Ranger Bill, warrior of the woodland, struggling against extreme odds, traveling dangerous trails, showing rare courage in the face of disaster, in the air, on horseback, or in a screaming squad car. Ranger Bill, his mind alert, a ready smile, unswerving, loyal to his mission, and all this in exchange for the satisfaction and pride of a job well done. There's something about a police officer pounding a beat at night that gives everyone a real sense of security. He walks along in the dark with his lead-weighted nightstick dangling readily from his hand while he stops here and there to check locked doors to make sure they're doing their job. Every once in a while he flashes his light into some dark corner to make sure that only the dark of night is there. The officer on the beat also watches homes to make sure there's no suspicious smoke coming out or people trying to break in. And then he's an awfully nice fellow to meet if you're walking home late at night. Now, in naughty pine, there isn't much in the way of excitement on the night beat, but officers O'Rourke and Ryan walk their beats just as carefully. Let's find out what happens on this night in the story River of Fire. Come on, Patrick, this is the halfway mark on the bridge, me boy. And the rulebook says you got to walk to the half mark. Ryan, you're a hard man. It's too bad you ever learned to read. You'll drive me to retiring by reciting that rulebook every time you look me squarely in the eye. Come on, Patrick, me boy, you can make it if you try. All right, are you happy now? I'm sure glad you never made sergeant. Say, and what's the matter with your nose? It's jumping around like a rabbit.  Smell what? Fuel oil. Certainly I smell it. Do you think my nose is stopped up? It's coming from one of them barges tied along the dock upstream.  Sure, and so's the breeze flat foot. You're standing downwind at the barge. Maybe you're right for once in your life. If you ever know the time, I wasn't. Take it easy, Patrick, me boy, on your next round.  Use your whistle or phone for a squad. Remember that for yourself, and stop smelling so good. Sure, now me aching feet give me more trouble than me nose. Too warm hearted Irish policeman having a bit of chin music at the end of their beat before they start back. Let's follow Pat as he slowly walks along, giving everything the once over. Wait a minute, Pat stopped. Has he seen something he doesn't like? No, he's just standing there. No, he's turning back. Pat's walking quickly now, back toward the river. Something's on his mind. Something's disturbing him. He's not letting it go by as a passing thought. Let's follow Pat as he heads back toward the bridge. Ryan, what are you doing back here? I might be asking you the same thing, all right. You got the river on your mind too? That I have. Let's go down and have a look. Come on. Flash your light on the water. A few lils smell as strong as day old fish. Now I have to agree with that. The river's covered with oil. And that it is, Milad. The whole thing is covered. And those barges must be leaking. Let's have a look. Barges? Where's the stuff coming from? Now, if I knew the answer to that, I'd be worth a million dollars right now. It's coming from up the river, sure as I'm standing here. The pipeline's over the river. You don't suppose it sprung a leak, do you? Where else could it come from? Let's pull the box over there and get the boys hot on it. Come on, Ryan. We've got to sound the alarm. One spark and this will be a river of fire. What's all the excitement about? Yeah. It's a fine time of me getting people out of bed. That's the way I felt until Pat and Ryan showed me that river. Well, let's take a look. Time the top ranger got here. Hello, Pat. Hello, Ryan. Time for them running to you, Bill. That's what it is. The top of the morning or the bottom of the night. I'm not sure which. Ha, now there's a youngster for you. Full of fire no matter how little sleep. Say, Bill, can you smell it? I'll say I can. Fuel oil. How bad is it? I'll take a look across the river. You follow the beam of me, flashlight. There's a regular blanket of the stuff floating on top of the water. Must be a couple of inches thick. You said it, pal. Have you found out where it's coming from? No, not yet. Pat and Ryan think it might be coming from the pipeline where it's bridged across the river. It didn't leak it in town. You're probably right. Come on, pal. Let's pick up Stumpy and Gray Wolf and take a look at the pipeline bridge. Yes, sir. I'll have the fire engines flood the river with water and try to disperse this stuff down rapidly. Right. You better send cars around informing the people of the danger, even though you'll wake them out of a sound sleep. Make sure there isn't any fire of any kind nearby. What are you going to do about that fire way over yonder? Huh? Where? The lightning. Looks like a storm coming on. And how? We've got to try and get that leak stopped before the storm gets here. All right. Let's go. Please. The river is covered with fuel oil, and the situation is very dangerous. You can help by staying in your homes until this emergency is over. Please do not go down to the river to sightsee. It's too dangerous trying to disperse the oil downstream. This is the sheriff speaking. If you refuse to cooperate, I'll have to ask the governor to establish martial law and to send troops into town to keep you home. Great. And this won't be necessary. Thank you. Naughty Pine Dispatcher calling Junction City. Naughty Pine Dispatcher calling Junction City. Come in. Over. Junction City Police. What's up, Naughty Pine? We've got a river covered with fuel oil, and it's moving your way. Naughty Pine Sheriff wishes you to notify Central City. Say, you fellas got your hands full. What's leaking? We think it's the pipeline. Man, that's not good. Pass the word to the Central City Police. Thanks for the water. Sonny, that's me. Pretty good size hole. I guess we all are thinking the same thing, fellas. What bothers me is what they've got in that line. What do you mean? What they've got in it? Isn't it all oil? Not this pipeline, pal. This is a freight line. You mean they sent batches of different stuff through that line instead of only one kind of fluid? Right. How do they pull off that stunt? It's a matter of chemistry. They know which liquids won't mix. Like they can put a load of Ethel gas between two loads of regular gas. Sovereign catfish. You mean they pump automobile gas through that line? Yeah, sure do, pal. That's smart trick. How they know where one kind begin and end in pipeline. They put a mass of radioactive substance in between each load. And by using Geiger counter as they can tell when a load begins and ends. Dad, for a fancy dangle of contraption. You speak truth. And company can send a lot of different liquids through line. That's what has me worried. What's next in line after the fuel oil? We won. This is Scotty Logan with the 5 o'clock news. This early morning, I'm sure, there are more listeners than usual.  Here's our sheriff to speak to you about the emergency situation of the flood of fuel oil on the river. Here's Sheriff Hopper. Thank you, Scotty. Ladies and gentlemen, Bill Jefferson and the Rangers are trying to locate the source of this fuel leak. I haven't heard from them yet, but I expect to at any time.  Those of you who have to cross the river to get to your jobs will have to do it on foot. And only across the Main Street Bridge, and only if conditions permit. If we feel dangerous and crass, the bridge will have to be closed to everyone. I wish to thank you for your wonderful cooperation by staying at home. It's made our job much easier. And again, I urge you not to become panicky, even in the face of the oncoming storm. The fire department is rapidly dispersing the oil as it comes downstream, and our fire chief feels that the danger point has been reduced considerably. Thank you. Henry, throw the spotlight along the bridge. Malcolm Gray speaking. Amal, Bill Jefferson, you've got a busted pipeline. No. Now where? I'm at the bridge over the Shady River, watching the fuel oil spill out by the hundreds of gallons. Is there room to land a helicopter close by? Yeah, plenty of room. Well, I'll be there with a crew in 20 minutes. Oh, the company man are in the air now, flying here from Canyon City. That's about all I can tell you right now, except the stuff is spilling out like crazy. That's fast work, Bill. Our thing's a naughty pine. Wonderfully quiet, everyone's doing his best to stay cool and calm. The fire boys are pumping water into the river as fast as they can. Fine, Cal, that's fine. I'll call you as soon as I know more, over and out. Well, here come pipeline men now. Yes, sir. And not too soon. That star is beginning to kick up and off of us. When's your toss of that copter around? Fast. There's no minute to lose. Yes, sir. Let's go, boys. Hello, men. Come on. Hello, Mal. Howdy. Hey, sure looks like a kind of a risky business out there, isn't he? You're right there, old timer. Bill, may I use your radio? Sure, help yourself. Thanks. QXBC 3, this is JMNX1. QXBC, this is JMNX1. Over. This is QXBC. Come in, boss. Cut off the line immediately, Fritz. Sure, boss. What's up? I'll tell you after you close the valve. Do it now. I'll wait. Right. Be back in a minute. The line is split open on the bridge. I'm afraid to ask you, but I've got to know. What's the load behind the fuel oil? I think I know, but let me check the manifesto to make sure. I don't want to scare the pants off you for nothing. Hurry up. Are you positive? I'm looking right at the manifesto now. If it were Kyle's milk, I might joke about it, but not 107. Okay, Fritz. Now, don't open that valve for anyone or anything.  Sweeney, what are you doing back here?  Boss, we can't work out there. The wind's too strong. Get out there. Don't tell me what you can and can't do. But, Mal, we've got all we can do to hang on. We can't repair that leak now. It's 500 feet to the bottom of that door. What kind of man are you? Get out there or I'll know the reason why. What's the matter with you? We might get killed. That's too bad, but it's part of your job. But maybe you figure the rangers should do your work, huh? Now get out on that bridge and fix that leak. Oh, all right. We'll try it. But I'm not making any promise. Get out there, dearhears. Stop blabbing and get out there. I'm going to talk to Fritz again. Okay, Mal. Use the radio all you want. Thanks. Boy, is he a gluttle and nerves all of a sudden like... You said it, honey. I smell a rat in the wood pile. I think same thing. He changed like wind after he talked to Valve Station. You fellas are pretty sharp. Pretty sharp. What do you think's wrong? I don't know. I'm waiting for Mal to tell us. Hey, wait until it's too late. I hope not. Here comes Sweeney's men crawling back on bridge, huh? They're hanging on for dear life.  Trying to plug that hole in this storm is like... Like trying to walk a tight wire on a one-wheel bike. Are you telling me what you're going to do? Yes, and if you don't like it, you can jump in the river.  Let's make him go out there. He's so smart, huh? No, I think we ought to throw him in the river.  He used to be a good boss until just a few minutes ago. And this thing's got you scared stiff. You mind your own business.  Wait a minute, Mal.  It's none of your business. That's where you're on. I'm top man here. This is government property, remember? Come on in the car. I want to talk to you. You aren't telling me what to do. Get in the car and make it snappy. We haven't got time to stand around and argue. Sweeney, you and your men take it easy. There's something wrong here. You can say that again, Ranger. I ain't looking for no fights, but I ain't taking any more of Bill's either. He'll get Mal straight now. All right, let's have it. I don't know what you're talking about. Listen, Mal, don't play Ring Around the Rosie with me. You change like night from day right after you talk to the valve station. What's in the pipeline behind the fuel oil? The next load is aviation gasoline. Aviation gas? Yes, 50,000 gallons of it. If the lightning hits that stuff, the whole county's going up. Bill, I'm almost to the point of nervous collapse. That pipeline comes down to the river in a long incline. I don't know how to stop that stuff. It just keeps draining out. I do. Well, how? We've got to cut the pipe open on the other side of the bridge and let the gas run on the ground. Yeah, now that would do it. Come on, we got work to do. Not to Sweeney. I'm ready to jump out of my skin, just thinking what could happen if that stuff spills into the river. Okay. Sweeney, gather your boys around. Okay. Come on, boys. All right. Let's go. Yeah, let's get this thing out of the way. Your boss is on the point of nervous collapse, so I'm taking over. No, I'm not taking over.  Aviation gas? That's right. Now, there's only one thing to do to save us from a catastrophe. You've got to open the pipe on the other side and let the stuff run out on the ground. That means we've got to cross the river. That's right. Can we go around? It'll take too long to go around. Come on, now. I'll lead the way. Henry, you stay here and man the radio. But that's in order. Yes, sir. Inform the sheriff what's going on. You and the copter pilot keep a close eye on us. You may have to pull this out if the lightning touches off the gas. Why can't we use the copter to cross? Too many dangerous wind currents over there in those canyons. We'll save the copter for emergency. Real emergency. Let's go. Every last one of us was in extreme danger crossing the pipeline bridge over the shady river. One misstep on the narrow catwalk. That would be all over. They might find our bodies down in dead man's gorge but they might never find us. The wind howled and angry gale and tried to tear each man off the catwalk and throw him into the river. I wasn't worried about the bridge itself going out even though it swayed like a rope. It was engineered for that. My big worry was getting the men across. And the electrical part of the storm hit us. The lightning played about us waitably. One flash after another so that I could have read a newspaper by it. I decided to hang onto a brace cable and let the men pass me so I could bring up the rear. That would leave me on the bridge longer. I didn't want anyone to panic and lose his life. I tried to encourage them as they itched their way along the grin sight. Watching the men crawl across the bridge and the eerie lightning flashes. I prayed that all would make it safe and sound. They won't make it, I tell you. Did I ever let them go and gas them?  Burn them to a crisp. Now keep quiet. Can't you see them now screaming and yelling and burning gas? Nobody to help them. I'm going to rescue them. I'm going to rescue them.   Mal, I'll come back here. Game point, US port. Sorry, Mal. Sorry I had to tackle you.  Henry Scott, the sheriff won at Nutty Pine. Henry Scott, the sheriff won at Nutty Pine. Come in, over. Sheriff won to Henry Scott, over. Cal, sending ambulance right away. I just had to tackle Mal, throw him on the ground, knocked him out. He was going off his rocker with worry. He was going to go out there on the bridge. Is it that bad up there? Yeah, it's pretty bad. What about the pipeline? Where's Bill? Bill's leading the men across the bridge to try and cut that pipe open on the other side. Let the gas run out on the ground. Gas? Yes, aviation gas. They're on this end and pray for those guys. They'll need all the help they can get. Charlie, get that cart away from here.  How long, sweetie? There's a small hole now, Bill. Maybe 10 minutes. We'll have it split in two. Can't wait that long. You'll have to. Need miracle men, you know. It's time to cut through steel. Pull right open in a can of soup, you know.  Are you cracking too? First you say cut faster, and now you say stop cutting. You say those rocks up on that ledge? Yeah. Will they open the pipe if they're dropped on it? Okay, get your men out.  But if the gas is coming through the line when the rocks hit, we won't find you after it's over. I'm not asking you to risk your life, am I? No, sir. I get you. Come on, boys, clear out. I go with you, Bill. You heard me and that's an order. Get out of here, scram! I climbed rapidly up to the top of the ridge. That is as rapidly as I could in the early morning darkness. Now I was glad for the savage lightning, because it helped me see where I was going. I thought of all the people and property along the river for a hundred miles. It would be in danger if the gas got loose on the river.  Finally, I made it to the top of the ridge. I stopped for a second, looked the rocks over with the help of the lightning. And I saw the key rock that would start the slide to crush the pipe. Put my muscle to work. The rock began to move. Pushed it over. It went crashing down. Taking more and more rocks with it. Where's the gasoline in that pipeline? As I was holding my breath, waiting for the explosion of the deadly gas. But it didn't come. Then I smelled it. The gas, that is. The rocks had smashed the pipe seconds before the first of the gas got there. I was still alive. I'll wait for explosion and breathe again after it's not come. I did too, Grey Wolf. Thank the Lord there won't be a river of fire. Kirk and Ryan realize how important their keen sense of impending danger was. The whole shady river valley was saved from a most disastrous holocaust. Well, see you next week for more adventure with...


Merdan fydd yma. Mae'r Llyfrgell Cymru yn ffasgau o'r cwbl ymddangos iawn... ...llewch ar gwybodaeth яr wirionedd yr ysgrifenni... ...yngoydd oclubodol Llyfrgell Llyfrgell. Mae yw Llyfrgell, yn ei wnaeth i'ch gwbl yn Bwyd, ac am gyfrifeddiol... ...a coleg yma ymgylchedd yw'r gyllid... ...yna mwy o gyfan mae'r Llyfrgell am yr Llyfrgell hon i... ...on purpose am ymlaen i ddweud ar y ffasgau'n hyn... Ie gwaith y cyfnod am y dyfodol ac yn gweithio y Darlwyr yn ein law, mae'n hynny'n wrth gwrs yma ar gyfer y cy tackle ac yn gyfwil yng Nghymru, a mae'r hynny'n ddechrau'r llyfr yn cael ei ddigon o'r llyfr yn gwybod, ac mae'n gweithio'r llyfr yn cael ei ddigon o'r llyfr yn cael ei ddigon o'r llyfr. Fel Lleisdyn Denham, Yr Profi Garethor. Yn cyfnod, mae'n dechrau'n gweithio'n cael ei ddigon o'r llyfr, ac mae'n gweithio'n cymryd ar gael, I will not be searching, so I will try to avoid myself. I am going to speak, I think, unless I run out of ideas till about a quarter to two. I am looking forward to questions, if you have any, or comments.  This is some kind of series called Pathways the 21st century or something, so I am trying to write for a non-lawyer and an international market and it is really quite tricky. The book is called Liberty and Security and it is about 40,000 words. How do you capture what you think to be the essence of this in such a short space in a way that is appealing to a readership that is not a legal readership so much unnecessarily and also an international readership? That is what I am sort of caught up in and I gave you guys a number of options that were sort of rubberising or trying to remember what I said in the last book or there was this and I was slightly anxious when you went for this because of course it is less easy for me than rubberising and trying to remember what I wrote in the last book. So here we go. I am going to read bits of it which are slightly for me complicated and then I am going to wing it a little bit and that will mean I can keep an eye on the time and I can look forward to critical questions. I have to say that there is another thing that occurs to me too which is this whole business of writing books during in an age of the internet and in an age of blogging and in an age of Twitter is really kind of preoccupying me a little bit because with the fair wind and this book delivered in May it will be out in 2013 and it seems so odd now and also the it is a package of stuff that I am not supposed to let anybody see until they go into a shop and buy it and I would like your opinion on how as academics who obviously want to be able to prove that they are scholars as a part of their job to get the money but academics who apart from needing to do that want to influence events how they should do it because I had a choice this morning I was asked to do a thing for the Guardian Unlimited I think they are called on the Court of Appeal judgement in the St Paul's Occupy case on Wednesday I spoke out in the tent on Monday night which was great fun the university, they have a university, a tent university I saw Trevor there actually, was it you Trevor or was it somebody else? Sympatical Leeds can turn people very odd so no you weren't there, very good, very good and I chose to work on this paper rather than do that it's quite an interesting, as a practical matter when you have spare only a limited amount of time what you choose to do, it's quite an interesting point you could endlessly blog and not do the work that you're supposed to do but if you do only the work that you're supposed to do and nobody reads it you do nothing anyway it's a thought, it's a thought so comment both on substance if you will and also I'd be interested in modes of expression so here goes first of all I'll talk a little bit about the meaning of these two words and I'll read from the start of the book I'll talk about the remit of the book or my ambition for it and then I'll talk about how it works as a structure so here we go there are a few words more dangerously confusing in their meaning than liberty and security the first has a range which takes it across a spectrum from the essence of human freedom at one end to a far narrower statement about the need for unrestrained movement at the other liberty is sometimes thought of as concerned with the individual cry individual and on other occasions with the individual within society at one moment the word seems to be about the need to be left alone by all authority while at the next it positively suggests active participation in the government of the day no one seems quite sure whether liberty is in any of its incarnations the same as civil liberties and even if it is there are as Jeremy Waldron pointed out at least four separate meanings to this term civil liberties as for the lawyers in pre-rights days they got into the habit of thinking of civil liberties as primarily concerned with the law on the control of police powers and this is the space that the subject still occupies in legal practice by the way that liberty security has a similar range and equivalent level of vagueness used in conjunction with liberty security has been historically taken to refer to national security to the protection from external and perhaps even internal threats of particular lands which are organised as states the field of counter-terrorism has grown out of this orientation of security towards protection from attack taking a different approach we now see also the idea of security being reconfigured for the global age as something called human security an idea of protection that focuses on people not places and which tries to get beyond immediate attacks on freedom to systemic failures in the public sphere that render us all in a much broader sense less secure so lurking in the background is the idea of security as a guarantor of well-being captured in the contemporary term social security which is now so familiar to us that we have forgotten the startling idealism and ambition that once oozed through those two words social security now paradoxically in a way I will explore this uncertainty over meaning the meaning of liberty and security does not detract from their power as positive signifiers the first liberty suggests freedom and unconstrained self a life lived to the full flourishing limit the second secures the space for such a life hedging it against the threats that might destroy it seeing off the intrusions that threaten to make this success impossible in this way as a signifier security communicates a kind of something like a platform for liberty a launching pad and a safe landing place for the soaring self these words echo across European languages and carry this implication so there is kind of oddity about words that you can show have various meanings which are difficult to one pick and yet words which carry positive connotations which seem unaffected by this range of meanings they're not rendered redundant by the variety of meaning that can be accorded to them so I was thinking about that and the book will be about what these words mean the shape that they have taken through time and from place to place how much they have been realised and for me this is the key thing and for how many people how can we have these doubts over meaning and at the same time have such agreement on their positive connotations how can words surrounded by such bonami be thought to be confusing well I think what matters about liberty and security and what I'm going to concentrate on in my book and what I think begins to answer that paradoxical point is the question of the reach of the benefits that each so powerfully evokes being the central question it is the for how many issue that will concern me it's these questions to whom our liberty and security to be extended is it to be to all or just the few if it is to be to all is it through community, state, regional or international action if it's guaranteed for all how practical in their reach will these theoretical commitments prove themselves to be or to put this in a cruder way for all the fine talk what will really be going on on the ground today the central arguments I say over liberty and security to which these qualifications about meaning are to some extent peripheral have always been about this issue of remit, reach rather to ask if liberty is constituted by freedom from external constraint rather than freedom to access the necessities for a good life is immediately to raise the question of whose freedom we have in mind our answer will reveal whether we are thinking of those already in a position to live a decent life and to want to protect it or those for whom presently it is a faraway dream equally when we talk of personal security or national security or human security or as I indicated earlier even social security it's immediately clear that our differences with each other will be mainly about who is to enjoy these valuable protections not what it means to be safeguarded in this way so here's what my argument is going to be in these 40,000 words this book will set out to track the breadth of these terms through time tracing the fluctuating range of beneficiaries that are to be found within their remit it argues for a particular approach one that regards the benefits of liberty and security as being rightly available to all and thereby capable of reaching, being required to reach the many rather than the few so viewing liberty and security in this all-inclusive way is going to shape my approach to the past work these words have done and the present meaning that I say should be accorded to them this is not as easy as it looks it's certainly a pathway of the type that I indicated right at the start I need but it's not as easy as it looks neither term has been routinely understood in such broad terms indeed, as we shall see the primary understanding of liberty and security in the pre-democratic era was always narrowly selective as to who was to benefit from the opportunities afforded the one and the safety delivered the other so that was a kind of pre-democratic reading of liberty and security and it was only when the radically egalitarian idea of community self-government took hold on a national scale that liberty and security found themselves open to being wrenched out of their elitist corrals and offered to all democracy gave the universalist readings of liberty and security an entry point and strong support but it could not by itself deliver effortless supremacy so I have the pre-democratic and then I have the democratic but the democratic period has certain defects which I explore, which I'll indicate this is because the democratic victory, the republican victory was in itself incomplete a freedom for all that was invariably not forged afresh but rather tentatively grafted onto pre-existing society a society that had been designed for the few old elite readings of liberty and security this persisted into the democratic era jostling for space with their egalitarian interlopers and now as we drift towards a post-democratic model of government or what I might call neo-democratic a third generation if you want of ways of looking at the world we see a polity that increasingly wears democratic clothes as a disguise rather than a proud necessity we see these old pre-democratic meanings of the terms returning into popular use underpinning and explaining readings of liberty and security which are ostentatiously universal but falsely so words that hide inequality and unfairness by seeming to reach all when in fact in their practical impact they are tailored to the few so here's, I'm put it another way because I wasn't sure that would be understood in the book and you have to draw all these people in so here goes my thesis my thesis is that we need to recover and re-energise true universalism in the way we use these terms liberty and security here are two words that grew to prominence when they worked they did was at the service of the few but which under the energetic influence of the democratic impulse became goals towards which it was right for government to work on behalf of all now that this expansionist trend has been halted by a drift away from democratic fundamentals and back towards elite readings of liberty and security albeit these versions remain cloaked in apparently universalist language an echo of past, more egalitarian times now that all that's happened the contention here is that we need to grab back and restore these democratic readings the version of liberty and security for which I argue the universalist version has three great allies products, two of them the democratic phase, I'll go through them these allies are in a way somewhat weak for reasons that I'll explain these three great allies have had a beneficial impact on the reading of liberty and security as universal the first is as I've already indicated this impulse for democratic government the second is the notion of the rule of law and the third is respect for human rights now the push for democratic government I would regard as the main driver behind the insistence that the privileges of the few should be made available to the many the second, the rule of law predates the democratic turn but compliments it maintaining that everyone must be subject to the same laws and just as critically that the maker of any given law should not at any one at the same time be its authoritative interpreter the third, the human rights movement of more recent origin at least insofar as we understand that idea today the very way that it describes itself reveals a commitment to an egalitarian vision of the world one in which we should all have a right to the freedoms that were once thought the privilege of the few and human rights today reach beyond the protection of liberty to encompass rich readings of human security the sort that democratic government once made popular so these three big ideas democracy, the rule of law and human rights are universalist in their structure they push societies that commit to them towards equality or in the language of this book liberty and security for all in this neo-democratic phase into which I argue we have drifted they present a problem a challenge to the version of truth that seeks to assert a new elite common sense because this victory is not yet complete neo-democracy has had to accommodate these contrarian pushes for universal freedom within its model but without losing the drive back to privilege which is its primary model the reason it has managed to impose itself in the first place so we have seen not just the wearing of democratic disguises for authoritarianism but also attempts to bypass the rule of law and to distort the meaning of human rights so radically that the term turns into a legitimate sorry a legal legitimator of oppression rather than the passport of freedom that it ought to be this neo-democratic term the world in which I argue we live increasingly today wants us to regard democracy the rule of law and human rights as outmoded old hat ideas incapable of coping with the challenges of the modern global world the rise of extremism climate change the movement of capital, population growth, refugees etc its proponents, conscious and unconscious are happy to see these phrases contaminated by misuse forsaken by those who should love them as creatures of illusion and hypocrisy liberty and security that is liberty and security for all and not just the already empowered few depends on recovering their finest meanings and using them as offensive weapons against the onward surge of the overprivileged minority whose ideal world would see liberty and security as their exclusive preserve alone so basically that's the structure of the book there are these three phases pre-democratic which I'll turn to in a minute versions of liberty and security then a democratic impulse which produces the democratic movement which is assisted by the rule of law brings on board the idea of the protection of human rights all of which stand for the universalist reading of liberty and security but each of which is incompletely realised because of the lack of deep embedding embedment of the democratic idea and of the republican idea and so that idea is never complete and it has these weaknesses and so when we move into the situation where in the moment I would argue where we are returning to the elitist readings of liberty and security we are doing so under cover of democracy the rule of law and human rights but that is a kind of camouflage for change rather than a genuine deployment of those terms I'm trying to make the book universal and I have in mind Russia it's a sort of democratic human rights rule of law at the moment it's a kind of sort of the dystopian future now the book then you know I talk about this pre-democratic and I do a lot I'm not going to read all this bit out don't worry on Hobbs because I think Hobbs is really important I did a big long paper on Hobbs and I've used a lot of that to try and get under the skin of this subject because I think Hobbs is very important to how we read liberty and security and also I think how England reads liberty and security is very important to the world we can't undo colonialism we can't undo the power of England and I use England not the United Kingdom of course so these tropes are having universalist dimension which is regarded as rude to point out because it suggests that only the top thinkers are English well I'm just commenting on influence and this is the way I read Hobbs's importance I'll read bits of it but not all of it in his first major work Elements of Law Thomas Hobbs saw liberty in fairly simplistic terms I don't mean that as offensive I mean that as a compliment actually as a capacity to act or to forbear from acting which capacity leads naturally to deliberation as between rival paths should I go with my appetites or let my fears triumph and this in turn produces a decision the will to act or not to act as the case may be what is marvellous about Hobbs and for its day highly original is how he relegates reason to a sideshow to the main event it's all about emotions feelings, wants, aversions in this world of blameless liberty we naturally desire what is good for us and seek to avoid what is bad for us and above all famously of course as people know what for Hobbs is bad is death and therefore fleeing from death becomes our thing and as Quentin Skinner upon whom I rely for a lot of this puts it in Hobbs and Republican liberty it was for Hobbs obvious that we have a natural tendency to do everything we can to preserve our lives now here's the move because this disposition is so very reasonable we must therefore have the natural right to act to preserve ourselves at all costs so arguably in the modern world he's the first human rights guy but this of course raises problems there is not enough of the world to go round there are too many of us exercising our natural right to do whatever we want at the same time we couldn't all be simultaneously satisfied that's why he ends up saying the life of man is solitary, poor, nasty, brutish and short and then quoting Skinner a lovely quote the desperate paradox on which Hobbs's political theory is grounded is the greatest enemy of human nature is human nature itself now the way out of this conundrum is lies and obliging ourselves to forbear from acting according to our will and power this requires submission to a sovereign to whom we are henceforth to be quote as absolutely subject as is a child to the father or a slave to the master in the state of nature because liberty is impossible our submission to the protective force of the sovereign is practically absolute Hobbs does have some sense of inalienable rights as far as I can tell but these do not figure prominently in his thinking and he never seriously contemplated any kind of right of revolution against an iniquitous sovereign as far as I can tell his description of his later book Leviathan was as a work that now stands that now fights on behalf of all kings and all who whatever name they have hold regal rights stands as a description I think of the kind of thing that he was doing so here's a story that produces an absolute abnegation of liberty in the name of security and a handing over of responsibility for security to an unquestioned monarch now that's one version of liberty and security which is pre-democratic but at exactly the same time there is emerging a republican reading of liberty and security and that's recovering past versions of freedom which see freedom as living in a free state so much broader than the narrow common sense approach of Hobbes and I use the obvious example of the levelers who've been written about very well by Martin Lachlan recently and also Stephen Sedley and lots of others they were an operation that were around the mid-1640s and they produced a document which Martin calls a landmark in constitutional history which apart from setting out the rudiments of a system of representative responsible accountable and democratic government demanded also that laws ought to be equal this is a quote from the levelers laws ought to be equal so that they must be good and not evidently destructive to the safety and well-being of the people so in this last phrase the safety and well-being of the people that the law should not be evidently destructive of that you have my vision of security which is sort of the word safety and liberty which is well-being for all the people so I put up these kind of alternative versions of liberty and security the first leading to absolute power on the part of the monarch the second calling for a free stay now on one version the second of those has clearly won the idea that you need to live in a free state a republican state a democratic state has become the norm and the rule of law is seen as facilitative of that and that in turn has produced versions of security that echo the levelers commitment to safety for all and I go through a little bit of this but not a lot the obvious highlights are the development of a kind of welfare system in Germany in the 19th century the web minority report the development of labour administration in the 20th century and welfare not warfare temple during the war and the four freedoms of Roosevelt culminating in the kind of human rights movement after the war so there's sort of a way in which democracy delivers versions of liberty and security that fit with my universal reading and the rule of law and human rights are part of that now you will already anticipate because I've already said my theories see democracy, republicanism version of liberty as vulnerable because of certain weaknesses in the embedding of republicanism, democracy in our culture and these weaknesses are to be found in the way in which democracy embedded itself and in its half complete or less complete triumph than we sometimes assume and that then leads on to certain problems in our approach to the rule of law and human rights and these three together have made us vulnerable to what I've called this kind of neodemocratic retaliation so that's what I'm going to do in the last few minutes I have so let's look at the ways in which I say that republican triumph has been less complete than the universal democratic narrative would have us suppose this is not entirely about form though of course the United Kingdom in common with many other democracies does remain distinctly non-republican in its retention of the monarchy and at least some other seemingly republican states find themselves applauding by their vote members of the families of elected rulers the obvious example are the Bushes but Lee Huan Huw in Singapore and a depressing number of similar examples drawn from post-colonial Africa the main point is that though the vote has been conceded and participation in the governing of the state guaranteed to all but the entirely incompetent this has not produced the renaissance of free born citizens that many proponents of this vote would have believed would follow the evidence for the imperfect success of the democratic impulse I would say is more importantly evident or seen in the continuing power of private money in the systemic defects in prevailing constitutional orders from a democratic point of view the conservative tendencies of state bureaucracies the lure of populist nationalism the temptation to indulge in a rhetoric of fear and the lack of energetic engagement in self-governance revealed by many citizens our republican democratic form of government does not operate in practice in the way that it was assumed by the optimist that it would the situation has been compounded by the tensions generated by the fear of external attack and internal subversion on which more shortly now that sort of part of what's gone wrong in a way are not gone wrong but what renders democracy less effective than you might have expected and therefore less invulnerable but there's another one and I think it affects it theoretically in a very important way a second aspect or a further aspect to the imperfect triumph of republican ideas relates to a failure to think through properly what individual liberty in a free state entails as a matter of personal as opposed to social freedom maybe it's because the language of human rights did not apply here with their focus on the individual with their setting up of a framework for resisting particular state action against individuals other than in defined and defensible circumstances whether or not this is the case it is clear that republican thought emphasised as liberty the living in a free state and security as the defence of the free state in a way that certainly didn't pay much attention to the individual and could be construed as practically Hobsian in the blank cheque that it gave to authority albeit this time a different kind of authority republican democratic rather than despotic in a free state matters of security national state security are too often left to a single actor without further accountability and that state's rhetoric of political liberty is a rhetoric about living in a free state not protecting individuals within the state so even that great republican figure John Milton was unabashed in his willingness to act against Catholics but perhaps more seriously from the perspective of this argument was perfectly happy to clamp down on sedition albeit he opposed and he's the best one he opposed controls on publication in advance but not laws against sedition the qualified nature of the republican triumph combined with this failure of democratic imagination when it came to individual as opposed to collective freedom served to generate a strong undercurrent of hostility to universal liberty throughout even the golden democratic age of freedom this insecurity has afflicted democratic states and when allied to this republican tendency to subjugate the individual to the needs of the republic has produced a series of harsh assaults on individual freedom that have taken place within and been justified by the free state rather than been in opposition and at odds with it well why has this been so easily permitted why has republican versions of freedom which have been so abusive of the rights of individuals in the protection of the state not generated more energetic opposition from the citizens themselves and this takes me to the second incomplete embedding which is that of law now obviously law the rule of law predates democracy but it has in those countries which have adopted republican forms of government led to a large number of cases where courts have quite explicitly supported executive action in the name of the security of the state and have done so without probing deeply into the individual circumstances before them the famous maxim is deployed in some of the cases in michael's and block I think from 1918 the salos populis supreme alex the safety of the people is the supreme law and so what we've seen is that law has taken its cue from republican concerns for security and not stood up for the individual within the system where the state's security has been at stake also increasingly in this neo democratic phase we're going through when laws engage on behalf of the state the response of the state is to bypass the law and so what we have at the moment in this country at the moment is quite a lot of efforts to marginalise the courts by being able to take decisions outside the judicial system in quasi judicial administrative frameworks which are without the same kind of level of engagement that courts would bring this is slightly it's a variant on the point support the safety of the state the old way or if courts flex their muscles and engage they find the state manoeuvring to avoid them and so you see special advocates control orders t-pims and a whole story about the way in which the administrative state is returning which is standing outside the framework of law so the courts are okay if they do nothing and bypassed if they do something but neither of those points is the one I want to just bring back to you here before I go on to the human rights thing and finish the point I want to make here is that Hobbes is connected to this in I believe quite an important way and let me see, I'll need to read some of this to try and articulate it Hobbes' theory required that liberty be extensive in the residual sense of being in the presumptive position and at the same time vulnerable to aggressive state action capable of being smashed if Leviathan judges such repressive action to be essential to the safety of the state it has been an English law that the residual theory of liberty promoted in the 9th century by Dicey among others has really bedded down enjoying to this day an eminence in constitutional law teaching that is only being very slowly eroded by the move to rights so you are free to do what you want unless the state decides that you shouldn't now Hobbes' combination of an outlandishly extreme commitment to individual freedom on the one hand you can do whatever you want with a deep precariousness so far as the protection of such liberty is concerned not if Leviathan moves against you is only experienced as precarious if the contingent nature of the exercise of your freedom is before you all the time if it is not if Leviathan rarely intrudes on you your family or your immediate community in other words the people you know then the fragile the fragility inherent in your liberty is not the foreground of your way of thinking it is the freedom you experience not the ease with which it is taken away so there are two kinds of people the people who enjoy liberty in a republic who don't really think anything is going to happen and the people who have the possibility of things happening at the forefront of their minds all the time because they know that Leviathan stroke the republic might move against them these may be for example alleged revolutionaries suspected terrorists tiff cullness foreigners who are said to seek to subvert the state from within but because they are not you or like you and of course you never meet them their vulnerability does not register in designing a system which turns everything over to Leviathan while assuring the majority that Leviathan will not challenge their freedom to pursue their individual appetites as they wish as long as they do not rock the boat Hobbes produced an artifice which has remained attractive long after the monarchs and despots for whom he has argued were slung from centre stage it has endured right into the democratic era a time when servitude may have disappeared but a recognisably hobsy an apolitical selfish passivity has if anything fuelled by its compatibility with capitalist modes of thought come into even more prominence so we do not experience the vulnerability that those who are possibly going to be moved against by Leviathan experience so that's the weakness in the rule of law which is in turn made possible by the weaknesses in the lack of a complete democratic engagement which is primarily about ignoring the individual well what about finally human rights now it seems to me that human rights are potentially the saviour of I mean it's funny I say this but the saviour of the democratic framework because they actually by prioritising civil and political insist on readings of society that are democratic but by focusing on the individual they remind you that liberty is about more than a theory of freedom that it has an immediate protective consequence for everybody now of course it can be mis-deployed as I said at the start and of course the neodemocratic trend does mis-deploy the language of human rights you can have a human rights commitment which is simply there as a constitutional requirement and which is ignored a bit like maybe Jordan's commitment not to torture people and when the European Court of Human Rights analyses it does sort of offence taken that it might be subjected to some empirical test or Russia's membership of the Council of Europe which it sees as not incompatible with the invasion of a fellow council member so you can have simply a sort of empty signification or you can have human rights which serve to legitimise in law human rights attacks and so you have systems whereby you can act against marginalised groups and insofar as any of the individuals in the groups then seek to assert their human rights you do have a judicial framework but the judicial framework is so designed to ensure that the end of the process produces an approval of the action as human rights consistent rather than human rights abusive so cases like the I don't know the Kettling case the protest which was compatible with their human rights the St Paul's eviction appeal which I think the judge was right but I'm not wearing a party propagandist point here but which goes through article 10 the right to freedom of protest which points out that actually it's not available in private property which says therefore the removal of the protestors anytime soon is compatible with their human rights is not in a front of them removes even the weapon of protest on the basis of the infringement of human rights because the answer is actually we've checked and your human rights are fine as you are removed you know of course that is a possibility and an even more an even more dangerous one in a way is the way in which the language of human rights has become a stick with which to beat other cultures so in this uriner your out which the republican idea I suppose of a sort of homogenous state lends itself to you have situations where you can define a culture as one that is supportive of the rule of law and supportive of human rights and supportive of democracy in the abstract and that somehow rather gives that culture an advantage over other lesser cultures which are not so supportive and that's an idea about human rights which is independent of practice and what you actually do and so that would be for example in its more extreme form what might you have argued for where you have the entitlement to engage in the lesser evil because it's lesser it's less evil even though objectively the thing you're doing might be the same it's less evil because you are defending your own culture and we see a little bit of that with the government's latest prevent and contest where they are defining extremism not as violent extremism but as a rejection of our values and so they're arguing for a move to prevent violent sorry a move to prevent extremist speech independent of any connection with violence so obviously the language of human rights can be mis-deployed it can be either just an empty veneer or it can be used through judicial action to legitimise what looks to everybody else as a breach of human rights or it can be turned into a positive weapon with which to beat other cultures and even underpin military action of course it can but the concentration that human rights gives you on the individual allied to its determination to have a democratic system which is a real one with most recently in this country the determination that prisoners should have the right to vote which is fantastic because it's getting us to think differently it's actually a way of addressing the weaknesses in the democratic achievement which weaknesses have made us vulnerable to this if you aren't using it again right at the end the Russian model vulnerable to a drift towards a camouflage authoritarianism and which enables us somewhat to both resist that and energise the rule of law and democratic ideas to resist so I'm really all-fashioned I think these were fantastic ideas I think they are universal and I think that we should not fall into the trap of believing somehow or other they're outdated, jaded, tired democracy, the rule of law and human rights because these are the three universals that make it possible to reimagine the society in which there is liberty and security for all Abef stop thank you very much


And if you went shopping through Central Square Mall and Grand Rapids over the weekend, you might have noticed multiple activities going on in celebration of Earth Day. The third annual Earth Day at Central Square Mall took place on Friday and Saturday to celebrate Earth Day and raise awareness of environmental issues. The event had talks from authors of environmental books, a movie showing for kids, and a bake sale in addition to literature about ways to protect the environment. I think our major mission is to raise community awareness because a lot of people aren't really thinking about what's happening, aren't paying too much attention, and we want them, we want awareness to increase. So we're trying to get people in, share information with them, however we can. While the event is typically a one-day event, this year was moved to two days in order to not interfere with Grand Rapids March for Science, which also took place on Saturday. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.


This talk is the second part of a proof of the Riemann-Roch theorem. So the Riemann-Roch theorem, as you recall, states that L of D is the degree of D plus 1 minus G plus L of K minus D, where as usual D is a divisor, that's its degree, this is the genus, and K is the canonical divisor. And in the first half, we prove Riemann's half of the Riemann-Roch theorem, which says L of D is equal to the degree of D plus 1 minus G plus I of D, where this mysterious factor is the index of speciality of the divisor D, which is something like the dimension of the space of obstructions to the Mittag-Leffler problem. And what we're going to prove today is Rock's half of the Riemann-Roch theorem, which says I D is equal to L of K minus D. This part of the Riemann-Roch theorem nowadays is usually proved as a special case of serduality. That's what Hauptschrone does, but serduality is a fairly major theorem about high-dimensional varieties, so you don't really need it for proving this part. Well, obviously Rock proved it without using serduality. In order to simplify the proof, we're going to work over the complex numbers, at least to start with, and when we've done the proof over the complex numbers, I will say a little bit about how you extend it to general fields. The big advantage of working over the complex numbers is we can use the residue calculus, we can sort of integrate over paths on a Riemann surface and apply Cauchy's residue theorem and things like that. So the residue calculus gives us two key facts. First of all, if we have a one form, which looks locally like f of z, d z, then it has a residue at any point p. This is a meromorphic one form, and the residue is given by 1 over 2 pi i times the integral around a contour of omega, where here we've got a point p and the contour gamma just goes once around p in a clockwise direction, whatever clockwise means. The second key point is that the sum overall points of a compact Riemann surface of the residue of omega at p is equal to zero, and this is more or less Cauchy's theorem. This only applies to compact Riemann surfaces, rather obvious counter-examples of the surface isn't compact. And the reason is that Cauchy's theorem says the integral around some path is more or less equal to a sum of the residues inside the path up to factors of 2 pi i. And if you've got a compact Riemann surface, then you can also apply Cauchy's theorem to the region outside a path just by considering it as the inside if you look at it from the other direction. So you find that if you've got any path on a Riemann surface, the sum of the residues inside the path is equal to the integral along the path, whereas the sum of the residues outside the path is equal to minus the integral along the path. And from this it's easy to see that the sum of all residues over all points of a compact Riemann surface is always zero. So these are the two facts that we get from working over the complex numbers. Now we recall that the index of specialization that we want to deal with could be more or less defined as R over R of D plus K of C, where you remember this was the space of rational or meromorphic functions on the Riemann surface and this was the ring of valuation vectors. And this was the set of obstructions to the Mittag-Leffler problem. So you remember the Mittag-Leffler problem says that we specify a singularity at each point of the Riemann surface and we want to find a rational function with those singularities. Well, the reason why we're interested in one form is that a one form omega is an obstruction to the Mittag-Leffler problem. And this is because if we've got any one form omega and we've got a function f, we know that the sum over P of the residues at P of omega f is equal to zero. And now we notice that this residue depends on the singular part of f at the point P. So this gives some condition that the singularities of f at all points have to satisfy in order for them to come from a meromorphic function f. More precisely, we get a bilinear pairing from the holomorphic one forms times this space of valuation vectors. Well, I guess we could question that by r and zero plus k of c to the complex numbers. So this is just taking one form omega and some set of singularities, which are rather sloppy writers f. And you just take this to the sum over P of the residue of f omega. So this is what we get if the divisor is just the zero divisor. More generally, we can do something similar for any divisor. So we get a pairing from one forms omega with omega greater than or equal to the divisor. And that means, remember, this is the divisor of zeros of omega and we want it to be equal to this divisor. And this time, instead of r zero, we take r of D plus k of C and this maps to the complex numbers. And we do exactly the same thing. We just take the divisor and multiply it by the singularities and take some of the residues. And you can check that this condition sort of matches up with this condition and make sure that everything is well defined, unless I forgot to put a minus sign in somewhere, which I quite often do. And in particular, we get a map from one forms omega with omega greater than or equal to D to the dual of r over r of D plus k C. And the key point is this map is injective. And it's very easy to see its injective because we can choose a valuation vector with any given singularity at any given point. And from this, it's very easy to get any map from one forms to C by choosing a suitable valuation vector. So showing this as injective is easy. It's also surjective, but this is considerably harder. So we know it's injective and we have to think more about whether or not it's surjective. Anyway, from the fact that it's injective, well, we know the dimension of this is L of k minus D and the dimension of this is just I of D. So from the fact that this map is injective, we find the inequality L of k minus D is less than or equal to I of D. So this is half of Roch's theorem. What we want to show is that L of k minus D is actually equal to I of D. In other words, we want to somehow prove the hard part of the surjectivity. Well, proving surjectivity directly is, well, you can do it, but it's a little bit tiresome. Unfortunately, it's not really necessary because it turns out we can actually deduce surjectivity from all the other things we know about the Riemann-Roch theorem. So let's summarize what we know. We know, first of all, we know L of D is equal to the degree of D plus 1 minus G plus I of D. So this is Riemann's part. Secondly, we know L of k minus D is less than or equal to I of D. And by changing D to k minus D, we also see that L of D is less than or equal to I of k minus D. So this is the sort of easy part of Roch's theorem. And a third thing we need to know is that the degree of k is equal to 2G minus 2. And we worked this out by explicitly calculating the degree of k and found it was equal to this by writing down an explicit one form on a plane curve with nodes and so on. Anyway, from these three facts, we're going to deduce that L of k minus D is actually equal to I of D. And to do this, we're going to use this twice and we're going to use this twice once in this form and we're going to use this once. So what we do is we just write L of D equals degree of D plus 1 minus G plus I of D. Well, that's just Riemann's part. And this is greater than or equal to degree of D plus 1 minus G plus L of k minus D. Here we've used this inequality. And now we apply Riemann's part again. So this is degree of D plus 1 minus G plus L of k minus D is now equal to degree of k minus D plus 1 minus G plus I of k minus k minus D. Which is just I of k minus D there. And now we apply this bit again, which is a variation of this for a different divisor. So we get degree of D plus 1 minus G plus degree of k minus D plus 1 minus G plus so I of k minus D is at least L of D. And now we seem to have L of D is at least equal to L of D plus this rather messy looking expression here. Well, if you look, degree of D cancels out with degree of minus D. So what's this going to be? Well, if we put everything together, we see that this is degree of k plus 2 minus 2 G. Which, well, we worked at degree of k is equal to 2 G minus 2. So this is just equal to zero. So this whole mess here just disappears. So let's see what what we've managed to prove. We've managed to prove that L of D is at least equal to L of D. Oh, well, that seems kind of trivial. So we don't seem to have proved anything. But if you look more carefully, what you find is we've shown that L of D is greater than or equal to this, which is greater than or equal to L of D. So in other words, this must actually be in equality and this must actually be in equality. And the only way this can be in equality is if these two things here are equal. So we've now actually managed to show that I of D is equal to L of k minus D. And this proves rocks part of the Riemann-Roch theorem and thus completes the proof of the Riemann-Roch theorem. Well, that shows how to prove it over the complex numbers. And I want to say a little bit about how you prove it over more general fields. So what about about fields of characteristic greater than zero in particular, when there doesn't seem to be any obvious way of doing contour integration? Well, there are two problems. Problem one, need to show that the residue of a one form omega at a point is defined. And the second problem is we need to show the sum over all points of the residue at p is zero. Well, the first problem looks kind of trivial. So how do we define a residue? Well, let's choose some local coordinate z at point p and a residue omega looks slowly like something of the form a minus n, z to minus n plus plus a minus one z to minus one plus a naught plus a one z and so on. We can expand it as a formal power series. And why don't we just define the residue to be a minus one? What's wrong with that? We seem to have a perfect good definition of the residue. Well, there's a big problem here. Problem is how do we know this does not depend on the choice of z? And you have to be really careful here because it turns out that all the coefficients a i other than a minus one do depend on the choice of z. And if you choose a different local coordinate, they all change. So it's only this particular coordinate which doesn't change. I guess I should have put a d z there because otherwise it really messes things up. So how do we check this? Well, let's take a look at what happens if we change coordinates. So suppose we change to a different local coordinate. Let's call it w. So we might have z is going to be now equal to b naught w plus b one w squared plus b two w cubed and so on. Again, just expanding as a formal power series. Well, of course, b naught is not equal to zero. And let's just try and work out an example. So suppose we've got a one form which we can write locally as a minus one z to minus one plus a naught z naught and so on. D z and now let's write this in terms of w. Well, that's quite easy. We get a minus one and then we we want z to the minus one which is going to be b naught minus one w to minus one plus various terms plus a naught times something. You don't really care about the others. And then we have to put down d zing, which is going to be b naught d w plus various higher order terms. So this is equal to a minus one d w plus higher. So a minus one w to minus one d w plus higher terms. And now you see the coefficient of w to the minus one d w is the same as the coefficient of z to the minus one d z. So, so for poles of order one, no problem. It's just very easy to check that the residue doesn't depend on the choice of local coordinate. The problem comes when you have poles of higher order. And then things become a little bit complicated. And I'm just going to do an example to show you that things really do get a bit complicated. Let's try and order two pole. So here we've got a function a minus two z to minus two plus a minus one z to minus one and so on times d z. And let's again change z to b naught w plus b one w squared and so on. Expand the other a different local coordinates as a power series in z. And let's try and figure out what happens to this power series. Well, it becomes a minus two. And then we've got to take z to minus two, which is going to be b naught to minus two w to minus two minus two b one w to minus one over b naught squared and so on. And then we've got to add a to minus one b naught minus one w to minus one plus various terms. And we've got to take this all and we've got to multiply it by d z is going to be b naught plus two b one w and so on all times d w. And this is beginning to get a bit of a mess. So let's collect together all the terms and see what we get. Well, we get a minus two b naught minus one w to minus two.  And this times this and this times this cancel out in a freakish accident. So we just get a to minus one w to minus one all times d w. And now what we see is that this is still a to minus one, but we get a weird cancellation. We get quite a lot of unexpected cancellation. And you should also notice this is not a minus two. So changing local coordinates really does change the coefficient of w to minus two. And in general it changes all the coefficients other than the coefficient of w to minus one. So how do we show that this coefficient of w to minus one d w stays the same? Well, if we take any one form a minus n z minus n plus and so on times d z. And we change z to b naught w plus b one w squared and so on. Then this term becomes some complicated coefficient times w to minus n plus some complicated coefficient times w to the one minus n and so on or times d w. And what are these complicated coefficients? Well, they're polynomials in the a minus n a one minus n and so on. And they're also polynomials in b naught b one and so on. And that also you need to take b naught minus one. So if you expand them all out, you get some mess. But it's it's obvious that this mess is going to be polynomials in these variables here. And furthermore, they're going to be polynomials with integer coefficients. And that's really all we need to know. And we want to show that the polynomial for w to the minus one d w is just a minus one. So all the other coefficients, this polynomial is going to be some horrible mess. And we want to show that everything cancels out. And this is in fact really easy to do without doing any calculation at all. Or we notice that it is a minus one over the complex numbers. So it is a minus one over if we work over the integers. And you notice that it's going to be the same polynomial with integer coefficients, whatever field we work over. If you're working over a finite field, it wouldn't really have integer coefficients. But if you if you do it with integer coefficients and then reduce the integers modulo p, that's what you get if you work over a finite field of order p. So it is a minus one over any field. So this is a really rather weird proof because we're proving something over a field of characteristic p by using contour integration over the complex numbers. And then observing that forces it to be true of any field. So the point is that Z is actually a subring of the complex numbers. So if you prove, so in order to prove an identity with integer coefficients, it's enough to prove it with complex coefficients. And for that we can use contour integration. And once you prove it over the integers, we can then just reduce it mod p and get it for any field. So this rather messy identity that we need in order to show the residue as well defined. The proof of the complex numbers does actually prove it over all fields with this rather kind of piece of black magic. It looks as if we're cheating, but it is actually valid. Finally, we want to prove that the sum of all residues of omega at p is equal to zero. And I'm not going to prove this in detail. I'm just going to sketch the main idea of the proof. First of all, it's easy to prove for the projective line p1. For the projective line p1, the residue is just a meromorphic function times dz. You can write a meromorphic function as sum of partial fractions and just check this by explicit calculation for each partial fraction. So we can just say proof by calculation. Now for any curve c, what we do is we map it to p1 by a finite map. And if we've got a one form omega on c, what we do is there's a way of pushing the one form forward to a one form on p1 by... This is sometimes called taking the trace of a one form. And what you do is you define this trace and then you check that the sum... If we call this map f, the sum over f minus one p of the residue of omega is equal to the residue of the trace of omega at a point p, where p is a point in the projective line. And if you can prove this, this obviously proves the sum of the residues of omega is equal to zero because the sum of the residues of omega over all of c is then the sum of the residues of the trace of omega and this is equal to zero by explicit calculation. So the proof that the sum of the residues of omega is zero reduces to this calculation, checking this here. And again, this is easy to prove over the complex numbers just by using the residue theorem. And you can prove it over all fields by using a kind of trick similar to the way we showed that the residue is well defined, that this turns out to be an identity between polynomials with integer coefficients. And since it's true over the complex numbers, it's true over the integers and therefore true over any field. Okay, so that completes the discussion of the proof of the Riemann-Roch theorem.


There's many layers of operational planning that falls within C2. When we look at from a lead wing perspective, we have the walk, the wing operation center, which consists of the A-staff element, the combat intelligence cell, and the special staff, and they will command and provide information within the lead wing to the mission generation force elements, the air base squadron, and even down to the contingency locations. The great thing about C2 and something that we're really working for in this exercise is you're not always going to have the connective tissue that creates C2. So something that RA-6 has done a really good job on is creating what we call pace plans. We want to work through your primary and alternate comms and work down the line. As we build those communication bridges and we can share information back and forth between the subordinate units, that information share also involves orders, so sending out mission type orders and things like that. So when that is severed, instead of reverting back to doing nothing, tigers up front are leading the way, executing the mission without that communication back forth. We're all on the understanding that we're going to get our orders from the AOC. When that is severed, it comes back to the lead wing being able to execute, but within the lead wing we also have those nodes. To be able to push forward contingency locations, to get our forces out there, multi-capable airmen out there, jobbing it, being able to refuel jets, put weapons on jets, so they can go out and do the mission, that is huge. So as they are refueling and rearming these jets to be able to execute the mission, they are in dangerous way, so the C2 nodes that connect those to the main hub are absolutely imperative for their safety. With a lot of coordination and command control enables that coordination, and that's what's key. It enables all the commanders and the different force elements to actually work together, pass information from one to another, and actually provide air power to where it's needed.


Jason and Jason you have the same main main. Oh, you know. Oh, is that I when I was texting Ethan earlier I had to make sure we cleared that up. Yeah. Yeah Honestly, but I was I was being honest is like you could take Burdo tonight No, but he's already had someone else picked out.   What are we talking about currently Jason?    Yeah, the big old Bowser blast It's kind of nice though Covering up where his giant schlong should be hard. This is my favorite mini game. Luxie I like this mini game a lot. Well come big schlong. It's really getting in the way of his like it's really dragging them down You are Give me something nice I wanted your attention the fact that you won your first Mario Party game recently. I did you're right You're right.  I'm proud of you. I just want to can you just keep raising it forever or? No Oh, I didn't know Double dice again I didn't know that you had to drop it. Oh, I like this one. I'm good at this one I feel like Jason's talent is Jason's good at every mini game You're good at a lot of them Jason. Oh my god my taint You're still in the first section. Oh my god, Rosalina. I can hate it's definitely Rosalina's fault. I Keep getting like a little bit of lag. Oh my god. I did something new record, baby It's wallowee g spindly legs and it has nothing to do with any of our of our talent. He basically like stepped up You know, he didn't even need to jump Yeah, I can't buy I Can't buy I can't buy No money Baby no money. So that says oh you get out of here Says to that. I'm just in general. I have 12 might as well, you know I'm thinking about the future, you know I got a little bit of like a shot glass Wait hold a hot dog like a shot glass What does that mean? You use it as a as a shot glass. How does that work? I was just wondering if hot dogs much like mouths are multi-tools. Oh Okay, okay Much like mouths. Oh, I love this one You have to go to the touchdowns Well, you never played a sport No, but being loves football doesn't she That's to be fair We were at like a Super Bowl party the other day and I have a video of her being the only the only person That's why I said that Look at that guy Hey guys if testicles had to be somewhere else, where do you think they should go the roof of your mouth? No, that's a uvula I told you guys about Spencer, right?  I want you to give me coins. I don't have coins That's kind of rude that they wouldn't see that you have none and give you some Normally they see that you have no money and they take more. Yeah Few net banks, I need coins real bad No, you got plenty Yeah, if you're doing so great. Listen, you're definitely getting this car for least amount of coins though So that's a hey. It's only turned five You're absolutely correct Last sometimes it's good.  No be birdo. What according to Jason's lore, it's a black hole in there, right? Yeah, and it's lubricated. Can you imagine Birdo with teeth like a lamprey? I'm sorry, but someone in my chat just said Waluigi could bottom from the other room. What does that mean? But his butt cheeks aren't long. Yeah, his legs are long Yeah, but but like his torso is kind of long too So you can just be in another room like having dinner and you know, you know y'all are in blast We are in the blast zone is making me very uncomfortable. I don't even think anyone's gone over yet Well now Ethan's gone over it. So yeah, Ethan is the first to start blasting. Mm-hmm at least tickle the blast.   Yeah, I got all the coins. You were like at like no coins and now you're good Yeah, what side do y'all rotate? Likewise, also, I immediately also do with the palm of my hand. I don't give a Different ones I honestly don't know every time Is it the right one? I don't know. I just know we didn't do good actually I just got a text from max that says how many people you think are gonna guzz in your gear plushie I Responded with I hope only you by the way guys. There's your plushie out now get it Don't give it actually for that reason. Don't get it for that reason.    I'm bad at them Ball sports It's a ball for me. It's a ball sport Look at us our homerun team. It's the only ball sport.   I'm getting really bad lag and that's why I can't hit any of the balls Oh, yeah, the lag. It's definitely the lag. There was Ashley Watch your toe play so many sport games.  I'm simply married to a softball gay I have to know how the game works max. I were talking about it last night How much we missed just sitting and playing garlic all the time. Did you get the glove though Ashley? I did get the glove What it's a lefty thing It's not just a lefty thing It's drawing on a on a screen because you're the skin of your hand will start to interact with the touch screen Because you know how like lefties right like upside down almost. Yeah, no, absolutely max is a lefty. Oh Okay, wait, are you right? Me I didn't really I guess when you're drawing me cuz I lefty How do you have so many coins?  You're talking about which hands you use You're kidding me I'm being robbed.   Oh Oh Wow, I was close to being able to steal a star if I accidentally steal coins from let's see by hitting random I'll feel like the worst person in the world. So Jason. I'm sorry Would you say toadette is going down? In an early around and going down No, no, no toadette's going definitely down on toad, right? Oh Oh, yeah, who's to say? Yeah, that's true. Maybe me birdo. Ah Yeah Do you think our toad and toadette related? I thought they were together I'm sorry. I have to go to the Mario wiki. Well the first thing the first Google auto complete is our toad and toadette siblings They are not siblings.  They hold hands and toadette winks while doing so Somebody asks if bean is my sister. I can just start saying no, we're adventure pals No, is Ashley my sister. No, she's my adventure pal Oh They hold hands while they do so You know, what's a fun question to ask chat, I think everybody should ask their chat what era they are in Ethan's in his male wife era That's a midwife.  We're gonna battle. Oh wait. We're battling.    Oh god, okay Can I just be in my old era? You are not old. I'm gonna punch you.  I lie embrace and I freaking love that my knees are feel terrible every day and you know my back hurts Literally have an even reached half of your life Oh Until you change Somebody said I'm in my lover era, which they described as being pretty cringe, but you're happy and healing Oh Great One of my mods said that you're in your glam metal era.  Yeah, my glam rock cheeky era No, I don't want to deal with this I'm putting it up to fate. Okay, cool. Please. Don't be me. It's always gonna be me I only wait oh Shit, please. Oh, please. I think you're getting close there. Yep.    Why are you has warrior where wallow? Weegee needs wallow?   Oh locks.  I would like to also find out.  Oh, she's gonna punch me. That's me. That's pure My chat taught me about war your chat how you about war. Yeah, I didn't know about war What did you learn about war? War I don't know probably like five or six years ago. Hey Jason. How you doing over there? Oh, I am doing well, and I never forgot that time you took the coins for me. I just want to My god listen chat my stream is marked as mature. All right, and so See you problem.  It's funny Tiptoe out of the room and Ethan's like what are you going guys? We're having really good The video just started I want to record a video really badly and it would be a hundred percent censored So I don't even know if this would be a good video to record but a video of doing like watching like the gauntlet of Fucked up videos that were like spread around in high school I would probably I would watch a video of someone where it's just their reaction cam to like the gauntlet Videos. Yeah. Oh I was just saying because you were saying you Right where I was saying that I need to be sat down you were in my chat and I was like I haven't seen any of these videos Oh, we need to sit down and have like you and Mika and Ethan and Ashley and Max all sit down and be like this is two girls one cup I've never seen any of those videos Wow none of them. We should all yeah, we should all sit down and watch them I don't know if I would like I think that's a very funny video idea Yeah, but you got a gold pipe out of it So you're fine. Honestly, it's better than I stole one then you would have three stars And then I would have been the target but guess who's the target now Ethan. It's Ethan Ethan's Ethan can I steal that star my star? Let's talk about this chat just said Ethan you need to apologize to Rosalina if you win And I don't think I do if I win then You know, it's just Rosalina's privilege coming back into play Very close to my asshole.  Oh Who needs the circumcision? I have a question for you. Does Birdo have a cloaca? That's how you say that word Yeah I don't know. I think I think we decided the other night. Yes, I think so because like we're does like a reptile But Birdo literally shoots eggs out of her mouth birds. Don't have that. Oh, the mouth is the cloaca First don't have a They don't have a post post.  I think it was because his balls hurt Imagine why 19 all right can hail Mary. Here we go I love the overcompensation of like using a triple dice to go far away. It really makes me Yeah, you and E for getting blasted what happens when you get blasted. Yo, honestly You know that is a massive conging right there. It's not like we can do anything with them Well, I mean, it is a colossal conging though Who purchased the most items I purchased a few me and me oh Shit when I keep that puts each back in first right now. Ethan's in first place. Come on Event spaces. I don't know who that is. This might be Luxie if Luxie gets it.  It's easy. Yeah, it has it for sure But like wow. Yeah What do you have to say about Rosalina now? Hey I thought if you won now you have to cosplay Rosalina.  Oh My god, you're right Yeah, like I honestly think you could probably find a use for that outside of the Rosalina


Hello, this is Hans van der Kwas, Senior Lecturer at IHE Delft Institute for Water Education. In a previous video, we have styled the catchments and streams of the Ruhr, as given in Chapter 4 of the book QGIS for hydrological applications. In this video, we are going to continue with that data. We're going to add cities and towns from OpenStreetMap, and we prepare the layout for styling, which will be covered in another video. First, we're going to install the Quick OSM plugin. You find it on the plugins, and it should install plugins. If you do a search, you can easily find it. In my case, it is already there, but I need to upgrade, so I'm going to upgrade this. Remember that you need an internet connection for this. So we open the Quick OSM plugin from the Vector menu. And if you want to know the keys and values, and if they are available as points, lines and polygons, you can click the Help button. Here, we're going to use Place, and from Place, we will first download all the cities, and we want it in the layer extent of the DEM, so that it also covers a bit around the catchment. And if you click the Advanced button, you can choose there the points and run the query. If the internet is slow, you can increase the timeout value. This one has loaded, and I'll do the same for towns. This one has also been loaded, so it's added now to the layers list. And what we see is that it has this chip symbol, which means that's a temporary layer. That means that it gets lost if we close Qchis. So I'm going to save this now to a Geo package. We give the layer the name Towns, and we also change the projection to the one from the project. And we repeat this procedure for the temporary file of City. Save features as Geo package. Make sure that Geo package is chosen. Choose the right database, and change the layer name, in this case, to City. And we change the projection to the one of the project. Now we can remove those temporary layers, and we can check our database. We need to refresh, and there we see that Cities and Towns are now also added to the Roar data. We are now going to style the RoarCities data. So open the Layer Styling panel, and there we are going to use the simple marker. We're going to use another marker symbol. Here in this list we find the TopoPopCapital, and now we can also label it. Choose Single Labels, and the field I'm going to label it with is the Name field. I'm changing the font to a Sensory font, which is better readable, and I'll choose Aerial. Make it a bit smaller, choose Nine Points, and use a Bold font. Go to the Buffer, and switch on the Text Buffer. Change the color, 191, for RG and B, comes with a softer background, and then we use a Blending Mode, Soft Light. This gives a nice effect that the buffer is not very disturbing, and blends nicely in with the background. We change the placement, increase the Distance to 2.5mm, and we choose a Cartographic Mode of Placing the Labels. Now we're going to do the same styling with the Towns. We switch to the Symbology, and we're going to change the Marker. We can change to All Symbols, and then we'll find TopoPopCity, and that's the one we're using. We can change the labels. Also here we will use Single Labels, and label with the Name field. We also choose the Aerial font here, and make it a bit smaller to Eight Points, and keep it as regular. We draw Text Buffer in the same way, so we change the color to the same gray, and use the Soft Light Blending Mode. For the placement we change the Distance to 2mm, and we change the Automated Placement Engine to not truncate the labels on the edges of the map, so we uncheck this box. We also are going to make a separate boundary of the raw catchment, which is not using the inverted polygon shape burst fills, so I duplicate the catchment polygon, and I'm going to style this copy with just a single symbol, and I'm going to remove the shape burst fill by pressing the minus, and I change the Layer Rendering again to 100%, and this gives us a sharp boundary of the catchment, which I'll need later. Now all the layers have been prepared and styled for making a physical map with a print layout. In the next video I'm going to demonstrate how to do that.