Hello and welcome to today's IIA webinar. My name is Dr. Barry Kulfer, the Director of Research at the IIA, and we're delighted to be joined today by Sam McBride, Northern Ireland Editor at the Belfast Telegraph, who's been generous enough to take time out of his no doubt hectic schedule to speak to us. Sam McBride is the Northern Ireland Editor at the Belfast Telegraph and is only independent. He also writes about Northern Ireland for the Economist and was previously political editor of the Belfast newsletter. His excellent 2009 book burned the inside story of the cash for ash scandal and Northern Ireland's secret of new elite became a Sunday Times Best Editor and was nominated for the Christopher Eward Biggs Memorial Prize. He has a regular presence on radio and television, giving analysis of events which impact on Northern Irish politics. Today, Sam will speak to us for about 20 minutes or so about the outcomes and implications of the Northern Ireland Assembly elections and the implications of which seem to change by the hour. Attendees will also have the opportunity to put their own questions to Sam before we wrap up at around 2 PM. You'll be able to join the discussion using the Q&A function on Zoom, which you should see on your screen. Please do feel free to send your questions in throughout the session as they occur to you and we will come to them or as many of them as we can once Sam has finished his presentation. A reminder that today's presentation and Q&A are both on the record. Please feel free to join the discussion on Twitter using the handle at IEEA. Without further ado, many thanks again for being with us, Sam, and I hand you the floor. Thanks very much, Barry, and good afternoon, everyone from Belfast. I'm going to try to answer five of my own questions here at the start and you will then be able to ask me proper questions to which I do not have the answers at this point. The storm of the election, which we've just had, has made headlines around the world. We've had the world's media in Belfast both before and after. It's had all sorts of dramatic, very dramatic and seismic outcomes we are told by some of those paper headlines. But is this election really as historic as has been made out or is it actually exaggerated? I think that what this election has done is clarify that Northern Ireland is now a land of three tribes rather than two. That is something which has been really getting clearer over recent years. It has been the clear trend since about 2007 when Martin McGinnis and Ian Paisley went into power sharing together. At that point, we also started to see when we look back now at the graph of how unionism and nationalism and those who are not defined by either of those two labels have performed. That is the point at which they start to move upwards gradually, incrementally, but really clearly. And when you plot it out over a long period of time, it is very stark. So in this election, it's not that that is a dramatically new event, but the fact that the others in the center ground of Northern Ireland politics are continuing to get bigger, they are continuing to put on more seats, particularly the MI Alliance Party, which is now really the dominant force in the center ground, which has not just eaten into unionism and nationalism, but has also eaten into other parties in its territory, into the Green Party in particular, taking both of its seats. That is a really significant moment, because these are the people who ultimately will decide Northern Ireland's future. There are three minorities now. There is unionism on roughly about 40% of the vote. There's nationalism on roughly about 40% of the vote. And then you've got these others in the middle with something like 20%. And it will not be those parties which will decide the outcome of a future border poll, but it will be their voters. So it's not about their voters being told by those parties how to vote. It may well be that in that instance, they will not say anything at all and they will sit on the fence. But those people are the people who, smart unionists and smart nationalists are trying to court and are trying to work out how can they strategize not to maybe get them into their camp in a storming election where they vote for Sinn Féin or the DUP or whatever it might be, but how do they appeal to them at some future point in a border poll? That's the big strategic prize now for politics in Northern Ireland. This has also been an election which has symbolically humbled unionism. Unionism lost its storming majority in 2017. That was the snap election after the cash for ash scandal. It was at the point where we now know Martin McGinnis was dying, where there was a change in the Sinn Féin leadership and in its strategy and its long-term approach to storming, which until that point had been really treating it as something that was sacrosanct and suddenly it said, actually, storming disney on the table as a negotiating tactic and it's something which we're prepared to haggle over. That was very popular within their electorate. There was a lot of distaste at Arling Foster, a lot of distaste at the RHI scandal, lots of unease within nationalism at Brexit, which had happened the year before, the vote for Brexit had happened the year before and that loss of storming's majority was a really significant, a really dramatic moment. And yet at that point, as somebody who reported that and who grasped the significance of it, even I didn't think that it was the point at which unionism's majority was probably never coming back. Unionism had gone from a position where it had 49% of the vote in 2016. Just before Brexit, there was an assembly election and things had never looked more secure for the union, arguably in the history of Northern Ireland at that point. And in the 2017 election, just a year later, less than a year later, the unionist vote went from 49% to 46%, but in terms of seats that had a much more dramatic impact. And when we look at things now, 46% actually looks like a very healthy percentage for unionism. Unionism is now down around 42%. It has not only lost its storming majority as a designation, it has lost the post of First Minister, it is no longer one of its main party, the ADUK is no longer the biggest party in storming. And so there is a continued weakening of the unionist position there. This election has also put pressure on the Good Friday Agreement structures, which have been creaking for a very long time. And I think that the growth of the others in the center ground is something which is really going to push reform there. It may not happen now, but I think that it is something which is now completely inevitable. It's just a question of does it happen now or does it happen perhaps when storming falls apart the next time? And the final significant element of this election are the geopolitical implications of this, both for the UK's relationship with the European Union and for what that means for wider politics across Europe. There is a clear hardening of unionism's position in this election. Unionism is both shrinking, as I've said, but it's also hardening. And that complicates things in relation to the Northern Ireland protocol. And we've seen that yesterday and we'll be seeing that over coming weeks and over the next year or so. But it's also important to say that while all of that is true and all of that is significant, the issue which has most dominated the headlines, the ascent of Sinn Féin to the top of storming is a wholly symbolic thing. It doesn't give Sinn Féin any extra power. It means that Michelle O'Neill can rub out the deputy in front of her title. She can say she's the first minister and despite lots of speculation, which was fueled very unwisely from the DUP's perspective by their refusal to say that they would go into government with Sinn Féin on that issue. I think it's very clear that the DUP will go in on that basis because they have nowhere else to go once the protocol is removed as an issue, if indeed that can be sorted. But once that happens, yes, it's a very symbolic moment, but it doesn't actually do anything to resolve either the problems with storming as a system of government or from Sinn Féin's perspective, it doesn't do anything to advance the cause of Irish unity. It does not in any way persuade people who are the bloc in Irish unity, people in Northern Ireland who up to now have not supported that, it doesn't do anything to persuade those people. The second question I want to answer is what does the protocol mean for Northern Ireland at this point and where is it likely to be going? And I think that there are really two aspects to this. There are the economic aspects and there are the political aspects. In economic terms, there are people who are doing very well out of the protocol. There are companies that are making lots of money. Some of that is quite crude in some ways. It's quite simplistic. It's as straightforward as Sainsbury supermarket is no longer able to bring certain products across the Irish sea border from Great Britain. And so therefore they have to turn to a local supplier for those. So that's good for that local supplier. But it is something which is not necessarily making a really dramatic impact on the Northern Ireland economy. There are more sophisticated and more significant economic aspects to this, benefits to this for companies such as companies in the pharma manufacturing sector, some of the advanced manufacturing companies in Northern Ireland, where having a food in both the single market for the European Union and the UK market is going to be a significant advantage. And we've seen some significant and some big investment by some of those pharma companies in particular. But the big question, which is curtailing some of that, I think at this point is the uncertainty as to whether what currently exists in the protocol is actually going to be the long-term position here. But that benefit to Northern Ireland economically is counterbalanced by the really breathtaking scale of a lot of the paperwork which now faces companies who are importing products from Great Britain into Northern Ireland. There are rules here, which would normally apply to a container ship or a container coming from China or India or Brazil or wherever it might be, which are now applying to single items or single pallets coming from Great Britain into Northern Ireland. And when you talk to companies, I think there is a gulf here between how small companies are finding that and how big companies are finding that. If you're a supermarket or a big company in that sort of area, you're able to take the hit to a certain extent, particularly if Northern Ireland is quite a small part of your wider UK or wider continental market, you're able to hire the best lawyers to understand how this operates for you, how you can take advantage of the rules. You're able to hire the best lobbyists to try to get around some of these rules. And we've seen the UK supermarkets in particular benefit from that with lots of these grace periods where they've basically exempted themselves from lots of the pain that would hit them most squarely.  And I think there is going to be this growing problem here that there is a disproportionate impact on the small person. That's going to have implications for competition in Northern Ireland. And it's also going to have very significant implications for consumer choice in Northern Ireland if the current situation persists for the long haul here. And I think that the most significant aspect of the talk about the protocol is that as it sits at the moment, huge chunks of it have not been implemented. I think that talking to both the EU and the British government and to business, the likelihood is that lots of what hasn't been implemented will never be implemented. There is actually growing political support for that from parties which are on paper supporting the protocol. They actually don't want lots of it to be implemented because now that people realise how particularly complex that would be, there is a realisation that actually some of it is just unimplementable. It could not be done. And so there is now an argument, I think, not so much about whether the protocol as it exists on paper and in law is going to be implemented. But how much of it should be kept and how that process should be overseen? Should it be done unilaterally by the British government? There is clear consensus from the parties who support the protocol in Northern Ireland that should not be the case, that that's dangerous, that that undermines the rule of law, et cetera. But I think that there is much more consensus here actually on the final outcome than might be apparent from some of the rhetoric here. But the second aspect of this is more complicated. This was never simply about filthy looker. It was never simply about economics, about trade rules for a lot of people. This was a fundamentally constitutional question. It was about where the border went. That cut both ways. It was very significant to nationalists if that was going to go at the land border. It was equally significant to unionists if it was going to go in the Irish Sea. I think that has been very poorly understood by the Irish government or if it has been understood, they have misrepresented that quite significantly. And there has been this sense that the only way to protect the Good Friday Agreement is to effectively adopt what is the nationalist interpretation of where the border can go. It can't go at the land border, but it can go at the sea border. I think the difficulty now is that the British government is moving in what Liz Truss said yesterday to accept the unionist interpretation of that and say, well, actually, there is this significant constitutional problem now. It's not just about us dealing with the practical difficulties, but that cuts both ways because that then means that if the British government is saying, as she said in the House of Commons yesterday, that there must be unionist consent as a minority for what comes out of this process, it means that there has to be nationalist consent for what comes out of this as well. And so this is a very messy and far from straightforward situation whichever way this is decided. And I think that there has been a profound destabilization, obviously, of Northern Ireland politics. It is far more rancorous than it was before Brexit. It is far more uncertain. There is far more of a sense from both unionism and nationalism that there is a lot to play for here, that they can make significant gains and they can also lose significant things if they get this wrong. And so that really has put things on edge in a way that was not the case prior to the vote in 2016. The third question is around whether the DUP can compromise on this protocol issue and get back into the executive. And the short answer to that I think is absolutely yes, definitively yes, they can compromise. I think if you look at their documentation around this, it is basically written to allow for compromise, but that doesn't mean it can come away with a fig leaf on this. It doesn't mean that their concerns are either not genuine or that even if they're not genuine, that they can spin something which is not serious as being very fundamental and representing real change. What we have seen in this election is hugely significant. We have had the most hard line stance by a unionist party in decades going into an election. They have gone into this election asking for an explicit mandate not to go into government unless they get what they want on the protocol. And what they want on the protocol is not some like touch changes. It's about, it is in their terms getting rid of the RAC border in its entirety. Yes, there is an argument around whether that involves the entire protocol going or whether it involves changing the protocol. I think that's quite a semantic argument which really doesn't matter. What they have said in simple terms which the person in the street will understand and which their voters will understand in these terms is that the RAC border, as it is understood, as it makes a significant barrier between Northern Ireland and the rest of the UK, must go. And that's a very high barrier for them to clear, a very high hurdle for them to clear now. And even having gone into this with such a tough message, if you like, such a recalcitrant message, they have seen huge leaching of their vote to an even more hard line party, the traditional unionist voice of Jim Allister. He took 66,000 votes in this election. That's a really extraordinary hole for somebody who in himself is very capable and is very widely respected on the right of unionism. But even there, there was not any great enthusiasm for lots of his candidates. They were quite low profile. There were not big figures in many cases and they got really significant votes, really surprising votes in areas where they had no hope of getting seats. So what we have seen here and what the DUP has listened to in this election is a message that basically says, unionist voters who are leaving it are going to a more hard line alternative. And the Austrian unionist party, which, while it opposes the protocol, is more pragmatic on this and certainly is not saying that they would pull down Stormwind over this. They would go back in tomorrow, regardless of what happens with the protocol. They're the party that is losing support. The DUP is not losing its vote to there. It's losing it to the right. And so if it does not get significant gains on this, I think it's in really perilous territory. The next question is, what happens if the British government actually does ditch the protocol and whether that's in all but name or whether it is literally getting rid of the protocol, I don't think really matters. The first thing there, I think, is that Sinn Féin have been remarkably coy as to what they would do in those circumstances. I was at the Sinn Féin manifesto launch about three or four weeks ago during the campaign and Mary Lou McDonald was asked this question, would you then boycott Stormwind? Would you then say, we're not going into the executive? And she didn't answer the question. And I think that was quite telling. I don't think that necessarily means that Sinn Féin knows how it would respond to that, but they're certainly not ruling that out. It would be quite difficult for Sinn Féin to do that because they have been really forthright in their very clear denunciation of the DUP for not going into government over this issue, saying that it's nowhere near as important as the DUP is making out and actually health and education and all of those things, such as the cost of living crisis are more important. But I think the reality is that both sides here care about this a great deal. It was easier, I suppose, for Sinn Féin to say that when they thought that they had won this argument to a certain extent that the protocol was going to stay. If it's actually going to go, I think that's much harder. And I think that the alternative here where the British government actually goes back on its word where it again, basically betrays unionism and having said very tough things in the House of Commons yesterday, it actually doesn't do very much or certainly doesn't do what it said it would do. I think it's going to be very dangerous on the other side. We're likely to see things move onto the streets. We're likely to see protests. We're likely to see lawless paramilitaries get more involved in this. And I think that there is a very long history of militancy within both unionism and nationalism at various points, but particularly within unionism over recent decades, there has been often an incoherent militancy, even at points where it's not logically in their interests, where it's not going to change things, where it may actually drive people away from unionism. We have seen in things like the flag protests and even what happened last year in parts of Northern Ireland where there was quite serious rioting and loyalist areas, that it really doesn't necessarily stop that happening. There is a sort of in really on clear and incoherent lashing out, which I think is likely to be a pretty visceral reaction to this if there is another betrayal by the British government. But I think that in terms of the DUP, if they do go back into government and if they are betrayed by Boris Johnson, I think that is potentially the sort of thing that is the end of the DUP as a serious political force. They were warned during the Brexit process not to trust Boris Johnson. They disregarded those warnings. They put him into par in Downing Street. They brought him to their party conference. They lauded him, they listened to him. And throughout this process, they were really clearly saying to people, you don't know what you're talking about. We know what we're talking about. And there was sort of arrogant swagger, which clearly was wrong in hindsight and in many ways was wrong in foresight as well. And I think that if they do that again, having been betrayed on multiple occasions, that is something which potentially for a party which is so wounded, which is so driven by internal contradictions and so lacking in ideological coherency is the sort of thing that potentially is just the end of the party as a serious political force in Northern Ireland. The final question I want to address is, is Northern Ireland doomed? Is it the end for Northern Ireland? Is Irish unity inevitable? And I think the answer to that as far as I'm concerned is not in the slightest. I think the surge here in this election was for a party in the centre ground, the Alliance Party, which was explicitly saying, let's basically park talk of a border pole. Let's not say we're never going to talk about it. Let's not say that we'll never have a border pole, but it's not on their radar as an immediate concern. And even for Sinn Féin, which saw its vote go up slightly and to incredible levels. I mean, when you look at the Sinn Féin vote of 250,000 people, it's an extraordinary vote. It's really a dramatic shoe of their electoral might in Northern Ireland. But it was in response to a campaign from Sinn Féin that was far more about things like inflation than it was about Irish unity. And some of that was tactical by Sinn Féin. They were not wanting to energize unionism. They were not wanting to wind up unionism at a point where they knew that they were ahead in the polls. They just needed to play things safe. But I think it was about more than that. I think it was about a realisation that even within Sinn Féin's voter base, there are people there who, yes, are very enthusiastic about having a border pole tomorrow or next week, but there are others who are much more cautious. They want to plan for it. They want to think about it carefully. They want to be clear about what sort of New Ireland they actually want because they're not quite clear right now. And I think that if there had been a campaign from Sinn Féin here, which had put Irish unity as a much more urgent and pressing matter, I think their vote would not have been 250,000. I think that that was a recognition that there are other concerns that are driving people in the more immediate term. And I think that when I say that Irish unity is not inevitable and it's not on the current horizon, that is really contrary, I suppose, to the zeitgeist, which not just within nationalism, but even among lots of gloomy unionists and lots of unionists are fairly perpetually gloomy about their prospects, says that there are really grave concerns here for the future of Northern Ireland from a unionist perspective. And there are reasons for really significant hope from a nationalist perspective. In some ways, both of those things are true, but I think that they feel to take account of the longer game here, the bigger picture. If you go back to 2016, Northern Ireland had never been more secure within the union. We've seen in the space of a few years, and actually it was true within the space of a few months there, that one vote, one big decision turned that on its head, something which seemed completely clear and something which had led to nationalism losing support, which had led to Sinn Féin losing support, which had really got nationalists very worried in Northern Ireland about where they were going. They were, in some ways, worried that Sinn Féin had been outfoxed by the DUP, that they had got stuck inside a stormed system that wasn't working for them, and that they were trapped within a Northern Ireland system that, yes, was much fairer for nationalists. It was something that was far more tolerable than what had gone before in the 1950s or 60s, but that wasn't what they wanted. They wanted something that was much grander than that, a far more significant political goal. And actually, I think that lesson, to a certain extent, has been forgotten by both nationalists and unionists. They look at the current situation and they think that that will persist forever. And actually there is every possibility that something is fine that is a compromise in the protocol, that things do settle down, that if the protocol actually does become in some way the best of both worlds in a genuine sense where a lot of the red tape has got rid of between Great Britain and Northern Ireland, but there is a food in both camps for Northern Ireland companies, that that brings economic benefits, that it brings economic stability, that that brings political stability, and that as one nationalist businessman said to me last year, why would anybody in those circumstances, if it works, want to stop it? If we had a United Ireland in those circumstances, we would lose these unique circumstances. It would no longer be unique. We would suddenly just be as the rest of the Ireland. And so therefore I think there is sometimes quite short-term thinking here. And if you go back to the longest running survey of attitudes on Irish unity, which is the Northern Ireland Life and Time Survey, it's overseen by Northern Ireland's two universities, Queens University Belfast and the Ulster University. It has been going on since the 1990s. And if you look at the figure, when people are asked if they would support Irish unity, if it was voted on tomorrow, in 2002, that survey found that 27% said yes, they would vote for unity tomorrow. In 2020, after two decades, and after Brexit and after everything that has happened, that had gone up to 30%. So it had risen by 3 percentage points. Now, I happen to think that the survey now, that for various reasons, it underestimates support for unity. I think that there are reasons why sometimes people in a face-to-face survey like that are sometimes shy about saying that they support Irish unity. So I'm not saying that is the true figure for the level of support for Irish unity. I think it's higher than that. But I do think that over a 20-year period where with the same methodology, you're asking this question, the same question, and you're getting those results, there is a significance in being able to track the shift in the public mood. And to move 3 percentage points in that period, given the really calamitous fallout from Brexit, given the failure of storming, given that that in many ways gives support to the old Republican idea that really Northern Ireland is a field state, that it can't work, that it won't work, that we've tried everything in terms of forms of governance and none of them are any good. And given the really shambolic leadership of unionism and a very unpopular British Prime Minister and Boris Johnson, I think that some Republicans ought to be looking at that and not believing their own propaganda, but actually thinking, hang on a minute, why have we only marginally shifted the dial on Irish unity? It is true that Sinn Féin have been brilliant at winning elections, but it's also true that they've been awful at persuading people of coming on board with the idea of Irish unity. That is the only way that they say they now accept we will get Irish unity. There is no other way. And yet they're not persuading people. Sometimes when that is said to them, as I wrote last weekend in the Sunday Independent, we get an answer from Republicans, which says yes, but that feels to account for the fact that unity will come about through other people being better persuaders than us. And to a certain extent that is of course true, there are more persuasive voices for unity than Sinn Féin. But I think that also is quite an easy answer for Sinn Féin, which feels to account for the fact that not only are they not persuading people, in many ways they are one of the greatest things which unionists in Northern Ireland say is an impediment to Irish unity. A question in a border poll for Irish unity without Sinn Féin in the picture would be much less problematic for some softer unionists, but particularly for those people in the center ground who are not unionists, who are not nationalist than the current situation. And just, just finally, I think that if we go back 100 years and look at what has happened, it's a good lesson in being cautious about anybody who says that anything beyond the next five or six years is in any way inevitable. Nothing in life beyond death and taxes is inevitable. There is nothing in today's Ireland north or south which would really have made much sense, I think, to Michael Collins or Edward Carson or Eamon de Valera or James Craig. They would have found it hard to comprehend a lot of what we take for granted. And so therefore I think people who say now that one thing or the other, either union or unity is inevitable are really feeling to learn the lesson of history. Thanks very much.


When looking at the axioms of Fano and Young Geometry, we see they differ in only one axiom, what we call axiom 5 for those two geometries. Which axiom 5 states something about the existence of parallel lines. Axiom 5 for Fano geometry said that parallel lines don't exist. Axiom 5 for Young Geometry says that given a line and a point off a line, there's a unique parallel line to the given line through the given point. So it doesn't just say that parallel lines exist. It says they exist up to some uniqueness criteria. Now because both are models of incidence geometry, we see that their respective parallel properties are independent of the incidence axioms. That is, the incident axes are not enough to determine the nature of parallel lines in geometry. So what we're going to do in this video is actually list three parallel alternatives.  These three alternatives we put on the screen right now, you cannot have all three of them. In fact, you can't even have two of them because they're mutually exclusive. If one of these statements were true, the other statements would have to be false in that geometry. And that's why they're often called parallel alternatives. I should also mention that in axiomatic theory, the word axiom and postulate are really synonyms of each other. You can use them interchangeably. But when one talks about parallel alternatives, the word postulate is typically more used than the word axiom. Why is that? Well, that's really just tradition. And it really comes down to Euclid's book on the elements where he essentially established the modern idea of the axiomatic system studying geometry. With Euclid's geometry, his fifth postulate was a statement about parallel lines. And that postulate has been scrutinized so much that the word postulate is always used when describing parallel axioms. And also it's a literative in English. That's kind of fun, parallel postulate. So you'll probably hear me call that, and they're all listed as parallel postulates, but postulate and axiom, the words mean the same thing. So what are the three parallel postulates that we're going to consider in this lecture series? The first one is known as the elliptic parallel postulate. These names will make a little bit more sense in the future, because in particular the elliptic parallel postulate, the Euclidean parallel postulate, and the hyperbolic parallel postulate, will be sort of the designator for elliptic, Euclidean, and hyperbolic geometries, something we'll define later on. But for the moment, just imagine that this is an axiom, a fifth axiom we could attach to the four incidence axioms and then get a different, a more restrictive geometric theory. The elliptic parallel postulate says that all lines intersect, and another way of saying that is that parallel lines don't exist. Axiom 5 of phano geometry was exactly this, the elliptic parallel postulate. We had the first four axioms, phano geometry, plus this elliptic parallel postulate. The Euclidean parallel postulate says that for every line and every point not on that line, there exists an exactly one parallel line 2L, which contains P. This was exactly axiom 5 of young geometry that we explored previously in this lecture series. This is known as the Euclidean parallel postulate because this is equivalent to Euclid's famous fifth postulate of geometry. In the elements, Euclid gave five postulates for geometry. These are the five rules of geometry, and everything else can be derived from that. Euclid's work in the elements on axiomatic geometry was breakthrough. There's no other contemporary or predecessor to Euclid that we know of that approached geometry in this axiomatic method. I confess that Euclid's methods were not perfect. There were assumptions that Euclid used that were not spelled out in the axiom, so his axiomatic system was incomplete. He didn't have all the axioms on paper. He had five of them, but there were some other implicit axioms he was using in his proofs that weren't stated. That's a big no-no for geometry. Euclid did this thousands of years ago, and so for his age, that was amazing. In modern standards, it's not good enough, but I should mention that his approach to geometry was groundbreaking. His fifth postulate in particular has to do with parallel lines. His fifth postulate is what makes Euclidean geometry Euclidean. It's named after him for a reason. Non-Euclidean geometries can have Euclid's first four postulates, but they don't have the fifth one. Long history of geometry that led into the modern era actually was people believed the fifth postulate to be a theorem of the other four postulates. And, of course, also the invisible postulates he didn't mention. But no one could ever do it because, in fact, Euclid's fifth postulate was independent of the others. You could take Euclid's first four postulates and attach the elliptic parallel postulate or the hyperbolic parallel postulate. Again, Euclid had some gaps in his lodge. You could have to fill in those gaps, but you could fill in those gaps and adopt a different fifth postulate, and you can get a consistent geometry there. Now, I should mention that this version of Euclid's, the Euclidean parallel postulate, it was not actually how Euclid wrote it. This version is actually due to Playfair. Euclid's fifth postulate is expressed a little bit differently, and we'll talk about that in a future lecture. For our purposes in the language of incidence geometry, Playfair's version is a little bit better. And therefore, because, again, you could have had some implications that weren't stated and assumptions that weren't stated. So Playfair's version is a much simpler, cleaner version for the realm of incidence geometry. Then the third parallel postulate that we're going to take on is the hyperbolic parallel postulate, which sounds a lot like the Euclidean parallel postulate, which says that for every line and every point not on L, there exists more than one line parallel to it. So the hyperbolic parallel postulate guarantees the multiplicity of parallel lines. You could have a line with a point off of it, and you could have multiple parallel lines that go through that point. That's what the hyperbolic parallel postulate guarantees. It doesn't necessarily guarantee how many parallel lines there are, but there are more than one parallel line given any point. The elliptic parallel postulate could be rewritten to be in harmony with the structure of these statements here. It could be written to say that for every line and every point not on L, there exists less than one line parallel to it. Well, if you're less than one line, there's zero lines parallel to it, so there exists no parallel lines. I wrote it this way just for the sake of simplicity, but it also is in this situation. So given any line and one point off of the line, how many parallel lines do you have? Do you have less than one? Exactly one are more than one parallel line. Those are these three alternatives. And when you think of that way, you can see why we have these three parallel alternatives. And they are mutually exclusive. You can't have less than one and exactly one parallel lines. You can't have less than one and more than one parallel lines. So these are mutually exclusive. You can't have more than one of them.  We have talked about that, that satisfy these parallel alternatives. Three-point geometry that looks something like this. Three-point geometry is an example of, well, it satisfies the elliptic parallel postulate. All lines intersect each other. That was actually one of the axioms of three-point geometry. Phano geometry, which looks a little bit more sophisticated than, of course, three-point geometry. We get the picture looks like this. Remember, it's the deathly hollows with three elder ones. Not my best drawing of it because these lines should be, we should be going through this part right here. We're going to bend my elder one for the sake of this diagram. But this is also an example of a geometry satisfying the elliptic parallel postulate. All lines intersect each other. That was axiom five. When it comes to the Euclidean parallel postulate, we've seen some examples of geometries that satisfy that. So if we take what we call four-point geometry, we get a picture that looked like this. For which if you take a line and you take a point off the line, there was exactly one parallel to it. If I take this point, there's your parallel line there. If you take a different line, take a point, there was exactly one parallel line. Same thing here. If you take this line and this point, you're going to get that parallel line. Remember, because even on the cross of the diagram, there's no point of intersection there. They are parallel. So four-point geometry is, in fact, it satisfies the Euclidean parallel postulate. It actually was axiom two for the four-point geometry. For young geometry, we also took axiom five for young geometry. That is the Euclidean parallel postulate. And hopefully I can do my best at reconstructing young's geometry on the fly right here. Let's see how well I can do. So we had our horizontal lines. We had our vertical lines. We had these slant lines. One right here. One like this. One like this. And then we had the other slant lines. One like this. One like this. And then, oh, now that I'm almost complete. Oops, sorry, that's not supposed to go there. It's supposed to go here. And then this one is supposed to go here. Nope, not there. Try that again. This is why color coding can help a lot. So, okay, now we get young's geometry. It's just a mess. It's on the screen right now. If you pick any line and a point off the line, there's a unique parallel line to that line. Take a different point, like this one. There's a unique parallel line. If you take, for example, this line and you take a point, you take this line and take a point off this line, there was a unique parallel line to it. No other lines going through this point are parallel to it. So the uniqueness is there. It was one of the axioms. Now, an example that we haven't yet talked about is, well, what's an example of a hyperbolic geometry? An incident's geometry that satisfies the hyperbolic parallel postulate. Now, I haven't mentioned this in the lecture series up to this moment, but in the homework for my students, you have been exploring this geometry, which we call five point geometry. Five point geometry satisfies the hyperbolic parallel postulate. We could draw a picture of a five point geometry by taking points of a pentagram, something like this maybe, a pentagram and a pentagon right there. The star forms a pentagram, the pentagon. This is five point geometry. This is an example of a hyperbolic geometry in that it satisfies the hyperbolic parallel postulate. That's what I mean here. If you take any line like so, and you take a point off the line, I can actually find two lines that are parallel to it. And by the symmetry of the diagram, every point I consider will look something like this. So there are two lines parallel to the given line through that point. So this is not Euclidean. This satisfies the hyperbolic parallel postulate. Now, given five point geometry in three point, four point geometry, I really should clarify that when I say five point, four point, et cetera, right? Well, this is the only three point, this is the only three point incidence geometry. This is not the only four point. This is not the only four point incidence geometry. There's another one which we'll talk about in a later slide. And there's two distinct four point geometries there. And this is not the only five point geometry. There's a couple of those. I'm not going to list all of them right now. But they do belong to a family, which is known as the handshake geometry. Handshake geometry, what it means is a line that only contains two points, because secant C says lines have at least two points. If a line only has two points, we call that a handshake because you can think of it as like as you go around in a meeting and you shake everyone's hand, there's a line between two points if they shake hands. When people shake hands, you can have three people shaking hands at once. That would be weird even without COVID-19. That would be a weird thing to do. And so a handshake is a line with exactly two points on it.  So you take every possible pair, right? And so in handshake geometry, if you take the set HN to denote the handshake geometry within vertices, there's going to be in vertices. And since every line is exactly two points and you have to have a line between two points, the number of lines in handshake geometry is the same as the number of pairs. And so the number of lines in handshake geometry is equal to N choose two, where that's your binomial coefficient N choose two. So for this one, handshake geometry H3, this is what we call three-point geometry. And three choose two is going to give you three of that situation. You have three points, three lines. H4, that is the handshake geometry on four points, that's what we've been calling four-point geometry. This is really the four-point handshake geometry. It has four points and it has four choose too many lines, which would be six. And then lastly, H5, this five-point geometry we've been talking about, this is really five-point handshake geometry. It has five points and it'll have five choose too many lines, which is 10. On the screen, I've now illustrated the six-point handshake geometry. It has six points and it has six choose too many lines there. With six choose two, you're of course going to take six times five divided by two. So you should have 15 lines in that geometry. Handshake geometry with the exception of three-point and four-point handshake geometry. Handshake geometry always satisfies the hyperbolic parallel postulate. Take six-point handshake geometry, for example. Take a line and take a point off the line. Notice that this line right here has two points on it since it's a handshake. And this point right here, I can form a handshake with the N minus two other lines here. Okay, so I have two points in play on the line. Then there's a third point here. So there's three points that are not part of the original line nor part of this point. Let me change the color scheme to make this a little bit better. So we have two points here, one point here. So if I take N minus three, then these three other points can be formed handshakes with the point in question. So I'm going to get three lines parallel to the original line that contained this point. And so I can actually tell you how many parallel lines there's going to be. So in HN, you're going to have N minus three parallel lines to parallel lines to this situation. And so, of course, when you take N minus three, when is that greater than one? Well, that happens when N is greater than four. So five, six, seven, eight. Handshake geometry is going to be hyperbolic when N is greater than four. When it was four, you had Euclidean. When it was less than four, you get elliptic. And you can't have a handshake geometry with only two points because point existence says you need at least three points and handshake H2 would look like this. That's not an incidence geometry.


Thank you very much for the invitation. It's a real pleasure to be here presenting this joint work with Jeff Nussiant. The first thing I would like to say is that the title is quite telling and let me just give an excited debate about data quality and inequality yesterday. I will start to open it for disclaimer. The title as I said is quite telling. I mean, the paper tries to look at what explains the reasons for the rigidity of labor regulation, not only across countries but over time. And we look at the roles of structural reforms as potential determinants of employment regulation rigidity and their impact, the impact of these regulations on growth and inequality. Then inequality will be on the correct side of the regressions according to what we heard yesterday in this paper. Then what is this paper about?  The emphasis here will be on less on inequality and more on this public policies. And we're going to be looking at the labor market institutions, which is obviously a very important topic, and in particular we're going to be looking at one of them. We're not going to be looking at different interactions between very important labor market institutions. We're going to be focusing on one. And the one we're going to be looking at are the laws and regulations. I mean, we're going to be looking at employment protection. I said something about the ceiling site, looking at this EPL index. And the ceiling site is essentially, well, if you care about reform, if you observe changes in this index, that would be an approximation to reform. And of course, if you observe, no change in this index is that would be a good hint that these rigidities are indeed important, or at least long-lasting. Then that's what the paper is about. I mean, can we come up with measures of the rigidity of these labor market regulations over time in the past? And try to explain them, and then go back and look at the implications of these changes in terms of both economic growth and income inequality. Hence, why this paper is in this conference. The contribution of the paper, if any, tries to be twofold. I mean, it's an empirical and a policy contribution. And the policy contribution, I think it's quite clear. I mean, the kind of empirical or academic contribution departs from kind of a caricature of this literature. And I kind of characterize it as basically kind of three features. Most of this literature is confined to the post-1995 period. When not confined to the post-1995 period, it focuses on two regions, which are OECD in Latin America. And third, I mean, this is the third feature I already mentioned, it focuses on levels as opposed to changes. It just occurred to me yesterday that this, if I describe the literature on income distribution, it's possibly a not very unfair caricature. But in any case, I'm talking about EPL, not about income distribution here. Then, the two main objectives. One is to extend the absolutely seminal paper by Botero et al. in 2004 that come up with this index for one point in time. And second, to assess whether or not our effort, our exercise, makes any sense. What's the worth of this exercise? Let me just spell out, because I don't assume that this audience is familiar with this work, at least not at the level of the detail required to follow what we're doing, because we're going to follow this very closely. This is one of the various papers by Djankov Laporta, Lopez de Ceylonis, and Schleifer. This is one of the quality of label one that came out in the quarterly journal in 2004. I'm sure you saw a number of them. This is kind of the theoretical philosophical basis to the doing business project at the World Bank. And this particular paper looks at label, label regulations. It focuses on 85 countries for year 1997. What we do is essentially we use exactly the same methodology. Extend it first for that particular time period to a considerably larger number of countries. They originally have 85. We go to 145, 150 countries, which is almost doubling the sample. And that would have, of course, implications to what kind of... As you can imagine, the countries that are being added, the very bottom of the income per capita distribution that increases the variability, the variance in terms of per capita income levels in this sample, and then enhance changes slightly the potential explanations of these changes. Then what we do is try to extend it backwards all the way to 1945. But the real action starts after 1906, and that's why we cut it out. Objective two, of course, is to assess this new measure. We call it LUNRIC, which is an index of the rigidity of label market regulations. And we do that in a number of ways. We try to replicate the Botero et al. result. They put forward three competing theories, three competing explanations. For those of you familiar with this line of work, the one that comes on top is legal origins. According to not only this paper, but a number of them, the origins of the country legal system plays a determinant role, a number of institutional features. I'll talk a little bit more about it later, but it's the contrast between civil English and French lot traditions where the action is in this particular story. The important thing to say here is that they find legal origin plays a very, very important role. And just the addition of all these countries at the bottom of the per capita income distribution, you can imagine bringing the role of, quite naturally, increases the power of what they call efficiency theory, which is level of development. That's one change that is not very surprising, but follows from the exercise. Then this is the first assessment we provide. The second one, well, now we have this measure over time. Then we see what happens in terms of levels and changes. Then how much inertia is there? Legal theories, legal origins still play a fundamental role in explaining levels over time or changes over time. We find that they do still play a role, but it's a much more nuanced story that we can put forward. We examine changes instead of levels. And because it's a more nuanced story, we need to search for other determinants. In some cases, per capita income disappears. In some cases, there's very little support for legal origins. Then what we do is we embark on a search for potential other determinants. I mean, in a very humble way, trying to assess whether or not this construction exercise, this data construction exercise makes any sense. There's no intention of providing a final theory or final explanation for these changes, but it's just to see whether or not they make some sense. And of course, at the very end, we do also look at the effects. Now we can endogenize the CPL changes. You couldn't before because you have one point in time whether or not they have any effect on growth and economic inequality. I'm going to give you the conclusions because I still have a zillion slides to go, and I'm not going to finish, obviously. They find that legal origins are very powerful explanation. We find that over time, particularly in terms of changes, if you care about labor market reform, legal origins play a much more less strong role. There is some evidence for legal origins, some evidence for the importance of the level of per capita income, but what we find that's quite interesting is that other structural reforms, we look at a number of other, we look at crisis, we look at structural factors, et cetera, and we find that other structural reforms play kind of an interesting role. In particular, trade liberalization seems to have a negative impact on rigidity of labor market regulation, and we have an opposite effect played by financial liberalization, which if you're trying to design reform packages, it's kind of an interesting insight. This is all done on five-year averages for 140 countries. A policymaker shouldn't take this as any sort of guidance, but it highlights the importance of these interactions between reforms and designing packages. The last one, I think, which would be the big interest to this audience, but the relief is that we do provide evidence for what we call the Freemont conjecture, which essentially says that this labor market, rigidity of labor market regulations have very little, it's very ambiguous effect in terms of growth, but they do indeed reduce income inequality and we do find support for that over time in a panel setting, which is obviously something that, if you don't have this set of measures, cannot be done. Anyway, the outline of the talk is introduction and motivation. We took up 15. Yes, excellent. Then I have the real talk that goes, how did we construct land rig? What does it look like? How good is it, this assessment? You know the results already and there are conclusions, maybe this afternoon I can get to that point, conclusions and next steps. I'll fly over these slides now because I presume you know what I'm going. I'm going to measure land rig in three easy steps into one checks and another one is balances. Then we take the Botero methodology and we combine it with a compendium of labor laws that the ILO has generated in the last five or six years. This is Botero, Botero employment law index has four components. I don't have time to go into them in greater detail, but I mean they can be mapped very straightforward manner in this data set. This is the website of the data set, of the not lacks data set and what it is essentially a compendium of labor laws. Okay, then we have different countries and the ILO very kindly classify each law in different areas. For example Australia, we have 2,506 laws since 1945 and they are classified over time in each one of different subjects. The list of countries as you can see is endless. The list of categories is also endless. An important thing for us is that they map into the four elements, into the four components of this index. We have labor contracts, part-time versus full-time contracts is one of the categories. This is for our junior, it's a random example. Cost of including hours of work, I'm sorry. I can't help you, I'm sorry, apologies. Right, hours of work, it's another category and then we have cost of firing is another one and dismissal. We're going to look only at these four boxes, 450 countries. You could kind of do something more refined but this is two guys and 12 research assistants. Okay, I was expecting zero. Okay, all right, plenty of time now, it's going to slow down now. First step then, we start with this EPL. The first thing we do is we know the result. They have like us a very detailed web appendix with a list of these laws and it's like an economics exam now. Imagine, discuss, pick a D, right, it's question one and somebody gives you, okay, this is the assay, this is an A, this is a B, this is a C and this is a D. This is a very kind of candid assessment of this literature and I hope you're getting the gist of it. I mean, there is no way you're going to come up with indexes that try to reflect anything important about labor market rigidity that do not involve a degree of judgment, okay. There are aspects of it that can be easily quantifiable. They are usually the less policy relevant ones, okay. And this is an issue, I mean, if you are very sanguine about data that is simply unavoidable in this literature, okay.  Then what we do is essentially, that's what we have. That's the starting point, okay. We know the laws from Botero. We know the grades that they give to these laws from Botero and we add to that the same laws for that five year period from Netflix, okay. And then we just essentially, we come up with a key, an answer key, okay. Once you have the answer key, we know exactly how it maps, we extend, okay, right.  And then we go back in time, all right, and mark all the exams all the way back to 1960, okay. This is exactly what we do, okay. You know, that's the second step.  And then third step, we just go back.  I mean, we're going to kind of block them in these five year boxes, okay. And then we have, you know, three steps and five steps, actually. One is checks and the other one is balances.  We generate 2000 and 2004 because, relax again, 2004 because of, it's the first vintage World Bank doing business, which is still very much, you know, in this tradition. I mean, I don't know how much you follow that work, but it has changed quite a lot after 2006.  I mean, we're quite happy to see that we can, you know, I mean, I don't know if we're doing something right, but, you know, we're not doing anything different from everybody else. And balances, I mean, it's, you know, Jeff is very keen on Middle East. You know, he's kind of searching the web and really bringing in history to check, to try to check whether or not this indicators make any sense. And I mean, we're still quite happy with them.  How does it look like?  I mean, these are laws. Then, you know, they change very slowly.   This is the first, an important comparison. And it's important for a couple of reasons. First, because in the Botero paper, I mean, it takes, I believe, five or six pages in QJA, okay. Portugal is obviously a French legal-origin system. New Zealand is obviously, or not the typical case of English legal-origin, you know, legal system. And they, you know, get a lot of mileage, finally. Thank you so much. I get a lot of mileage out of this difference, okay. You know, Portugal is much more rigid label market than New Zealand, and you can say, well, you know, does it matter to look at overtime? Well, if you do look overtime, and if you choose, you know, how the point of comparison, you can, you know, draw a very different set of conclusions if you look at the beginning of the sixes, then if you look at 2004. There are a number of individual studies of, we don't know for Portugal, but for New Zealand, we do know individual lawyer efforts to measure, and the behavior of the index is very much like ours, then that's the checks and balances bit, okay.  There's action. This is China, India, and Brazil. You're not going to see it very clearly either. And there are a number of very interesting patterns, and legal-origins, when you start to look at these changes over time, you know, you know, it's less clear whether or not it's that type of pattern emerges, okay. These are the Botero and Etol results. We essentially replicate them. I'll just summarize what we found very quickly. I mean, I have a number of slides, as you can see, and I'm not going to be talking about them. Then there's some indication that it's going to go very fast. There was this, you know, that trade liberalization as a negative impact on labor market reforms and the other effect by financial reforms. And then, oops, oops, okay. Then we tried to, you know, replicate the original results. These are the original results. I'm sorry. This is cross-section, pulled OLS, and you can see it's pretty much, you know, follows it very closely. And then, you know, a couple of sample splits where, you know, there are some interesting differences that I don't have any time to talk about. Then we start to look at changes, and you can see suddenly all the significance from the legal origin starts to disappear, okay. And that's, I mean, what prompted us to look for other determinants. Then we go on and on looking for different determinants and don't find much other than those structural reforms. Okay, I mean, look at different types of crisis. It's going to go very fast. You know, look at different political crisis and factors. And the slides are going to be online. That's why I'm flying. And then we have some evidence on the Freeman conjecture in particular. Okay, it's not moving. It's not my fault. In the sense that on the left-hand side, the first three columns, I mean, you can see that long rig has a negative and significant impact on income inequality. Caveatria, this is weed, not sweet. It's weed true. I mean, then when we send the extended abstract, we're planning to use a number of different measures of income inequality. But I mean, this is the one we have right now. And in the columns four to six, you have the results for growth.  Okay, then for this audience, I mean, you can of course say, oh, we knew this all alone. We haven't seen evidence that, you know, suggests that there is a lot of us or, you know, some strong support for the Freeman conjecture in a cross-country panel setting. And I think this is, we find it interesting, but that obviously just us. Then just summarize if I can. Okay, all right. I really appreciate it. It's extremely generous. Then I think the paper offers a new index of labor market rigidity, legislation rigidity. I mean, it's totally the yure. I mean, I don't think, you know, I don't want anybody to have a different idea. It's a panel since 1960. You know, you can see quite a lot of interesting action. I mean, revisit the original explanations, potential competing explanations for these changes and they find slightly different results from before for reasons that I think are quite clear. I mean, not surprising. And there are two kind of additions to that list of findings. The first is regarding the importance of different reforms in terms of important implications in terms of design of reform packages and the other this evidence supporting the Fremont conjecture. Thank you very much. Apologies for running both.