When I started this podcast, I really didn't know exactly what it would be like. I decided I'd start with the war on drugs and then do the antebellum period through reconstruction and then go from there. But I wasn't really sure what kind of format the podcast would be and in my mind, to begin with, I was thinking more like audio lectures, something you would find in a classroom. But as I got to working on the scripts, I found myself really enjoying diving into the details, the minutiae and the context that you don't ever really get from lectures because it's just too much. The podcast has taken on more of a storytelling narrative and I found that I like this format a lot and I hope the rest of you do as well. But it means that the six episodes I had originally planned for the drug war turned into twelve episodes. And the twelve episodes I had originally planned for the antebellum years turned into twenty-four episodes. Because I've been able to maintain my one episode per week rate of production so far, that's nine full months. When I started outlining the series on the Civil War itself, I realized what a big project I was about to try to take on. I mean, of course, I knew that this was a pretty historically dense four years, but sometimes you don't really think about how true that is until you start diving into the details the way I have been over the past few months going over the 1850s.  If I ever do a series on World War II, that could easily prove much more enormous, but that's only because I would want to include the relevant history of all the other countries involved. But the war from 1861 to 1865 is pure United States history. So I found myself in a dilemma.  I could definitely expedite it by reducing it all to lecture format, giving the bullet points of the more significant events, Gettysburg and Antietam and all that. But that's the kind of thing you can find anywhere. Just as I hope I demonstrated in the previous series on the 1850s, what I tried to do anyway was show that there is so much more to this history than we are normally taught. And I would like to do that again with the Civil War, at least to the best of my limited ability. If I'm going to tackle a major event like the Civil War, I want to do it justice. I'm going to go ahead and say that I'm going to fail. No matter how much I include, there will always be things left out. Since the Civil War ended in 1865, there have been so many books published about it that they amount to more than one book a day, something like 65,000 books to date, just on those four years of American history. There are still questions to be answered and questions that can never be answered and questions that still have yet to be asked. No matter how much I or any of us learn about this conflict, there will always be so much more that we don't know. And mix this with the tremendous emotional attachment people have to this history that still rages into the present. There are still people who take sides in the conflict, almost as if the war is still being waged, and people feel the need to defend the Union or defend the Confederacy and this certainly colors the history that's being told. I don't want to do this, but I certainly have my views on things biased by my own value judgments about secession and aggression and war and government, and I've no doubt that my personal judgments will seep through at times, no matter how much I try to avoid it. I've no doubt I'm going to leave something out that other people consider of great importance. That's just the nature of tackling the history of the Civil War.  There are wonderful single volume and multi-volume histories of the Civil War, but there will never be a definitive history and this series will certainly not be a definitive history either. But the enduring controversy of the Civil War is exactly what makes it a topic worth taking on in any historical podcast, let alone one whose title embraces controversial history. But for me to do this series as much justice as my limited abilities will allow, it's going to be a long run. I've already made a basic sketch for the war from Fort Sumter to Lincoln's assassination, and without me finding new things or realizing that there's a bigger story about some event than I previously realized, this is the kind of thing that led me to adding a six-week foray into the Nicaragua in the last season, for instance. Even without any of that, I believe that this season will take me at least a year to get through if I'm going to dive into the details that I enjoy. So I appreciate everybody who listens to the show regularly and who enjoys the historical minutiae the way that I do, and I hope that you all find this investment in time to be worth it. I'm Chris Calton, and this is the Misesense to Toot podcast historical controversies. This season is pretty much going to pick up right where the last season left off. Since I'm not taking breaks between seasons, it almost seems weird that I'm dividing these two up the way that I am, and I get that. Part of it is just because dividing them up helps me to organize the history when I'm outlining the episodes, but that really isn't the primary reason I'm treating the Civil War history as a separate story than the antebellum years. Obviously they're related, but there is a very significant divide between the two things, which is the difference between secession on the one hand and war on the other. People treat the antebellum years as a lead up to the war, and in a broad sense, that's obviously true. Chronology alone makes that true. But in a more substantial sense, the antebellum years were only the build up to secession. William Freeling's famous two volume history, The Road to Disunion, aptly demonstrates this recognition in its title. It is not the road to war. And that's because war is certainly not an inevitable outcome of disunion. Whatever opinion we may have about southern secession, whether it was good or bad, justified or unjustified, regardless of what their motivations for secession were, none of that makes war the inevitable outcome of secession. Ludwig von Mises in his great book Theory and History, as well as in Human Action and the Ultimate Foundations of Economic Science, Mises reminds us that history is a science of human action. He says there are two sciences of human action, praxeology and history. Praxeology being the a priori logical deductive science of human action, which includes economics as its most developed sub-discipline, is the one most people are familiar with if they're familiar with Mises at all. The other science of human action is history, employing the empirical method Mises called thymology. In his earlier works such as Human Action, he just calls this understanding. But Mises' assertion that history is a science of human action seems pedantic when we state it that plainly. Of course, history is a study of human action. It seems so obvious, but in practice this is not commonly how history is treated. Whether consciously or not, historians often treat history as mechanical. We have the benefit of hindsight and it makes it seem so obvious that what occurred must have occurred as a result of the events that came before it. This is true in the sense that human beings do not exist in a vacuum and the actions we take are influenced by our environment, our culture, our ideas. Our actions are influenced by what happened in the past to some degree or another. But the point that Mises was making is that our actions are still choices that we make. They are choices that we make even though we could have made other choices. Sam Harris in his essay Free Will talks about philosophical determinism. Basically he's arguing that Free Will is an illusion. He uses the example of his choice to drink coffee the morning that he wrote the essay and he says sure I could have chosen to drink tea but I chose to drink coffee and it's meaningless to say that I could have chosen otherwise. Mises would entirely disagree. When looking at history or any science of human action, Mises would say that it is incredibly meaningful to say that human beings could have made different choices than they did. And when studying history we want to know why they made the choices they did. We can hardly answer the question of why some historical figure did something if we consider it meaningless to say they could have done anything else. Because our question relates to what influence they're reasoning. What were the ends they sought? Why did they value those ends? What were the means they chose in pursuit of those ends? And why did they think those means would be the most effective? Were their decisions correct? Did they successfully achieve their desired goals? These are the broad questions of history and they are empty if we consider human beings to be acting without some conception of Free Will. Ludwig von Mises rejected Sam Harris's notion of Free Will. Mises called it fatalistic determinism but this is the concept that we typically just call determinism. Mises said that instead historians should adopt the philosophy of activist determinism. This would be one that acknowledges that there are things in reality outside of our control. The laws of physics operate regardless of the choices we make and as a result our environment and our perception of the world is something that human beings take into account when making their decisions. The goals they pursue and the means they employ in pursuit of their goals. But and this is key. In Mises' activist determinism human beings still have Free Will or at least Mises says that we should assume they do. He doesn't take a hard philosophical stance on the doctrine of Free Will but he believed that as long as we couldn't perfectly explain human volition we can understand the world better if we assume that Free Will exists. So with this notion of activist determinism the historian has to consider the context of the episode. The events unfolding around the historical figures, the cultural environment in which they lived, the state of their knowledge of the universe and so on. All of this exerts an influence on the decisions people make but human beings still possess their own volition and their actions are determined by their own personal ideas and for historical change to take place at all ideas must have some degree of originality. So to bring this back around to the division between secession and war and why I think it's important to divide the two seasons is because the previous season on the antebellum history is a lengthy attempt to answer the question of why secession took place. Why did the south finally decide to break away from the union? Fundamentally I believe that it's silly to contend that anything other than slavery was the primary reason for the first wave of secession. There may have been other variables involved. Monocosal historical explanations are almost certainly incorrect in any situation but slavery was quite clearly the primary element. But historian Eric Foner, pretty much the leading living scholar on the reconstruction era, he reminds us that the question of what caused secession is different than the question what caused the war. These are separate questions and they have separate answers because human beings make choices regarding the actions they take and because it is not meaningless to say that they could have chosen otherwise because we do consider it important to understand what options they rejected and why they rejected them as much as it is to understand what options they acted upon and why. We have to attempt to understand why people in the north and the south made the decisions to fight. Why did Lincoln and his administration decide to go to war? It is not meaningless to say that he could have let the south secede in peace as many people in the north thought he should have done. Why did poor non-slave holding whites fight on behalf of the Confederacy? I've already covered in previous episodes the fact that it is entirely plausible and quite clear from the evidence that even southerners who did not own slaves believed that the institution should not be abolished for various reasons and as such many non-slave holders supported disunion because they valued the continuation of slavery. This is empirically true from the records even though it is not universally true. But the answers to questions like why did Lincoln wage war and why did poor Confederate soldiers fight cannot be answered by pointing to slavery and that is because the decision to go to war as a response to southern secession is a very different thing from the decision to secede in the first place it is a different decision made by different people for different reasons. The simple answers which are not complete answers by virtue of their simplicity are found in the very words of the people involved. Lincoln made clear that he considered secession to be illegal and that he was not fighting to free the slaves but to maintain the union. Those are his words that can be placed in the context of the time with an understanding of Lincoln's personal history northern sentiment and his wartime actions that can demonstrate that his stance on unionism seems to be the honest motivation behind his actions. Whatever Lincoln's personal views on slavery and I'll be talking about the complexities of trying to pin down Lincoln's personal views versus his political views in later episodes it does seem clear that he was willing to fight and preservation of the union and professional historians are pretty much in consensus about this. The idea that Lincoln fought to free the slaves is the product of public school education more than it is professional researchers despite their possible generosity to Lincoln in their own value judgments and the answer to why did poor non-slave holding Confederate soldiers fight is even more difficult to answer because each soldier can have his own personal motivations but the oversimplified generality that seems to best explain this question is the off-quoted story of one early Confederate prisoner of war. This anecdote is found in the two most highly read Civil War histories Shelby Foote's three volume history of the war as well as James McPherson's one volume history the battle cry of freedom. Shelby Foote is generally considered to be more sympathetic to the South and McPherson is probably more sympathetic to the North but both agree on this motive. I'll read the passage from Shelby Foote's answer to this question. I don't usually quote anything that isn't a primary source but Foote put it well. He wrote quote perhaps the best definition of the conflict was given in conversation by a civilian James M. Mason of Virginia. Foote quotes Mason. I look upon it then sir as a war of sentiment and opinion by one form of society against another form of society. Foote then goes on to write. No soldier would have argued with this but a few would have found it satisfactory. They wanted something more immediate and less comprehensive. The formulation of some such definition and identification became the problem of opposing statesmen. Meanwhile perhaps no soldier in either army gave a better answer. One more readily understandable to his fellow soldiers at any rate than a ragged Virginia private pounded on by the Northerners in a retreat. What are you fighting for anyhow? His captors asked him looking at him. They were genuinely puzzled for he obviously owned no slaves and seemingly could have little interest in states rights or even independence. I'm fighting because you're down here. He said. End quote. I'm fighting because you're down here. This is one simple statement from only a single soldier but these words hold powerful meaning and that's one reason why this is such a commonly cited anecdote. Secession was primarily driven by slavery. The second wave of secession as we will see had greater motivations at play but the first catalyzing wave of secession was clearly motivated by slavery above all else and non-slave holders supported this for various reasons. Some enjoyed the higher status of a free but poor white over an enslaved black and many Southerners were afraid of living among free blacks even though there were already free blacks in the south. Many people in the south weren't so much concerned with the abolition of slavery per se but they saw it as a slippery slope. The first history of Fort Sumter was written by a man who had been stationed there named Wiley Crawford. He was a unionist but he despised Lincoln and he despised abolitionists. He believed that Lincoln would be a puppet of abolitionists and they would free the slaves and this was dangerous he thought because the next step after abolition was equal rights for blacks. He wrote quote any proposition to lift the Negro to the social level of the white man is to me monstrous and insane. End quote. Some non-slave holding Southerners simply believed that slavery was a right, a constitutional right and any attack on slavery was by extension an attack on rights in general. The reasons for non-slave holders supporting slavery are numerous and complex and vary from person to person and of course there were Southerners who opposed slavery such as the abolitionist South Carolinians, the Grimke sisters and more moderately the Missouri Senator Thomas Hart Benton but slavery was the primary motivation for secession nonetheless but for somebody to pick up a gun and risk their life for slavery that's a much harder argument to make even for somebody who owns slaves and the records left behind by soldiers give us very different reasons for their willingness to fight James McPherson in a less well known work from the battle cry of freedom studied the personal letters and diaries of civil war soldiers from both armies this is his book for cause and comrades why men fought in the civil war and in that book he found that two-thirds of the soldiers from both sides genuinely believed that fighting was their patriotic duty they believed that they were upholding the legacy of the revolutionary war heroes the northern soldiers believing they were preserving the government that the founding fathers established and the Southerners believed they were upholding the right of secession of independence of self-government that compelled the revolutionary war veterans to fight so many decades before the idea that the war was fought over slavery is simply not true sure there were a handful of union soldiers here and there who genuinely did enlist in the union army because of their opposition to slavery but these people would be outliers they were not representative of the union cause and the war could not have been fought at all if this were the only motivation for participation in the south there were politicians and other wealthy slaveholders who were more concerned with the preservation of slavery than anything else but even among this demographic slavery is not a driving motivation that explains the question of why the war was fought very well as the war went on as we will see in much later episodes there were plans to offer slaves the opportunity for freedom in exchange for service in the military there was recognition that a Confederate victory might require the ending of slavery or lead to it at the very least these ideas were never a matter of consensus they were matters of debate but the fact that they were debated is meaningful other people the most prominent example being Robert E. Lee believed that slavery was not a cause worthy of fighting a war and Lee said he would rather free all the slaves in the south than fight the war but he fought for the Confederacy because he like many Southerners considered himself duty bound to his state first he fought as a Virginian more than he fought as a Confederate and he was not fighting to preserve slavery though he was a slave owner himself I say all this not because I want to make a definitive argument as to why the war was fought today this is a question that will be present throughout the series and it will change and evolve as the war progresses so it's a question to keep in mind but not one that we should consider settled by this or any other single episode you may or may not find my answers convincing at the conclusion of the season but these are among the questions that I will have in mind as I'm telling this history because it involves the motivation for the actions that the various historical figures took over these four years so secession in the war involved distinct questions with distinct answers and all too often people including historians let this mechanistic deterministic narrative of history seep in with the logic that because slavery triggered secession and secession triggered the war it is logical to say that slavery triggered the war this interpretation is simply bad history this is effectively algebraic thinking it's the transitive property of algebra if a equals b and b equals c then a must logically equal c that's true in math but it's nonsense in history because it negates the complicating element of human volition individual autonomy free will choice making ideologies and so on so I split these seasons up partly because I want to highlight the division between these events and abandon this mechanistic algebraic view of the history of secession and the civil war there's another misconception in the history that I want to address as well before we start talking about the war and that's the term civil war as a label for this conflict I often hear people argue that calling the American civil war a civil war is a misnomer it's an accurate the war these people argue was not technically a civil war at all and then of course other people disagree so is the term civil war a misnomer? in this case I will speak in greater absolutes because we're dealing with a precisely defined term which makes the question definitively answerable yes the term is absolutely a misnomer the term civil war refers to a war for control of a specific government that is the technical definition of the term regardless of which side of the conflict you might favor and regardless of which side you favor it is beyond dispute that the confederacy was not fighting for control of the union government this is simply the objective facts of the matter I've heard people try to defend the term civil war in the context of this technical definition some people have pointed out that the confederacy could have marched on Washington DC in this case in which we're debating the semantics of the word rather than the motivation for human action it actually is meaningless to say that the confederacy could have done this the fact is they did not attempt to invade Washington DC there was at one point some officers advocating this but the idea was rejected by Jefferson Davis and even their idea wasn't actually take over the union government it was just to take control of all territory in which slavery was legal and Washington DC was included in this but even had this taken place it would have been a territorial war not a civil war but regardless the war was not fought over control of the same government and calling the war a civil war is indeed inaccurate but the most common alternative to the term civil war is also inaccurate among people who do not want to use a technically inaccurate term I typically hear the alternative the war between the states this is just as much of a misnomer as civil war it was not a war between the states it was a war between two distinct confederations two distinct central governments in which various states were members it was not a war between Georgia and New York and Arkansas and Maine it was a war between the union government and the confederate government calling it a war between the states is at least as much of a misnomer as calling it a civil war another common alternative is the war of northern aggression this is pretty much a blatantly pro-southern term the problem I take with it is not one of historical accuracy but one rather of subjective value judgment the term assumes that the north was the aggressor now that may be true but it's a value judgment whether it's true or not and as we will see in the next episode the matter of who the aggressor was is a lot more complex than people realize the standard interpretation is that the south fired the first shots which is technically historically true and therefore they're the aggressor but most people when defining aggression will consider the threat of violence to be legitimately classified as aggression and therefore a legitimate threat is the initiation of aggression in the legal world this is the distinction between assault and battery right assault is the cocking of your fist and battery is landing the punch if I understand these concepts correctly so the question of who was the aggressor cannot be answered according to most definitions of aggression by simply saying who fired the first shot that's clearly an oversimplification the response to the accusation that the south fired first is usually met by people pointing out that Fort Sumter was in confederate territory and by having union soldiers in the fort southerners felt threatened this is also historically true but this brings up the more complex question of what constitutes a legitimate threat we can't define aggressive threats on the mere notion of somebody feeling threatened because any individual can feel however they want about anything this is the same fallacy of making laws against offensive things since anybody can be offended by anything it doesn't mean that offense or threat are non-real it just means that they are subjectively felt by an individual so there is some necessary gray area and questions about legitimate threats Fort Sumter was on union-owned land and of course some libertarians will counter that the land wasn't legitimately owned because of Locke and Homesteading principle but that isn't helpful historically because the people involved in Fort Sumter were not basing their actions on these modern libertarian interpretations of John Locke but it's also true that the federal land was in confederate territory it's true that confederate appointees attempted to meet with the cabinet of the Buchanan and Lincoln administrations to arrange a peaceful sediment of the territorial dispute regarding union-government lands in confederate territory and it's true that Lincoln would not allow the negotiations to take place because he believed it would be seen as a tacit admission of the legitimacy of secession it's true that Lincoln allowed the troops at Fort Sumter to be resupplied and it's true that he informed the confederate officials that he would not be supplying them with any weapons or ammunition but it's also true that this was a lie and the ship was carrying a secret cache of weapons and they were also carrying 200 troops that the confederacy knew about so did this constitute a legitimate threat? well that can still depend on the personal views of the person judging it but the historical details should be enough to demonstrate that the question is much more complicated than people typically make it out to be and again in the next episode I'm going to go much deeper into the story and we'll see even more complications but my point here is that there is an element of subjectivity in calling either side the aggressor and for that reason calling the war the war of northern aggression is a value laden title meaning that it depends on your personal views of legitimate aggression there's nothing wrong with that as a personal matter but if you're wanting to argue that this is a better objective name for the war being the name that everybody should adopt you're necessarily saying that your personal value judgments should apply to everybody and I don't believe that's a good approach to history so I don't like the term war of northern aggression regardless of whether or not I believe the north to have been the aggressors the final common alternative I hear is the war for southern independence at first glance many people also take this one as a south-centric value laden title for the war but I think this one actually is the most objectively accurate the reason it seems at first to be value laden is because people have a tendency to view independence as a positive thing they tend to have a pre-existing value judgment on the idea of political independence in other words but whether or not something constitutes political independence is not a matter of subjectivity this can be objectively defined and apply to the concept of southern secession and the war that followed the reality is even if you personally don't believe that southern secession was a right you might believe it was unconstitutional or that because it was motivated by slavery it was wrong or simply that you're a patriot who hates the idea of our nation being split in two regardless of any of these views it is still true by definition that what the confederacy was fighting for was political independence from the union government that is a simple clear historical fact so it may be the case that the people who use that term tend to be more sympathetic to the south but that's a matter of happenstance it is still true that on technical definitional grounds the war for southern independence is the most accurate term for the war that I've yet heard proposed but as you've probably noticed if you've been listening to this podcast I don't use the term war for southern independence I use the term civil war that has actually been the merit of some criticism I've seen on articles I've written in comments on some earlier episodes so it may be something that I should have addressed earlier why do I choose to use the technically inaccurate term the civil war the simple answer is because the term serves the function I need which is to communicate to people what military conflict I'm referring to when talking to people who are raised in the United States if you say the civil war they aren't going to be confused about what war I'm referring to some people who like to harp about the misnomer which I find to be often a way of avoiding the actual history will fame credulity but this is just a silly argumentation tactic griping about the misnomer serves no historical significance it can be instructive I think to talk about the misnomer as a way of bringing up questions about aggression and motivation as I hope I've done here because those are all legitimate questions but at the end of the day if I want to talk about the history of the conflict I choose the term that people in this country are universally familiar with fixating on the technical semantics of the word as a distraction from the history it's also worth mentioning on this point that the adoption of the misnomer civil war is not as far as I can tell a matter of propaganda as some people have given me the impression they believe the term civil war was on people's lips a decade before the war actually started it was just the term of the conflict that people anticipated as a result of the slavery question in my episode on the resistance at christiana I cited a newspaper headline from 1851 that claimed that the resistance marked the first shots fired of the civil war being the first instance I know of that the term civil war was used obviously historically we do not mark that as the starting point of the actual war but it does demonstrate that usage of the term and how it got misapplied to this conflict furthermore even though I don't think the term civil war is a propaganda title the north did have a term for the war that was a matter of propaganda employed to drum up support for the union but that term was war of rebellion this is what the Lincoln administration was calling the war trying to underscore their argument that secession was legally impossible and the actions of the southern states constituted rebellion which they wanted to paint the conflict as because it opened up legal arguments for certain actions that they took such as the suspension of habeas corpus though there were still constitutional problems with the suspension of habeas corpus and other actions by Lincoln under the pretense of suppressing rebellion but I'll cover all that in later episodes so in short the term civil war came about as a matter of history and the title stuck simply because that's what people knew it as it serves the purpose we need in history not because it's technically accurate but because it is the name given to the conflict that people are universally familiar with at least in this country so it is technically true that the civil war as a proper noun was not a civil war as a lowercase general noun but the technical language in my opinion is of relatively little importance and I will continue to refer to the war as the civil war because I consider that the best term for communicating this history to a general audience so I'll wrap this episode up and the amount of time I spent simply prefacing the history of the civil war probably represents the lengthy history we are about to undertake this is a dense four years with a great deal of contentious historical questions as well as a lot of compelling stories that are worth telling just for the entertainment value and I want to do this history the justice it deserves so we should be prepared for a long run the story of course begins usually with the bombardment of Fort Sumter but before the bombardment of Fort Sumter which took place in April of 1861 there was a great deal going on in the politics of the Union, of the Confederacy and even for several weeks of South Carolina which stood as a lone new nation and it is that nation of South Carolina when it succeeded before other southern states joined it that we will start discussing in the next episode for more content like this visit mesus.org


Greif iawn. The first item of business today is Time for Reflection and our Time for Reflection leader is the Rev. Morris Calachan Parish Priestess and John the Baptist, Port Glasgow. A years ago, I read a short story, and it was about a city called Omalas. Omalas was one of those fabled places that is beautiful, peaceful and prosperous, and all of its citizens wrth gwrs, yw'r lleion. Yn y bethau i'r byw yn yma'r eich bwlygu o'r gweithgol, yn ymddangos o'r rhaid o'r gyllid yn y profiad yn y gweld, rydyn ni'n ddiddordeb yn awrwyr, maen nhw'n ddiddordeb o'r ddiddordeb yn 10 yn yr ysbryd, ond yn yn 6. Mae'r ysbryd yn y llwyddiad ar y dyfodol, ac mae'n rhaid o'r rhaid i'r llwyddiad, no whinever speaks to this child.  The child though hasn't always been in this room, but although it cries and screams, sometimes says, I will be good, but nobody replies to this and the door is locked again. The people of Omelass all know the child's there. They know it has to be there. For a sort of contract exists for every child in that city between the ages of eight and 12, it's taken into the room to see this child. It's explained to all of them that everything good in the city, the happiness, the beauty, the prosperity, it all depends on that child being kept in this room in these conditions. The youngsters are of course very upset when they hear this, but the vast majority learn to live with it, except that every so often one of the youngsters does not go home. They leave the city and they don't go back. They walk away from Omelass. The contract of Omelass isn't just a fable, it's a reality of the world. Pictures show it better than words. A dead, drowned Syrian toddler in the arms of a Greek soldier because Europe's borders have become a deadly barrier. A burnt-out tower block in a wealthy London borough because cost competes with safety and furbishing poor people's homes sees that a full of plastic melting ice caps starving polar bears and deadly droughts because we need our lifestyle, my good at the expense of others misery, the contract of Omelass. Certainly, Omelass is more of a mindset than a place. Good religions always see this, good politics, good humanity have always seen this. It's all connected. The kingdom of God within me connects with the kingdom in you, the Buddha nature in you, the conscience in you, everyone, everything, it all matters or it's all diminished. Discount one child, discount a polar bear and then we're back in Omelass.


yna'r gwaith ar y cyfnod ymlaen. Yn ymlaen, yna Llan south o Codwm Llan, ac mae'n Chris Crisione a Tim Chilvers yn ymdweud. Yn ymdweud, Chris. Fy enw'r fawr, ddweud ymdweud, ymdweud, ymdweud. Yn ymdweud, mae'n fawr. Yn ymdweud, Chris Crisione. Yn ymdweud ymdweud ymdweud ymdweud ymdweud. A rwy'n gweithio'n gweithio'r gweithio'r gweithio'r Gweithio'r Tim Chilvers gan y bydd per macaronu llan nesaf. Dyna'r amlynedd ac er ôl i eich fulio iawn i chi Hyrwyr Cywr醬ais hynna'rifer y gall fod yn ei wycheth y Llan south o Codwm Llan. Roedd fy hun hynod eich lastiadau cyntaf, a bobl gwneud foundations iwer ym Uni朝 a oedd rhaid ei hynny addysg Abertaol. Rhaid, ymddw'n enthyg iawn, ond dyfnydd yn digwydd Shirell, a chael y bydd yn gweithio. Rwy'n defnyddio i'r cyd-gwysig i'r cyd-gwysig, mae'n nhw'n gweithio. Tim wediなるほど bryd y gwirionedd a clywed o'r pethau mewn cyd-gwysig, wedi bod yn ffysg y cyd-gwysig i'r cyd-gwysig i'r llyfrnedd y Llyfrgellau. Mae'n dweud i gyda'r cyd-gwysig i'r cyd-gwysig i'r cyd-gwysig, a ydych chi'n gweld â'i ffordd oherwydd mae'n golygu gyda'r cyd-gwysig can ni allu cyd ros i. Os mai fyddwn Parsel yn gyd curfodoli? Yn agilydd beth ydym isbê arall, wedi cael nodi.  Yn wedi'i o центр I guaranteeiem ddechrau siarad yma yn y dedarb Silbysbysysaidd CymruOOP. but the A is quite obvious in any case. That is for appropriate commercial uses set out in that policy. Area B for elements about the recreation and ecological mitigation. And then within our control we have what's known as area C or as many people will know the lakes and so that's down here it's just the two lakes with obviously the TA lake above that that's out of our control. And so plans are for wider generation. I'll move on to the next slide and so it's no secret that we've been at this for a while. And it's been a thoroughly detailed process, many iterations of proposals from mixed use to what we see here on site or here in the proposals now. The good thing that's come out of that slightly sort of protracted process is the sheer volume of engagement that we've had with local residents. And so now we feel that this scheme is in a place that reflects their wants and desires out of such an asset really on the lakes for the most part, but also what they want to see on area A and B. And so that that is, you know, a sort of run for of where we have been. We've had free public consultations over the years that I've most certainly been part of, and every time we've had a great deal of interaction with local residents. And so that has led to what we currently see. So I'm not sure what the noise is now, but handily, I'll pass on to Tim to run over the vision for the land south of Coulthamside. Great. Thanks, Chris. Yeah, if you want to pop down the slide to the next one, that'd be great. Thank you. And yeah, good evening everyone. As Chris has said, the context behind this, these sort of three parcels of which we own is the local plan, the 2018 local plan, so it's up to date. And it sets a very clear framework for the council's expectations are in terms of the development and type of uses that need to come forward and the interaction between these parcels as well because it's an area that is quite naturally severed with the rail line and various uses. So there's really an emphasis on making this as linked as it can be. So parcel a there you can see, we can run through the other slides but parcel a is now coming forward. We're putting it forward for a commercial use. Historically, we had proffered and looked to come forward with more of a mixed use offering. Obviously, the desire was to see a commercial only scheme and that's what we are looking to do. Parcel B then will be used wholly for ecological ecology mitigation, bearing in mind the various designations of the land in the area and the fact that we need to offset biodiversity requirements. And the lakes, you know, clearly there's, there's a long history of the lakes and problems associated with what could be a really, really good asset for the local community. We're as keen as anyone to get this sorted for the long term, and to make these a real usable place that residents can enjoy. And so the scheme would undertake, you know, quite a significant programme of improvements to the lakes and make them safe and accessible and we will open those up so that members of the public can make use of them, as I say in a safe way. So we just run through the next slide, of course that will give people a slightly more zoomed in prospect of what we're looking at. So parcel A, which is that L shaped area, which obviously has the tins running through the middle. There'll be a commercial uses on both elements of the land there with a grade separated crossing so that there's no conflict between pedestrians and cyclists and any kind of vehicular movements. This, this area we would be applying for an outline so what you see there is purely illustrative as a to give a flavour of what could come forward. But really, you know the details of some something that come forward as part of reserve matters. On to the next slide please Chris. Parcel B, as I said earlier, we're really looking to do a light touch proposal here of biodiversity mitigation. So really not a huge amount of change to what's currently in situ on the site, but there will be enhancements to habitats predominately for invertebrate species. And then the most exciting element of the scheme from our perspective and and no doubt from the communities as well is the lakes. And so this would be a part of the site we apply for in detail so that there's no kind of time lag or delay between, you know what we're putting forward, hopefully obtaining a permission that's implementable. We can bring forward the works that are required to bring the lakes forward. And, and really for these lakes we are. We're not looking to over engineer anything at this stage and we don't want to kind of preempt what the community might want to bring forward. You know in the years ahead here, because the way we see is this is a local asset for informal recreation and use only we don't want it to be. And nor do I think the community really want it to be a major draw or kind of traffic generator or anything like that because there are other country parks in the vicinity of this site which fulfill that role and don't have the physical constraints at this particular parcel of land does. And that there you can see, for example, just a zoom in of some of the plans that are emerging just to show that these are detailed plans. As I said earlier, not over engineers are very much timber natural materials, nothing intrusive or urban and look and feel. And I just just two images which show what the what the current condition of the lakes are in and really we just got to build on what's there because they really are incredible on site at the moment aside from the Angling Club and certain permits for birdwatching and the like. It's closed off to people and that's that's a sad state of affairs. It makes it right for trespass and you know the sooner we can resolve this I think the better really. Next steps very quickly are we've we've put in for an EIA scoping opinion, just to make sure that the technical evidence based upon which we're basing our plans is is robust and and satisfactory. You explain EIA please. Of course can environmental impact assessment. So procedure you go through for major applications where there's, you know, more severe potential environmental impacts than a normal application of a normal scale. So you just have to go into more detail in assessing traffic and quality noise, those kind of considerations. The planning application itself we've been we've been working closely with the with the city council and the highways authority also through pre app and we will be looking to submit the application. Next month and obviously that builds on many many years of consultation and engagement with the public to shape where we've got to. That public engagement will obviously continue and it will continue through throughout the course of the determination and they'll be engagement in relation to the lakes which obviously we've got to manage and we're very sensitive to in the months ahead and as the and as the weather warms up but that last bullet point there I think it is absolutely crucial from from our perspective is, you know, in bringing forward a for that local plan commercial development. What that will enable us to do is the early and upfront delivery and improvements of the lakes. And that that is key, I think. There was Councillor Daunton a question submitted in advance that related to trespass on the lakes and Tim's touched on that. And I think in early and upfront delivery of that parcel. And really the focus is on sort of early prevention clearly in summer is upon us thick and fast. And so we will take the necessary steps to manage that and I can go into detail and in the question time. And in effect the way we see the solution to the, the trespass to the antisocial behavior and so on is through opening up lakes and so that's our sort of central mission and aim at this point in time. The last slide is just to say, you know, we'd be happy to take questions. If you do want more detailed. If you have any descriptions on the proposals, please do visit our website, because that will effectively go through what we've just presented but also some more information on top of that. And our contact details are also on there as well so we're more than happy to take questions via email. Thank you, Tim. And thank you, Chris. And just before we go to the questions in the chat, there was another question sent in in advance. Would Anderson's please stop referring to the lakes as Burnside Lakes. A possible name might be for example Cherry Hinton Lakes so that's something for you to. I mean, so we've, we've, we've been having this, this conversation for years and our central sort of focus when we sort of labelled it Burnside Lakes way back when and was to make sure that people weren't calling it the Romsey beach because that was attracting hundreds of visitors on weekends in the summer. We were moaned at for calling it Cambridge Lakes we were moaned at for calling it Cherry Hinton Lakes, all for various different reasons and we so we settled on Burnside. However, moving forward, we are speaking with local representatives, as well as residents about what they want to call the lakes as they come forward to become the urban country park and I think that that should be where our sort of efforts are on making sure that what it's called in this area is something that's reflective of local opinion. We're certainly live to the issue of associated with the Burnside reference so so that's that's eminently sensible and we'll make sure that's taken into account. Okay thank you. And so if you could take your presentation down now we'll go on to the questions and Chris Chris Carter, and if I could take the first question first. Yes please. Yep. So, Ruth, it's Claire Daunton here and it's Daunton D-A-U-N-T-O-N, not Dawson. And if we can have another meeting in the near future well I should just explain that because of COVID we missed two meetings last year. And so we do realise that we've got a lot to get through in this session and we normally meet every three to four months and we will now be getting back to that schedule. As I mentioned at the beginning, alternating between city leading and south cams leading. So we should be meeting more often than we have done in the recent past. Over to you now Chris Chris Carter. Thank you. Yes. Further point from Ruth. The future of the lakes should be tied up with the future of Snakey Path and of the Brook. I've suggested in the past that the path needs to be remodelled with perhaps additional land taken from the school to permit a widening what options are currently in play. I believe the city and county councils are taking forward proposals to remodel and look at Snakey Path and some widening there. We've had discussions with them on that and I understand that they've got monies set aside and they're looking at initiatives to do exactly that. Obviously it's land that we don't control. I think there's every chance that we may be asked to make some kind of offsite mitigation contribution to it. I think that's open for discussion. We certainly wouldn't say no if it was reasonable and put to us. Thank you. In addition to that, we've had meetings before with the friends of the Cherry Hinton Brook, very conscious of their opinions on that part of the area. For us, I think that the proposals we see to date do respect the Cherry Hinton Brook and the special nature of it, but also in creating that cycle and pedestrian access at the northern part of the lakes parcel. That will effectively take away a pinch point and a sort of one central access that we see at the moment. In that respect, I'd argue that the proposals are reflective of those discussions. There was a question sent in by David Brooks on the improvement to Snakey Path and I think if you've not covered that in your answer, you'll be taking that up later on, I think, from the written question. Thank you. Yes, the next question. What is the current situation with the methane from the old refuse tip? Yes, so we've got, you know, an incredibly extensive amount of monitoring going on and it has been going on for many, many years now. So, you know, the gas report will form part of the very detailed geo environmental report and monitoring for form part of the application. It's not actually gassing much at all anymore, just due to its age so actually it's really, you know, very, very settled and you know gas mitigation measures will be put in place as a matter of course, both during any construction and obviously post construction as well. But in terms of actually what's happening in the ground at the moment, nothing from the monitoring is indicating anything of particular concern. Thank you. The next question is, are you able to comment on where the access points will be for the lakes, vehicles and people? Yeah, yeah, I mean I alluded to it in my last answer but we've tried to shift the emphasis to access from the tins that's the most actively used area or sorry cycle network. And so we want to allow ready access from that area. The car park that exists at the end of Burnside that will still remain but purely for use by the private fishing club and obviously access for those who need to maintain the lakes going forward. So that will be the only vehicular access to site. Okay, thank you. The remaining comments relate to the name and I think we've covered that already so chair that's the end of the questions as I see them. Thank you. And we had one written question sent in advance from Claire Castle, and if Claire is here in the meeting, I think colleagues from the Greater Cambridge Partnership Transport will take that question and get in touch with you get back to you about that. Thank you, Chris.


The lethal dose of hydrogen cyanide gas which has the formula HCN for an adult is about 120 milligrams. First of all I want to know what's the volume at STP of 120 milligrams of HCN and then we'll work out how many molecules of HCN are in this volume. So let's take this first problem first. We're going from a mass to a volume. So that's our strategy. The conversion factors we're going to need are the molar mass of hydrogen cyanide and the molar volume of the gas at STP which we know is 22.4 litres per mole. Now there's one other thing. This mass is expressed in milligrams not in grams. So we're going to have to include a unit conversion to get that mass into grams so that the units will cancel out nicely with the molar mass which is in grams per mole. So let's work this through step by step. First we write down what we know, 120 milligrams of HCN and then we're going to convert this into grams. So we want the conversion factor for milligrams to grams and we know that there are 1000 milligrams in one gram. So I'm going to put the milligrams on the bottom so that they cancel and the grams on the top. Alright so if I were to calculate this out now it would give me this mass in grams. But I'm going to keep going so that I can make it one single calculation at the end which is slightly more efficient. Okay I have changed my mass from milligrams to grams. The next step is to change the mass in grams to moles. So I need the molar mass as a conversion. I haven't calculated the molar mass yet so I'm going to need to go back and do that. And I'm going to need the molar masses of hydrogen, carbon and nitrogen which gives me the molar mass of 27.026 grams per mole. Okay there's my conversion factor. Now I need to put it into my calculation. I have grams on the top. I want to cancel out the grams. So the conversion factor is going to be written with its grams on the bottom and moles on the top. Alright I've now converted my mass into moles. The last step of my conversion is to convert the moles into volume using the molar volume as a conversion factor. I have moles but I want to go to liters so I want the moles to cancel. So I'm going to write the conversion factor with the liters part on the top and the moles part on the bottom. Moles cancel and I'm left with liters. Now I run through the calculation. And when I plug that into the calculator I don't forget to put the bottom in brackets so that the order of operations is preserved. And that gives me the answer of 0.09946 liters. I go back to check my sig figs. The original mass that I was given has only two sig figs so I need to round this off. Becomes 0.099 liters which is about 100 mls of gas which really isn't very much.


And then also, and it said, thanks to the job of chemically. OK, so now we start our first talk of the day. Actually, lecture of the day, taking a series of questions. Thank you. Thank you. A little walk, no? Yes? OK, can you hear me? No. No? Can you hear me? Yes? No? OK, like this, no? Can you hear me? OK, what if you come closer to me?  Anyway, so can you hear me? It's OK now? I mean, I have the feeling it doesn't work. It's not working. Do you want me to take the? It's working? Is it working? Yes? OK. OK, if you can't hear me, then raise your arm on the. OK, it's desperate. OK, I will try to speak louder. OK, so I would like first to thank Tamara Grava for putting all this work and organizing this event, making it possible. And so my course will be about Dyson Trigger Equation and Random Matrices. So the point is that random matrices provide a great example of complicated system where the eigenvalues are in very strong interactions. And somehow there was a need to get new tools to study them. And Dyson Trigger Equation are one of them. And this is one tool which I hope to convince you is very useful. And today I will show you how it works, how you can use this equation, this set of equations to analyze the so-called Gaussian ensembles. So the GUE, the GUE matrix. So this is somehow the simplest example that we can consider. And the GUE matrix is just a matrix which is a Hermitian with IID and independent entries, entries above the diagonal, so x, n, i, j are independent. And they are Gaussian. So they are complex in the case of the GUE. So this is a Gaussian complex with variance 1 over n. So if i is smaller than j, and so you can think about that as a sum of two independent Gaussian. And they are real complex, they are real Gaussian with covariance 1 over n on the diagonal. OK, so that's the basic example of random matrices we'd like to study. And what you would like to understand is a spectrum of these kind of matrices. And what is nice with the GUE ensemble is that you have an explicit joint law. So if you let lambda 1, lambda n be Ziegen values, then you can see that the distribution is quite explicit and is given by what is called a Coulomb gas law. Sum of lambda i squared. And here you have some normalization. OK, so this, if you would have chosen real entries here instead of complex, you would get the same type of expression. But you would have to multiply to replace here the exponent 2 by beta and here beta over 4. So beta equals 1 if the entries are real. And 2 otherwise. OK, but the point is that this kind of distribution is quite complicated to study, typically, because you have an interaction which is very strong, which is given by this Coulomb gas law. And this Coulomb gas actually is also interesting on its own and can be generalized to a higher dimension, for instance, by taking complex numbers here. And what we would like to find is how to, what I want to show you is how to analyze this kind of distribution by using the Dyson-Schwinger equations. OK, the type of question I will address here is mainly about macroscopic asymptotics. So what we would like to show is that there is a convergence of the distribution of the Ziegen values. So if you take test function f, can you show that this is going to converge? So this is one of the goal. And this is going to converge almost surely. And then the next question is about the fluctuations. So if you remove the limit, can you show that this converges in distribution toward some Gaussian distribution? OK, so yes. So n is going to infinity. So it's for this distribution, under this distribution. So usually what you do is you use Borel-Cantelli-Lemma to show almost all convergence. So this means that somehow you, of course, I'm not going to construct for you the sequence which is going to converge almost surely, but you have from Borel-Cantelli-Lemma a canonical way to extend your probability measure so that you give sense to almost all convergence. So that's really the meaning of the convergence. OK, so that's the goal. And the point is that, as I said, it's not easy to prove this kind of theorem because you have this strong interaction. And so Kertjo and Son, I think, was the first to use. So I think it's 97. Use a Dyson-Schwinger equation to prove this kind of convergence. Well, in a more general context, here instead of lambda square, you have a potential. So this is what is called matrix models. And what I want to show you today is how to use for the GUI. And what I will do in the next lecture is first to show you how to prove it for matrix model in perturbative situations. So this is matrix models. It's typically this kind of model, but where you have replaced the lambda square by a more general potential. Then, eventually, this can be several matrices. And then I will show you how to throw that out. In this situation, there are two settings which are quite different, which is the so-called one-cut situation where the limiting measure E of f, so this, you have to think this is replaced by, eventually, by V. So sigma will depend on V. So this means that V of x is something like epsilon x square plus some perturbation. So you are not far from the case of the GUI. So in this case, so you have the one-cut situation. So this is a perturbative situation. And then you have the non-perturbative situation where you take a general V. And then in this case, you have two types of difficulty. The case where the limiting measure here that we will show to exist, so sigma is some sigma of V, has connected support. And the case where it's disconnected. So this is a several-cut. And the last thing I will discuss in this class is an extension to discrete tiling, to discrete setting, to discrete measures, and random tiling. OK, so that's somehow the plan of what I want to discuss here. There are lecture notes. And I will not always do all the details, but I will try to give you at least the main ideas. And of course, you should not hesitate to stop me if you don't understand, because my understanding is that there are people from very different backgrounds. So you should really feel comfortable to ask questions. OK, so that's somehow what you want to do, is to understand this kind of questions. And to do that, as I said, we will use these Dyson-Schringer equations. And the idea that we will get equations for this type of observables under this type of distribution. And we will then solve this equation to eventually prove this kind of theorem. Let me tell you more precisely the result we want to prove for the GUI. So what I want to prove for the GUI is the following thing. So the expectation of 1 over n, the trace of xn to the k, I want to show that this is, I can expand it as a function of the dimension. And what I want to prove is that if I look at any family of moments, where ki are some integer numbers, then this will converge towards a Gaussian joint, so p joint Gaussian variables with socovions, which I will denote c, k, i, kj. So this is what I'm going to prove for you. And this will answer this question, at least for functions which are polynomial. So mgk is the number of graphs that, let's say, maps of genius g built over a vertex of degree k. So what is a map? It's a graph, a connected graph, that you can draw. You can properly embed onto a surface. And what I say that the minimal genius of such a surface has to be g. So you can do a drawing. So here I have a vertex of k of degree k. So k is equal to 6.  So here you see that this is genius 0. You can draw this on the plane. But of course, for instance, if I do this, we will get a genius 1. And ckL, so the covariance of the Gaussian process, is going to be the number of planar maps. So this means that genius is 0, built over a vertex of degree k and 1 of degree l. So that's what we want to prove. So here you have to be careful that when you do the counting, you can think about the half edges here as labelled, because you have drawn them on the surface. And you have actually, here I rooted. I should have rooted maps. And so this gives you a full expression for this. This is the so-called Arer-Zage formula. And you can reconcile this with this question I asked at the beginning by the following exercise, which is that if you look at the m0 of k, it's going to be the integral of x k under the semicircular law. So where sigma is the square root of 4 minus x square dx 1 over pi. So why? Oops, nobody said anything. But this should have gone to 0 with this normalization. You should not renormalize, get something on trivial. So you can show that this is true. And so what this implies over these results, all this theorem, what this theorem implies is that the expectation of the integral of 1 over n, the sum of f lambda i, this converges to the integral of f of x is sigma of x. If you take f to be a polynomial. So by density of polynomial function in the set of continuous function, you can extend this to continuous function. So here, this is only L1 convergence. But you can see, in fact, that you can get almost no convergence by estimating the covariance. We said to use Porel-Cantelli lemma. And so you can use this. So this implies a fegrant point. This implies that 1 over n, the trace minus x expectation, where so this is finite. This is going to be smaller than some ck over n squared, because this converges towards a Gaussian variable, once I have multiplied by n. And so by Borel-Cantelli lemma, this implies that this goes to 0 almost surely. So then you can also extend this to a continuous function. So this proves this. And then if you look at the second question, well, if you just take any polynomial function, you just have to sum one of these. And so the second point, maybe I should write this A and B. So B implies that the trace of any polynomial function, so this converges towards some Gaussian variable with some covariance which depends on P. I should have said that this is centered. In fact, if you look at geo-imatrices, so if you take the real entries, you will not get something which is centered. But OK, when you take geo-imatrices, you get a centered Gaussian process. OK, so is there any question? Or can I go to the proof of this kind of thing by using the Eisen-Sringer equation? Yes? Here? Yeah, OK. So the third phase here, so you can see that here, well, it's very bad in drawing. But you should add that to somebody doing geometry. But OK, so you can think about here that somehow I can draw this vertex on this surface. And when I do that, it's properly embedded in the sense that the edges do not cross anymore. Clearly, when I embed it on the plane, it's not properly embedded because the edges are going to cross. But so the point is that here, your graph, you can always draw them on a surface in such a way that the edges do not cross. So of course, and then of course, you could imagine that you are going to draw them in a much more complicated surface, eventually with something like this.  So the genus of the graph is really the minimal genius of the surface in which you can draw it. So you should not do that. Yes, so this is the Catalan numbers. I do not remember the formula. I'm sure that lots of people do here, but yeah, exactly. So you can compute the genius by saying that 2 minus 2j is, so let's see, number. So I have to remember number of vertices. So here there is only one. So here there are two, but plus number of faces, minus number of edges. So exactly. So you can compute the genius by this formula. So here you have only one vertex. The number of faces are the part, the number of parts that you, if you look at this embedding, for instance, when you cut along the edges, you will get faces. And the number of edges, so here you had 6 half edges, but after the matching, you have only three edges. You can compute the, yeah. So the Ckl is, so maybe I can take this from again. So you have, let's say, two vertices. Actually, I could also take even here, but the total number need to be paired so that it's non-zero.  So for instance, I have this, something like this. And so this has to be plan R to contribute to this number. I'm counting all these possible matching so that the result is plan R. Okay, okay, so now let me discuss how to prove that. So the original way that was used was simply to express all this in terms of the Gaussian variables of the entries just by using the formula of the trace. And you could also do that here and compute the moments. And compute the, actually the idea will be to compute the moments of this guy and show it converges to the moments of this guy. And again, if you have convergence in moments, it implies convergence in law. Okay, so the limit is a Gaussian variable. So you could do all this by just expanding everything in terms of the entries. But as I said, I want to generalize this strategy to a more complicated system, and then there is no a priori definition in terms of independent entries. So I will show you how to prove this by using Dyson-Tringer equation. Okay, so first I have to say what is Dyson-Tringer, what are the Dyson-Tringer equation? In this case, Dyson-Tringer equation. Okay, so for the lemma, that one, if I look at my moments, I will define this as m and k, then this will be the expectation of the sum L equals zero to k minus two of one over n, the trace of xn L, one over n, trace of xn k minus L minus two. So that's the first one, and the more general one is that so if I set, I will set yn of L to be the trace of xn L minus its expectation. Then if I look at the expectation of the trace of xn k one times the product of yk i, i equals two to p. Of course, I will not have the room to write it, okay? So this will be the expectation of, yeah, I should, yeah, let me go over there because otherwise you will not be able to read it. So the expectation of the trace of xn k one pi of equal to k i. So these are any kind of choice of integers. So this will be the expectation of, so the sum L equals zero to k minus two, one over n, the trace xn L, one over n, the trace xn k minus L minus two times the product of the yk i, plus the sum from i equal two to p of the expectation of one over n, the trace xn k one plus k one plus k i minus two times the product of g different from i of y kj. Okay, so what are these equations? So that's, these are equations. So I have two sets of equations, which are an equation on the product of the expectation of moments. Okay, my observables, all these trace of x to the k, and what I'm giving you with these equations is some equation on only these observables, the expectation of these observables. So the point which makes the GUI much easier than any other system is that you can see that that's somehow a recursive equation in this case because if I look at the total degree in the xn, here I have the total degree which is sum k i, and here I have lower degree. If I look at the total degree, if I sum all the degree, I have the sum of k i minus two and here as well. For you see actually it's an inductive, it's an equation which is inductive and the expectation of the moment, and so in fact it defines uniquely all these moments just because it's inductive. So it's very natural that I am able to analyze it at the end to show you this type of result. Okay, however again what I'm going to do now is to show you how to analyze it asymptotically because this is somehow the way I will proceed in other more complicated situations. So further proof maybe of this Dyson-Tringer equation so it's integration by parts. And to do that you just have to notice that when you have GUI entries, so if you want to do integration by parts, so if you take the entry ij to the expectation and you take any kind of function of the other entries, all the entries. Okay, so you have to remember that this xij is a complex Gaussian, risk of variance was over n. So you do integration by parts and what you find is that this is going to be the derivative of f with respect to, and this is where you have to be careful, xji. Okay, so if you have a complex, just one real Gaussian variable, it's well known that Gaussian variables are characterized by the integration by part formula. Okay, so that's the usual thing. Here you just have to be careful that here you have gi and here you have ij because just it's complex. Okay, and when it's real, it's still true because it's ij and gi. So you just have a factor one over two coming because I took, no, actually you don't have a factor one over two in this case. Okay, so that's the formula of integration by parts. So how can I use it to prove, for instance, well, I can prove directly my business formula. So I want to get an equation for this guy. What I just do is that, yeah. Okay, so I take a function f, which is smooth, and with the, yeah, infinite support. Yeah, I mean, any kind of smooth function. I mean, if you don't like it written like this, you just should think about the fact that this, because here you have the derivative of this guy, minus the derivative of this guy, this is going to be f prime x just by integration by parts on the, so the parts that you are maybe worried about is just this one. Okay, and when you go from minus infinity to plus infinity, it's just zero. So it's just this written in terms of the entries of, okay, so that's important because actually we will do a lot of integration by parts. So now if I want to apply it to get a formula for this, what I do is that I just write that this is sum over the ij of xij, and then I have xa k minus one g i, okay, okay, product of the ykl. And now I am going to do integration by parts with respect to this guy. So what I get is the sum, so I put the sum outside. I will have the one over n, and the expectation of the derivative with respect to sji of xn k minus one g i, the product of the ykl, okay. So now to conclude, I need to compute these derivatives. Okay, so it's not very complicated to compute this derivative because you just have, you're just dealing with polynomials in your random variables. So if you have something like this, no, it's not a good choice of, okay. If you try to differentiate something like this, what you will get is just the sum over the place in the polynomial that you will differentiate. So it will be xn m, so sj. S l minus m minus one, i t. And the sum, yeah. The sum of all the possible m from zero to l minus one. Okay, so we should use that to compute this, the derivative of this guy and the derivative of this guy. What you see that the derivative, if you apply this to, so it's g i, so this will be the sum of xn m, g g, xn l minus m minus one, i i. And when you differentiate this guy, so l, so what you will get is the sum over, so you have to think that you're taking the sum of the derivative of x, so maybe I should write it, okay. So this is just a trace, okay. So you use this formula, the sum of m and the sum of s, and then you can make the summation of s and what you get is just l xl minus one and ij. And so when you put these two formula inside here, okay, you get exactly this formula. This term is coming from the differential of xl and g i because you are going to sum over g and i. And this term is going to come from this derivative because you have to remember that you are multiplying by this guy, xn k minus one g i. Okay, so that's just differential and actually another interesting thing is to do this when you have several different random matrices independent and you take instead of xl, x to the l words in these several matrices and you can do exactly the same kind of computation in this case, so the several matrix case is exactly the same. Okay, so now I have still 20 minutes, so I want to show you how to analyze this equation. Everybody understood the derivation, it's okay. And so how do you analyze these equations? Well, the first thing is to see that, as I said this, in this case, the Dyson-Tringer equation give you really an equation with a unique solution. In particular, you can derive two a priori estimates, which is rich or crucial, which is further concentration for the lemma, is that for all k, there exists ck and dk finite, such that independently independent of n, such that you can bond your moments and you can also bond the covariance. And so that's, sorry, concentration and compactness somehow. So this is somehow the compactness and this is a concentration of measure because it shows you that the trace is very close from its expectation in moments. And so the proof is very easy, so it's just by induction over, so k and the sum of the ki. So how do you do that? You look first at the case where this is zero or one. So if it's zero or one, it's very easy because you get zero. Okay. Sum ki equals zero, one, ck is equal to dk equal, well actually, c zero. c zero is one, c one is zero and d zero, well d zero is d one is zero. And then you assume you have shown this bond at four k and the sum of ki smaller than k and you put it back in your equations. And so what you see that this, you can recenter it, so what you get is a covariance. Okay, so maybe I can show that. So you get from one that mn of k.  Okay, and again what you see that you are doing the induction on the sum of the coefficients, so here you are reducing them from by two. So if you have proven this estimates previously, you see that this is smaller than dk minus two and this is also going to be smaller than the sum of the cl ck minus l minus two. So it's going to be bounded. So by induction, mn k is bounded. So it's smaller than the sum. I can put that the l ck minus l minus two plus dk minus two times k minus two, which I put to be ck. And similarly for the expectation of the yl because I have this formula, I recenter it with the expectation. You can show it with the expectation of yk i. So this is going to be this guy times the product of the yk i minus its expectation. So minus the expectation of the sum of one over n trace xn l trace of xn k minus l minus two times the expectation of the product plus the extra term, which is a sum from i equal two to p of the expectation of one over n, the trace of xn a1 plus ki minus two times this product. And now you just write in this right hand side that the trace of xk is just yk plus mn k. And you can see that the right hand side will only depends on quantities that you already bounded. So by induction, you can show that this is also going to be bounded. All right, so that's good. So in the next example, I will discuss it will never be possible to deduce from the Deysen-Schringer equation this kind of bound, but we will have other tools to do it. But once we have the Deysen-Schringer, this is bound, the idea that we can analyze asymptotically the equations. Okay, so how do we do that? Well, if I come back here, for instance, once I have this uniform bound on this moment, I know this is going to be small. So I know asymptotically that I will have, okay, so I have no more blackboards, it's terrible. So I know asymptotically that I will have an equation for mn, okay? So I have mn k, which is the sum of mn l, mn k minus l minus two, plus something which is a further one over n square. So now I can prove by induction that this is going to converge. I know that mn zero is equal to one, mn one is equal to zero, and by induction, mn k is going to converge to mk, which is solution of mk, which is the sum of ml, mk minus l minus two. Okay, and there exists a unique solution, so that's the point also that you have a unique solution. And now if you want, you can find out that this is this number of planar maps, because this is the same induction relation. So this is m zero k, and the way you can see that this m zero k satisfies the same induction relation is by looking at your description of m zero k, and you see you want to count the number of possible matching so that this is drawn on the sphere, and so what you do is that you look at the place where this would be matched, and then what you see is that once you have matched the root, you obtain two planar maps. And this time with a vertex of degree, which is here l, and here, so it's the remaining vertices, which is m, so k minus l minus two.  Okay, so this is just to say that this limiting equation has a unique solution, and because it's, and it is also an equation which is satisfied by this number m zero l. Okay, now we can do the same thing for the covariance, for instance. Okay, so for the covariance, so here I started to write the equation, so I have the expectation of yk, yl, which is the expectation of one over n to the thumb. I think I put an extra one over n, sorry, again. Going to be the sum of the trace of x to the m, trace of xk minus m minus two, yl minus, so the expectation for the product of the expectation of this times the expectation of this, but which is zero in this case, okay, because yl is centered, and plus the expectation of the one over n, the one over n, the trace of xk plus l minus two. Okay, and then what you do is that you recenter these guys to get just something which depends on yl on the m. So what you get is a sum of mn, m, mnk minus m minus two, times, well, this expectation, so this is zero. And then the expectation of, so we'll have mnm times the covariance of this guy, k minus m minus two, yl, and then mnk minus m minus two, the expectation of ym, yl, and plus at the end, and here I forgot l, plus l over n, mnk plus l minus two. Okay, so here I think I forgot something, so it's, let's see, trace, so this is zero, okay, this is zero because this is centered, and here what I see that I have the covariance, but again with a smaller exponent, zero as well, and so I can see that by induction, I can again show the convergence, and what we get, what we get is that the expectation of yk, yl will converge to some quantity which is ckl, which satisfy the equation that this, so this term, and this term are actually the same because you sum, so it will be m, m, m, it's not very nice, s, the covariance of k minus s minus two, and l plus l mk plus l minus two. Okay, so it's the same thing, on now again you can play the same game and see that the number of planar maps that you can build over two vertices of degree k and l will satisfy this very same equation.  So that's, and now you can continue, so maybe I think my time is more or less complete, oh no, I still have five minutes, so you can continue for instance for if you want to compute m and k minus its limit, okay? And then maybe I'm not going to do it, but imagine you want to do that while you suppressed m, k, e, and then you're going to subtract also the limit. You recenter with respect to the limit, and again by induction, you prove that this difference, once you normalize it by n square, which is the size of this error term, will convert towards some induction relation, on this induction relation will be just the induction relation which is also satisfied by maps, which this time are of genius one. And now you can continue like this, I mean it's done in the notes to show that if you look at the general polynomials in the yk, they will converge towards the moments for the Gaussian variables. Okay, so I think you got the idea, I mean it's just a bit painful to do all this computation on the blackboard, but what I wanted to show you that because it's very easy in this case, it's just induction. And still it allows you to get quite nice results in terms of enumeration of maps and why the topological recursion appear in this context. So the topological recursion are in a very basic form, this type of induction relation where you see genius enumeration of all maps of any genius driven by this kind of equations. And so next time I want to show you the very same ideas generalize to much more complicated questions, and namely so next time I think I will do a perturbative cases where you don't have Gaussian matrices, but you have something which is not too far, and where we can use the same kind of ideas. Thank you very much.


Spring Cleaning is here and Appalachian Wireless has the deal to get you started. Get a Samsung Galaxy S8 for a penny or a Galaxy S8 Plus for only $89.99 on the region's best network. Better service, bigger savings, that's today's Appalachian Wireless. So your agreement requires you store for details. The Chatteroy Church of God hosted the annual Mingo County Special Olympics today. Every school in the county brought a group of athletes to the historic Williamson Memorial Fieldhouse to participate. Each student competes in three games. There's a first, second and third place winner, each student leaves with a medal. It gives those students that don't get to play a regular sport, this is their day. They get to come out and shine, everybody cheers for them, so I think they need this. The Mingo County Special Olympics has been around for several decades. This is the third year the Chatteroy Church of God has hosted. They say each year the crowd grows and it's exciting for those competing. Members of our church, they will come just to cheer them on and I know that this year we have a lot more parents and volunteers coming out. So it's just a great atmosphere for them and they love it. I just think it's awesome getting to compete in these Olympics, getting to see some people that I've never seen before. Some I have seen before. I'm just pretty happy to be here and I actually have competed a few times. I'm just proud of everyone who's competed today and I'm proud of all my family and friends who have supported me. So guys, if you're watching this, hi! Mingo Central High School and Tug Valley High School students as well as members of the church volunteer during the Mingo County Special Olympics. In Williamson, Shelby Porter, EKB News.


What's going on guys got Kyle here with Layton sports cards, and we are ripping this is three boxes for Joshua G We've got one twenty twenty two twenty twenty three Don Russ basketball fast break We've got one twenty twenty two twenty three court Kings basketball, and we've got one twenty twenty two prism draft picks basketball Good luck. Mr. Joshua. We'll start with the draft picks here. I'm getting pretty close to full guys I don't know that we are yet. I'm getting pretty close. I've got about an hour and a half left About an hour and a half left. All righty. Good luck. Joshua Righty. Good luck, sir. Let's see a palo here Start with a palo. Let's end with palo. Let's just palo everywhere Silver Larry Bird Indiana State and our first auto is gonna be Keyante George still at Baylor there on the Silver Auto Not number Keyante George Auto. I believe he's still at Baylor. I don't know if he graduated this year, but he was last year There's a LaRavia hyper Rookie got Orlando Robinson Red Rookie that one is number two two ninety nine and we've got a blue variation Jason Tatum This color match on the Tatum there to one ninety nine Jane Hardy base rookie Too scared to send it Randy. That's fair man. That's fair They you do hear some some horror stories sometimes, but I've never had a problem with shipping on eBay or anything Silver is BI and our auto is gonna be Paul Atkinson, Jr. Out of the Irish, Notre Dame Paul Atkinson, Jr. On the blue auto that is number two one forty nine Hyper of Kareem. We got Isaiah Thomas blue blue wave two forty nine Shade and sharp. We've got a silver brilliant Steph Curry for Davidson there Looking like a high schooler when he played for Davidson Looking like a high schooler a couple years in the NBA as well, but He's lighting it up. So it didn't matter. There's J. Dubb. We got a silver Jalen Brown out of Cal and This is gonna be Ron Harper, Jr. On the auto out of Rutgers number to 75 blue ice Ron Harper, Jr. And Ron Harper, Jr. And Scotty Pippin, Jr. In this class got a hyper Christian Brown This is Jean Montero, rookie blue. It's a one ninety nine. Murray. There's a chit base I'm not Cooper. I'm not. I don't think so. I don't believe Forrest has any in the in the mixer later There's tie-tie Washington Silver rookie and our last auto is gonna be Sasha Stefanovic Sasha Stefanovic out of Purdue Boiler maker there on the Penmanship Silver auto not numbered Dwayne Wade hyper we've got a shea blue cracked ice ice color match there for Kentucky big blue to 99 Jordan Walsh rated prospect That is Jabari Smith fireworks hyper Mr. Bari Keegan Murray base and a Devin Booker We'll go to the court Kings now for you here. Good luck Joshua some court Kings I'll see it level four Palo something really nice You Refresh the orders again We might be full guys. We might be getting close to full People must get a box or two in just to close us out. I could do that But we are getting pretty dang close got about an hour and a half here left. Good luck on the court Kings First up. We have our base. We got Andrew Wiggins We've got Garland and giddy and our first red is gonna be Luca on the watercolors numbered one of 149 That's a Luca red watercolor there So 149 we've got number to 75. This is oh This is auto masterstrokes auto of John Lucas Throwback there for the Rockets on the masterstrokes auto. That is definitely a throwback That one is 21 out of 75 and we've got game use Jersey. This one is gonna be LeBron James nice one there Artistic endeavors on the game use LeBron Jersey Definitely a Lakers Jersey there with the purple Definitely cannot be Cleveland or heat with that one nice LeBron game worn not numbered Take that Then we've got a watercolors Zach Levine This is Steph Curry on the paint by numbers short print there nice Steph Don't see these very often paint by numbers Steph Curry Take that one as well There you go, Joshua Curry paint by numbers and the LeBron game used We got a Blake Wesley level one rookie and Johnny Davis on the back level two Alrighty now. We just got the prism fast break or sorry optic fast break Good luck here Joshua. Sure. We got the right one. Yeah Yeah, not bad dude not bad the uh got the game use LeBron That uh that paint by number step is pretty pretty short printed. I don't think I've even seen one yet Don't know what they do or anything, but I know they're pretty short printed in that set Nice box there for sure a lot of cards in here a lot of cards in this one There's a Bryce McGowan's For the Hornets and we've got a Christian brawn That one is numbered 17 of 25 nice hit there on the pink pink disco rated rookie Could be a world champion here in just a few days about a week or so Christian brawn there to 25 very nice hit Nice little number rookie there Didn't idea redemption Redemption Kenneth Lofton We've got a disco Jay Sean Tate. I'm not numbered Christopher Den Whitty Rui And our redemption It is gonna be ready of rookie signatures fast break pink. I think that's the 25 again car 218 of Patrick Baldwin, Jr Warriors rated rookie there on the auto Believe that should be the 25 as well. Um the base rated rookies the 25 so I'd imagine Nice Patrick Baldwin there for the Warriors rookie got a Rui on the back I hope that was another redemption. He's just a turned around card here No reason at all There's disco all-stars and beat and cats and a Darius Basely Yeah, I agree Steve optic is a lot of fun, man both the optics I know that football has a little more chase with the downtown and stuff with the basketball you can hit freakin hard here, man You can hit hard There's a Caleb Houston rated rookie and a Christian brawn on the base disco rated rookie now You base disco rated rookie Bring an Ingram like a low number rated rookie auto of a big guy like really really sells The low number in general Rated rookies also sell. It's a really fun product. We got purple disco Mike Connelly to 99 and Disco Jimmy Harden Dylan Brooks Yeah, this is the fast break variation as well Cooper. There is the the hobby as well On this one comes with the discos there's some of knots. We've got Jeremy Grant number to 99 purple disco to 99 Jimmy buckets Hemi Tyrese Martin. We've got a hollow Luca Luca on Schroeder There's a shade on shark base rated rookie Bran on and we got a disco Kumminga Devin Vassel go Knowles Throw that one in there. It's a Christian Coloco rated rookie We've got optic of Otto Porter and a disco Devin Vassel go Knowles Got it in there twice. Let's go And last pack for you. Good luck Joshua Really nice couple hits in this box so far a couple boxes Jalen Duren how you doing? And this is going to be Jalen Brown on the blue disco to close us out number to 49 Jalen Brown potential free agent going to go somewhere else I don't know if it's potential for you. I think he is a free agent but uh Potentially going somewhere else All right, Joshua that will do it for your three box break there. Thank you so much. We'll get it right out to you