you're welcome back to the breakfast and plus TV Africa it's now time for today in history and on this day in history July the 1st 2003 it wasn't a very good day for Kobe Bryant because there was a misconduct charge against him so a female employee at a Colorado resort basically went to the police to file a sexual misconduct charge against the basketball star Kobe Bryant on July 1st and a few days later an arrest warrant was issued for Bryant and the ensuing case generated lots and lots of media frenzy. This particular incident really affected Kobe Bryant because he faced intense scrutiny he lost many of his endorsement deals as a result of the rape case because he went on to actually admit it that he went on to admit that they had you know something together but he maintained that the accuser all rather than he was consensual with the accuser and this particular female employee had said you know Kobe Bryant assorted her but he insisted that it did happen but that it was consensual. The accuser her name and her identity was mistakenly made public as a result of the court's clerical errors and this you know thrust her into the limelight and she began to receive many personal life and death threats but in early March 2005 Bryant and the accuser settled their civil lawsuit for an undisclosed sum and that's what happened today in history. Sadly he is no longer and the year 2020 took Kobe Bryant basically but you know I think we've said it before that you know no matter how beautiful your career is just one tiny mistake can ruin a 10 15 20 year career where you've put in all the work and sacrifice and worked entirely hard to build just one mistake. Same thing you know with someone of course that didn't make the news this morning which is Bill Cosby if you've been following the news also you must have heard that he has been released but of course he made his own mistakes that ruin his career you know and even if he hasn't set free from you know from jail he's been released from jail you know it's never going to be completely wiped away that he's been accused of multiple sexual assault crimes basically and same thing with Kobe Bryant. But we forget Crip quite easily here in Nigeria I mean look at the Babaay just a case with all the alleged sexual misconduct and you have lots of people rallying around him supporting him I wouldn't be surprised if he's shooting blockbuster movies in the next few days and Nigerians rushing to the cinemas to watch despite all the allegations so I guess it's just different different approaches to the council culture Nigeria and over there. Yeah you know so I think it's also because we we we're really hypocritical you know a lot of times and we also need to do better with taking a stance against certain things shameful you know when I saw the tampon tampon sorry group and their message to those actresses really really shameful I was ashamed of you know and you know all those people there really really ashamed and really just for me just meant that a lot of them maybe had skeletons in their closet and they had to you know stand for each other you know so that if they are called out in the future they will be able to you know find somebody to defend them it's really really shameful how the whole thing played out but what he's granted will I believe that he's gonna go back to court and I I hope you know that you know we continue with the court case I don't want to say more than I should. Alright on this day in history in 2007 if you lived in England then you must have heard that England banned smoking on this day but not smoking it wasn't a complete ban on smoking it was a ban on smoking in enclosed areas it of course came with it with its own controversy it was it made it illegal to smoke in enclosed workplaces in England and it came into force on this day in 2007 as a consequence of the Health Act of 2006 the ban of course before the ban of course a lot of people who are not businesses who in who voluntarily introduced ban on smoking mainly as result of public feedback but there was a legal blunder with this ban because there was no actual punishment for flouting the rule until the 16th of July in 2007 while the ban affects almost all indoor workplaces smoking is permitted in private residences also and of course although it is not used in areas such as a shared workplace in flats with communal entrances or shared corridors these must all be smoke-free eventually I think late in the year then it was also enforced in public transportation and other places that had to do with the public so on this day basically the ban on smoking in England came into play and came to force I think later I'm sure Legos also has a or somewhere I think Nigeria also adopted a you know similar ban on smoking during the last administration good like Jonathan's administration there was a similar ban on smoking that also was placed you know was thought about here in Nigeria okay but anyway this happened in the year 2007 fantastic and after about 10 years after that you know in the UK they began to have reports surveys as to what impacts this ban on smoking in public places have had and some reports show that people were now trying to actively quit smoking because there was a ban on smoking in certain places so it did improve their health in those ways and researchers also conducted a found that after that ban on smoking in public places air pollution in the UK bars reduced as much as 93% so it seems to have have had a great effect on the health and of course air yeah and then there's also places that you go to in Nigeria the you know clubs that have a lot of patronage that you go to and you can't smoke inside because I think they understand yes yeah so you can smoke outside they I don't if they have smoke rooms but I know that you have some have places where you know this is just for smoking and they have played you know they have a way they divide it where you can't smoke here yeah yes so so I think it's because they understand that not everybody wants to be in an environment and you know I well girls always complain that you know they have their old you know hair and clothes melon smoke and it causes headache for people like me oh it does yes okay yes so anyway the point is you know from 2007 it now became a popular thing to ban you know smoking in enclosed places across the world I'm not sure how much they enforce it here in Nigeria but I think what happens here is you know people just voluntarily decide to place that ban in their you know business places and their lounges and the likes alright 2007's what we shared with you and of course we're also wearing back to the year 2003 could be brined and that's sexual assault charge and let's take a break here and we'll return shortly


Hi, Dr. Jared here recently saw this patient the last time they were in was two years ago The patient was three years old and they weren't able to tolerate x-rays, but they did have decay on teeth number B T s I and then down here on L and K as well I just went ahead and placed glass anemone and all these teeth and we were gonna put the patient on a three-month recall Unfortunately, they didn't show up till today two years later and you can see Riva self-care HV is the product I used in this case Really serve this kid nicely and not having to do Conventional dentistry and sedation if you want to learn more about minimally invasive dentistry I'd like to invite you to join me next week on Friday at the Iowa State Fair or I'll be in New York at the Greater New York Dell meeting giving a Shorter but similar talk on minimally invasive dentistry and the things that are changing in the field and how you can utilize them Successfully at your office. Have a great day


It is July 2008 and a controversial local landmark is being removed. It has been here for nearly a decade and, strangely, is the grim reminder of an environmental disaster. Officials, locals and the wider public have argued whether it should stay or go, but the decision and money has been committed and the multi-million dollar project has started. The landmark in question is not a statue or a piece of artwork, but instead a wrecked remains of a transport ship. The removal and wreckage represents a legal argument that was used to make the ship's owners responsible for its running aground. I'm John and this is a brief history of. Today we're looking at the Oregon New Carissa disaster. A little background for a big ship. Our story starts at the end of the 1980s, some 19 years before the wreckage removal, with the laying down of a new dry goods transport ship. The ship was built by Imabari Shipbuilding Company in Japan using an all steel construction, beginning on 30 August 1989. She was named the new Carissa and was 195 meters long and 32 meters wide with a draft of 10.8 meters when fully loaded. The vessel had a complement of 26 sailors who were in charge of the ship's gross weight tonnage of 36,571, pushed along by an 8200 horsepower direct drive diesel engine. The ownership structure of the new Carissa like many naval operations is rather complex. She is registered to Panama, but her owners, much like her builders, are very much Japanese. She is under the operation of and owned by operator and managed to Haukeian Co Ltd and TMM Co Ltd respectively. Although ownership is via a Panama based subsidiary Green Lane Shipping. This registration is a flag of convenience, allowing the owners to hire sailors under the working rules and conditions of the ships registration country. But to add another level of complexity, the ship's home port was in the Philippines and her crew consisted of a Philippine captain and other personnel. I told you it's a confusing web or maybe it's just me. The new Carissa would be pressed into service carrying wood chips used in the manufacture of paper between Japan and the US. Part of this would require entering US waters and a law brought in in 1990 meant that any operator must be held financially responsible for any environmental impact in the case of an accident. Like with any potentially financially damaging risk, operators insure against this and the new Carissa was no different. Approximately 23 million US dollars of environmental liability insurance was provided by Shipowners Insurance and Guarantee Company Ltd of Hamilton Bermuda. It is the beginning of February 1999 and the new Carissa is doing what she does best, heading towards the USA to collect wood chips. She is running with an empty hold and is bound for the port of Coose Bay, Oregon. She at this time has around 400,000 gallons of diesel and lube oil aboard. All aboard the ship are Philippine nationals. On the 3rd of February and not far from their destination, a local pilot is assigned to guide the vessel into port. As the evening drew in, an ocean storm with winds that reached 39 knots was hitting central Oregon. The pilot, due to the weather conditions, was unable to reach the vessel. He informed the captain that he would not be able to assist until the morning and as such, entry to the port should not be attempted. Healing the pilot's warnings, the captain ordered a turn away from the bay to open the empty holds and drop anchor. By now, the new Carissa was around 1.5 to 1.7 nautical miles from the bay. Only one anchor was dropped, but little did the crew realize that the chain was too short but a 20 to 25 knot winds. The evening gave way to the early hours of the morning of the 4th and the storm continued to rage. Slowly, the ship began to drag her chain. Poor watchkeeping of the crew meant that the movement went undetected for quite some time. She was dragged closer to the shore. Eventually the movement was noticed and the crew set to raise anchor to try and maneuver away from running aground. In the heavy storm and strong winds, nothing could stop the Carissa from moving closer and closer to the Oregon shore. Around 3 miles north of Coos Bay, the new Carissa ran aground on a sand bank. The collision was reported to officials at 9 o'clock in the morning and immediately a recovery operation was set into motion. The new Carissa represented an environmental issue with hundreds of gallons of fuel aboard. The immediate recovery attempts tried to make use of the new Carissa's own power but the stricken vessel couldn't free itself. A unified command consisting of representatives from the Coast Guard, the State of Oregon and other rescue party operations was set up as soon as officials were first notified. Three objectives were set out for the unified command, to save personnel, save the ship and prevent spillage. The poor weather affected any immediate rescue when the only tugboat available in Coos Bay couldn't be used due to safety concerns. As long as the ship was still intact, refloating was the preferred option. The high winds prevented the crew from being rescued immediately but eventually the Coast Guard helicopters were able to evacuate the sailors aboard and replace them with salvaged specialists. During this time a survey of the ship was undertaken by air and so far it looked like it could be refloated but there was a problem. No suitable ship was in the area that was powerful enough to drag the new Carissa off the sandbank. The nearest suitable vessel was based in Astoria, Oregon, roughly 170 miles away from Coos Bay. She was called the salvaged chief but she had not sailed for over a year and required provisions, fuel and the sourcing of a suitable crew. The turnaround time to ready the chief was going to be 18 hours, a long time to wait especially in addition to the 24 hour journey time that she would take. All during this the new Carissa sat precariously putting more strain on her hull. The salvaged chief would not arrive at Coos Bay until the 8th of February, four days after the new Carissa ran aground. The waves and high winds continued to batter the stricken vessel pushing her further along the beach. Although rescue had arrived the additional 600 feet the new Carissa had been pushed jaw-wood put her out of the salvaged chief's reach. Not long after Tarbull started to appear on the beach hinting that the Carissa was leaking oil meaning she had developed a crack somewhere on her hull. Because of this the three main objectives for salvage were changed, to ensure safety of personnel and the local community, minimize damage to the environment and finally salvage the vessel. The now leaking ship posed a serious risk to the local ecosystem. Cleanup activity preparation began almost as soon as the ship got beached but the leaking fuel had already covered wildlife and had leaked into the vulnerable local environment. With another storm on the horizon and a high probability of salvage causing the ship to break up rescue workers were confronted with a horrible last resort decision whether to burn the ship or not. You see setting a light to the vessel may sound like a bad idea but this could mean the toxic fuel would not contaminate the environment directly. Obviously there was still the environmental cost but by now it was a case of least worst outcome. This rock and hard-placed decision was made for the salvage team when it was decided that the ship was a complete structural write-off and thus movement was out of the question.  The unified command attempted the first burn on the 10th of February using a combination of napalm and incendiary devices but to the disappointment to all involved only one of the ship's tanks set alight. Time to bring out the big guns. A navy explosives ordinance disposal unit from Whitby Island, Washington was employed to have a second crack at burning the fuel. The unit used 400 pounds of explosives to rupture the fuel tanks and to sustain the burn a locally brewed napalm mixture was employed. The fire would last 33 hours and result in between 165 and 255 thousand US gallons burnt. Other things would get worse for the vessel. All during the explosions and grounding the main structure was weakening and its integrity couldn't last any longer. At around midnight on 11th of February the vessel broke into two sections and a now separated ship started to drive in different directions. On the 26th of February the salvage teams managed to float the 440 foot bow section and prepare it for towing. By the 1st of March the tugboat sea victory has successfully towed the bow from the beach and out to sea but a return of stormy weather resulted in the cable snapping. The bow now loose free floated for 14 hours until it ran aground near Waldport, Oregon on the 3rd of March roughly 80 miles to the north of the original grounding site. It was refloated again on the 8th of March and towed out to 280 miles off the coast where it was sunk with explosives and cannon fire from two US Navy ships, the destroyer USS David L. Ray and the submarine USS Bremerton. Interestingly the cannons and explosives didn't fully sink the bow requiring an additional torpedo before it was sent to the seabed. The stern however would remain on the beach for nearly a decade but we'll come to that in a bit. Like with most disasters the authorities set out to find the root cause of the disaster and like most disasters everyone blamed everyone else. With the government blaming the crew and the insurance company, Britannia Steamship Insurance Association blaming the less than useful Coast Guard charts and the pilot not telling the ship to drop anchor where it did. This resulted in two lawsuits, one from the insurers claiming around $96 million and a counter from the US government claiming around $7 million. Both parties would reach a settlement of a net amount to the government for $6.5 million in 2004. But this wasn't the end of the legal proceedings. In an interesting tactic Oregon State demanded a $25 million bomb to cover the dismantling and cleanup costs as well as charging the ship's owners a rent of $1,500 per day for storage costs. Needless to say the ship's owners and insurers refuted these claims and the case went to trial. Let's take a moment to appreciate the case here. The state of Oregon was asserting that the crashed ship was actually trespassing on state property. Bold claim. But it did actually pay off when on the 13th November 2002 a jury sided with the state's argument and the $25 million was put into an escrow account as appeals and alike were hashed out. The shipping company would get back around $5 million after an appeal in 2006. Now before we come back to the implications of this legal case and the stern, we have to look at the criminal side of the investigation and what happened to the crew. Captain Morgado and his Filipino crew had some questions to answer after the grounding and this required them to stay in the US for several weeks as the Coast Guard questioned them. The captain pled the 5th amendment for most of his questions which is a smart move and after their testimonies they were finally allowed to return home. The investigation did find the captain and his first and third officers responsible for the crash but not enough to prove criminal wrongdoing and they would not see any charges brought against them. Bearing in mind the stern was still beached representing a constant reminder of the disaster the result was pretty unpalatable. Okay now we can get back to the landmark previously known as the stern of the new Carissa. The state of Oregon had kind of painted itself into a corner with its trespassing trial as their whole argument would have been pretty much seen as a cash grab unless the stern was actually removed and this leads us back to 2008 and the somewhat controversial dismantling and removal of the last few remaining sections of the new Carissa. The removal of the stern proved to be more difficult than originally anticipated as years of waves and storms had wedged the wreckage into the sand up to 20 to 30 feet in some places it was decided that the remains be dismantled by the use of jack-up barges which allowed crews to work on the ship cutting her up piece by piece. By September 2008 most of the visual wreckage was removed leaving only a few small pieces. By November the recovery crews and barges were gone and thus the new Carissa was no more but although no humans were killed the death toll from the fuel that did manage to escape into the ecosystem was thought to be responsible for over 3000 shore and seabirds. Rather worryingly if it wasn't for the burning of the ship this toll would have been significantly higher. I'm going to rate this disaster 4 on my scale and a 5 on the legacy scale. What do you think? Let me know in the comments. This is a plainly difficult production. All videos on the channel are created common attribution share alike licence. Plainly difficult videos are produced by me John in a currently wet and windy south-eastern corner of London UK. Help the channel grow by liking, commenting and subscribing. Check out my Twitter for all sorts of photos, nods and sods as well as hints of future videos. I've got Patreon and YouTube membership so check them out if you fancy supporting the channel financially. And all that's left to say is thank you for watching.


The Equitable Life Assurance Society presents This Is Your FBI. This Is Your FBI, the official broadcast from the Files of the Federal Bureau of Investigation. Presented as a public service by the Equitable Life Assurance Society of the United States and the Equitable Society's representative in your community. Among the many life insurance plans offered by our sponsor, the Equitable Life Assurance Society, one is of particular interest to home owners. This plan combines a money-saving mortgage with life insurance security all in one package. For further information on this Equitable Society Assured Home Ownership Plan, listen carefully to the middle commercial in about 14 minutes. Tonight's FBI file, The Fugitive Traveler. There are more than 5,000 crimes committed in the United States every day. When you pause to think about that fact, your mind conjures up the dark streets of a big city late at night. But the experience of your FBI in dealing with crimes in every one of the 48 states is that crimes don't happen because of geography, but because of people. Crimes are being committed tonight in crowded tenement slums and in peaceful moonlit valleys because there is a criminal president in each case. It is true that there are more crimes committed in big cities. But no section of the nation is so remote that it remains isolated from the crime wave. The night's FBI file opens in a farmhouse located in a hilly section of one of our eastern states. It is early evening. A young girl is seated alone on the back steps of this hillside dwelling. In a valley below, a passenger train moves swiftly through the dust. The girl watches the train, her eyes follow it intently. Well, what is it, Aunt Bessie? I've been calling you for the last five minutes. Sorry, I didn't hear you. Did you bring in some wood? Yes, ma'am. Did you feed the chickens? Yes. Did you bring in the eggs? I think I did. Well, where are they? Uh, didn't I put them on the kitchen table? No. Oh, I must have left them in the barn. In the barn? Why? I just forgot them, I guess. Well, go get them. Oh, Aunt Bessie, please, not right now. Just let me wait till the train goes around the hill. Oh, good heavens, child. When will you stop this foolish nonsense, moaning over trains, moaning over books, moaning over going to power off cases? I'll get the eggs. If you just give a little more thought once in a while to the fact that I'm an old woman trying to run this farm all by myself, and at least that a strong young girl like yourself can do it. I'm getting them, Aunt Bessie. I know. Let me go in the house. What else is in that house? Is that all? Yes, just the two of them. How did you get here? Where did you come from? I put off a train, a freight train. Oh. That's how you were hurt? Yeah. Yeah, that's it. I see. Look, I just want to rest a while, and I'll get out of here. But you're bleeding, so you need a doctor. I'll find my own doctor. Did you come from far away? What's that to you? I just wondered. Len! Len! What is it? My aunt, I've got to go. Wait a minute, wait a minute.  Don't, don't tell her I'm here. Why? Just do me that favor, please. All right. I'll come back later. Some 50 miles away from the lonely farmhouse in a nearby city at the local FBI field office, special agent Jim Taylor is approaching the desk of the agent in charge. You wanted to see me, Mr. Henderson? Yes, Jim, come in. All right, sir. Jim, you're about finished with the Brooks case, aren't you? Yes, I dictated my full report this morning. Good. We just received a teletype that you can go to work on. Oh, what's it about? Criminal named Ralph Alias Rip Gibson was being transported here from the penitentiary to testify to federal trial. Yes. He was traveling by train, had an armed guard with him. I see. While on road, he requested to go to the washroom. Guard consented. Once he was in there, Gibson smashed the washroom window and jumped off. While the train was in motion? Yes. When did the guard discover this? Almost immediately. He heard the glass crash and rushed to the train platform, saw Gibson rolling down the embankment, fired at him, believed he wounded him. But Gibson still got away. Yes. When did all this happen, sir? Several hours ago. Many trace of him since? No. The train was stopped, searching party was organized, but Gibson must have found some means of transportation that took him out of the immediate neighborhood. Well, if the guard did wound him and it's serious enough, he'll most likely be needing medical attention. We have already notified all doctors in the escape area. Local police are cooperating to him. Oh, good. I want you to stand by, Jim. All right. As soon as we get a definite lead, we'll go to work. How's your arm? Okay, I guess. I brought some bandage from water. Maybe you'd like me to take care of it. All right, go ahead. I'd have been out sooner, but I had to wait till my aunt went to bed. You didn't tell her about me? No. I've got to rip your shirt sleeve. It may hurt a little. All right, I won't mind. Are you... Sorry. Okay. Now let me bathe it. Yeah, sure. I've got to get the wound cleaned first. The bullet went right through, didn't it? What bullet? The one the guard fired at you. What are you talking about? I know who you are. What is this? I just heard the report on the radio. Your name is Gibson Rip Gibson. You escaped from your guard, jumped from a moving train. He shot at you. Look, I don't know what you're talking about. They gave you a description. Now just lift your shoulder a little. Did your aunt hear this report? No. Do you tell anybody else? No. Please lift your shoulder. Okay. That's fine. Now I can put the bandage on. Look, Miss... Nan. Nan Carroll. Nan. Why didn't you blow a whistle? What do you mean? Why don't you call the cops and let them know I'm here? Doesn't matter. I want to know. I know what it's like to be caged. Huh? To not be able to get away, to be free. I've spent my whole life right here. Anyone who can escape from anything, I envy. I get it. That's the best I can do with the bandage. Well, thanks. I better go now. There's some milk and cheese that I brought out. I'll bring you a real meal in the morning. Well... Good night. Good night. Mr. Henderson. Yes, what is it? If you've got the time, so I'd like to have you give a report on Ralph Gibson. Let's have him. All right. Well, two hours ago, we received word from a witness who saw a man answering to Gibson's description hop a freight train about half a mile from the point where he jumped. I see. This witness was a railroad employee. He said the train was a westbound freight. Its destination was a point about 50 miles down the line in Centerville, to be exact. This was two hours ago? That's right, sir. The train should be there by now. Yes, I know. I've already contacted the yards. Some railroad detectors are going to search the train for me. No guarantee. We have no guarantee, of course, that he didn't jump off somewhere en route. I know. Excuse me. Sure. Henderson speaking. Yeah, just a minute. For you, Jim. Thanks. Hello. Yes. Oh, hello there. Really? Or did you pick up any other clues? I see. Well, thanks a lot. Right. Goodbye. That was the Centerville Railroad Police. What did they have? A coat that they positively identified as belonging to Gibson was found in one of the freight cars. But no sign of him. No, they feel he jumped off somewhere en route. Oh, by the way, there was a bullet hole in the coat, and it was quite heavily stained with blood, so he was wounded. Jim, I suggest that you alert the local police all along that 50-mile route. Right, sir. Then arrange for a crew to cover the tracks. See if you can pick up any evidence on where he jumped off that freight. Yes, Aunt Bessie. Where did you been all morning? I just went out a half hour ago. Well, where did you go? I took a walk. What were you doing in the barn? The barn? I just saw you coming out of there. I was putting away some tools. Oh. I think I'll go... Wait a minute. What? I played in your hand. That's my best china. What were you doing with it? I just picked it up. You had it in your hand when you came in. Well, if you must know, I used it to feed the chickens. My best china? I'm sorry, Aunt Bessie. Wait. Huh? What's that all over your apron? Where? Right there. Looks like blood. Who's blood? I cut my finger. Let me see it. Please, Aunt Bessie. Leave me alone. Now, just a minute, young lady. There's no point in making a fuss over just a little cutter. I'm going to go upstairs and fix it right now. You were able to move. Yeah. I thought you wouldn't come back till later. Something's happened. What? It's my aunt. She knows I'm here? No, but she saw me come from the barn before, and she saw the plate and some blood stains on my apron. I didn't know how to handle it. That's why I came here. What should I do? Let me think. I won't let her come into the barn. I promise you that. Even if she wants to... Wait a minute. Tell me something about her, would you? What? She got a car? Yes. Is it around here now? Yes. How is she fixed? I don't know what you mean. She got dough, money. Well, she has a bank account, yes. How much are you keeping it? I don't know for sure. What about how much? Well, the last time she gave me her bank book to take him to town there was $800. There you go. Not too bad. Why do you want to know all this? Well, I'll tell you, honey. I feel sorry for you. Real sorry, see?  I'm going to give you that chance. Huh? By taking you away from here. Oh. Well, of course we're going to need some cash and a car. That's got to get from your aunt. Oh, she'd never help us. I'm sure she wouldn't. Honey, she won't have much to say about it. Huh? We're taking. Oh, I couldn't do that.  This is your chance, baby. Your chance to bust out. I know, I know. If you don't take it, you'll spend the rest of your life in this trap. You can sit here watching trains. Wait. Huh? Look out the window. My aunt's coming. Coming here? Yes. I'll stall her. Keep her off. Hold it. Let her come in. Let her come in. I'll let her find out what it feels like to be caged. Tonight's case from the official FBI files will be reopened in just a moment. Where Claire and I have lived together all these happy years. Where Sonny took his first steps. The place and all the world we love the best. If that's the way you feel about your home, then it's time you knew about the Equitable Society's Assured Home Ownership Plan. It's a money saver, it's a home saver. It's America's finest plan for home ownership. A money saver, you say? That's right. Just listen to these four advantages of the Equitable Society's Assured Home Ownership Plan. First, if the owner dies, the Equitable Society cancels the mortgage. It's paid off in full. What's more, every dollar previously paid on principle is returned to the widow along with the canceled mortgage. Second, mortgage interest is only 4%. And there is a libel allowance to help cover title search, lawyer's fees, and other closing costs. Third, during the owner's lifetime, a special cash fund is built up in this plan, ready for use if sickness or unemployment threaten home security. Fourth, as your mortgage shrinks, the cash fund increases. You can use it to pay off a 20-year mortgage, for example, in approximately 14 years. Well, that sounds good to me, paying off my mortgage in 14 years with that cash fund. Yes, you might be very glad by then to get rid of further payments. All in all, a man is mighty lucky if his health, age, income, and the location of his home qualify him for an equitable, assured home ownership plan. Well, how can I find out if I qualify, Mr. Keating? Ask your Equitable Society representative. Get full information on the plan that protects you against the two major hazards of home mortgages. Death and hard times. Look in the phone book or send a postcard care of this station to the Equitable Society. That's E-Q-U-I-T-A-B-L-E. The Equitable Life Assurance Society of the United States. And now back to the FBI file, The Fugitive Traveler. The night's case from the files of your FBI points up two important morals. Important because they concern you. The first is that wherever you are, however hidden your shelter may be, the crime wave in this country is your problem because it is a wave that may wash up on your shore at any time. The second moral and one which your FBI cannot impress upon you too strongly is that you, the decent citizen, should have nothing whatever to do with any criminal. You do not help him by condoning his crime. Instead, you only endanger yourself and become an accessory to his crime. When you come in contact with a criminal, your duty is clear. You should do one thing and one thing only. Notify your local police. The night's file continues at the FBI field office. Special Agent Jim Taylor is just reporting to the agent in charge. Mr Anderson. Yes, Jim. Sending out that crew to cover the railroad tracks is what results. Really? What happened? They're pretty certain they've located the exact spot where Gibson left the freight train. Good. It's about 25 miles east of Centerville and they're a community called Ridgewood. Well, I know Ridgewood. I'm a good sheriff up there. Name's Morgan. Yes, that's right, sir. I just talked to him. Oh, fine. The track crew called him in on the case as soon as they established where Gibson had jumped. He's taking over right now. I think you better get right down there, Jim. All right, sir. Get Morgan to work with you. I'm sure he'll be helpful. Good. I'll let you have a report, sir, as soon as anything breaks. Nan? Yes. How's your aunt? I just brought her some soup. You didn't untie her? No. She would go from mad at me. Well, she's lucky we brought her in her house. She could still be tied up in that barn. How do you feel? I'm okay. Did the walk-in from the barn tire you? No, no, I'm doing fine. Rip? Hmm? When do we leave here? Just figure that now. Look, what about this bank account? My aunt? Yeah. What is it? Savings or checking? She writes checks. Would the bank take your signature? Oh, no. We've got to get her to sign it. Rip, I wish we could just leave here and forget about the money. Are you kidding? You wouldn't get as far as that next corner. Well, she'll never sign a check for you. I know she won't. Where's the checkbook? Over there in her sewing basket. Bring it here. I'll get it assigned. Sheriff Morgan? That's right. Hello, I'm Jim Taylor. How you doing, Jim? I'd know you. Any word on Gibson, sir? Nothing yet, I'm afraid. We have a number of searching parties out looking for him. I see. Our bad break was at a drain last night. What do you mean? Well, as you know, Gibson's presence in this territory was established by that railroad crew who found blood stains leading down that embankment. Yes. When I got out there, I picked up Gibson's trail. I followed it to a stream about 100 yards away. It's a shallow stream. Gibson waited into it. Obviously, to avoid detection. Right. Just at that point, the rain started. Both sides of the stream up and down for several miles. But we weren't able to find any trace of where he came out. The rain, of course, had washed it away. I see. Sheriff, could you determine if he was bleeding much? I think he lost quite a good deal of blood. Then he couldn't have gotten very far. I know. I've set up a house-to-house search for him. Oh, I'd like to join you in that, if I may. You certainly can. Did you drive down here? Yes. Well, we'll divide up our assignment. I'll give you half a dozen farmhouses all on one roll. Okay? You'll have no trouble finding it. Fine. Let's have that list, and I'll get started. Did you sign the check? Was there any trouble? Of course not. She was very happy to do it. That's not true. You didn't hurt her. I didn't have to. What time is it? Almost one o'clock. Does this bank stay open till three? I think so. All right. You'd better get into town and cash us. How much is it for? Five hundred. Dollars? What else? Keep going. Rip, I don't think they'd give me that much money. Look, you've got to check here with your aunt's signature on it. Tell them that she sent you in for the doll. Tell them she needs it to take a trip. Yes, but I... They know you at the bank, don't they? Yes. All right, then get it. Rip. Shhh. Get rid of whoever it is. I'll hide it here. Yes. Are you Miss Carol? That's right. My name is Taylor. I'm a special agent of the FBI. Yes. Here are my credentials. What do you want here? Well, I don't wish to alarm you, but we have every reason to believe there's rather a dangerous criminal at large somewhere in this vicinity. Oh.  No, sir. I have the man's picture here. I'd like to have you look at it, please. All right. How would you try to remember him? And if you should see anyone resembling this man, get in touch with your sheriff at once. I will. I understand you live here with your aunt. That's right, but she's upstairs taking a nap. Oh, I see. Well, just pass this information on to her, too, will you? Yes, sir. Thank you. Oh, uh, by the way, would you mind if I took a look around in your bar? No, go ahead. Thanks again. Goodbye, Miss Carol. Goodbye. He was from the FBI. Yeah, I know. I heard the whole thing. He's gone to the barn. He won't find anything. He cleaned up around where I'd been. Oh. Now look, you wait long enough for him to pull away from here. Then get into town and cash that check. How'd you make out? I didn't get a thing, sir. I drew a blank, too. Look, I'll tell you what. I'll review all the calls I made and see if by any chance I missed a farmhouse. Go ahead. By my first call was a family name Pastor, a man in white. Right. You have any trouble getting in? No, I... Well, they're not usually very sociable as strangers. They were very cooperative. My second call was a man named Stuart. Oh, Pop Stuart. You had to shout at him, I bet. He seemed pretty dead. He is. My third stop was at the Carol Farmhouse. Who'd you talk to, man or Aunt Bessie? The girl, man. I was thinking of that. Probably just as well. Aunt Bessie's a man-hater. Oh? She won't have one around the place. Wait a minute. Not even a hired hand? No, sir. Hasn't been a man around there in years. Sheriff, I think we ought to go back to the Carol Place. Stay behind the door just in case. Well, how'd you make out? They cashed the check. Good, baby. Let's have the door. Just a minute. Here. Okay. Small bills. That's good. Where's the car? Out back. Give me the keys. Are we leaving right now? Let's have the keys. Don't you think we should do something about my aunt first? We just can't leave her tied up. Honey, will you give me those keys? Sure. Here. I'll go get my bag. Wait. I've changed the schedule. What do you mean? You stay here. Oh, no. You heard me. But everything we planned, the reason I did all this was to get away. You've got to take me with you, Rick. No, Dice. You promised. Look, sweetheart, you're better off here. I don't want to stay here. I want to go with you. Honey, I might as well tell you right now. Going away with me was strictly a routine. What? What would I do with you? All the things you said we'd do together. The places you'd take me, the clothes I'd get. Baby, did you ever look at yourself in the mirror? What do you mean?  I'm getting out of here. No, wait. You can't leave me. You can't. You can't. No, no. Don't change.  Hello, Gibson. You saved us the trouble of coming in for you. Who are you? A special agent of the FBI. What? I was just showing the sheriff here why I came back to this farmhouse. Your footprints there in the mud. Now I think we should arrange to put you back behind bars. Ralph Gibson was returned to prison after being given an additional 20-year sentence in a state court for his brutal assault on the elderly farm woman. And thus, another criminal was brought back after escape by your FBI and a lyrical local policeman. Another instance in which local authorities led a very important hand to the Federal Bureau of Investigation. Your FBI has stated before and wishes to repeat that it owes a great debt of gratitude to local police departments all over the nation for the cooperation it has received from those departments. And on this official broadcast, it wishes publicly to thank every local law enforcement agency in the United States. In just a moment, we will tell you about next week's exciting case from the files of your FBI.  That's right, Joe. And don't forget, you get a lot of good things in that plan. A mortgage that's paid in full if the owner dies. If not, a cash fund to be used in financial emergencies. And mortgage interest at only 4%. No wonder it's called America's finest plan for home ownership. So don't delay. See your equitable representative soon. Or write to the Equitable Society care of this station. That's E-Q-U-I-T-A-B-L-E. The Equitable Life Assurance Society of the United States. Next week, we will bring you another colorful story from the files of the Federal Bureau of Investigation. The curious cameraman. The incidents used in tonight's Equitable Life Assurance Society's broadcast are adapted from the files of the Federal Bureau of Investigation. However, all names used are fictitious. And any similarity thereof to the names of persons living or dead is accidental. Tonight, the music was composed and conducted by Frederick Steiner. Your narrator was Dean Carlton. And special agent Taylor was played by Stacey Harris. This is your FBI is a Jerry Divine production. This is Larry Keating speaking for the Equitable Life Assurance Society of the United States. And the Equitable Society's representative in your community. And inviting you to tune in again next week at the same time when the Equitable Life Assurance Society will bring you another thrilling story from the files of the Federal Bureau of Investigation. The curious cameraman on This Is Your FBI. This is ABC, the American Broadcasting Company.


A group is recruiting families and businesses in Bemidji who want to make the switch to solar energy. Solar United Neighbors held a public information meeting tonight. The nonprofit's goal is to make solar energy more mainstream. They help by forming bulk purchase groups in communities so everyone participating can get one-on-one help with the process. They already have groups in the cities and thought Bemidji would be a good next step. So the Bemidji group kind of brings a whole bunch of neighbors together. You get assistance, understanding what the technology is, kind of walking through all the aspects of it, and then you get to have good pricing from our selected installer, which is WolfTrack Energy. So the group is open. It's free to sign up for the solar co-op group. That way, participants can really determine if going solar is right for them. There are site assessments and the people in the group work with the installers directly to figure out pricing. Solar United Neighbors adds the panels that they are a 25-year investment. Well, I think it's a great time to go solar. The costs have come down a lot in the last five years, but we kind of hit the bottom of that trend. So I think the timing is good. And with solar right now, there's a 30-percent tax credit, so you'll get that the year following the installation that's based on the entire cost. Yeah, and you can sign up through August 31st. We have the link on our website with this story.


An organization in Brainerd is holding their annual big event this weekend to raise money to fund scholarships and programs for students in the Brainerd public school system. The Brainerd Public Schools Foundation is hosting the big event this Saturday at Kregens Resort. This is the foundation's sixth annual big event and the major fundraiser for the foundation. This year's theme is game on and in addition to the event an online auction is available for anyone to bid on all with all the proceeds going to the foundation. Everything we've got going on that night is game related. We've got some really great raffles and things of that nature. We're going to do some terrible gambling like electronic horse races and just some unique things that we've never done before so it's going to be a lot of fun. This event wouldn't be possible without our generous sponsors and our community partners and we cannot thank Lindar, Avantek and TriVent enough. They have been our premier sponsors every year since we started. The Brainerd Public Schools Foundation was established in 1987 to provide scholarships, programs and funding to enhance the 4As, arts, academics, athletics and activities in the Brainerd Public School District. Along with providing scholarships, the foundation has provided funding for cutting-edge technology in the schools such as virtual reality and a new makerspace. We're having opportunities in a little town like Brainerd. It's nice to be able to compete with the bigger, the bigger schools, the bigger communities and so we've got cutting-edge stuff. We've got virtual reality. We're working to fundraise for augmented reality right now. Flexible seating and furniture. There's so many things that we're able to provide our kids locally here to enhance what the school district's already doing. Tickets for the big event are sold out but anyone still interested in attending can purchase a Crash the Bash option which will get them into the event at 8.30 p.m. for $10. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


Hi good morning So we're gonna have a change of pace from yesterday there's gonna be Well, I'm not sure what it's gonna be there's gonna be less chemistry I hope that I don't I because I don't know any chemistry. So whatever I'd say would be gibberish I want to start by showing you this picture We heard about DNA linking yesterday and how does DNA do this in fact? There's some things this kinetoplast DNA Which is actually linked on purpose and actually the little loops there's some purpose and the big loop for the for the processing of the Cell so there are macro cycles and there are little cycles and the little cycles are in the right place So not only do you have these things that duplicate they duplicate and they stay linked together It's not just that you have how do they manage to duplicate while they're linked together and then come apart These actually go back together in a special way So I'm not going to talk about this kind of linking All right, but this is the kind of linking I have in mind I'm thinking of linking of things that are physical links Where you can't pass things through each other yesterday somebody said who said it are you here? Yesterday somebody said oh, well, I'm not going to talk about energy She's already she's already gone. Okay. She's all right But of course she was talking about energy if you try to like pull if you pull two strands of DNA hard enough They will break and go through each other. So topology and energy are always, you know, deeply interconnected It's just a question of scales I'm going to talk about work that started some time ago with Gareth who's up there and Brian Chen who's not up there and Ended recently with some work with Ricardo Mazna from Brazil So Here's a story. Here's your first introduction of the crystals.  I've never seen one. Okay, but this is what looks oops. This is what oops. Oops It was so much easier when you had transparencies you could just drop them. All right, anyhow here Is a nematic look at crystal When you look at a nematic look at crystal Through cross polarizers and I'll explain everything in a moment you see places You see these black lines and you see these places where the black lines come together into four fold places And sometimes into two fold places. So let me tell you what you're looking at in case you don't know So this is how it works. There's a light. There's a polarizer There's another polarizer that's at 90 degrees, which is called the analyzer if you send light through cross polarizers you get You get Nothing exactly Okay, but the liquid crystal molecules in there the nematic liquid crystals are Elongated rods from the point of view of mathematics. They're just line fields But they're molecules that are long ellipsoidal and long and stretched and they're birefringent And as a result if they're in here They actually help rotate the light if you if you like light you would say well There's the ordinary wave the extraordinary wave and they go at different velocities and they get to the other end of They don't cancel or if you like polarizers You can think of them as a third polarizer inserted between the cross polarizers The upshot is is that when you see light coming through it means that the molecules Which are lying in the plane of the polarizer and the analyzer are Letting light through and it means that they're not along the polarizer direction of the analyzer direction if they were Along the polarizer direction you'd have two polarizers like this and one like this that would still give you nothing right the second polarizer would be redundant and so These black lines are the pre-image of the direction of the polarizer in the direction of the analyzer So there you go to apology in a nutshell right you take a picture with cross polarizers and you can actually see the root the pre-image of these two directions and Why do you see four? Well, I told you it's a line field So I'm drawing a line field in here notice that I don't have any heads on these lines if I have a Defect here a place where I can't tell you which direction the things go everywhere else I have to have a well-defined line field. So as I go around this point The line has to rotate by 2 pi one way or the other way And you get four brushes why for I get black whenever the molecules are along P or along a So you get four brushes because it goes through the polarizer once in the analyzer once in the polarizer again in the analyzer again four brushes four times It doesn't matter how as long as it goes around by 2 pi you get four brushes By the way fancy pants it means that these here where you get to Tell you that the molecule is symmetric under rotations by pi look at that I took a picture with something that was invented in the 1800s polarizers with light this is a picture taken with a microscope something that Galileo could have built and You can tell something about nanometer size molecules That they're the same whether they're like this or like this. It's pretty cool, right? They don't have to do that much Once you know mathematics, okay? This again, so that's the pneumatic phase if I were a mathematician I Would classify The defects how would I classify them? I'd have my sample here Here's the sample. It has a bunch of defects in it Here is the direction of the line field, so this is an angle phi And what I would do is I would look at some path around this defect and I'd make a map from this path To this space. All right, so this is a map from the circle to the circle So it's a map from the circle to the circle and so I can classify those defects by the fundamental group of This thing which I'll call the ground state manifold It's the place that tells me all the directions that are ground states after all the ground state of the liquid crystal the ground state of the line field is all parallel lines and Now I tell you that as I go around some defect the direction rotates and I can tell you how much the direction Rotates because it's an angle and there's maps from the fun from this path Which I went around to that path and I see a black line Any time I'm here or here or here or here for instance But I don't want to talk about pneumatics the next talk. We'll talk about pneumatics I want to talk about something which is a little more subtle which we don't understand And I hope that I can entice you to work on it with us or work on it yourself solve the problem and Mail us a copy. All right here is a smectic a smectic is A crystal and what I mean by that is that there has one dimensional order It's like a building right so there's a stack each layer of the building can do whatever it wants Each layer of the building can be a liquid no organization on each floor, but the floors are separated Like a department store. Okay, but by the way, this is a real picture of a smectic This is what a theorist writes down they draw always parallel layers But real smectics when you look at them and cross polarizers are very complicated things But Everywhere that you see the smectic Locally it looks like this Locally a smectic looks like this So how would you describe a smectic one of the reasons energy is not that interesting here is that the Ground states or the things that you see not the ground states the things that you see are quite complicated Let me just tell you what we do we write down energies We'd write down energies that say things like the layers want to be equally spaced and they don't like to bend But I'm not interested in those what I'm interested in is how do I describe the layers and I describe the layers by Writing down level sets of some phase field phi The density of stuff is proportional to cosine of phi Phi equals zero is the first layer phi equals a is the second layer phi equals 2a is the next layer and so on and Because phi cosine phi is the variable of interest you'd say this is exactly what I did before After all phi, which is telling me where the layers are is also lives on the circle Because phi and phi plus a to the same so you'd say oh, it's the same thing. I Would classify defects and objects like this precisely the same way I would find some point where I didn't have nice order. I would go around the point in the sample That would be a circle measurement here, and I would have a circle measurement here But that's not true. It turns out smectics are more subtle and The reason that smectics are more subtle is because this order is periodic in space. It's actually in space It's not in some internal manifold like telling me what the direction is So unlike the pneumatics So one of the things about pneumatics Which you could realize for looking at this is all I need to do if I actually am classifying things in a fundamental group Pi one of s1. Oh by the way, I should I shouldn't keep it a secret from you These are just the integers and so since they're just the integers the fundamental group I can add things together, and it's true if I take two defects where the rotation is 2 pi and bring them closer together Far away. I'll get eight brushes It'll look like I've gone around 4 pi and if I've gone around plus 2 pi and minus 2 pi as I bring those four brushes together They're all cancel with each other. They'll all link up, and I won't have any brushes at infinity. So in fact This is not nice a billion group. I can add the defects together because they're classified by this object But smectics are different. There's a real theorem by Ponaru. It says look suppose that you have a system Wait hold on Measured foliation Measured foliation means locally You can always zoom in on whatever the thing is and it looks like this Looks like a smectic except for a few points, which are singularities That's what the all these words mean measured foliation is the important one It means that you can locally make things look like layers and Pornaro proved that you can have a Defect that looks like that see here is a texture if I asked myself. What is the normal direction to the phase? Right the normal it goes around by 2 pi. I Could talk about this here the normal goes around by pi That works because the normal and minus the normal are the same here. Nothing happens here It goes around by minus pi minus 2 pi minus 3 pot minus 3 pi and Ponaro prove that you can go all the way this way You can have any negative charge you like But you can't have any positive charge in fact plus ones as high as you can go Now You can read this it took us a long time to understand it here's the problem a group is a group and We say this thing in the United States what state what happens in a group stays in a group and so here's this group I Should be able to combine two objects that are classified by This winding how come I can't join them together the group operation would tell me I could join them I must get something with winding number two and a winding two or an index two zero Why don't I get one and put our approved you can't do it and it's this thing that locally I always have to have my layers look like this And we didn't understand the theorem I mean we could read the all the words and We could read even sentences, but we realized to us what was going on was much simpler in our minds is I Told you we have this field Phi level sets of Phi tell me where the layers are So I'm going to talk about a two-dimensional Smectic because I can't draw the three-dimensional one this green thing is just the graph of Phi It's not a physical object It's a mathematical object and level sets are easy You intersect this green surface with the surface by equals zero And that's this level set and the next level set and you get all the level sets and you realize that Asmetic is nothing more than a topographical map And it's important this thing about it being measured means that at every place there's a slope that isn't zero And so Here you go, right? You get to basically use the idea as a Morse theory to talk about the Smech-tik and it's different when you talk about a Smech-tik instead of talking about Layers as the objects or the direction as the object the phase you think oh it's really something that lives on a mountain range and The mountain range level sets of the mountain range tell you where the layers are and it's great. The layers never cross The layers never end You can tell that you're at the top How can you tell that you're at the top of a mountain good? In Europe and you're you know you yeah in Europe. It's easy because you can buy a coke Right. There's always a coke. Yeah. Yeah, it's not like that. There's a coke. There's a chop You can buy lint chocolate everyone Switzerland the top of every mountain you can buy lint chocolate, right? It's true right but in the u.s. It's what you said you get to the top and every way else is down Okay, all right, and you know all right and so here's the and if it's every way Oops, oops. Sorry if every other way is down it means that as you go around you have these closed loops Which are the plus one index zeroes? And the thing is you say how come I can't bring two of them together And you know the answer because there are mountain passes in between and there's this thing the mountain pass theorem That tells you if you bring try to bring two mountains together You always in train a pass and a pass is precisely a minus one index and So as you try to bring the two mountains together you lose the pass in between them and the charges all cancel So it's not so simple. However, it's not as simple as you can bring the two plus ones together They always in train this extra minus one in there How can you have any negative charge you can have a situation where you have you know 35 mountains? And you have one pass That goes down to the 35 valleys that's not allowed in Morse theory that would be a degenerate Critical point, but it's allowed in my picture Okay, so it's not quite Morse theory. I should probably have some other symbol here that isn't equals So the idea is you can have any negative charge, but you can't have any positive charge It means that classifying these defects is not as simple as having a group If we're a group I'd be able to take two plus ones and add them together and Has something to do with the fact that you have this spacing and that you have this measure everywhere now Smectics get to enjoy something else now Nobody stopped me You guys all nodded when I said oh, it'd be just like this problem The original problem thematic and here's a situation where it is the same problem as the pneumatic because now I Have a phase field and the phase field rotates by 2 pi or the phase field changes by pi or 4 pi And what do I mean by that? These are called dislocations. These are different than those index defects That was something about a defect in the normal to these surfaces But the normal to the level sets now. I'm talking about the level sets themselves and In the US, I'm sure it's true everywhere. Oh, I know where it's true. It's true in Bristol Who's from Bristol? Excellent. Okay. It's definitely true in Bristol Sometimes you have these buildings that are joined together One was built like before the war and the other was built after the war I'm talking about World War two and and the war they come together and There's more floors in the new building Somehow over time they improve the technology you need less space between the floors and people got shorter or Whatever they didn't use much space, right? And so what happens is you have nine stories here and you only have eight stories here The buildings are the same height and you have to like mush them together somehow you do it like this You relabel them one two You always call this the mezzanine Right one of them is the mezzanine with three and so forth and The weird thing would be is that if you weren't paying attention to what you were doing You could be wandering around the building. You could start here. You could go up one floor Here you are here's the ground floor, but you start on one See I'm adapting for you guys. Okay. You start on one you go up to two You come over here. Now you want to leave the building So you go down two stories because you were on two you're just you think you're on the ground floor, but you're not You're on the mezzanine. You've messed up. You can't get out. You're trapped. You have to get a coffee and so That's a dislocation. You're not where you thought you were because there's this extra layer That is the phase field changing. What am I doing? I'm looking at grad the gradient of that phase field Phi and I'm adding up the changes And I went like this and I added up one and then I went over here and I went down to So when I did some integral of grad Phi It wasn't zero These are classified by maps from the circle to the circle So, how do I mix these two things together? I just told you that a smectic so they get to enjoy this kind of defect I told you that a smectic is a Topographical map I told you topographical maps can't have ends to their lines So how do I manage this that I'll be allowed on a topographical map. I Can ask you a question How is it possible even draw a surface that does this What kind of earth or what kind of planet or what kind of map or actually what kind of mountain range would give you this Here's a hint remember the graph is up. It's away from the surface and you're so here's the surf Here's the XY plane and I'm telling you that as you walk around the circle Phi changes by Or to pie or whatever units you like That means you've gone up though. That's a staircase. It's a spiral. It's a helicoid You say, how can I work a helicoid in here's a helicoid? What's wrong with this helicoid if you get the answer wrong I get extra fun. It's a negotiation The problem is far away the helicoids flat So it's not measured. It's not a smectic. I have to have a slope Another way of saying is I want the ground state to be equally spaced lines So I don't want to have something which goes to flat. I want something a mountain range. It looks like this infinity So I can I combine the two things together? Of course I can Right. Here's the helicoid and I can stretch it and there it is It's a stretched helicoid and I stretched it up. You know why I stretched it up I stretched it up so that on the circle Phi and Phi equals zero and Phi equals one and Phi equals two are Exactly the same thing. I'm making this space the mountain range live in a periodic space Instead of living in R. It's living on the circle. Haha the circle right And so then I can fit it in and it works and so here. Oh, I don't know what's going on Oh, but you get the other version of it. I don't know why okay Here's a picture of it. Now watch me take level sets of it. You ready?  Do you see there's two extra layers coming in? There's the dislocation watch there it is see It's a dislocation two extra layers And I can go and I can even get the other geometry If I want the one where I get one extra layer is a little more singular Because I have to have only half of a helicoid, but you can do it, too So here you have the situation where you have dislocation. So if you make a mountain range That lives on the circle instead of the real wine Then you're good then you can actually completely describe the defects and smectics And you can say why am I telling you about this? What's this workshop on anyhow? It's on links and knots, but I'm going to try telling you that the story of links and knots of This object is very complicated All right, I'm not talking about vortices and superfluids Or defects in nematica crystals I'm talking about defects in a very complicated system because it has all these extra problems The defects don't add even the blame simple story the defects don't add nicely. There's no group I can't use homotopy theory so easily So we've been exploring this system. Our goal is to really understand it Our method is to just find problems that we can solve that we can understand So let me go from two to three dimensions. Oh Do you have a question? You have question ask me you you it's okay. Who says that? Well, of course, I have a theorem for you everything shown at this conference is too deep Okay, but I'm not but here is a picture. See there's the extra dimension y Okay, this is the xyz plane. This is a section in the zx plane I have complete symmetry in the y direction. So this is an edge dislocation Look at the light blue line only the light blue line. You have one come in and you have two going out to infinity Here's the dislocation these different colors Phi equals zero is the blue color Phi equals point one is this darker blue Phi equals point two is this even darker blue Phi equals point three is this pinkish color and so forth I'm drawing all the values of Phi all the level sets of Phi not just Phi equals zero and Phi equals one all of them They're all there the phase to wrap around has to be defined everywhere and This point here is the place where I've added an extra layer There's an extra two pi of Phi in here. I've squeezed in an extra whole two pi I can write down a phase field if you like, but I noticed something Suppose I draw the normals to the surfaces The normals to the surfaces around this point wrap around So this is an index one Defect in the normals, but I have this funny boundary condition. It's that measured foliation boundary condition far away The normal points up The normal isn't zero if I were a superfluid. I Would say far away grad Phi is zero But here grad Phi isn't zero grad Phi has to point in some direction there has to be a slope And so now I can use the mountain pass theorem again if I want to call it that that's I think overkill I have a situation here where the line points down Near this defect and I have a lot and I know out here the line points up Somewhere the line must vanish There's another zero Grad Phi has another zero grad Phi has a singularity here and it has a zero right here And that means that here I have a place where the I have a plus one index Dislocation or plus one index zero of the director field or the normal But here I have a minus one index one there are the two points the plus one and the minus one and they're separated And they make the dislocation Did you see that you have these? Disclanations the things you saw in the pneumatic and put together they make this extra layer in the Psymectic, but I have to have them they always have to be in pairs in other words if I want to add an extra layer I am forced to have a disclanation pair a pair of Singularities in the orientation It's unavoidable Yes No That's right, but I'm just talking about the topology you're saying it could be that the energy is so high You just get a giant spot in the middle that blocks all of them. I agree Well, then I have to worry about what I do on that boundary And typically as you know, it never really goes to zero. It just decay it goes it gets it gets smaller So what happens if I look at this system? So here's this edge dislocation going through the sample I've added an extra layer suppose now that I want to tilt it. So instead of it going along this way now It's going to be more 3d Okay, now the dislocation goes like this This is still where the layers are this is the layer normal So the whole thing gets tilted a little bit But it's still true when I look at a section perpendicular to the defect line. I will still get these Layers there'll be a different spacing. They'll be stretched out But I'll still have this hyperbolic point and this Dislocation point or if you like the mountain and the saddle until eventually I have a helicoid Remember that helicoid. This is the boring helicoid, right? This is a defect. Look at this. Here's Phi That's the level the phase field. I look at a level set Phi equals zero So Z is arctangent Y over X. It's a nice helicoid. This is a defect in the smectic Which is allowed a 3d smectic and This doesn't have to have this hyperbolic point because these guys just go around. There's no condition on grad Phi in the XY point Right here. There was a condition in grad Phi in this funny tilted XZ plane But here there's no such condition and So you lose this property a screw dislocation, which is what we call this because it was like a screw Doesn't have to have a hyperbolic point, but this one does So I become interested in how do you link together defects in these materials? Are they linked? Are they linked the way that DNA is linked or? Are they linked in land-out theory where you have two superfluid vortices and you say well They're linked because there's some energy costs to have them pass through each other But that's a very small energy Compared to breaking apart two pieces of DNA and what I want to know is are they topologically linked when I mean That is can you actually pull them apart or just apology force you to leave a thread behind? as you pull them apart So here is my screw dislocation You see blue might be the level set Phi equals zero and red is Phi equals, you know Two-thirds and green is Phi equals one-third and blue is again Phi equals zero and Here's the screw dislocation and out at infinity it fits on the flat layers, and that's okay Now suppose I have an edge dislocation going around it Watch carefully So what do I mean by that an edge dislocation is a place where two red layers become one red layer? The mezzanine in the second floor just joined to be the second four So here's the edge dislocation. It's a closed loop in the XY plane What do I have to do? I have to pinch together the two red layers over here But as I go around because the screw dislocation is changing I have to pinch together the two green layers here and in back. I'll have to pinch together two blue layers So what I see is that on this edge dislocation There's actually a winding The winding is what color do I pinch together as I go around? You could say to me why don't you just keep pinching the red together? Well, I can't I would have to stretch everything in some terrible way it would effectively I would have to tear the smectic to do that. I'll make this more precise. Here's a picture I don't know which picture helps more. I think the picture on the left Doesn't help me at all. It's like some drill that was badly made, right? So here's a screw dislocation in infinity with one less layer than the screw dislocation that's going up the center Another way of saying here here are the level sets. What I'm doing here is I'm rotating around the central axis So here's where the screw defect was that helicoid. I'm going around it Here are the two here the here is the edge dislocation. Do you see as you go around the color changes? In other words, what's happening is there's a winding on The edge dislocation that's being induced from the boundary conditions at infinity The fact that in infinity I have layers is forcing me to connect those layers to the edge dislocation on the inside You don't get that usually usually when you talk about Superfluids or superconductors or even pneumatics at infinity everything's constant And you don't have to worry about this, but now you do Right. It means that in fact I have a problem. I Can't compactify my my sample Usually I could say that every point on the boundary of the sample is the same I can compactify the plane to the sphere But I can't do it here because at infinity. I don't have constants So I either have to do it in a finite region or I have to have some kind of really strange I have to have a defect at infinity Right, and so here's the structure It turns out it's in here here. You have a structure where you have a dislocation going around a screw dislocation. You see as You go around these lines over here. It looks like a dislocation over here It looks like a dislocation But as you go from the left to the right the lines of constant color have a shift in them They have a jump and there's no way to get rid of that So that if I tried to take these two lines and bring them back together I would have to have a singularity in the phase To me this means they're really linked There's no way to take if you had a screw this location here and you start running at it You can do this with dogs. You can do this experiment. I have my college roommate My college roommate his mother was a veterinarian. They went to the beach and They they they just they had two dogs and they decided to keep the dogs from running away. They would just tie them together Forgetting that dogs are pack animals. They don't run apart. They run together So they went around the beach taking everybody out with this rope in between them But that's exactly what this is here. The things are running. Okay. There's no way to take that rope Cut it and rejoin it that would mean cutting all these phase lines and rejoining them There'd be a terrible singularity in the phase lines So these are linked. These are linked like ropes tying dogs together They're not linked like superfluid vortices or vortices in a liquid which are energetically for you know suppressed from crossing These are topologically suppressed from crossing knots I've people have already seen this table, right? So I Feel better though. I can't imagine that any journal would ever accept a title like this anymore the first seven orders of naughtiness Q imagine that I mean Maybe the New York Times It turns out you don't know this in the US, you know, people aspire We want to publish in nature and science, you know all those things people really want to Publish in the Times literary supplement, right that that would be the pinnacle of your publication, right? So here are the knots. I'm going to explain to you how this invariant I'm talking about is closely related to knots and actually is much simpler from the point of view of knots so suppose instead of having a Tangled set of defects. I had a knot in my smectic Okay, Mark Dennis. He sort of introduced this idea to me this idea that you have a knot But the field around the knot It goes to the whole knot The knot just happens to be a simple part of the whole field, but the field has the knot in it So this is also Mark Dennis and and John Hane's beautiful picture. They say let's think about how link and twist and writhe work I don't know why this is Edinburgh, right? I'm bringing that this is Trieste. Okay Trieste. Sorry, so They said look everybody knows link equals twist plus writhe Here is a situation where I only have writhe And here is a situation where I only have twist So what does it mean? To have only writhe or to have only twist So here I have my belt Okay, so and You can see the two stripes. So now what I'm going to do is I'm going to rotate it give it a two-pile twist Like so Now you see these things. So this Configuration is twist. How do I know that? Because sometimes you can't see the red and the green stripes There are times when the red and the green stripes wrap around each other That's because there are places where there's always no matter what projection I give you There's always a place where you can't see the belt But this is writhe because you always see the red and the green Rithe is when the red and the green cross at the same time So that you always see them non-local crossings and twist is when they have local crossings And you can convert one to the other see how simple that is Okay, this beautiful way of interpreting things. I Lost my advanced sir It's okay. I'm wearing I'm wearing underwear. It's alright. Okay Boxers, okay, so anyhow Here we have link is twist plus writhe. Let me think about something Hello Maybe I've gotten too far away. I'll just touch the computer. So here's a knot. Here's a trefoil knot. Here's its cypherd surface All right, what I'm going to show you is That there's a natural framing of this knot There's all this work beautiful work about how how is link equals twist plus writhe What's that word? generalized to whole fields and to whole fluids and the Helicity of the fluid, but here I have a much simpler problem. I have a system where here is my knot Here is its cypherd surface the cypherd surface defines one framing of the knot. We see it The remote is dead. Oh, there you go So I'll remind you this is from Mark Dennis here is a trefoil knot Here is its whole vibration in cypherd surfaces, which is quite pretty see each of those as a smectic layer You see a fiber knot is naturally a smectic so let me make my vibration here is the unknot and I can make a cypherd surface for it and then I can the cypherd surface is orientable so it has a normal everywhere and What I do that I call this an epsilon ball around the line. Is that what you call it an epsilon tube, right? what a tubular neighborhood tubular neighborhood around this line and I intersect the tubular neighborhood with the cypherd surface to get another curve this one and then as Tom Michonne would tell me since the normal is everywhere to find I can take that new curve and just push it off the surface And that means that these two loops are not linked Okay, the link is zero, but fortunately I have another framing Right, so I can talk about if I talk about this guy. I'll call this the surface where phi equals zero It's one of the level sets, right? And so this is the line I get I'll call it eight zero. It's the line I get from that cypherd surface defined by the symmetric But fortunately I have another frame. I have this point here You see I don't know the value of phi at this point where the dislocation is because it has all values of phi But the place where there's a saddle where grad phi vanishes is perfectly well-defined and this guy always has one with it So I can use this curve as the other curve So I have a framing from H and I have a framing from H zero if you like and Because the framing is a such that I'm gonna put the H's and these the D is the green curve Here's the not the projection of the knot the framing is always in such a way That the H curve you can always see it. It doesn't twist around the green curve Right. It's because it's always just it has to do with the gradient of the phase field And so now I can talk about this and we know from my belt and from Mark Dennis that The red and the green curve it's pure Rive No link no twist all Rive So Here we go. I'm gonna take Link equals just plus Rive for two different curves. Here is D and H That was H is the induced one from the symmetric. Here is D and D zero. I guess I called it eight zero That's the one that I get from the ciphered surface This one has no link the Rives cancel. I can subtract And I discovered that the winding Which is my topological invariant that's telling you how the color goes around as you go around this location There's nothing more than the linking number of D with H So the smectic gives you a natural framing of the curve the defect curve Until something terrible happens Davide do you know You're taking up my time You know yeah Do you know the answer if I take my knot after all the knot is a three-dimensional object Why couldn't I rotate it? Why is this projection have to be in the XY plane? Why can't I rotate it so that the defect starts pointing straight up? When the defect points straight up I lose H Remember I told you that if you I have a helicoid the helicoid doesn't have a natural hyperbolic point And that's a problem because as I do it now the defect tilts up and it's gone I don't have my framing anymore. What do I do and I say to you here's the math question This is about the boundary conditions So I can't take my sample and Compactify it. I have to take a finite sample. So I take a cylinder All right cylinder fine. It might be an infinite cylinder this way and it doesn't have to be infinite It can be you never have to be infinite. It's just a cylinder And I have boundary conditions on the top and bottom and on the sides I have these graduations right the phase going through phi equals zero phi equals one and so forth As I take my edge and try to tilt it up That other curve. This is supposed to be green I picked red white and green. I was trying to be patriotic. So here are the two things this guy moves further and further away as I take this guy This line and tilt it out of the XY plane and try to point it up the z direction This guy moves further and further away Until it goes off to infinity That's why it's gone It doesn't disappear because it merges with this point. It disappears because it gets pushed away Now I can't there is no infinity in my system. I have a cylinder It means that at some point this passes through the cylinder and violates whatever boundary conditions I had on the cylinder So if I do the topology right and keep everything inside I Can never let this guy pass through the wall of the cylinder Another way of saying is I can't take my knot if I try to take my knot and rotate it arbitrarily Arbitrary rotations will violate the boundary condition on this cylinder Which has graduations right these are these are phi equals? one zero minus one two Three and so forth. So as I move up I have my finite cylinder if I try to rotate the knot arbitrarily. It'll mess up these boundary conditions So this doesn't solve the problem It just points out the same problem because I have this measured foliation Infinity is problematic their boundary conditions at infinity or on the cylinder actually come back in and create Linking on the inside that I can't get rid of and because I can't get rid of it. I can quantify it It's two pi times the linking number That's the end. Oh, I don't need that. Okay. Thank you