My name is Jeffrey Tucker and I work for laissez-faire books and I would especially like the other speakers like to thank Hans and Gulchin for inviting me to this wonderful event. Of course the surroundings are spectacular, Josler and I were just talking about the amazing food. We both have a sense that of regret of having to go back to the United States, you know, we thought we lived in a place with wonderful food. Now we know it's all just terrible. I guess, you know, Americans are specialized in the distribution of massive quantities of food to the masses at very cheap prices, but of course it's all deadly.  So, it's thrilling to be here. And of course the laissez-faire books were very honored to be the publishers of Hans's new book, The Great Fiction, which is out on the table. So my speech today, like many other speeches, will cover... Can you all hear me well? So my speech will, like many of the other speeches, will chronicle the decline of civilization, so I hope it's nice and uplifting for you. In this case, I will not be talking about the decline of mores or values or anything else, but the very strange way in which the law is being used to deliberately take away from us all the advances that the market has made over the last century, in particular and then going back in time. It's a very strange thing that's happening in the U.S. It doesn't get much attention, so I hope to chronicle it in some detail in these few minutes. Well, I remember too well back in 1989 when socialism fell apart in Eastern Europe and Russia, and there was a great moment for any believer in liberty, and I recall thinking at the time, I can't believe it. Everything I've dedicated my life to so far has already been achieved. Now the whole world will have to embrace freedom completely, now that it's been obviously proven superior to every form of statism. It seemed to me the battle had been won, and I wondered what I would do, actually, with the rest of my life. I rushed to the library several months after the great events and dug up many of the proto-socialist journals of the time, the Marxist journals, the Stalinist journals, to see what they had to say about the failure of socialism. To my astonishment, I didn't rattle them the slightest bit. I was alarmed by the sheer calm of these journals, the sense that nothing had really gone wrong at all. Over time, of course, we've seen vast increases in the size of the state, not just in the US but all over the, and many other parts of the world. So then I began to look through Mises' great book, Socialism, 1922, to try to understand what I had misunderstood. See, up to this time, I had thought that the purpose of socialism was to, the belief was that socialism would enhance human well-being and make us more materially better off than we were before. That it would bring a kind of garden of Eden to the world of wealth and prosperity and equality of distribution, and that humanity would be vastly better off under socialism so they believed. And this is what Mises directly addressed in his 1928 article showing that this was an impossibility, in fact. Every step towards socialism was a step away from prosperity and material wealth. So he conclusively demonstrated that socialism could only lead to the opposite of its intentions. But by 1922, he writes this book, Socialism, he covers other forms of socialism besides the one that believed that socialism could make us more materially better off. And he covers a whole variety of types of socialism, and in particular, I was drawn to the section addressing what he called chelastic socialism, which is a version of what Rahim addressed in his first lecture here, which is a kind of a millenarian theory of mostly religious origins. The chelastic view originally dates from a kind of a Jewish sect that mutated into a Christian sect and mutates into our own time into a secular sect. The view is this, that we once lived in a golden age where everything was perfectly balanced and beautiful in every conceivable way. Man was united with God, man was united with nature, all human beings were equal. Whatever your view of the golden age is, this is what once existed at some point in the past, and then some corruption into the world to cause this golden age to turn into the present misery. So it's the job of the chelastic view of the world to expunge from the world the evil so that we can restore the golden age. And this turns up in many different forms. We saw it throughout Christian history with Murray Rothbard's very well and hilariously in his history of economic thought. And Mises saw it even in the 1920s. He saw that there was a view of socialism that had nothing to do with enhancing material well-being of humanity, like the old socialist views, but rather had this much more mystical view that we could expunge from the world some source of evil and restore some golden age of whatever it may be. And this is the type of socialism, and I didn't understand this at the time, that had come to dominate socialist thinking in the United States. It was no longer about making us more prosperous. It was about bringing about some kind of utopian view through some kind of change in the world that the socialists themselves would enact. And Murray Rothbard in his pamphlet on equality and primitivism in the division of labor likes to identify John Kenneth Galbraith's book The Affluent Society from the 1950s as the beginning of this type of chelastic socialism in the U.S. where Galbraith observes that the market had made the world vastly more prosperous than we ever imagined. But he said the affluence alone is enough. In fact, affluence is the problem because the expanse of private wealth has come at the expense of the public sector. The public sector is getting increasingly impoverished. And our human well-being really should be defined not by how much money you have in the bank, but by how much money the government that's really new has and how many resources it has at its disposal, and that's the real source of wealth. So we needed high taxes and high regulations and a vast transfer of wealth from the private economy to the government in order to achieve this kind of vision. It's kind of an early view of this chelastic position that we need to restore a golden age where the government was big and ruling everybody. His view of the golden age was the New Deal or something like that. Well, there's another book that came out in 1962 by Rachel Carson called The Silent Spring. And maybe you know something about it or you've heard something about it. Ironically, the same year that Man Economy State comes out. So Rachel Carson comes out with this book, The Silent Spring. Last week I wrote a kind of bitter criticism of the book and I swear to you that I've received more email about that column than anything I've ever written from the partisans of Rachel Carson. It turns out she is not just a writer who wrote a book 50 years ago. She is a modern saint. Not just a saint. She's like the mother of God or something, I mean the way people perceive her. I mean she's the founder of the environmental movement, I guess many people believe. Her book was a gigantic bestseller at the time. It was an example for the American left, a rare example where a book, one book, completely changes the public culture and has this gigantic effect on law itself. So it was a kind of a model for them. Rachel Carson herself was not really an academic. She was just a worker for the government, actually, the Fish and Wildlife Service or something like that. But for some reason her book of 1962 really took off like no book in the post war period had up to that point and ended up causing a gigantic shift in American public policy. Most famously her book ended up in banning DDT, which was the cool chemical that caused us to vanquish many evil insects from the world like mosquitoes' bed bugs. This was a great uptick in life as far as I'm concerned. Well her book ended up in banning DDT and we see the effects all around us, not just in the United States but around the world. More importantly, it turns out her book had served as the purpose of modeling a kind of a new socialistic view and I want to just read a few passages from her because she goes way beyond Galbraith. It's said to be a book of science that documents how chemicals are killing birds. So the one day that spring will come and we'll wait for the birds to hear and there will be no birds outside of our windows and this will be a result of evil chemical companies spraying to get rid of insects and they inadvertently kill birds and so we have a silent spring. This is the vision of the world that she creates. It's like the ultimate nightmare for the suburban housewife or something. No longer will the hummingbirds dance outside the window, outside the breakfast room and this is all because of chemicals. So her book raises this specter that chemicals are taking its way from the golden age. But more importantly than a book of science and her science has been debunked through many, many books in the meantime and there have been dozens of books that have come out attacking her book Silent Spring and its scientific specifics. More importantly, it really is a book of philosophy. Its advances, exactly what Mises called the chelastic view of the world. So I just want to read you the opening of her book, it's a very strange thing. Something you could only believe in 1962 really, where there's no mosquitoes around you and every life seems happy and everything's wonderful and you can now have washing machines, all this technology, everybody's bored out of their minds and they decide to destroy the world. So this is what she says, the history of life on earth has been a history of interaction between living things and their surroundings. Okay, I mean, right, okay, we can get that, we can get that. To a large extent, the physical form and the habits of the earth's vegetation and its animal life have been molded by the environment. That's a little bit suspect, right? It's been molded, the environment is molded, okay. Considering the whole span of earthly time, the opposite effect in which life actually modifies its surroundings has been relatively slight. So to the extent that you and I have done anything to change the environment, that's a relatively small period of time. Only within the moment of the time, only within the moment of time represented by the present century has one species, man, acquired significant power to alter the nature of his world. Only in the 20th century has man altered his environment to his own benefit. According to her, that's right. Only in the 20th century. So, I mean, what did the 20th century give us, really? I mean, well, a few things like we got internal combustion in the car and like running hot, running water in every household and like the air conditioning and the heating and flight and other cool things like that. But this, to her, all these things represent the first time in the history of the world that man ever presumed the right to alter nature to his own benefit. And this, she says, is what we have to stop, beginning with chemicals, chemicals. That's the great evil. So that's the opening of the book and I'll read you the closing of the book. The control of nature is a phrase conceived in arrogance, born...  It's a phrase conceived in arrogance, born of the Neanderthal age of biology and philosophy when it was supposed that nature exists for the convenience of man. What arrogance? The concepts and practices of applied entomology for the most part date from the stone age of science.  It is our alarming misfortune that so primitive a science has armed itself with the most modern and terrible weapons and that in turning them against the insects, it has turned them against the earth. So she recommends, she says, only by taking account of such life forces and by cautiously seeking to guide them into channels favorable to ourselves, can we hope to achieve what she calls a reasonable accommodation between the insect hordes and ourselves. So we have to kind of sit down with the bed bugs and with killer mosquitoes that are killing millions of people around the world. We have to have like a negotiated settlement or something. This is her view of the... This is her view. Of course, she's a moderate by any standard of today. You can go out into the libraries and pick up practically any book on sustainability and find that people have far more extreme views now. It's not just the last hundred years that are corrupt, but it's like the last, you know, couple hundred years. Really, everything's been going wrong since the industrial revolution. And the further back historians have dated the industrial revolution, the more radical the achelastic socialists of our time date the beginning of the end and date the golden age.  And so we need to reverse all these things using the power of the state. And this view of socialism, you know, the problem from the socialist point of view is that insofar as you allow man to be free, he is going to adapt his environment to his own benefit. The goals of this movement is by enhancing, transferring the power from you and me to a state to control us. And this is essentially what we've seen playing itself out in the whole post-war period of American economic regulation. I mean, a systematic issue by issue, slow going unraveling of all the achievements that we have achieved in the twentieth century. And it's been going slowly and systematically through a whole series of products and you have to keep your eyes open to out for this because otherwise you'll miss it. It's unbelievable the expanse of the central planning that's taking place in America right now that's systematically unrolling all the advances of the twentieth century, including, you know, every form of indoor plumbing and internal combustion. And you name the advance of the twentieth century, you'll see a attack on it in a regulatory form. So I make part of my, what I like to do is to investigate these things and find the regulatory source of the problem. So I've made a list here and I don't know how many of these things I can get through, but I want to talk about some of them. Let me just start at the top here. For one thing, in the 1970s, and this continues all the way up to now, there's been a systematic attempt to take all phosphates out of detergent. Now phosphates essentially are the things that make things clean. Okay, it's not soap, it's stuff that takes the soap out and whatever the soap gets out of stuff like dirt and pulls them out of your clothes or off your dishes and results in clean stuff. And basically that's what phosphates do. But these have been banned largely in detergents in the United States, systematically a little bit at a time. The way that most of this legislation works is that like Congress passes something, it's sneaked into some big piece of legislation. It's not like an immediate ban, it's like five years out or ten years out. It's like goals for industry and industry immediately gets on board with these things. There's a slogan in American capitalism called new and improved. So under the new legislation, nothing's ever new and improved is always new and worse than it used to be. So like almost all products are worse now than they were a few decades ago. Industry doesn't like to talk about it because they don't want to advertise to consumers that actually the soap is kind of crappy compared to our most recent release a few years ago because that's not good for marketing. So nobody wants to tell the truth about what's happening here. The phosphates were taken entirely out of dishwashing soap. In the late 1970s, not dishwashing soap, it was soap for clothes. Any soap that you use for washing clothes was taken out of there, resulting in far dirtier laundry than it used to have in the past. And it's almost impossible to find, in fact you can't find any laundry soap anymore in the US that has phosphates in it. And the same thing has happened to dishwashing soap more recently, only within the last ten years. It's a very interesting thing to me because many American households, millions of American households discovered that their dishes were dirty when they were coming out of their dishwashers, sometime in the last five years. So many people went and replaced their dishwashers to get better dishes. Only to discover the dishwashers they bought were actually worse than the previous ones because they had to be energy efficient. And this combines with several other effects I'll talk about here. Now there's a hack for this. There's a way to get around it. You can actually buy phosphates and add them, but those are increasingly under attack too. Air conditioners are another one. Now this is obviously, Doug French has written the mighty treatise on the glories of the air conditioners. But back in the 1970s, we saw the first attacks on CFCs that, you know, on Freon that makes the air conditioner work in the US. So industry replaced it with a different version of CFC. Well, that was banned too. And just within the last four years, basically because of international treaties, we've had a new form of coolant introduced that only works on something like 5% of air conditioners. 95% of air conditioners run the old form of coolant. So when you're free on it and your air conditioner runs out and you call the repairman, he will tell you that unfortunately, yeah, it will cost you about $1,200 to replace the coolant in your air conditioner with that old form of coolant because it's severely rationed right now, severely rationed. So your best bet really is to buy this new kind of air conditioner. They use this new form of coolant that's much cheaper. So you should spend about $2,000 doing that.  And most American households are bamboozled into doing this because they don't know any better. There's a gigantic black market right now for a CFC. There was a guy arrested and put in jail the other day for having imported tons of it from China where it's made very, very cheaply. And it can be sold without any problem in Mexico. And I'm not sure about Canada actually, but in most places of the world, you can use this stuff in the United States. So there's a gigantic black market that's developed for the thing. I have to raise the subject of toilets because one of the things you'll discover when you come to the United States is that your toilet doesn't work. Sorry to report this to you, but it's just true. It doesn't work. And the reason is that they lowered the amount of water that can go into that could be held in the tank. There used to be something like six gallons or more so you could flush down like a ham or something. But now, it's like nothing flushes anymore. You have to flush like 20 times and it's extremely dirty.  That's why I'm concerned. This is a disaster. Hot water heaters, you can no longer get hot water. Like the showers in this hotel, you turn it to hot, it's hot. Great. The US, all the hot water heaters are shipped so that they can only get as hot as 120 degrees. If you ask your plumber to hack it, he's forbidden by law from changing it, forbidden. So you have to do it yourself. You have to get a screwdriver and get it out. Unbelievable. The dishwasher itself, an amazing thing. Just within the last year, new regulations are mandating that new dishwashers, they don't work anyway because the detergent is so crappy. But now they have to be reduced from using 6.5 gallons in the course of the load to using five gallons. Only five gallons. So you've got cold water washing dishes with crappy soap. Using only a mere five gallons of water in the course of the load. And everything comes out dirty. So what are you gonna do?  This is what they're driving us back to. Hand washing. And there was a testimony about this in a regulatory hearing the other day where a woman who's a real serious dishwasher expert explained them, do you understand what this regulation would do? Do you understand this is gonna drive the American bourgeoisie away entirely from dishwashers? To hand washing their own dishes? And the answer was yes, of course. We do understand that. That is exactly what they're intending to do. Get rid of them completely. When these appliances were first introduced in the 1940s, there's a common phrase in American culture. Women proclaimed the liberation from drudgery. That's what the washing machine did. That's what the dishwasher did. These are glorious inventions. So much for liberation from drudgery. Drudgery is going to be back. Refrigerators with ice makers. When I was a kid, you had to attack the freezer like every few months. They would build up this ice ring around the freezer.  Now the innovations are that these freezers don't freeze up anymore. And also you can get water and ice out of the front door. It's fabulous stuff. The physical capital of stuff. Capitalism gives us cooler, greater things every single day. Well it turns out this uses a little bit more energy than the old machines. And the government doesn't like that. So now the energy controls are so severe on the new forms of freezers and refrigerators that they're having to eliminate some of these features like ice makers or to the extent that they use them. The energy used in the ice maker has to come from the functionality of the refrigerator itself. So now in the old days people would buy a refrigerator in the 1930s and use it until the late 1950s or something like that or buy one in 1960 and use it until the mid-1980s.  So you end up spending ever more money. The things are being depreciated by law. Drain on cloggers. Lie is no longer legal in the US. If you get a clogged drain, forget it. And you are going to get a clogged drain because your water pressure is by law extremely low. And of course the water's not hot. And of course your toilet doesn't work. So everything's gonna be clogged but you try to unclog the clog. Lie is banned. That's a strange one though. It wasn't done for environmental reasons. It was done in the name of the war on drugs. I don't understand the relationship between lie and the war on drugs but there you go. Light bulbs, incandescent bulbs are under fire. Even now when you go to the Big Back's hardware stores in the US it is hard to find light bulbs. Mostly what they have are something else. These light oriented things. I mean you're called fluorescence.  It's terrible. So you're getting rid of incandescent bulbs. Congress keeps putting off the final regulation like one month at a time. Just barely intervening right before the regulations kick in. So lots of Americans are right now hoarding light bulbs like as never before for fear of this. Makeup is another one that's under fire. The regulations are so severe that American women will report to you very quickly that makeup doesn't work anything well as well as it did a decade ago. Mentioned gasoline briefly. I don't know if you know this, but gasoline in America is increasingly made out of corn syrup. So America has the thing about corn. We love corn. We love our corn growers and things. So Congress decided that we should make practically everything out of corn really. Everything should be made out of corn. But especially gas.  And 40% of the American corn crop is not going to feed the poor. It's going to be burned up in our gas tanks. And unfortunately this stuff is really, really evil. It's called ethanol. And it gunks up your gas, or gunks up your engine, which causes it not to work very well. And also you can't store it. So for example, if you have a can of gasoline that you're keeping over the course of a season for fear that maybe during hurricane seasons, a tree is going to come and fall on your back porch or something. So you want to put the gasoline into your, what's it called? Chainsaw. You pour the gasoline in there. It doesn't work because the gasoline separates the corn and the real gas, you know, separate over time and wrecking the whole thing. So you're stuck. But since I brought up gas cans, this is amazing. So I ran a gas one day in Opelika about six months ago. And because my gas gauge stopped working, probably because of the ethanol, I don't know. But I called up a guy, said he can bring me some gas. And so he shows up from the gas station, and he starts to pour gas in my gas tank. He goes, I don't know what the hell's going on with these gas cans these days. They just don't work like they used to. Of course, my ears are very sensitive to this, right? Oh really, what's happened? He goes, well, I don't know. He said, they don't put little plugs on the end anymore, so you can get a good circulation of the gasoline so it can go in quickly. It's all this kind of solid state enclosed thing. So the gas kind of gulps out and big belches, you know, blah, blah, like that. So it takes forever to fill the thing up. He said, I've hacked some gasoline cans back at the station, but this is the new kind that doesn't allow any kind of air filter to make the can work properly. So I said, well, that's very interesting. Do you think the government has anything to do with that? And he literally said, everything is wrong with the world the government did. That's what the guy in Alabama said. So sure enough, I got back quickly. It took one search only to find that within the last 12 months, new regulations had regulated the gas cans so that now they don't work anymore. They don't actually pour gasoline out of them. You have to actually drill holes in them and hack them.  And on eBay, the price of the old gas cans is soaring now. This is what's happening. But let me finally get to the question of insecticides because this is the one that Miss Rachel, St. Rachel Carson is most responsible for having banned any development in insecticides in the U.S. And increasingly, you can't get anything that smells like insecticide at the stores anymore. You certainly can't get DDT. And the consequence of this is that the U.S. is undergoing right now a bed bug epidemic of epic proportions. Bed bugs first revisited the U.S. about three years ago. And it was kind of a big news event. CNN covered it, oh look, isn't that interesting? We've got bed bugs, isn't that strange?  And then suddenly the news shut down. Well, thank God somebody started a bed bug registry because you could look at a map of the U.S. and see where they're infesting. They're infesting the whole country. There are something like 200 reports a day appearing on the bed bug registry and it's getting worse by the day. I don't know that I need to go into the details of what a bed bug does.  That you expect to have gone entirely in the developed world and the civilized world. They have not gone, they've come back. They crawl out of your mattress. They lie dormant for up to a year. They crawl out of your mattress in the middle of the night and they first bite your back in a way that takes away that sense of feeling so that you don't know that they're really there.  And then the morning comes and they sense that you've woken up and they all crawl back inside the mattress. And you go, this is what bed bugs do. And you know what? When they show up, they're sort of small and black and when they leave, they're large and red. That's what bed bugs do. This is Rachel Carson's fault. Not just because of the banning of DDT but because of the regulations that prevent any innovations whatsoever. I had a lot of mail where people wrote me. I said, oh, you can't use DDT on bed bugs anymore. If it doesn't work, nobody will use it. No, it's still gotta be bad. So I'd like to try it anyway. I'd like to try a little DDT. Just to make sure. In any case, we don't have any innovation in insecticides anymore. I've said before that the only thing on this planet that's killed more people than governments are insects. And it's extremely dangerous to unleash these things in the world that's exactly what these kind of regulations have done. But let me end on a hopeful note here. Just like our friend who is a smuggler of freon from China and people who hack their gas cans and people who drill holes in their shower heads so you can get a decent shower and people who open up their hot water heaters to crank up the temperature gauge and people who buy phosphates from sketchy, phosphate black market companies and add them to the dishwashers. All these kinds of activities represent a kind of revolt against the state in small but important ways. A very popular show on television in the United States is called Breaking Bad.  He decides to go into the production of methamphetamine and sell it. And he's a very good methamphetamine cook. Now you're thinking this is a very bad man, right? Watch the show, you will cheer for him episode after episode after episode. However implausible that sounds. I'm only in now third season, he's making about $6,000 a day, he's doing pretty well for himself, you know? Breaking Bad is very interesting. It occurs in the first episode where he first begins to cook methamphetamine and a kind of a local drug dealer comes up to him and says, you know, what's his name, do you remember his name? Mr. White. Mr. White. Mr. White, when did you start breaking bad? Right, breaking bad. That's sort of doing things illegal in order to survive and preserve yourself. Breaking bad is the new theme of American life. You have to break bad.   You have to find ways around it. And fortunately, this is happening. I urge you all to have a look at this book by Robert Neuarth called Stealth of Nations, where he documents something like two thirds of the workers in the world that are working in the informal sector. They're in full-scale revolt against the state's attempt to control and regiment our economic lives. They're going outside the law. This, my friends, I'm afraid, is the only path to freedom left to us. In fact, I think it's the best one. We can and must build our own liberties, our own world of liberty, and our times and our lives, even if it means breaking bad. And I'm afraid that the preservation of civilization itself absolutely requires this. Thank you very much.


Good evening. I like to call the Monday, October 1st regularly scheduled a select board meeting to order to my left is Pete Kelly Wayne Lamerton to my right is Jeremy Hansen Angelina Kaffron and With us also is Dana Hadley in our town town treasure Diane Isabel And Editions or changes to the agenda. I have no changes Public comment Hearing none treasure report Diane. Yeah, okay. We have if you look at the trial balance We have a savings account for six thousand three eighty eight thirty seven and That that money also sits in a sub-account. Well long time ago. We didn't have a sweep account for our checking account So the the treasure would use the savings account and just move money, you know, so she get more interest Well, that doesn't just isn't the same, you know, just doesn't really work to me I don't think you know, we're not getting enough money out of it So what I'd like to do what I'm going to do because it's not reserve money or anything is money Not money was voted on I'm going to move that money out of sub-account Just put into the general fund because I'm still making interest in general fund So I want to make you aware next time you look at the trial balance for the October trial balance It just be moved in general fund can just try to consolidate these accounts and get fewer accounts Especially those that are not really doing anything for Diane What does the sweep account do it every night at the end of business once we have all our Deposits let's all our checks the bank maintains a balance of X amount in our checking account 100,000 and the remainder of that goes into a sweep account as a repurchase agreement. Yes, yeah And we got what $50 worth of interest last month or something like that Yeah, we have a lot of money in there. So, you know for six thousand six thousand three eighty eight in the sub-account You're looking at maybe a dollars worth of interest a lot. Yeah, it's so I'm just like I said I think what you're trying to do is kind of try to streamline the the accounting a little yeah I want the reserves to match of those sub-accounts. Yeah, and that since that's not a reserve And it's not some of the auditors have said anything about okay that they care about but I imagine it simplifies things It will quite a lot. Yes, it will quite a lot Okay, and then the auditors speaking of them are coming in tomorrow and Wednesday And otherwise not anything else like that is in the agenda I guess a discussion requiring the change of meeting day for the select board. We had started that a couple weeks ago Angelina wasn't here last month. So I mean last meeting so we didn't continue it And I guess I just wanted you to Finalize the discussion on it whether you were changing the day or not changing the day We had talked about Thursday changing into a Thursday Tuesdays and Wednesdays The room is usually busy between Planning Commission and DRB You know in Thursday, it's not in Thursday's not And I had a chance to look back over my schedule and Thursday actually works quite a bit better for me At least this semester because I have classes right at 8 a.m. on Tuesday morning So when these meetings go late that means I'm sure showing up. Yeah showing up there Without as much time the evening So still the first and third Thursday. Well, that's what I was thinking but of course More for me. I'm gonna check my schedule All right, I Guess it doesn't matter all right If if so, I'd like to just start that in November and Because I'm trying to schedule public hearing for the next meeting So if we could do that that's great That would give me a chance to make Announce it and post it and so we should probably formally move move that yes, you should please move that we schedule our Regularly skit our regular schedule for Berlin select board meetings to the first and third Thursdays of every month Starting at 7 p.m. All those in favor Opposed motion carries We will we will change it on the website and I'm gonna miss your first meeting now that I think of that So that worked out but I'll figure that out I want to make sure he doesn't mess Show her if you don't know anybody here. Well, Dave hasn't been here lately. I felt kind of hurt You know, I did a lot of something I said. So all right, so we'll begin that in November Give us a courtesy call for the first month absolutely Okay, and review of bridge and road reserve accounts. Yes, okay, I'd like to begin with that I guess that I'll begin with the bridge. Okay, and I've given you it like coverage a cover sheet I have gone looked in the minutes. Okay, I've since 1988 on and I looked at every single one of them to try to find what was happening why they created this So they had what they called a bridge transfer account that started in 1988 And the reason they did it is they said it was recommended by the auditor take money left over from fiddick Account plus money from Partridge bridge and just start having this bridge account. So Through the years they have you move money in and out of bridge account They've used it for bridges and then it became dormant in 2005 and or even before that time actually but in 2005 The treasure had moved it and then she moved it back into this to this account So this the trans the bridge called the bridge transfer account that is in another Fund balance. It's a fund balance all by itself Now we also have what we call bridge maintenance and the bridge maintenance go back to goes back to 2010 and That one in the minutes was started because and this is a reserve Okay, so we've got one that's a reserve and one that's a fund balance and The one that is the reserve it says reserve the funds in the bridge maintenance fund to build up reserves for work to be Completed on the glenus road bridge and the work has been done since that time But there's still money that remains in there So in the fund balance that has its own separate fund balance the amount there is 19,398 46 in the bridge maintenance account, which is in the reserve account That's 34,798 68. So we've got just add the two together here 53,000 basically For bridge maintenance, so are you saying you want to put it in one fun? I do want to move the fund balance account into the reserve So at least we have it in one place because it's both for the same purpose. Yeah So the nine three hundred dollar debit in 2012 was for bridge maintenance. Yeah Yes, and that that one I think there was a grant on that as well So if we move it all into the fund balance, can we use it for our portion of the culvert? No, it's the bridge bridge But it was voted on by the select board this is not Money that the taxpayers voted on directly. So it was a select board. So then in that case the select board could Repurpose it. That's my understanding. Yeah, okay. I was wrong. That would be my understanding. Yeah, I Think that would verify that with the attorney first. I would I would but I think it sounds like I can certainly move it I think into the one reserve account. I think it makes sense I mean what we're trying to do is stop having all these funds for the same thing In this way you would also see it because when you're looking at the trial balance I know you're looking at the general fund part of it. You don't usually go further into the trial balance and see But the different accounts are You know anything in these funds go before the board before they get Used anyway, right. It has to be approved. Yeah What is our portion of the mirror like culvert our portion is 33 thousand dollars So I just I want to make you aware that I'm going to be moving it, you know to the reserve But also make you aware to keep that in back of your mind that that is not me that's available at this point for bridges Okay, then the second one that I have to discuss today is what they call capital road project And that one also has its own separate fund and there's 29 thousand five sixty one seventy in that one that one was established in January of 1999 and it was There's discussion regarding trying to budget for a plan to improve the gravel roads rather than just maintain them So that was what the purpose was like I said that was in the minutes from 1999 And there has been money going in and out of that since 1999 But I don't know when the last time let me put this way is before 2005 The last time it was used in 2005. It hasn't been used since I was hoping to use those funds as the money that we need To make up the remainder of the traffic light project We needed I think 23 thousand dollars 295 you've got 295. I mean would it make sense to use the 295 and clear that fund out I think the thing is in my view Funds are great and to save them, but if you just have them to stay in the books Yeah, since 1999 has been touched in 13 years Or should at least be used yeah, yeah, I mean if we use the 295 and then we would not hit the operating budget quite as well by six thousand dollars I'll make a motion that we use the Kappa roads project capital road project fund balance to have 295 60 170 to Pay toward the traffic signal upgrade on Fisher Road and close the account second Are you for the discussion? Carry none those in favor Those opposed motion carries and then I'll move To take the bridge maintenance fund and combine it with the bridge transfer fund and Establish one bridge maintenance account and eliminate the other reserves in the reserves second Any further discussion? Carry none those in favor. I don't know those opposed motion carries We have been Getting these more organized in the last year and a half and we've talked to the board about it before I still have a few more to go You know, I think things happen as you go along and My ideal goal is to have the reserves all the money that's in the reserves has a sub-account each one separately So when the audit comes around it will be a lot faster because a lot of time is spent on Explaining where the money is. Yeah, well, yeah going through it this way I think everything would be mirrored and I'll be right there in front of you certainly pending or Immediately necessary bridge maintenance or repair. It's out there. I'm not aware of any Small bridge down by us the one of the guard rail posts have been hit and the only thing standing there is for rebuy Well, there's a bridge on three miles Yeah, so maybe you have Tim, but that's the type of thing we could use that for an album mention that Tim We do have I think we need to pave lovers lane bridge Tim was concerned that there was a whole forming in there, but it's just the tire that's Bunch done. So maybe I'll also ask him if it's necessary to do any Washing or painting. I'm not sure what's necessary with the bridges that we they have done Some bridge washing in the last Year anyway, I'm not sure how probably they should do it every year, but I'll speak to him about it so back to using it for culverts we can we can Consider a large culvert a bridge if we so choose I don't know have to look up the definition, you know, and I got it I Think that we had just talked about we could even change the purpose of that one I mean, I would check that which with Rob, but I think we could change the you know, no, sir I'm not necessarily Advocating that we take the money out of that fund towards we're a lake, but I'm thinking about we have others We have Richardson that is going to need that we didn't get a grant on that's going to need to be addressed So third definition of the Mary Webster is a bridge over a culvert for culvert See it works for us, doesn't it? So but you also said that that was designated by the select board not by the voters Correct, so it could take an act of the select board to call it a bridge or a culvert fund as well I mean you could just say, you know, this was put here for that exact circumstance, you know, maybe there was originally envisioned for For the bridge over in Clintus road, you said but I mean I think that had been repaired I don't believe they're going to have anyone who's going to object to using and not money Yes, yeah Now is there a culvert fund? No, or any court maintenance No, not that I know of okay There is now yeah, sorry to call so after all of that Motion that I made and that we approved I Would move that we change the bridge maintenance fund to the bridge and culvert maintenance fund Any further discussion hearing done those in favor high those opposed motion carries Is that it yes, that's we weren't going to hit you with all of them in one night There's more to come Okay, thank you, thank you Appointment of Ted long is alternate member to the public works board you met with mr. Long at your last meeting He has expressed an interest to be an alternate on the public works board. I think he went to the last meeting he did and Tom has submitted to me an email asking That he be appointed as an alternate position to the public works board to a point head long as the public works for second be for the discussion Hearing none those in favor signify by saying aye Those opposed motion carries and Ted's name is really Edward just for the fear occasion Next is appointment of Molly Mcmurkridge There's an old Paulie Mcmurkridge now Paulie Mcmurkridge It's all in it to the DRB and you met with mrs. Mcmurkridge at the last meeting I think she's very knowledgeable. She was very familiar with the planning commission and faced him and would very much like to Serve in a committee and I think this is a good spot for her And to point Paulie Mcmurkridge to be an alternate on the DRB He for the discussion those in favor Opposed Okay, please door proposal received I received one door proposal and I've been hoping to get more I did have four Vendors to look at it, but the reason I wanted to bring it to your attention was it was a lot more than what I had thought It was going to be For the two doors, it's about eleven thousand dollars from this from this quote So I wanted you to be aware of that I am hoping I have called the other for the vendors and I hope to have some more vent Quotes for this meeting, but it didn't happen It is something that has to be done, but it's a lot more than what I thought and I guess it's the The style of the door the steel door in the frame and what were you originally thinking the price was going to be Well, I think we had thought that it was going to be less than five thousand dollars Which according to our policy we could have used three quotes I mean the board can do what whatever it decides to do, but normally over five thousand dollars We would have bids I put it out for bid didn't get any When I was more informal I did get more interest We tried Well, I don't yeah, I'm not asking you to do it now, but I thought it was I was very surprised at how much Yeah, I mean if you are then Then I guess I am If it's less than five thousand dollars at this point Exactly Okay So anything so you want to see about I'm just I gave that to you for your information And I will see what else I can get for pricing and I'll be back. Okay. Yeah, okay Private Rome road naming film was way. This is here This is a private road that is off of Bartlett Road it is property that was developed by Sandra and They have asked that the road have a name. It's still going to remain a private road, but the board needs to bless the name Tom has Gone with Vermont E 9-1-1 and there are no issues with that. He's also had we have a letter from Ray Washburn from Du Bois construction Saying that the film is way meets or exceeds the town's standard What we didn't know we didn't know where the name Thelma's way came from That's from me It was the name of my great aunt Who was the matriarch of our family here in Vermont and? she actually owned 80 plus acres and Williston and It's where my love for nature came from and Why I wanted to name it that okay super. It was her last Roebert So they're asking that the name Thelma's way Be accepted by the board to name the road in question thumbs way second Any further discussion those in favor? I motion carries Thelma's way great. We will need a street sign So we can order that but we're going to bill you for it. Okay So we just need to know who to send the bill to okay and Yeah How what if I just send it to Sandy because I know I know we send it except that I'm no longer All right, where would you all right you can send it to let me just have you write your information for me, would you? You should do is just writing capital letters exactly what my father wanted to road And it came in I Think it's still in our garage really They didn't spell road Oh my god, I wish you were here to make that joke That's the best joke I've heard all day What else do you need us to do now that it's been named is there someone that you're waiting to have? Someone's waiting to hear about this road or yes, so The boundary line adjustment. Yeah, so Tom probably knows that okay. Yeah, all right. He'll know tomorrow morning that it was accepted So, okay, is that all we? Yeah, okay He's got a chain of events. He's trying to get a septic. Okay. All right. He's actually everything but The drive way is going in exciting Stephen I went to the great school Yeah, yeah, we're Junction Row people. Oh, we're not gonna hold that again So questions for the board or I think we're good, right Go over. All right. Thank you very much Thank you Proof of slick word minutes from September the 6th 2018 and September the 17th 2018 the September 6 minutes I had changed the fact that select board member Kelly was absent And I sent you the wrong ones in the packet. I think it's but I have fixed that I was wondering I Just did it for make sure you were looking just to keep you. Yeah Move to prove the September 6th 2018 minutes You for the discussion all those in favor high high Stose pose one extension Motion carries and Motion on the September 17th move to approve the September 17th minutes second Can you for the discussion all those in favor? abstaining Okay motion carries one abstention to abstention And Thank you, and See here Ten ministries reporting Yes, I have a few things First of all, I'd like to let you know that they are starting to work on the traffic lights Tim will be over there this week to dig a new trench for the new electrical service that's going in The cameras will be in place before the paving begins And the electrical box they're working on it so it should be done Hopefully in the next few weeks For the work we're going to do this year we have Tim has been asked More than once and I'm just putting this out for the board to think about as you know driveway culverts is Responsibility of the person whose driveway it is and I would Maintain that a person would still be responsible to buy a culvert In some cases I'm wondering if it might make sense for Tim and the highway crew to install the culvert And maybe I should have Tim talked to you a little more, but they have had some issues with culverts This came from someone who asked because they didn't have resources if he could Install the culvert and I said no we can't because it's We don't but There'd be a fee for that that would be paid to the town that I hadn't thought about that, but it's certainly a Possibility and people that maybe don't have resources. Maybe they could pay in Over time or Something like that. I think it's in the town's best interest to have it done Correctly, they would be able to oversee it instead of this culvert failed. This is so replacement or is this yes the one I'm talking about Yes, it needs to be replaced really a modest Budget item just to sort of meet them part way something I mean in the case of you know where it's failing and it's gonna it will affect the road and that's you know, I Think we have to be you know Be on top of it before it becomes a major problem so if you're amenable to that maybe I'll write a policy and Think about it someone We received a thank-you note from for supporting the They call it now the the community with the the gleaning of the of crops Allison Levin and she's got a better name than what I gave it, but I thought that was nice that she sent a letter The underground storage tank at the Garage We have decided to discontinue that We are going to use an above ground tank in a in a cement containment and Continue to buy the fuel from Gillespie And that again will probably cost what was to close out the old tank will probably be looking at three to four thousand dollars when we're done the issue over at the Pond with the gentleman who was sleeping in his truck. We talked about that a little bit last time Sergeant Bessette really addressed that and I think that that issue has been resolved No, still this she's there this morning. Okay a couple hours ago. Okay. Well, then I will speak to Sergeant Bessette I'll just depending on his status if he has any mental illness or And is frequently home and homeless there is a Organization and Barry called Pathways Vermont and they will help him get an apartment Okay, they will find him housing. Okay, so Sergeant Bessette is pretty knowledgeable on those things but I appreciate that and I will mention it mention it to him if that's an issue yep So People want to know that. Thank you the fire department is having a Memorial dedication and recognitions recognition service on October 20th Saturday in honor of fallen and founding members of the fire fire department, so they've been they've asked if the select board would attend They're gonna have a luncheon immediately following the service and if you can go I would be glad to RSVP for you to Carol a house The 20th is accepted It's at 11 a.m. last Week I attended the psychiatric inpatient planning stakeholders meeting at the hospital Which is The hospital has 21 million dollars or I should say uvm plus the hospital has 21 million dollars and they're looking to establish more psychiatric beds here at Central Vermont and They expect that this Stakeholders group will take 18 months for them to Come out with some plans So the first meeting that I went to last week when I was completely out of my element and they were talking about How many beds if they added would solve waiting times? Basically, they're talking about waiting times people who are waiting to Get into a psychiatric bed So that project is this on the way and I'll try and bring whatever I can but it's not my This this right up here area the hospital here The new psychiatric board? No, not the not the state psychiatric hospital. This is the medical center the medical center Okay, because a lot of folks that don't have beds in other facilities First they go to the emergency room right and there's no place and they and they sit there and they end up waiting in the emergency room For many hours, right? So this one has filled up. I just heard stories over the you know, so the state I'm not sure I think the state you get admitted to the state under different type of this is more of an emergency This is more of an emergency. Yeah, there was a there's a colleague of mine whose child spent Five days real And that's been common throughout the state because they've they've done studies. They they did a lot of work on Coming out with wait times and if they added so many beds how how that would affect so naturally I'm very I'm very interested in how it will affect the town If it does bill wolf is also on that Committee and brad is welcome to come anytime So I just thought I'd give you that Um, I wanted to just mentioned As wane knows tom has been working on a program to Capture the cost of fire protection for the water division He is discussing I guess it's water protection for Residential customers who do not have Are not connected onto the water system because basically if you're connected on the water system, you're paying toward the bond He's done some calculation and it's somewhere in the vicinity of 1100 dollars That they could capture I don't think he's come to any conclusions yet But He is proposing a policy Um, I believe it's this board that would have to really approve it and some There are communities that do contribute to the water division for fire protection And I don't know The the issue that has been brought up has been that at when the water division was first discussed Um, people were assured that that if they did not Take part in being a water customer that they would not have An obligation to pay on this If if the town paid the 1100 dollars, which has been one they would be participating Um And we're talking about very small amounts and it's not the dollars that I'm really talking about But I'm just talking about the principal of the thing So 1100 1140 is what figure you gave for the residents. Oh, yeah And And I believe the business ones they were already on the water. So that's why he could give me that I know that you know a little bit more. So so the discussion here is You could have a hundred thousand square foot building And not tie into the municipal water But have a hydrogen in your yard And save on fire insurance because now you have public water available available The second discussion is You could have one bathroom in a hundred thousand square foot building And sprinkling your building with the municipal water and pay a hundred dollars a quarter For what is the fires free because the fire is free But you did choose to hook up correct, so It's interesting because when you do some research in different municipalities in the state Some municipalities have a fire protection charge and a water domestic water And as a user of this Municipal water the fire protection is more important than the water out of the water So I understand that and I understand why he's We could have built a six inch water main around town if nobody tied into the sprinkler system to it But we had to build a 10 inch so that they could But there are folks that aren't using municipal water but are getting the fire protection so Hence the discussion Is this policy something the public works board wants us to approve the public works board is still discussing I don't think you've made a decision yet. Yeah It's just a heads up. Yeah. Yeah, I honestly don't know how I feel I think that the fire protection Is a very important element of the public water system And that that I wouldn't be opposed to pay For the ability to sprinkle my building But probably not all people agree with that Well, and I think there's a big difference between the fact there's a fire hydrant in your yard that you didn't put there or near your yard Or that you have hooked up use a minimal amount but have maximum fire production at your disposal Those are really two different things probably remember You we don't meter fire protection, right? But you have it But you have it you didn't before so it isn't like we can if there's a fire We can say hang on a minute. Are you are you on the list? It's more of an insurance thing. Yeah Yeah So I don't know so I knew the board hadn't your board had not Voted for that yet, but I thought it was fair that I brought it right. No, we're so this yeah discussing on everyone has a Difference I don't know where Of course Yeah, you see in the circumstances vary from Person not person a person, but there's probably two or three different start circumstances Where you feel one way yet um I think personally that the the residence is the $1100 we're talking about They didn't sign it for this they asked for a hydrant in the driveway It is what it is Right, but the commercial buildings that can use the water for their sprinkler and fire protection is a different story They've hooked up Because you can't sprinkle your building if you're not hooked up So that's a little different Yeah Okay, so that's what um The you've had two meetings. I think it's been with the barry town thunder chicken snowmobile club And they're asking the board to draft an ordinance allowing travel On shed road cross town road black road and brookfield road um at your at two weeks ago No, I mean to the meeting before the last meeting um I believe the gentleman was here and you Discuss having a public hearing at that time to get input from residents or citizens um on that request um, and so I was I have drafted a letter to everyone on those roads and I haven't sent it out yet waiting for this meeting, um, and Just to check with you if you wanted me to set up a public hearing in two weeks on the 15th of october Now this on the this is for your uh For the four-wheelers to go up and down the roads, right? I believe that I'm understanding it with snowmobiles And four-wheelers What do they call those ATVs? And the request for separate he was clear about that right So they so I'm not sure if it's both or maybe they would consider one Yeah So it's sort of obvious for snowmobiles, but does this mean ATVs year-round? I doubt it because they can't write on uh, they're not allowed on snowmobile trails. I'm pretty sure yeah, but not a lot of snowmobile trails So they would only be in the summer or when there's no snow Yeah, so ATVs when there's no snow snowmobiles when there is snow, but never the two together All right But as I said before I think We've heard from the police chief. Oh, I hear you. I we've heard from but We probably need to hear from the public Because we're just hearing from from employees right now. We're not hearing from our from our employers. Right, right So I'll go ahead and notice the meeting and we'll hold it. I appreciate I'm on 15. Okay very good I have no update on the option agreement for the the well sites. I haven't heard any any forward progress on that And that is all I have Okay, uh Round table p I am set Wait Jeremy I have a couple things. Um, so I was asked to do my duty at my jury This week I've asked to be let go from it, but this week is the leagues meeting So I was wondering if anybody is going to be available if I need to be doing jury duty While I'm representing the town at the league annual meeting So, I mean I can I can let you know tomorrow But if anybody's available and willing to do that I'm happy to hand off the reins if I need to What day is that man? It's Wednesday. It's in south Burlington. That's first of all new Like new to uh three But you don't know yet. I don't know yet. I was supposed to be I was supposed to have been told today I still don't know. Is it for Burlington? Uh that's uh in We to get called up for Oh You know Yeah, you want to send an email out tomorrow is that I should be able to tell you tomorrow. That's why I've got a couple meetings now Wednesday, I know I have one in the morning one in the afternoon I hope they're sympathetic because I'm also closing on my house on Wednesday morning Wow, which would be so do you think you could add one more thing? All right If that were to occur I I'll need to notify the league to change who was on who has the I will let you know as soon as I okay, and I would have to try to change the meeting in the afternoon If I was going to try to attend so we'll play it by ear. Okay. Okay. You get the ball in let me know um, and then um, I happen to um Talk to dianne over in the police department. We're talking about police records And this is something we've floated in the past They're the physical space that they have available for their records that they're required to keep They're running out given, you know, unless we're going to build a new building Don't think we are We should probably consider if not Building the capacity to put those records in some electronic format at least think about Putting some money away in the next budget.  We do a little bit of that here But if you've ever seen the sort of the shelves that are everything has to be manually filed and refiled when things get moved around and and expired It's It's pretty it's a pretty bad tight situation over there We as you remember purchased a software system for us to start filing things electronically And we're still learning it and learning how best to utilize it, but it's going to be great I mean, it's really going to save us a lot of space and much easier to Access things and I remember you saying that is that something that they can use over in the police department That's going to be I don't think they'll be able to use hours because they'll tell me that they don't want to share our server But but yes, I'm sure that You know, I'm sure that They could purchase the system and have a server themselves to have a server I think that would be worthwhile to To talk about in the next budget cycle. Okay So can you bring in like a professional person that just this is what I'm going to do in six months? I have no idea how you do it. Yeah, and then somebody comes in they use our stuff They sit down scan it And put it in place and work it out. I mean, that's that's more expensive than you know digitizing the stuff You know as it's going out or Not not not that Diana really has the time and Her schedule to do that. Yeah, I guess it would boil down to that I mean once it's brought up to speed to maintain it or keep it current is no big deal We decided to And we we will go back as we can but we decided we would start now What happened before we're not as worried about and the issue with having someone come and scan it because I've thought of having like an Intern come in and scan it But we would still need to file it Because someone else wouldn't know really Weird of what it was because you have to title it and then you can put key words that You know you have to think about what someone might call it. You might call it this I'll call it that you know, but you need something for the system to retrieve it I think in the case of the records that we're talking about back there I think there's there's probably standardization in the materials that are there. So I mean there are certain forms You know intake and evidence and all of these sorts of things that are going to be pretty pretty standard and hopefully Hopefully would be easier to Bring into a system. I'll be true Because people in 15 years from now need to go back and You know if you spell the 15 years from now, they're going to come in they're going to say Who was that guy? But I mean, you know, we don't start with z in the alphabet. We start with a you know But even in the short time we've have it. I mean it is just so much more efficient and Defined things so like thumbing through a binder right exactly somebody dropped Yeah So one last thing In the place where tim short up the the cemetery over on rawl hill road Yes, I drew by today and somebody set up a little table with some chairs there right in that little little flat area It's kind of a nice just kind of a funny Attitude I don't know if tim's been tim's been over there, but the space is being used Apparently people are they set up a chair isn't that the table? Yeah, it's a little you mean like a little picnic area. Yep Okay That's all I got We're over there lunch age later round table um I don't know what this check is for What's it? Yeah, did we ever get to the license permit? No, you haven't done that. Oh, okay. Well Anything for round table? No, okay The approval licenses permits vouchers and applications everybody's seen the paperwork Yeah, I see that and I'll be able to see if I can tell you what it is sure It is postage But but look at the number at the amount on the check and look at the amount on the bill Right, but this is to have money in our bank at the postage So that the total postage so it's so it's paying in advance of us exactly exactly with the stamper Yeah, right So I move that we approve general fund accounts payable warrant number 19 g 07 with checks 18492 through 18528 in the amount of 169,726 dollars and 13 cents Also payroll warrant number 19-07 for payroll from september 16th 2018 through september 29th 2018 in the amount of 42,002 dollars and 50 cents So any further discussion? Hearing none those in favor so you can talk by saying aye Those opposed motion carries anything for executive session tonight dana. No, I have nothing to adjourn


Today, we are going to consider some of the problems for the Newton's method. So, we look at the f x is equal to 0, we want to find the root. So, approximation to this root is obtained by Newton's method. In Newton's method, we have proved that there is quadratic convergence. In fact, that is the advantage of Newton's method. So, we will look at a specific example and in that we will show that the quadratic convergence is achieved. Then we will look at one more example for finding approximation to square root of a function using Newton's method. After that, we will consider some problems for solution of system of linear equations. So, we will calculate condition number in terms of maximum magnification and minimum magnification of the coefficient matrix A. Then we will look at the residual obtained estimates for the residual and also we will consider the condition number, how it depends on the scaling. So, our first example is we want to find root of this function f x is equal to e raise to minus a x minus x, where on a our condition is that 0 should be less than a less than or equal to 1. We will show that this function is going to have a unique root in the interval 0 to infinity, then the x 0 is the initial approximation in the Newton's method. So, if this initial approximation you choose to be bigger than 0, then we will show that modulus of c minus x n plus 1 is less than or equal to 1 by 2 modulus of c minus x n square. c is the exact root x n plus 1 is the n plus first iterate in the Newton's method. So, this is the error in the n plus first iterate c minus x n square that is going to be the error in the nth iterate and error in the n plus first iterate is less than or equal to 1 by 2 times error in the nth iterate its square. So, this will illustrate the quadratic convergence of Newton's method. So, the first thing we are going to show that this function has a unique root in the interval 0 to infinity. So, let us look at the Newton's iterate. It is by definition x n plus 1 is equal to x n minus f x n upon f dash x n, n is equal to 0, 1, 2 and so on. So, I am recalling how the error in the n plus first iterate and error in the nth iterate they are related f of c is equal to 0. Write down the Taylor series expansion for f of c. So, that is going to be equal to f of x n plus c minus x n f dash x n plus c minus x n square by 2 f double dash of d n. This d n is going to lie between c and x n. Then what we do is we divide by f dash x n, take this term on the other side.  This will be equal to f double dash d n. These two you are dividing by f dash x n and then c minus x n square. So, now this is nothing but x n plus 1. So, the left hand side is x n plus 1 minus c. I am taking modulus. So, it is modulus of c minus x n plus 1. This is equal to modulus of f double dash d n upon 2 times f dash x n and multiplied by c minus x n square. In this particular example, we want to show that modulus of c minus x n plus 1 is less than or equal to 1 by 2 into modulus of c minus x n square. So, that means I need to show that this coefficient of c minus x n square is going to be less than or equal to half. So, here is proof of unique root in interval 0 to infinity. Our function is f x is equal to e raise to minus a x minus x. So, f dash x is going to be e raise to minus a x minus 1. x n plus 1 is equal to x n minus f x n. So, that is e raise to minus a x n minus x n divided by f dash x n. So, it is minus a e raise to minus a x n minus 1. So, denominator you have got negative sign. Here this is negative sign. So, this will become plus. Then x n and this x n it is going to get cancelled. So, you are left with a e raise to minus a x n multiplied by x n and then from here plus e raise to minus a x n divided by a e raise to minus a x n plus 1. So, we are starting with x 0 to be bigger than 0. Now, look at x 1. Our a is lying between 0 and 1. So, this number is bigger than 0. Exponential is always bigger than 0. x 0 is greater than 0. Similarly, the denominator will be bigger than 0. So, that will mean that x 1 is bigger than 0. You continue and then you get x n to be bigger than 0. In fact, I am not showing that f has a unique root. I will tell you how it follows.  If f dash x is less than 0, that will mean that f is going to be a strictly decreasing function. When you consider f of 0, f of 0 is going to be equal to f of 0 to 1.  So, f dash x will be less than 0. So, f dash x will be less than 0 on 0 to infinity. This implies f to be strictly decreasing. When you consider f of 0, it is going to be equal to 1. So, it is bigger than 0 and as x tends to infinity, f of x will tend to minus infinity.  So, by definition, this means that for some m, whenever x is bigger than or equal to m, f x is going to be less than minus 1. Now, you look at interval 0 to m. Your function f is continuous. At f of 0, it is 1. At m, it is going to be f of m will be less than minus 1. So, by intermediate value theorem for the continuous function, there has to be some c in the interval 0 to m such that. So, we will have c. So, there will exist c in the interval 0 to m such that f of c is equal to 0. So, that means we have proved existence of 0 of f and now strictly decreasing implies f has a greater than or equal to 0. So, this was the proof for showing that our function f has a unique 0 in the interval 0 to infinity. Now, we are looking at x 0 to be bigger than 0. If the initial approximation is bigger than 0, we calculated formula for x n plus 1 in terms of x n and using that formula, we saw that x 1 has to be bigger than 0 and then use the same argument. x 1 bigger than 0 will imply x 2 bigger than 0 and in general, your x n's they are going to be bigger than 0. Then, we look at c minus x n plus 1 and then c minus x n. So, we obtain x n plus 1 to be this much.  The second derivative is going to be a square e raise to minus a x. So, when you consider modulus of f double dash d n divided by 2 minus a x minus a x minus 2 times f dash x n, this is going to be equal to a square e raise to minus a d n divided by 2 times a e raise to minus a x n plus 1 and now, this is going to be less than or equal to half. Why? Because our 0 is less than a less than or equal to 1. So, a square will be less than or equal to 1. e raise to minus a d n, a is bigger than 0, d n is going to lie between our point c and x n. So, that is why e raise to minus a d n also will be less than 1 divided by 2 a e raise to minus a x n plus 1. So, this number is going to be something bigger than 0. So, I can dominate 1 upon a e raise to minus a x n plus 1 by 1 minus a x n plus 1. So, that is why e raise to minus a d n also will be less than or equal to 1. So, numerator is less than or equal to 1, 1 upon this factor is going to be less than or equal to 1 and then you have got 2. So, you get this to be less than or equal to half and that gives you modulus of c minus x n plus 1 less than or equal to half c minus x n square. So, this illustrates the quadratic convergence of the equation. Now, why was it necessary to obtain this expression? Using this expression we show that all x n's they are bigger than 0. Our c is in the interval 0 to infinity. So, we have got c is in the interval 0 to infinity, x n is in the interval 0 to infinity, and d n it will lie between c and x n, x n can be to the left of c or to the right of c. So, d n also will be in the interval 0 to infinity and then using that you get e raise to minus a d n to be less than or equal to 1. So, in order to obtain this estimate we need to look at what is x n plus 1 and then we have proved the quadratic convergence. So, now in our next example what we are going to do is when we want to find the square root of a positive real number then we want to apply Newton's method to that to find an approximation to the square root. So, our function f x is going to be equal to x square minus a, where a is bigger than 0. So, we want to find the root of this. So, x square minus a is equal to 0 and let us decide that we want to find the positive square root. So, to this function we will apply Newton's method then that will give you a formula for finding x n. Now, remember the Newton's method may not converge always when it converges it is going to converge quadratically. We have got our formula x n plus 1, x n plus 1 is equal to x n minus f x n divided by f dash x n.  If these x n converge to a point then that point or that number is definitely going to be 0 of a function. So, let me repeat the Newton's method defines a sequence of real numbers. If that sequence is convergent then the limit is going to be 0 or a root of a function. If there is convergence then the convergence is going to be quadratic provided that the your 0 is a simple 0, but there may not be a convergence. We have seen some sufficient conditions for which guarantee that there is a convergence in Newton's method. So, we are going to look at Newton's method for finding root of x square minus a is equal to 0. We will show that the sequence or the Newton's iterates they converge. So, this is our next problem. So, we start with a to be bigger than 0, function f x is x square minus a, x n's are the iterates in Newton's method. About the initial approximation our condition is x 0 should be bigger than 0 and x 0 should not be equal to root a. We want to show that x n's they are strictly decreasing x n's converge to root of a and root a minus x n plus 1. So, that is going to be the error in the n plus first iterate. This is equal to minus 1 upon 2 x n multiplied by root a minus x n square. So, here is error in n plus first iterate. Here is error in nth iterate and then it is square. So, once I show this then that will mean that we have got quadratic convergence. We will keep a track as to where we need x 0 to be bigger than 0 and x 0 to be not equal to root a. If x 0 is equal to root a then x 1 also will be equal to root a and the sequence generated by Newton's method is going to be a constant sequence. So, here that means you have found the root f x is equal to x square minus a. Its derivative will be given by 2 x n plus 1 is equal to x n minus f x n divided by f dash x n. This is equal to x n minus f x n will be x n square minus a divided by f dash x n which is 2 x n. So, to start with when I look at x 1 I am going to have x 0 in the denominator. So, that is why I need x 0 to be bigger than 0. x 0 we say it should not be equal to root a because if it is equal to root a then what will happen is x 1. So, x 0 square will be equal to a. So, this term will be go away and you will have x 1 is equal to x 0. So, you get a constant sequence. So, this is equal to 1 by 2 x n plus a by x n. You have 2 x n square minus x n square divided by 2 x n. So, that gives you 1 upon 2 x n and then this a upon 2 x n is written here. So, x n plus 1 is equal to 1 by 2 into x n plus a by x n. A is bigger than 0. So, that will mean that x n they are going to be bigger than 0. x 0 bigger than 0 implies x 1 bigger than 0 that will imply x 2 bigger than 0 and so on. So, this is our first step x n plus 1 is 1 by 2 x n plus a by x n. Then let us look at x n plus 1 square minus a. So, square both the sides and subtract a square of this is 1 by 4 x n square plus a square by x n square plus 2 a minus a. So, this will be equal to 1 by 4. Now, here you have got 2 a by 4. So, that is going to be a by 2 and then this is minus a. So, you will have minus a by 2 and that gives you x n minus a by x n square. So, this will be equal to nothing but x n square minus a divided by 2 x n whole square and that gives you x n to be bigger than root a for n bigger than or equal to 1. So, we start with x 0 to be bigger than 0. Then your x 1 it is bigger than root a and this condition will be satisfied by x 2, x 3 and so on. So, your first x 0 you have got 0, you have got root a. So, your x 0 which you choose it may be to the left of root a or to the right of root a, but after the first iterate x 1, x 2, x 3 they are all going to lie to the right of root a. Now, this becomes important because we are going to show. So, we have got now x n to be bigger than root a. Now, we will show that they are strictly decreasing. So, if you have got a monotonically decreasing sequence which is bounded below, then such sequence is always convergent. That is a property of real sequences that monotonically increasing sequence which is bounded above that is convergent or monotonically decreasing sequence which is bounded below that is going to be convergent. So, we have got x n to be bigger than root a for n is equal to 1, 2 and so on. So, we have got a sequence which is bounded below and now let us show that it is a decreasing sequence. So, x n plus 1 is 1 by 2 x n plus a by x n we obtain this expression look at x n plus 1 minus x n. So, we are subtracting minus x n from both the sides. So, what you will have will be 1 upon 2 a by x n here it is 1 by 2 x n minus x n minus x n minus x n minus x n so that is going to be minus 1 by 2 x n. So, this is equal to 1 by 2 a minus x n square and then there should be divided by x n. So, we have got x n plus 1 minus x n is equal to 1 upon 2 x n a minus x n square. Just now we have proved that x n is bigger than root a for n is equal to 1, 2 and so on. So, this will mean that x n square will be bigger than a and that implies a minus x n square is going to be less than 0.  So, this implies that x n is a decreasing sequence. So, we have got a decreasing sequence which is bounded below and hence it will converge. Now, just strictly decreasing bounded below it tells us that it is convergent. Now, why it should converge to root a because if the sequence generated in the Newton's method if it is convergent it has to converge to root of your function f roots of our function are plus root a and minus root a. The sequence which is generated it is going to be sequence which is bigger than 0. So, if it is convergent it has to converge to root a it cannot converge to minus root of a. So, thus we have proved that the sequence generated in the Newton's method it is converging to root of a and now let us show the quadratic convergence. So, x n plus 1 is 1 by 2 x n plus a by x n it is converging to root of a. So, let me look at root a minus x n plus 1 that will be root a minus 1 by 2 x n plus a by x n. Now, this is going to be equal to minus 1 upon 2 x n. So, I am taking 2 x n as the denominator. So, I will have here x n square then you will have 2 root a x n because there is minus sign here it will be minus 2 root a x n plus 2 x n plus 2 root a x n is taken out. So, it will be a which is equal to minus 1 upon 2 x n and root a minus x n whole square this is e n plus 1 minus 1 upon 2 x n e n square. So, we have e n plus 1 is equal to minus 1 upon 2 x n e n square. So, e n plus 1 upon e n square this is going to be equal to let me take the modulus this will be 1 upon 2 x n this will converge to 1 upon 2 x n. So, 1 upon 2 root a because x n is tending to root a. So, this will mean that 1 upon 2 root a that is going to be our asymptotic error constant and if I recall the earlier notation then p is equal to 2. So, that is quadratic convergence limit as a intends to infinity modulus of e n plus 1 by mod e n square that is equal to 1 upon 2 root a and that is the asymptotic error constant and we have got quadratic convergence. We want to consider some of the problems which are related to system of linear equations. So, when we talked about the condition number we had obtained a lower bound for the condition number which was condition number of a is bigger than or equal to norm c j by norm c i where c j is j th column c i is i th column. So, using this estimate we had said that if the columns are not balanced if they are out of order then your matrix is illiterate and your matrix is ill conditioned. But, one says for the columns it is true for the rows also. So, the result about that condition number of a is bigger than or equal to norm c j by norm c i I had left that as an exercise. So, that is what now we will do we will define what is known as minimum magnification of a relate the minimum magnification of a to norm of inverse and then we will obtain condition number as ratio of maximum magnification divided by minimum magnification and then I will recall one of the example which we had considered of a 2 by 2 matrix. So, that matrix was ill conditioned. So, we showed that you change the right hand side slightly and perturbation in the solution is too big. So, here is the problem a is an invertible matrix minimum magnification of a is minimum magnification of a is minimum of norm a x by norm x x not equal to 0. If instead of minimum we have maximum here that is our definition of norm a. So, we want to show that minimum magnification of a is nothing but 1 upon norm a inverse the proof is straight forward we start with minimum magnification of a this is our definition. So, this will be same as minimum x not equal to 0 vector 1 upon norm x divided by norm a x. So, this becomes equal to 1 upon maximum x not equal to 0 norm x divided by norm a x when we have got a to be invertible matrix then x not equal to 0 vector implies a x not equal to 0 vector. So, proof of this result is where a x is equal to 0 vector it will imply that a inverse a x is also 0 vector I am applying a inverse and this will mean that x is equal to 0 vector contradiction. And if a x is not equal to 0 vector then x cannot be 0 this is for any matrix that if you have got x is equal to 0 vector a x is equal to 0 vector a x is always 0 whatever is the matrix whether it is invertible or not. So, for a invertible matrix we have got this if and only if condition. So, now look at the minimum magnification of a. So, here we are taking maximum over x norm x upon norm a x let me put x is equal to y. So, y is equal to a x then when I this will be same as 1 upon maximum y not equal to 0 for x we have got a inverse y divided by norm y and that is nothing but 1 upon norm a inverse. Now, once we show this the condition number is norm a into norm a inverse norm a is maximum norm a x by norm x x not equal to 0 vector and then this norm a inverse which is in the numerator I write as 1 upon norm a inverse in the denominator. So, this is maximum magnification of a just now we showed that 1 upon norm a inverse is minimum magnification of a. So, the condition number is going to be equal to ratio of maximum magnification of a divided by minimum magnification of a. So, now let me recall the 2 by 2 examples which we had considered for this matrix it is infinity norm is 1999 infinity norm that means row some norm take the absolute value of the entries look at the first row look at the second row take the sum whichever is the maximum a of vector 1 1 is going to be 1999 99 divided by this. So, you have norm x infinity is 1 1 norm a x infinity is going to be maximum of these 2 numbers. So, you have for this particular vector norm a x divided by norm x is equal to norm a infinity. So, this 1 1 is going to be the direction of maximum magnification for this matrix. Now, let us calculate or let us find out the direction of minimum magnification. So, the direction of the minimum magnification is going to be direction of maximum magnification for a inverse. So, a inverse is this matrix it is infinity norm is again the same as before a inverse of minus 1 1 is going to be this vector 1997 minus 1999. So, minus 1 1 is the direction of maximum magnification for a inverse this relation you can write as a of this vector is equal to minus 1 1. So, this vector defines direction of minimum magnification by a the direction of maximum magnification by a. So, this vector defines direction of maximum magnification was 1 1 and minimum magnification will be decided by this vector. Let us go back to our system of linear equations. So, we have got a x is equal to b we obtain an approximate solution x cap or it is our computed solution. There is some error because you are using computer. So, we have got finite precision or you may be using some indirect method such as Jacobi method or Gauss-Seidel method. So, what we want to do is. So, residual is something which you are going to calculate like I find a computed solution x cap I will like to know whether this x cap is near to the exact solution exact solution we do not know. So, what we cannot calculate norm of x minus x cap or we cannot calculate the relative error what we can calculate is a x cap minus b. If x cap where exact solution is x cap then a x cap will be equal to b and the residual will be 0 otherwise it will be something non-zero. So, what one wants to know is if the residual is small then whether I can say that my computed solution is near to the exact solution we have got computed solution x cap I calculate a x cap minus b. So, suppose this number is small its norm is small in that case whether one can say that x cap is near to x. So, that is the question now that once again it is going to depend on the condition number. If your condition number is small then the residual small will mean that x cap is near x. If the condition number is big then it may not be the k. So, let us prove the corresponding result. So, a is invertible matrix x cap is approximate solution r is the residual b minus a x cap and then this is going to be the relative error in the computed solution. This will be less than or equal to norm a into norm a inverse the condition number into norm r. So, what it means is if this number is a big number then even though this is small it can happen that the residual it can happen the relative error in the computed solution can be big. If this is something reasonable then the small residual implies the nearness of the computed solution to the exact solution. So, we have a x is equal to b r is equal to b minus a x cap. So, that will mean that a x minus a x cap is equal to r just from these two equation a is invertible matrix. So, x minus x cap is equal to a inverse r norm of x minus x cap will be less than or equal to norm a inverse into norm r. Now, norm b from here will be less than or equal to norm a into norm x. So, we get 1 upon norm x to be less than or equal to norm a into norm b. So, in the earlier estimate what I had written there should be norm r by norm b. Now that is something logical here you are taking relative error.  So, here also you should look at the relative error. So, that is norm r by norm b. So, if this relative error is small and if the condition number is not too big it will imply that this relative error will be small and then other way inequality is similar. So, we have got a x minus a x cap is equal to r. So, do not apply a inverse from here you can say that norm r is less than or equal to norm a into norm of x minus x cap a x is equal to b. So, you have got x is equal to a inverse b. So, norm x is less than or equal to norm a inverse into norm b. So, from combining these two you will get 1 upon norm a into norm a inverse norm r into norm b to be less than or equal to this relative error. Now, we want to consider an example about scaling when you multiply a matrix by a non-zero number. You multiply a matrix by a non-zero number it does not change the condition number the condition number remains the same if I multiply the matrix by a non-zero number, but if I multiply say one of the row by a non-zero number then the condition number is going to be affected. So, we are going to look at a 2 by 2 example and in that we will try to determine the non-zero scalar alpha by which if I multiply the first row then the condition number is minimized. So, that is the scaling that the matrix is given to you. So, you look at its rows and columns and try to see that they are not say out of proportion. If you multiply a row by a non-zero constant you do not change the system it is the same system as the original system, but new system may have a better condition number. If you multiply a column of the coefficient matrix by a non-zero scalar then your solution gets changed it is a new system, but there is a relation between the earlier solution and the solution which you will obtain in the new system and that is if you multiply the j th column by a non-zero constant the corresponding solution will change only in the j th component. So, that we have seen. So, we are going to look at a 2 by 2 matrix or a 2 by 2 system. So, we have this is a matrix what I want to do is determine alpha. So, that the condition number of a alpha with respect to the infinity norm is minimized. Now, here is the 2 by 2 matrix so, I can calculate its inverse infinity norm is specified. So, what we are going to do is look at a alpha look at its norm a alpha infinity calculate a alpha inverse calculate its infinity norm and then we will have to consider 2 cases and in both the cases we will see that we get the same alpha. So, we are trying to find alpha which minimizes the condition number of our coefficient matrix. So, we have this is our matrix a alpha when you look at the infinity norm of the matrix that is rho sum north you have to take the modulus. So, first rho its sum will be 0.2 into mod alpha the second rho its sum is 3.5 and norm a alpha infinity will be maximum of these 2 numbers you look at a alpha inverse the inverse of this matrix a alpha is given by this our alpha is going to be not 0. So, this is the inverse now we will calculate its infinity norm. So, norm a alpha inverse will be the first rho gives us 2.5 plus 0.1 mod alpha divided by 0.3. So, this is the inverse of the norm a alpha and the second rho gives you 1.0 plus 0.1 mod alpha divided by 0.15 alpha. So, the maximum of the 2 number is going to be the first number which you can simplify and get 50 upon 3 mod alpha plus 2 by 3. So, we have got norm a alpha to be maximum of the 2 numbers norm a alpha inverse is given by this quantity case 1 will be 0.2 mod alpha will be less than or equal to 3.5 that means mod alpha will be less than or equal to 17.5 when I take the maximum of the 2 now the maximum is 3.5. So, it will be 3.5 times this. So, this is going to have minimum to be equal to 17.5. So, you will have minimum of norm a alpha norm a alpha inverse to be 17.5 and in the second case also you are going to get exactly the same value. So, now in the next lecture we are going to start new topic and that is the approximate solution of initial value problem. So, thank you.