks to a capacity to create or destroy jobs on net, but trade is assumed to create, change the composition of jobs. So as the economy gets richer, as we specialize in more high value-added activities, then the jobs should be shifting in those directions. We no longer produce garments and clothing. We have far fewer people producing steel. Labor-intensive industries have been, I wouldn't say seeded, but there are certainly far fewer workers in those industries. The case of manufacturing overall is an interesting one because the issue gets conflated. Manufacturing in the U.S. is as strong as ever. It still accounts for the largest share of global value-added. Year after year, U.S. manufacturing achieves new records with respect to output, value-added revenues, often profits, return on investment, except when we go into recession, cyclical recessions, but we've been trending in that direction forever. When people complain about manufacturing, they're complaining about the loss of manufacturing jobs, and manufacturing jobs peaked in the United States in 1979 at $19.4 million and they've been on a downward trajectory since. Manufacturing as a share of the U.S. economy peaked in 1953 at about 28%. It's now down to about 12%. That doesn't matter. In absolute terms, manufacturing is still growing. The reason it's shrunk as a share of the economy is because the rest of the economy has grown faster, the services sector has grown. So trade like technology and other factors perhaps expedite the shifting in jobs within the economy. But you don't hear too many people asking to put a moratorium on Apple products and on technology in general. It's widely perceived as good for us as is trade. They both create a larger pie. The question of how we divide that pie is trade is not to be burdened with that question. I think it's a matter for other areas of policy. Shouldn't we worry about the fact that we don't make anything here anymore in the sense that there were good union stable jobs that could provide blue collar expectations or building American cars that manufacturers no longer exist or owned by Fiat and things like that. There were this huge amount of things in the blue collar workers. They didn't have to be ashamed of themselves. Now they're changing jobs all the time or they're serving tables and we're moving to the service economy, which includes a lot of things that aren't building anything. So everything is built overseas. It all gets shipped back here and we're not building. And if a war starts, we have no ability to build things from internally. So we've created this inequality problem and that's something we should be worried about. Do you really believe that? You're trying to give me fire. You're perpetuating a fallacy here. What is the fallacy? Well, we build lots of stuff here. Again, we account for about 22% of global manufacturing value added. So for not making cars and t-shirts, what are we making? We're making a lot of business-to-business products. You hear the complaint all the time. It's a cliche. You know, I went to the store and everything says Made in China or Made in Vietnam, Made in Brazil. U.S. manufacturing doesn't make products that you're going to find on the retail store shelves. We don't make sporting equipment and clothing and hand tools anymore. We make pharmaceuticals and chemicals and components for high-tech equipment, airplane parts, technical textiles, things like that. It requires fewer workers. But to answer your question, Trevor, yes, we do need to make sure we need to have policies that enable the redeployment of people that lose their jobs. We used to be pretty good at it. Between the quarter-century leading up to the Great Recession between 1983 and 2007, the trade deficit increased by 15 times or something around that number. The exports went through the roof. Yet we created 1.8 million net new jobs every year. So the economy, and you know, it's a value judgment as to whether or not a high-paying union job is better than one in the services sector and various degrees of jobs in those sectors. The argument has been, oh, these are all hamburger-flipping jobs, but they really are not. A few years ago, the average wage in the services sector exceeded the average wage in manufacturing. One of the reasons that we hear that, hey, we had all these great high-paying manufacturing jobs in the past is because unions really stuck it to management. They were being paid more than they should. And as a result, that hastened, I think, the demise of some of these industries. So we should be concerned about having an economy that is able to redeploy workers. But we need to look at what is inhibiting that. And I think, you know, we have superfluous regulations. We have the highest corporate tax rate among OECD countries. We have an unsettled immigration policy, unsettled trade policies, energy policy. There's stasis here in Washington. I think if policymakers were to be more straightforward and get out of the way, we would see many more channels widening for job creation. One of the things that gets proposed to address job losses from trade, especially the manufacturing sector, is by American laws. Are those – well, first, what are those? And are those a good idea? No, I don't think they're a good idea. Should it be something – even if it's not a law, should it be something you strive to do?  But by American provisions have been around since, you know, the early 20th century. And these so-called local content requirements are sort of metastasizing around the world. And they're designed to – as jobs programs, basically, when state and local and the federal government spend money written into laws governing how that money is spent are requirements that certain ingredients, certain components be purchased from U.S. producers or they have to be U.S.-made products. The Department of Transportation has the most onerous of the by American provisions where you have, you know, all the steel, all of the cement, all of the labor has to be made in the United States and you can actually divert and actually entertain a foreign bid if the price that the U.S. bidder is asking is 30 percent higher. So you're already committed to a 30 percent loss in efficiency. States have been adopting these laws. Brujaha at the end of last year in New Jersey and the New Jersey legislature passed a very stringent by American provision that would have excluded from consideration lots of companies – the products of lots of companies that are foreign headquartered but operate here in the United States and ultimately Chris Christie vetoed it. But the concern here is because of globalization, it's pretty impossible to understand the DNA of a product or a company. You know, what is an American product? What is an American company when you have cross-border investment in these global supply chains? So really all it is is a sop to unions and it makes guarantees that taxpayers get a smaller bang for their buck and it's causing other governments from the world to emulate us and that hurts our exporters. So it's not a good idea. It's just garden variety protectionism. For those people who lose their jobs when industries shift around them or some computer manufacturer that used to manufacture computers that in Indiana moves to Mexico or we have the – what was it, the giant sucking sound that was Ross Perot's phrase of all the businesses going to Mexico. That kind of did happen on some level, I believe. I mean, computers are manufactured there and a lot of stuff is manufactured. And then someone is left here is like, well, I used to be able to build computers. I used to have this good job. Now I can't and I'm 55 years old and I have a skill that is now being practiced by people in Mexico who are undercutting me in wages. Should we be helping that person with retraining them or should we be sympathetic to that person? We should be sympathetic to that person for sure.  Earlier I mentioned the job – manufacturing jobs peaking in 1979 at $19.4 million. NAFTA was implemented in 1994 and the first six years of NAFTA we added about 600,000 manufacturing jobs in the United States. And if you listen to the left as it packages its anti-trade agreement narrative, you would think that we lost all these jobs in manufacturing and we didn't. I'm not going to say that NAFTA created those jobs in the United States, but the idea that there has been this giant sucking sound doesn't really – isn't supported so much in the data. But it could have shifted the jobs. There has been a shift. Certainly there's been a shift. We've lost jobs. There's been manufacturing job losses all over the world and the same technology that we're deploying here which reduces the demand for labor is being deployed elsewhere. But there's this sort of myth that there's this race to the bottom that we are – that investment chases low wages and lacks environmental standards when in fact what investors are most concerned about – what Western companies are most concerned about is minimizing the total cost from product conception to consumption all the way through. And by investing in countries where wages are low, that usually means that they're inefficient and then that the labor cost is high overall. They really want – investors are looking for places where the labor skills are suited to the activity that they're intending to do there where access to ports is good, access to infrastructure is good, risk of asset expropriation is limited. Sudden nationalization by Hugo Chavez in the situation. Exactly. So there's lots of – my point is a lot of the factors that weigh into outsourcing decisions weigh in favor of investing in the United States and in the United States we have more foreign direct investment than any other country in the world and our manufacturing sector attracts a trillion dollars of foreign direct investment. So if there were really a race to the bottom, why is there so much investment here in the United States? The investment is here. One of the factors is it's a pretty large market, skilled workers, relatively secure political climate, economic climate. And when companies invest abroad, instead of there being this – people think in their heads of this factory being disassembled in Ohio, bolt for bolt, rafter by rafter, and being resurrected in Mexico or China to produce for export to the United States, the numbers show that 90% of the output from foreign invested companies abroad is sold abroad. So it's not shipping jobs abroad to sell back to the United States. That only accounts for a very small percentage of it. But your question was, you know, what do we do about the people that lose their jobs? Well, we have something called trade adjustment assistance, which has been a part of our trade repertoire since 1962. It is widely considered to be a failure. It is a failure.  So it doesn't work, but workers do need to be retrained somehow and on whom does the onus fall? Well, the workers, manufacturers or the companies that would want to hire them. So I think that there should be some sort of incentive for manufacturers, companies in general, to hire people that don't have the skills to pay them, to train them to acquire these skills in exchange for their being willing to work for a year or two for them. Something like that. Certainly get the government out of this process because the government doesn't know what skills are going to be necessary next year or the year after. But isn't it, I mean, to push back a little bit, if investment in the United States is worth so much, I mean, then why is Nike in Southeast Asia running sweatshops and chaining people to their factory lines and expand? I mean, you have to admit that the companies go to where the labor is cheap. It depends on what you're making. And then exploit the workers. Come on. That's the argument. I'm doing a pretty good impersonation of it, but you know that's the argument. That's one of the other kind of concerns about free trade. It's like, yes, it may enrich us, and even if it doesn't destroy American jobs and make it more archiport, that we are from a moral perspective, that $6 t-shirt that we're buying at Walmart is... It's covered in the blood of children. These exploited children and that if we were willing to pay $8 or $10, we wouldn't be exploiting poor people, powerless people overseas. Well, I don't know that we're really... I don't think they feel that they're being exploited. I think some... Certainly there are some exceptions. There are sweatshops. There is exploitation. In some cases, that's the exception, not the rule, though. I think the left likes to paint a picture that this is the manifestation of capitalism, but people that work in factories and develop in countries are usually pretty happy to be working there as opposed to out in the fields. Farming is very difficult. Yeah, out in the hot sun. And I've made this argument before, and in fact, I did one of those point counterpoints in some publication, I think the New York Times online or something like that, where the premise was liquid capitalism has wrought these Western companies that are exploiting foreign workers. And as I clicked on the internet to read the rest of the article, we saw, not Nike, but all these retail brands who are advertising on the New York Times website. They, too, are benefiting from this. It was exposed in that little episode. But when Western companies invest abroad, they are mindful of the fact they have a brand to protect. And when there's exploitation of workers or the environment, when shoddy products are made, when dog food is infected with poisonous ingredients, that ruins their bottom line. So there is self-interest that is motivating companies to do their due diligence and to pick and choose the factories with whom they work abroad. They tend also to pay higher wages because they want to get the best workers. They tend to use mechanisms, production mechanisms that have been tried and trued by Western environmental protection agencies, things like that. So they're raising the standards. And without U.S. or European or other Western investment in developing countries, the options, I think, would be much more limited and the process of development would be slowed significantly. Remember, the United States was a developing country at the beginning of the 20th century. And as we got richer, we started creating child labor laws and environmental provisions and things like that. And that's kind of a luxury good. Well, the interesting thing is in the United States, if you just follow the garment industry, which is often a prototypical sweatshop, it begins in earnest in Lowell, Massachusetts, using women in these really interesting company towns where they're working 12 hours a day, 6 days a week, but they get a day off. You never get a day off on the farm. People always complain about child labor, but children always work on farms. It was always industrialized child labor that was the issue. They got a day off, they learned to read, and then it became too expensive to employ them in Lowell. So they shut down there and moved to South Carolina, moved around their country and then eventually went to China. Do we have any really good instances of some of these places where because of foreign investment, because of these kind of factories, the country is richer now than it was before. Is there any sort of good causal chain there we can draw? They moved on because now the labor is too expensive there, so now they're to a different place. That's what we would want, right? Absolutely. China is an excellent example. There is a lot of reshoring from China to Vietnam and Cambodia. And even Nicholas Kristoff has pointed out that we shouldn't disparage apparel cut-and-sew operations in Cambodia where the options confronting young women were picking through garbage dumps, prostitution, and other more difficult toils. So, yes, we're seeing countries get richer as a result of this. You know, you say it started in Massachusetts, it started in Manchester, really. Really, yeah, exactly. Manchester then to New England, and then from New England to South Carolina and South Carolina to China, China to Vietnam and Cambodia. So, there is a process here. What's very different today from when the United States was coming online and when Adam Smith was writing, and the classic economists were writing in the 19th century, is this is getting back to the comparative advantage thing. It's no longer about exchanging wine and cloth. It's not specializing in production of a particular product. It's specializing in a function on the supply chain. And right now the United States is still at the top of the global value chain. Germany and Japan are a great at precision manufacturing. You've got countries that are very good at mid-level manufacturing like China and assembly operations. And that's where the specialization happens. You see a lot of jobs on the supply chain going accordingly and respectively to these countries. It's not static, and you need to have good policies to stay, or to get to the top, or to stay there. And we are having this global competition right now for investment. And it's really a competition of policies, and I think it's a great thing. Globalization is putting every government's policies on trial the way federalism was supposed to among the states. What about the argument, and this is one when we post stuff about trade on, say, Libertarianism.org's Facebook page, and we get comments from our readers that are along the lines of, yeah, free trade between nations is great in theory, or it's great if everyone plays fair, but when other countries do things like manipulate their currency or take away their environmental protections. Yeah, environmental protections, things like that, that gives them a unfair advantage. Don't give labor rights. There's a good one, yeah. That sort of thing is not just bad for the people in that country that the policies may be harming, say, but that it somehow makes the trade worse for us as well. Yeah, I think in most cases you're looking for we're looking at excuses for reacting and imposing some sort of a countervailing tariff to mitigate the alleged benefit that is accruing. The problem with analysis of trade is that it does seem to focus commonly at the national level. Like this policy is good for the United States. We need to do something about Chinese currency manipulation because it acts as a subsidy for Chinese exports and attacks on imports so that hurts U.S. exporters. Is that true? More or less that, yeah, we could say that. However, tons of Americans benefit from Chinese currency manipulation. U.S. import using industries that rely on imported products or components from China get a discount. Consumers get a discount. U.S. exporters face attacks more or less if in fact the currency is undervalued intentionally. But I don't think that's that big of a deal. In this particular example that we're talking about, I know, Aaron, your question was broader than that, but in this particular example, because of globalization, products are made in multiple countries. In China's case, for example, about 50% of the value of exports from China is Chinese value added. Chinese components made with Chinese labor and overhead. The other half comes from other countries. So that means that it purchases those components and assembles them in China and exports them. So if the currency is undervalued, it's paying too much for those components so its cost of production is higher. And if we insist that China raise the value of its currency, then all those components are going to be lower, lower priced, and they're going to be able to reduce the price for export, which will mitigate entirely the effect on import competing industries here in the United States. So I think what is hurtful to certain interests is beneficial to others. We are not just a nation of monolithic producers. We have so many different entities on the supply chain from the consumer up to the producer. So broadly speaking, we have tremendous advantages that other countries don't have. So if some countries don't want to enforce their environmental laws or their labor laws, again, I think it's the exception and not the rule when this happens. We have tremendous advantages here having the world's largest market, having the most innovative society the world has ever seen. Why are we innovative? Because we allow competition of ideas. There's no reluctance to criticize somebody's idea. We have access to these capital markets to research institutions. We have the rule of law. For the most part. But we have these huge advantages that are much more advantageous than low wages or lax environmental standards. So when you were talking about just for an example about the value addedness of something like it's this very long production line, as you mentioned, that's different now. And you said between the wine and the cloth, for example, that was all integrated within Portugal and England. Now it goes across. So we have an iPod, right? What does it say? It says something like... Designed by Apple in California. Manufactured in China. Exactly. That's exactly what it says. So the value added is some of the ideas which we grew here and came up with them here. But they're components that aren't all built in China. They're built in maybe vows or something. So you can imagine the entire genesis of an iPod beginning in all these different countries all benefiting from the ideas coming out of Cupertino and building up. And what is most of the value getting added? Do you know when I can iPod? There's also, don't forget on the other end, the retail. Yeah, exactly. Well, yeah. This has become an iconic story in this globalization debate. I think in 2007 the first study came out. I think some economists at UCAL, Davis, wanted to figure out the components of an iPod and where they were made and the contribution to the total value of the product. Since then there have been kind of tag-on studies, one doing the iPhone, one doing the iPad. But the conclusions are basically the same. I remember the numbers for the iPod approximately. It cost about $150 to produce the iPod. Most of the components came from Japan, Korea, and Singapore, some from the U.S., very few from China. And it turned out that of that $150 cost of production, $6 was Chinese value added. So when we import that $150 iPod from China, it registers as a $150 import from China and it sort of exacerbates our bilateral trade deficit and adds fuel to the fire of the deficit debate. But then that iPod is retailed for $300 in the U.S. and that covers logistics and advertising. But there are pretty big profits for Apple shareholders and those profits are, some are returned to the shareholders and some are retained earnings that go into R&D for the next generation of products. But if the iPod didn't sell for $300, if we didn't avail ourselves of labor abroad and it cost $500 or $600, it never would have been quite so ubiquitous. There wouldn't have been the momentum that spurred all these new industries, the app industries. Podcasts. The podcasts. Exactly. And all these accessories, you know, the stuff, you know, good jogging, the equipment and everything else that's going with it. So, you know, earlier I said 50% of the value of Chinese exports is Chinese value added. And the high-tech industries, and I consider Apple products high-tech, it's much smaller. It's, you know, in the area of 5% to 10%. But you'll hear Americans who, you know, want to do combat with China on the trade front say, you know, according to comparative advantage, we should be making the high-tech products, but we have this huge high-tech trade deficit. This is exactly what has had they come to those numbers. It's that through that iPod. Only 5%, 6%, 8% of it is Chinese value. The rest of it is from other countries, including the U.S. Shifting gears a bit. One of the organizations that draws a lot of ire from people who are opposed to free trade, people who are opposed to globalization, the ones who march in the streets in Seattle, is the WTO. So what is the WTO? What does it do? It's a nefarious, lunatic-run organization, correct? Besides that, yes. Look, it's not just the anti-globalization left that has questions and impunes the WTO. I get calls from libertarians on this on occasion as well. I'm a supporter of the WTO. It is not, it doesn't live up to this sort of nefarious definition that we've heard. It's not a bunch of faceless bureaucrats and some foreign capital running roughshod over U.S. sovereignty. Basically, the WTO is the embodiment of 50 years of multilateral trade liberalization. So after the Second World War, we started the general agreement on tariffs and trade, the GATT, which was the U.S. and a bunch of European countries in Cuba. And it was an endeavor that from 1947 until 1994 through eight or nine successive rounds liberalized trade and reduced tariffs around the world. The last successful round of the GATT was the Uruguay round, which was concluded in 1994, and it created the World Trade Organization. And it said that all of these rules that we've agreed to are here, and this organization is going to operate by consensus, and it will be here for a couple of purposes, one, to adjudicate disputes that arise, and also to sort of commit to the idea of further trade liberalization going forward. The WTO doesn't have any sovereignty. It is consensus-driven. And it has been quite successful in the sense that there have been 480 or so cases brought to the WTO. So if a WTO member feels that a trade partner is violating its obligations under the various WTO agreements, it can initiate a dispute. What kind of things would be violations? Raising tariffs, not implementing your anti-dumping law according to the agreement on anti-dumping at the WTO. We'll talk about anti-dumping next. But basically governments have committed to trade liberalization and to operate within a set of rules. And when one government feels that its rights have been violated because another government has violated those rules, it can bring a case. And the process is you start with a request for consultation. So the U.S. brings a case against China. The first process is U.S. and China will try to talk it through to see if they can resolve it. If they can't, then the U.S. can request formation of a dispute panel. And the dispute panel will then hear the case. And at the end of the process, they don't say, China, you're violating your commitments, do this. Or China, you're violating your commitments. The U.S. you can retaliate. All they say is China is violating Article 2.42 of the anti-dumping agreement. And we recommend that China bring its measures, rules, regulations into conformity with the agreement. China doesn't have to agree. The U.S. doesn't have to agree. In fact, the U.S. is out of compliance more than any other member of the WTO. This is something that we don't hear in U.S. discourse very often. So how do we get the U.S. to comply if it hasn't? This is the genius of the WTO system. It allows the complainant to ask to withhold concessions, basically to withdraw its concessions, basically to raise tariffs to compel the United States to change. And the WTO say, okay, you're entitled to do that. But during that period, the U.S. is going to have a debate because the retaliation list is created by China or Europe or whoever the complainant is. And it identifies citrus in Florida, motorcycles in Wisconsin, textiles in North Carolina as the likely victims of this retaliatory tariff. And the retaliatory tariff is in place saved because there's a steel tariff in place that was the offense. What this does is it causes the United States to have a conversation within itself. So all the industries get together and say, hey, this is going to be the cost of our failure to comply with the WTO's reasoning. So it's not telling the United States what to do, but it incites the United States. It's a catalyst for the U.S. to have this conversation and sort out what its priorities are. And it's worked reasonably well. A lot of people think that the WTO is issuing victims that need to be heated or else that is far from the truth. And I think of all the international economic organizations, it is the least intrusive actually and has worked the best. Now we talked about going to dumping, which is something you know a lot about. What is dumping and is it a real thing? Is it one thing and is it a problem? I guess if yes, then is it a problem? Right. Well, it's not a problem. There's no real rationale for dumping law. What is the idea? Well, the definition today is the sale of a product in a foreign market at a price lower than normal value or at a price lower than what you would charge in your home market. So it's price discrimination basically. So under U.S. law, a foreign company is dumping if it is selling its widget in the United States at a price lower than it charges in its own market. Is there anything wrong with that? I mean price discrimination happens all the time. I don't know why it would cost the same at all. Well, but this comes up so you could analogize this, the concern I think if you analogize it to companies operating within the U.S. there's this fear like chain stores versus independent stores. Predatory pricing. Yeah, predatory. So you've got the mom and pop music store and then the big chain store comes in, sets up a outlet and then can price its stuff because it's nationwide and getting money from other sources and whatever can price the CDs in its store at a loss even and drive the mom and pop out of business and then once it's done that it can cackle gleefully and jack its prices back up and now we're all paying too much and we've been screwed. Right, that is the textbook argument for those in favor of having a dumping wall that through predatory practices the foreigners drive the U.S. companies out of business and then they raise prices. So it's a pro-consumer law, that's the argument. But really the rationale and we've tried to get to the bottom of this and the best we can figure the rationale is if a foreign company's selling a lower price in the U.S. than it is at home that must reflect some uneconomic or distorting policies in the home market. The company operates as a monopoly or it's protected from competition, something that enables it to reap supernormal profits at home to sell so cheaply abroad. The fact is in a dumping investigation that question is never even entertained. They don't examine whether that is going on. All they do is look to see whether the price is lower in the United States than it is in the home market.  You're actually comparing X-factory prices. Of course you'd expect the prices to be different because of movement expenses and selling expenses, etc. But the idea is to the Commerce Department calculates the percentage by which the U.S. price is lower than the home market price on average for all the products and then say it's 10% underselling than a 10% duty would be imposed on future imports of that product. But to get a dumping order imposed, the domestic industry has to demonstrate that it's been materially injured and that case is made at the U.S. International Trade Commission where they show, hey, we've lost revenues or profits. Our capacity utilization rate has gone down. We've laid people off. And they have to demonstrate that the cause of that injury is less than fair value imports. That seems like a really attenuated thing, a difficult thing to show even if it was true. Well, the Commerce Department looks at the dumping side, looks at the dumping margins. And the International Trade Commission looks at the question of injury. Commerce almost always finds a dumping margin and they have a variety of procedures and methodologies that they use in order to skew the comparison. And I've gone into this in detail in some of the papers that I've written. I won't bore you guys with it here, but what I find to be the biggest problem with the dumping law is that its rhetoric is appealing to politicians. It's to protect upstanding Norman Rockwell-type American businesses from these predatory foreigners and to save jobs and to level the playing field. But in fact, most anti-dumping cases nowadays, since the turn of the millennium, are on imported intermediate goods. So what happens is that a domestic monopolist, a domestic producer of magnesium, can bring a case against foreign producers thereby depriving all the U.S. users of magnesium like the magnesium auto parts industry of alternative sources. So they're just using it to keep out competition? They're using it to keep out competition. It's just a ruse, this whole protecting American businesses. It's U.S. businesses going after other U.S. businesses. One of the worst cases happened in the mid-2000s on Chinese wooden bedroom furniture. The petitioners in this case were the North Carolina industry. And they were really going after the Virginia industry, because the Virginia industry was heavily invested in China. The North Carolina industry was heavily invested in, I think, Indonesia. And so they brought a dumping case against China to cut off the, you know, to impair their Virginia competitors. Most cases are actually U.S. companies inflicting, doing battle against other U.S. companies. This has been written, this has been on the books for a number of years. This is unlikely to change the law. But if you're compared about U.S. companies competing in the global economy, if you're concerned about that, you need to recognize that you're raising the costs of production. The downstream companies don't have any standing in these proceedings. And the International Trade Commission does not evaluate the impact on downstream industries when it does its analysis. The producer wants relief and wins it and can demonstrate these very basic, easy-to-reach hurdles. They get it. They get it. So you mentioned GATT, which it seemed like you're generally a fan of. But then you also mentioned NAFTA, which you said was not a free trade agreement, was a managed trade agreement. And there are some libertarians, like Ron Paul, supposed NAFTA in that way. What is that distinction? Is NAFTA something we should be for as a lesser of two evils? And what is that distinction between free trade and managed trade? Sure. Well, like I said, I get a lot of hate mail from the left, but I also get similar-toned emails from libertarians. And it's a legitimate question. Should free traders support free trade agreements? The GATT, the General Agreement on Tariffs and Trade, yeah, it's an agreement, but it's a multilateral agreement. NAFTA is a trade agreement between three countries, so it's more narrowly focused. But let me answer your question this way. Free trade agreements are not Adam Smith's, the manifestation of Adam Smith's ideas. Free trade agreements really reflect business's priorities. Business leads the charge. It's about opening foreign markets and using our markets as leverage. We will only open our domestic market if you open your foreign market. Now, who does that benefit? That benefits U.S. exporters. So U.S. consuming industries and U.S. consumers are just along for the ride. Shaping the pursuit of these free trade agreements is other interests like labor and environmental groups and things like that. My view is that trade liberalization achieved through trade agreements is still good. Consumers, we benefit residually. Our objectives are not driving the push, but we benefit when trade barriers come down here in the United States, and so we should be thankful for that. The problem I have with some of these agreements is that they have protectionism sort of baked into them, these managed trade agreements. So for the most recent agreement, the topical agreement is the Trans-Pacific Partnership, which the left calls NAFTA on steroids. They love those buzzwords. Yes, they like to engage in a bit of hyperbole. But in this agreement, we will not liberalize our rules of origin with respect to apparel and textile and apparel sales. It is likely going to take 25 years to eliminate our 2.5% tariff on automobile imports and our 25% tariff on trucks. So in other words, we are consenting to allow the government to be gatekeepers through these agreements, and we are consenting to allow U.S. companies to still have access to protection. We also have these pretty trumped-up intellectual property rules that we're pursuing. IP rules, patent and copyright rules here in the U.S. that we are supercharging in this agreement, it seems. The terms of the agreement have not been released yet. Some information has been leaked. We'll see. There is also what I would consider to be protectionism in the form of something called the investor-state dispute settlement mechanism. This is a business wish list, and business isn't always acting in the best interest of consumers. We have to keep our eyes on it. So we're going to evaluate the TPP when it comes out and sort of score it. And if it's net liberalizing, we're going to point out the flaws and say we support it or we don't support it because of what we find. It's got to be net liberalizing, but we will identify the flaws in it. How optimistic are you about the future of free trade? You know, there are always going to be interests trying to make special cases, special exceptions to free trade. In the United States, tariffs are relatively low, about one and a half percent on average. We have tariff peaks in certain products, and I think that we will continue to bring those peaks down and I think we will liberalize. And I think the rest of the world will, too, because in order to compete in the global economy, you need to be part of these global supply chains and you need to get rid of frictions and impediments. You're competing with other countries and I think that bodes well for free trade. And it's also a good recipe for foreign relations. The more interdependent economies are, the higher the cost of potential conflagration ever comes to that. Yeah, you don't bomb your own stuff. You don't bomb your own stuff. And in fact, you know, there's this transatlantic trade and investment partnership which is on deck after the TPP. And the Balkan states of the EU very much want that to come to fruition because they want U.S. investment in Estonia and Lithuania and Latvia because they figure that would be a buffer against any aggression from Putin. But the context of trade can really be used to facilitate a long-term relationship between the United States and China. There's a lot of contemplation about what direction that's headed in. Some people think it's inevitable that there's going to be, you know, hostilities at some point. But the more, you know, it's just the negative aspects of the relationship that get the most attention. There are actually lots of beneficial aspects that it doesn't bleed so it doesn't lead. But I think the more investment, cross-border investment there is between the United States and China, the more we become dependent on each other through our supply chains, the less likely there will be hostilities between us. There's another school of thought, of course, that, you know, proactively some governments will see themselves becoming too dependent in that interdependence and then preliminarily or prophylactically do something aggressive. In fact, we're having a book forum on that soon. I think Justin Logan is hosting that. But I think expanding free trade is a good tonic for quelling the tendency toward hostilities.


Hi guys, so today I wanted to talk about LPNs, or License Practition Nurses, I think license practical nurses. I don't know, LPNs. So a lot of people ask me, you know, what I think about LPNs versus RNs versus going just to an RN program versus going to an LPN, then an RN program. And I am going to be 100% upfront and honest with you guys. In my entire nursing career, which has only been a year and a half, I've only worked with one LPN. So my opinions aren't super well-knowledge educated and whatnot. So I'm going to give you my perspective on things. LPNs are really phasing out a lot of major hospitals. There are still hospitals that hire LPNs, but the majority of time, LPNs are working in nursing homes, long-term care centers, kind of those step down, not acute center hospitals. And LPNs, for the most part, can do most of the things that nurses can, but there's a few things that they can't do. Some LPNs can't give IV medication, like push drugs. Some can't hand blood products or start IVs, but sometimes there are certifications where you can separately get that certification to be able to do that. So again, I'm not super knowledgeable on this topic. My opinion personally is if your end goal is RN, then it doesn't really matter how you get there as long as you get there. Whether you go LPN first and then RN. Some people can take to the year program for LPN, be done with it, and then it's like, well, I can work as an LPN while I finish my RN program, and some people want to just directly go to RN. So I wanted to open up this discussion for you guys and let us know in the comments below your thoughts on LPNs. If you are an LPN, if you're an LPN school, if you're thinking about it and whatnot, I honestly don't have the right or the passageway to really talk fully on this topic because I work with strictly RNs. I don't work with LPNs anymore, and there's not LPNs really in hospital settings because hospitals would rather hire RNs. So let's open this up. Let me know what you guys think in your thoughts, and thank you guys for watching this video. Hopefully we can answer some of your guys' questions in the comments below as far as LPNs because I'm just not super educated on it. But I know one of you guys wanted me to do a video on this. So thank you for watching. Give the video a thumbs up and subscribe to my channel, and I'll see you guys next time. Bye.


Yeah, my time at Purdue, it's been pretty crazy. Here's Boudreau from D. Splash! Evan Boudreau has been splendid today. You know, I knew coming into this season that we only have a couple of seniors. Being able to be a guy who leads by example and does the right things all the time sets a really good precedent for the guys who are younger. And you like to get rewarded through playing time. But it always doesn't work out like that. And I kind of found that out a little bit last year. And you kind of just have to keep your head down and keep working and doing the right things. And obviously, it's gotten to a point where seeing the courts helpful, but being able to keep your head down and consistently be a leader as a senior, I think it's really important. For the R, Kevin Boudreau buries the triple. And Evan's parents are behind us with a smile on his dad's face after that three was pushed. My family's been incredible. My mom, who's one of the hardest working people I know, she stopped working for two years to watch me play high school basketball. My dad obviously went through some health issues and cancer. And throughout all of that, he was trying to rebound for me in open gyms and coming to every game. I think I can count on both my hands the number of games I've missed throughout my whole career. So it's hard to put into words what they meant for me. But having them there the whole way was really special. Boudreau was breaking into the corner.  And Boudreau in the double fingers. I obviously came from a place where we didn't necessarily play in front of the biggest crowds. But to be able to come to a place like this and see the kind of support blew away every expectation I had, really glad I made the decision to come here. I really wouldn't trade it for anything.


So, we are in the middle of proving Jordan Brouwer theorem and Brouwer's invariance of the main theorem. We prove these two statements, modulo two important lemmas. So, these two lemmas, we need to prove now. The first lemma says that a subset of Sn, homomorphic to ik between 0 to n, k is between 0 to n, the reduced homology group of the complement all vanish. The second one statement says that if we subset homomorphic to sk now, for k less than or equal to n minus 1, then the reduced homology groups of the complement all 0 except at the level n minus k minus 1. At that level, it is infinite cycle. So, we shall prove 4.7 first and then we will prove 4.6. So, while proving 4.7, we will use 4.6 and then once we prove this one, all the four plus the two statements namely Jordan Brouwer's separation theorem and Jordan Brouwer's invariance of the main theorem will be proved. So, this is what we need to prove now. Not this one, this proof lemma. So, we have to use Mary Vitry sequence and apply induction on k. For k equal to 0, Sn has two points and Sn minus these two points is homomorphic to equivalent to Sn minus 1. If you remove one point, it is homomorphic to equivalent to a days. If you remove any two points, it will actually deformation to track to Sn minus 1. Strong deformation to track to Sn minus 1. So, in particular, it is homomorphic to equivalent. And we have already computed the homology of Sn minus 1. So, the statement is true for k equal to 0, right? k equal to 0, h, hn minus k is 0, n minus 1 of Sn minus Sn is infinite cyclic and all other things are 0. Okay, reduced homology. All right? So, k equal to 0 is true. Assume now the statement is true for k minus 1. Now, take a b which is homomorphic to sk. It can be written as union of two open sets, two closed sets a1 and a2, both closed sets. Each homomorphic to ik. ik is two disks, right? It is a disk. So, a1 and a2 are two disks intersecting along the boundary. So, a1 intersection is homomorphic to sk minus 1. Both Sn minus ai, okay, if you throw away the closed subsets, they are open sets in Sn. Hence, we can apply meriture sequence. So, h i twiddle of q plus 1, Sn minus a1 direct sum Sn minus a2, okay, two hq plus 1 twiddle of Sn minus intersection to this is the largest set, Sn minus a1 intersection a2, okay. Sn minus a1 and Sn minus a2 going there. Then hq of Sn minus b, the smallest set, okay, which is the intersection of a1 and a2. Sorry, complement of that. So, Sn minus b will come. So, this is the smallest set. For this open set, I have written like this, two hq again of same thing repeating, okay. Now, 4.6 says we know the complement of disks, right? Sn minus 1 of a, Sn minus a, Sn minus c and this one, these are all 0. The reddish homology groups are 0. If this is 0, this is 0, this arrow, the middle arrow must be an isomorphism, okay. So, isomorphism from a lower dimension, q dimensional thing to q plus 1 dimensional thing. This is Sn minus b, okay. This is Sn minus a1 intersection a2, which is a circle. For this, we have proved the statement. So, from that, we will get a statement for this one. So, first you have S0's, then a circle and then a sphere and so on, 1 by 1 induction. Now, it is k dimensional. So, this will be k minus 1 dimensional. So, you can apply theorem to this one and then write this one. Now, 4.6. Here also we induction on k. Now, I have to prove that Sn minus any disk, which I am assuming i k for convenience for k equal to 0 to n, the complement of that is or has all the reduced homology is trivial, okay. If k equal to 0, what is it? It is just a point, okay. A is a single point and we know that Sn minus a is actually homomorphic to a disk. So, it is contractible. Hence, all this reduced homology looks vanish. Now, assume the result for k minus 1, okay. Now, suppose hq twiddle of Sn minus a is not 0 for some q. So, we are going to prove this one by contradiction. Suppose for some q this, we want to prove for all q it is 0, right. Suppose it is not 0 for some q, then you should have a cycle, okay, q cycle representing a non-zero element in hq twiddle of Sn minus a. A q cycle means what? A q cycle is represented by a q change, such that boundary of that chain is 0. That is the meaning of q cycle, right. A q cycle consists of summation n i from sigma i, where sigma i are q simplexes, singular simplexes. So, how many of them are there? Finally, many of them. So, the support is going to be a compact set. So, this is the technological fact that we are going to use now, okay. So, take h to be a homomorphism from i k to a, okay, because that is what we assume. a is homomorphism to some i k. Write a as a1 and a2, where a1 is, now this, this, this disk is going to be split into half. Along i k minus 1 cross on the last coordinate 0 to half, i k minus 1 cross half to 1, okay. So, cut it in the measure, you see along the last coordinate. Both of them are copies of, again, the disk itself, i k, i k minus 1 cross 0 half is also homomorphism to i k, okay. So, I can apply the hypothesis for a1 and a2, but there is no hypothesis yet now, okay. But we can apply a marivitra sequence and conclude something. This is similar to what you did in, for example, Cauchy-Gurza theorem, okay. So, it is similar, the proof is similar here. So, and easier, apply marivitra sequence to open sets s n minus a and s n minus a1 and a2 to obtain exact sequence, hq plus 1 to the middle of s n minus intersection, hq to the s n minus 1 a is the top thing, then the direct sum of these two things, okay. And then again, s n minus a minus intersection, the union of two things, all right. Now, what we have assumed, we have assumed that there is some element in hq to the middle of s n minus a, which is not 0, okay. So, a1 intersection a2 is homomorphism to i k minus 1. So, here we have induction hypothesis. So, these two, this group and this group are 0. So, there is an isomorphism here. So, this is what we have achieved now. If this is not 0, then one of them must be 0. Not only that, actually what should have happened, look at this, how is this defined, hq of s n to hq of this. So, these are defined by inclusion maps, right. Therefore, what should have happened? If this comma this is not 0 here, it should not be 0 here or here. The image of the same c here, whatever I have taken not 0, either it is not 0 here or it is not 0 here, because it is an isomorphism. If it is 0 on both of them, then the image will be 0, that means c would have been 0, okay. So, this is what a eta i from s n minus a to s n minus a i, a i smaller, a is larger. So, this is the inclusion maps.  So, eta 1 star eta 2 operating upon c is not 0, means one of the coordinate must be not 0 in the direct sum. So, you choose that as your preferred one, okay. The half, among the two half spaces, you choose the one in which the image of c is not 0. Repeat this process. Now, that is what you do Cauchy-Gerr's theorem. Repeat this process. Now, a 1, you continue it to half, okay, a 1, 1, a 1, 2 if you want and choose the one in which one of them, both of them are, you choose one of them, one of them in which the image of c, further image of c and so on. So, image of c I will keep calling, they are all inclusion maps, inclusion induced maps. The image of c is not 0. Keep doing that. So, what we are going to gain? So, we keep getting a sequence of cells, half cell, a 1 is half of it, a 2 is half of it, a 3 is half of it and so on, okay. Along the same x axis, last coordinate, nth coordinate, okay.  So, it will be one single point along the last coordinate. So, i k minus 1 cross a single point. So, this t is the image of c, okay, in h q 2 to the power s n minus 1 is non-zero. For all r greater than or equal to 1. But by induction, h q 2 to the power s n minus t will be 0 because this is i k minus 1, okay. So, what is the meaning of this? When you come here in the image, in the limiting image, it is 0 means what? It is boundary of something, okay. There exists a q plus 1 chain tau such that boundary of tau is c. But this q plus 1 chain has again finite combination of q plus 1 simplicity, right, therefore it is a compact support, okay. So, what are these s n minus a is an open set, contained inside s n minus a 1, contained in s n minus a 2, contained in s n minus t. So, finally s n minus t is covered by the increasing union of these open sets, the complements of a s. And I have a compact subset there. So, it must be contained in finite stage, okay, which means this q plus 1 chain tau must be contained inside some s n minus a r plus 1. But there, we have assumed that by repeated application, the image of c is not 0. That is a contradiction, okay. So, s n minus t is union of this increasing union versus minus a r. a r is closed subset. So, these are open subsets, okay. So, every compact subset must be contained inside some s n minus a r for the mark. And there c is 0 is a contradiction. So, we have chosen a 1, a 2, a 3 so that the image of c is not 0. So, all this because we assumed that h q of s n minus a is not 0. So, therefore h q must be 0. So, that completes the proof of the lemma and all the theorems that we have proposed so far, okay. As I told you, these two lemmas, they give you much more information than the theorems. And they will be quite useful as well also. Okay, now I would like to make a few comments on Jordan Curve theorem itself. This theorem belongs to a class of problems or results namely s 1 contained inside s 2 or a plane, okay, embeddings of s 1 is a plane. So, more generally, net apologists are interested in embeddings of one sphere in another sphere. These two lemmas tell you a lot about them, but there are many, many more things of interest which lemmas do not tell you. So, some of them are useful also, okay. So, Brauer while proving this, he did not prove just one single result, but he has done a lot of work. But now let us understand in this slide, let us understand these problems in general. Let us consider embeddings of s k in s n, okay. Embedding means just topological embedding, 1 1, okay, continuous 1 1 map onto the image that is all, okay. Being compact, escaping compact in the s n v host or automatically it will be a homeomorphism onto the image, okay. Two such embeddings are said to be equivalent if you can move one embedding to the other embedding. This moving we have already defined homotopy, but here homotopy will not work a homotopy with a restricted condition namely at each stage it must be an embedding through embeddings, okay. These are embedded objects you are you can move it from one to the other, okay. Through embeddings do not collapse and make it overlap each other or cross cross each other and so on. So, then these two are called equivalent. That means I will more specifically you must have a continuous function h from s k cross i to s n such that for each fixed t x goes to h of x t is an embedding for each t, h of x 0 is f x and h of x 1 is g x. Then we can say that f is isotopic to g.  This is also transitive therefore it is an equivalence relation. So, one is interested in knowing equivalence classes of embeddings, okay. So, this is a general problem. Now, quite a bit is known and quite a bit is unknown. So, I would like to just give you some information here no proofs, okay. Consider the case k equal to 0. What is the meaning of k equal to 0? You have s 0 that means two points embedded in s n, okay. If this n is also s 0 then there are only two possibilities either identity or the transposition and you cannot connect them one with other. So, there are two classes. If it is bigger than 1 bigger than equal to 1 namely s 1, s 2, s 3 and so on. Then we know that all s n are connected and an isotopy of a point is nothing but just a homotopy nothing more than that which is same thing as just a path. So, since s n's are all path connected for n greater than or equal to 1 any two embeddings of s 0 in s n are what isotopic to each other. So, take two points take another two other points you can join them so that the two paths do not intersect each other. That is not very difficult to see, alright. So, let k equal to n, okay. k equal to 0 I have a definition. It is a classical result. What is the meaning of num embedding? Some homeomorphism from s n to s n, okay. By the way this needs a proof. Can you have a homeomorphism in embedding of s n inside s n which is smaller than s n not the whole of it. That needs a proof. I am not going to tell you the proof here. So, when you have k equal to n it will be on to surjective, okay. It follows from whatever we have done also but I am not going to do that one now. You have to think about that, alright. So, it is now question is it is called these are what are the homeomorphisms of s n which are equivalent in this case isotopic to each other. So, this was a classical problem at least in the differentiable case it was solved quite long back by Smale and Hersch and so on. So, there are exactly two classes, okay. So, when you talk about topological classes, topological mapping there are always more difficulties are there. Sometimes these are not true and so on. In the differentiable case namely the defumorphisms there are exactly two classes. This is the standard result, okay. Namely homeomorphisms of s n orientation preserving ones and orientation reversing ones they are distinct classes and there are only two classes, okay. Now, in general lemma 4.7 is very effective tells you that the complement of any embedding as trivial homology except in dimension n minus k minus 1. So, in some sense to distinguish between two embeddings it is useless. So, he is a very good theorem but it is useless as far as distinguishing any two of them complements are homologically same. So, what to do there is no other way. Whereas in some cases namely when k equal to 1 and n equal to 3. So, I will come to that case there are other things like this which are useful. So, before that I will tell you a deep result in PL topology tells you that instead of topological embedding what you call as piecewise linear embeddings. If the co-dimension which is named n minus k is bigger than equal to 3 then any two embeddings are isotopic. So, this is a fantastic result. So, s1 embedded in s4, s5, s6 or s2 embedded in s5, s6 and so on there is only one embedding essentially. In other words what you can move them around and bring it back to the standard embedding. So, that is the meaning of that any two embeddings are isotopic features. So, the complement must be at least three dimension that must a room must be there then you can move it around and bring it back. This is the result in PL topology. So, the most important thing is now the complement being equal to n minus 2 that means 2 k equal to n minus 2 and k equal to n minus 1 these two things remain to be settled. The case could n minus 2 itself is that means co-dimension to embeddings of spheres this goes under the name North theory which is a quite a deeply studied branch of algebraic topology okay and lot of applications in many, many other sciences like chemistry, physics and all of them use this North theory okay. Even physics very high physics I mean string theory and so on. So, we shall not be able to discuss this problem this particular thing any more detail except I want to tell you the case when n equal to 3 and k equal to 1 is the most interesting one that is where lots of problems are there and classically the only thing that was done was to look at the fundamental group of the complement. Look at Jordan Brower separation theorem all these theorems are two lemmas they do not tell you anything about the fundamental group they tell you only about the homology. The fundamental group okay can be computed by what are called as floating representations and so on using some hybrid when it comes to theorem actually. So, that will give you a lot of information yet up to 1980s lot of problems were unknown the group theory was not able to give you enough thing till CRF Jones came into picture and cracked the whole thing and opened up a new way of thinking completely. So, it is now quite flourishing branch of algebraic topology okay. So, finally k equal to n minus 1 let me give you a little more information on this one for n equal to 2 this is Jordan Kuru theorem okay here we have very strong theorem from complex analysis namely Jordan Schoenfritz theorem which is an extension of Riemann mapping theorem which says that any two embeddings of the circle inside r2 are equivalent in other words if you have any simple curve you can bring it to the standard circle by this isotope okay with a little more extra assumptions the same thing can be done in all other dimensions the extra assumption from it was first it was major and then the assumption was weakened by Morse and then further by Brown but still there is some assumption I do not want to go into the technicalities of that. So, you can read it in Bradon's book or some of one of the thing Brown's paper I have given you Brown's paper is very readable paper so you can look into that one the last thing that I wanted to tell you is that what is suppose you remove the extra assumption namely any topological embedding of s2 inside s3 that is the first thing right so that was cracked by Alexander Longworth in the negative. So, it is called Alexander's horned sphere obviously the embedding is somewhat wild okay wild embedding okay so he is going to put horns to these spheres and what happens is it is the actually the embedding of the disc d3 the boundary is obviously a sphere two sphere but the complement is a complicated complicated usually if you standard sphere d3 what happens the complement is also d3 so complement we are able to show that is not simply connected therefore it cannot be a disc okay so for lack of time I will not be able to present that one but I will just give you the picture the original picture of this Alexander's horned sphere okay so this is supposed to be the disc okay if you cut it away here it is just a twisted disc with a two horns the horns here this is a big horn this is another horn they each of them grow two horns again like stags okay two horns okay and then those two horns all the four of them they each of them grow two horns again so they are all trying to get interlinked as they keep growing they are coming closer and closer and at the end they do come closer in the limiting case so there will be a counter set of points wherein they meet finally okay so one can show that the complement the inside thing will be still a disc complement inside means inside this one this is a this was a disc we have started growing horns okay so this inside thing will be a disc and so boundary will be a sphere but the complement is complicated okay so that's all I can tell you for this one so let us stop here thank you