Welcome, weirdos, I'm Darren Marlar and this is Weird Darkness. Here you'll find stories of the paranormal, supernatural, mysterious, macabre, unsolved and unexplained. If you're new here, be sure to subscribe to the podcast on Apple or Android so you don't miss future episodes. This is a special 12 Nightmares of Christmas episode. Each day from December 13th through December 24th, I'm posting a new episode of Weird Darkness featuring material from the new book, The Spirits of Christmas, The Dark Side of the Holidays by Sylvia Schultz.  Just like superheroes, all paranormal researchers have their own origin story, the event that launched them on their careers as investigators of the unknown. Author Stephen Lancaster came to his first supernatural experience earlier than most. He was just 10 years old when he was attacked by an invisible entity in his bed. Lancaster remembers the date vividly. It was December 14, 1987, and he was living in a small town in western Maryland with his parents and younger brother. The family had moved in several months before. Stephen recalls that the Christmas was to be their first in the new house. As the older kid, his little brother was just five, Stephen felt perfectly justified in claiming the top of the bunk bed set when the family moved in. The boy's bedroom was chilly at night, the house was heated by a coal furnace, and its warmth struggled to reach the second floor. Up on the top bunk, it was even chillier, but it was worth it to Stephen to have the prized spot. On the night of December 14, the boys had gone to bed at 9 o'clock, but of course going to bed and going to sleep mean two very different things in kidspeak. Stephen and his brother hoarsed around for a while, keeping quiet to stay off the parental radar. After a couple of hours of covert play, Stephen's little brother was ready to actually go to sleep. He dropped off almost immediately. Stephen, on the other hand, lay awake for a while, tossing and turning in the chilly room. Around one in the morning, Stephen clocked out too. He came fuzzily awake to something pulling on his ankles. He couldn't see much in the dark room, but something was tentatively grasping his ankles and pulling gently. Of course, Stephen assumed it was his little brother. Stephen hung his head over the side of the top bunk, peering down to the bottom bunk. His brother looked like he was sound asleep. Stephen shook his head. Leave it to a pesky little brother to try a trick like that. He snuggled back down into his warm nest and closed his eyes. He had almost dozed off when he felt another tug on his ankles. This one was harder. Again, Stephen poked his head over the bed rail, hoping to catch his brother diving under his own blankets with a muffled giggle. But again, he heard nothing, and his brother looked dead to the world. At that point, it occurred to Stephen that his brother might not be the one responsible for the ankle tugging. His sleep-fuzzied brain was waking up and he was beginning to realize that it was virtually impossible for his brother to invade Stephen's domain, give him a tug on the ankle, then slip back under his covers, undetected and pretend so convincingly to be fast asleep. Stephen was mulling over this puzzle. He realized that some invisible something was slowly pulling his blanket down towards the foot of his bed. He reached for his blanket to pull it back and something grabbed both of his wrists. Imagine someone grabbing you around the wrists. You know what that feels like. This felt exactly like that. Something was holding on to me and not letting go. The skin around my wrists was actually indented as if someone were physically grabbing me. Stephen would write, much later in his book, true case files of a paranormal investigator. It is a straightforward description of stark terror. The unseen entity had hold of Stephen and whatever it was had no intention of letting him go. Within moments Stephen felt weak, drained of energy and the entity was still pulling him down to the foot of the bed. Moments before Stephen had sat upright to reach for the retreating blankets. Now the phantom yanked him forward, flipping him so that his feet were on the pillow and still he was tugged, pulled relentlessly toward the foot of the bed. Stephen tried to drag in a breath to scream but it was like trying to yell in a dream. Instead of a full-throttled holler for help, Stephen's cries of mom, dad came in thin whistling gasps and yet he still struggled, fighting with wiry kid strength against the invisible monster that had him in its clutches. Suddenly Stephen broke free. He'd been tugging so hard he overbalanced and crashed into the wall. The back of his head hit the wall so hard it left a dent in the wood paneling. Stephen found his voice. Mom! His parents came running. His little brother was roused from sleep. Everyone piled into the room as Stephen stammered out his incredible story. Despite the evidence of the head-sized dent in the wall, Stephen's parents wrote the story off as an amazingly vivid nightmare. The boys were soothed back to sleep but a paranormal investigator was born that terrifying night. There was an interesting post-script to this story. In 1987, Stephen's parents both dismissed his tale. theirs was a Christian home and such talk was discouraged. But many years later, Stephen was talking with his mother about that long ago night and she decided to share a secret with him. When Stephen's mother was herself 10 years old, the exact same thing happened to her. Her encounter with the invisible entity was so violent it left visible marks on her wrists where she was pulled toward the foot of her bed. This story happened in Liverpool, England in the early 1990s. It has never been explained. The story begins one foggy December evening in 1991. On the evening of December 20th, at 7pm, the Edwards family of Dovecott decided to do a bit of late Christmas shopping in the Liverpool city center. Mr. Edwards drove his wife and four children to town in his old Volvo estate. Many people had similar plans for the evening and finding a place to park was a chore. Mr. Edwards trolled the streets looking for a parking spot while his daughter and three sons, too excited to fuss, watched the spectacular Christmas decorations slide by the car windows. Abby, the youngest at six years old, was especially entranced with the colorful lights. As Mr. Edwards grumbled about parking, Mrs. Edwards pointed to a secluded side street called Bold Place. That's perfect, Mr. Edwards said. He turned and drove up the poorly lit Cobblestone Road which ran past the back of St. Luke's Church. As soon as the car was parked, the kids jumped out of the vehicle bubbling with excitement. Meanwhile, an icy fog began to roll down the street. The family was about to start off for the shops when Mr. Edwards suddenly stopped short and glanced around the short street. Where's Abby? Everyone looked around. Mr. Edwards peered into the windows of the car but his little daughter hadn't lagged behind. It was a tremble and Mrs. Edwards' voice, where is she? Three boys looked around but there was no one else on the street. Then they all heard a faint voice scream out in the distance. Daddy! The voice sounded like Abby's. It seemed to come from the end of the lane where Bold Place met Roscoe Street. The Edwards family rushed up the Cobbled Road with Mr. Edwards leading the way. Abby! He shouted, where are you? The gates at the back of St. Luke's were open and Mr. Edwards figured that Abby had wandered through the gate and onto the grounds of the old church. He hurried into the churchyard, followed closely by his wife and their sons and again they heard Abby call out for her daddy. But the little girl was nowhere to be found and the fog was getting thicker by the minute. Mr. Edwards didn't want to say this in front of his family but he was beginning to wonder if some stranger had grabbed Abby and taken her into the ruins of the old church. He handed his wife the car keys and told her to get a flashlight from the vehicle. When Mrs. Edwards came back Mr. Edwards climbed up onto the ledge of the church window and shone the light into the deserted church. The interior was in ruins with nothing but rubble scattered around. Mr. Edwards knew that the church of St. Luke had been gutted by an incendiary bomb in World War II during the Blitz, only the shell of the building had survived. The church had been left in that condition as a reminder of the horrors of war. Even though it was in ruins though Mr. Edwards couldn't shake the thought that Abby's voice had been calling for help from inside the church. As he clambered down from the window ledge, Mrs. Edwards said, Listen! The faint eerie sounds of organ music drifted through the open window. The family went to the police station and told the desk sergeant about their lost child. The sergeant alerted all the patrol cars in the area and told the officers in the city center to be on the lookout for the young girl. The family then rushed back to bold place to keep looking for Abby. They searched the grounds of St. Luke's once again and found nothing. They were about to go to the car to warm up when something happened that continues to puzzle the Edwards family to this day. A tall man wearing a top hat and a long black coat came out of the grounds of St. Luke's and walking with him, holding his hand, was little Abby. When Abby saw her parents, she ran to them and started to cry as her father picked her up. The sinister man in black looked like something out of the Victorian age.  He stood outside the gates of the churchyard and said in a low, creepy voice, please accept my sincere apology for any distress caused. Then he turned and walked slowly back towards the rear of the ruined church. A police patrol car came tearing down the road and Mr. Edwards told the officers about the stranger who had just returned his daughter. Three police officers bolted from their car and rushed into the church, but the police found no one. The church was empty. More police came. The grounds were searched with powerful flashlights, but the place was deserted. Some of the officers also heard the faint sounds of organ music, but they never could find where the mysterious music was coming from. One of the policemen asked Abby where she had been. And that is when things got really weird. Abby said that an old woman in a shawl had grabbed her and dragged her into the church where a mass was being held. There were many people dressed in old fashioned clothes. The women wore big hats and the men were all dressed in black. Abby had screamed for her father, but the old woman had put her hand over the girl's mouth to keep her quiet. Sometime later, a tall man had come into the church and pulled Abby from the woman's clutches. He had been the man who had taken Abby back to her parents. The intrigued policemen continued to interrogate the little girl, and he asked her if the man had spoken to her about what had happened. Abby shook her head, then said, the man said he had been a long time dead, that's all. A cold shudder ran up everyone's spine when they heard Abby's reply. Since that strange incident, the Edwards family refused to go anywhere near St. Luke's, especially during the Christmas season. On December 17, 1959, the William Meyer House near Gutenberg, Iowa was the scene of excitement that had nothing to do with the upcoming holidays. A poltergeist took over the house and soon no one in the family was in the Christmas spirit. One evening, as the Myers were sitting in their living room, a crash thundered through the house. The couple raced into the kitchen where the source of the bang was immediately apparent. They found the refrigerator tipped over. As they watched, horror struck, a flower stand flew across the room and exploded against the stove. Movement near a basket of eggs on the window sill caught their eye next. One egg lifted out of the basket, floated across the room and smashed itself on the kitchen floor. The Myers were dumbfounded. Mrs. Meyer was terrified. The inexplicable was in their home, in their kitchen, the heart of the home. What on earth was going on? The Myers hadn't had supper yet, but Mrs. Meyer was far too upset to cook in that kitchen. The couple went out to eat instead. Out of the house, among the chatter of the other diners, the Myers could almost forget the high strangeness of earlier. Mrs. Meyer's felt herself relaxing. Surely there was some rational explanation for what had happened. When they got home, the Myers got ready for bed. It had been a sorely trying evening, and all they wanted to do was go to sleep and try to forget the destruction in the kitchen. Mrs. Meyer got a glass of water and put it on the nightstand. Then she got into bed and reached for a book. A little light reading would relax her. There would be no relaxing reading that night. The glass rose from the nightstand and hovered over Mrs. Meyer's head as her husband watched in horror. Then the glass was squeezed in a powerful, invisible hand. It exploded, drenching her with water and shards of glass. Mrs. Meyer screamed. Her husband Bill, just as terrified, insisted they move to the guest bedroom. Mrs. Meyer dried herself off and they moved to the other bedroom. They scooted under the covers like children frightened of the boogeyman. Before Bill could even turn off the light, Mrs. Meyer shrieked again. Little black specks were appearing on the blanket. The Myers looked up, mystified. Soot was falling on them from the ceiling, appearing out of nowhere to shower the bed with black grit. In the morning, Bill called the sheriff, who came out to the house to investigate. He was called away in the middle of his search, but he promised to come back. When the sheriff did come back several hours later, the Myers met him on the front lawn. They had been spooked yet again. The sheriff hadn't witnessed any activity during his walkthrough of the house, but after he left, several chairs had skidded across the floor. Even stranger, every single window in the house had cracked, but the Myers hadn't heard any sounds of breaking glass. This was the most excitement Clayton County, Iowa had seen in decades. People from Gutenberg and other towns started to show up unannounced at the Myers home, searching for ghosts. One of these visitors was a Mississippi River towboat captain who came with some friends to investigate the strange tales. He admitted to the Myers that he didn't believe in ghosts. Mrs. Meyer, a gracious hostess despite her supernatural troubles, offered the men the use of the guest bedroom for the night. The captain turned in while his friends stayed in the kitchen with the Myers drinking coffee and getting better acquainted. A ruckus in the bedroom brought the group running. The befuddled captain was still lying on the mattress. The mattress, however, was on the floor, eight feet away from the bed frame. After a few months of poltergeist activity, Bill Meyer and his wife had had quite enough. They moved away, leaving the house empty. Curiosity seekers and amateur ghost hunters made the abandoned house their haunt for a while. The Myers eventually sold the house to their former neighbors, the Finnegans. To combat the vandals that had started using the house as a playground, Wallace Finnegan turned the house into a barn. Now filled with hay instead of ghosts, the house lost much of its spooky appeal.  Billy Plummer snugged the covers up under his chin. He was finding it hard to fall asleep on that December night in 1939. He sighed, then turned over. Suddenly he jerked. It felt like his wife, Gert, was tickling his feet.  A sleepy mumble met his ears. Billy looked over at Gert, who was just waking up out of a sound sleep. Then her eyes widened and she twitched away from him. Billy, gosh, stop, that's me and I hate being tickled. Gert, I didn't do, ugh, Billy squirmed. I said stop. I didn't touch you, I've been asleep. Then Gert made a face and clambered out of the bed. If you didn't touch me and I didn't touch you, we need to check the bed for bugs. Billy sprang out of bed at the mention of bugs and switched on the light. Together Billy and Gert stripped the bed. Sheets, pillowcases, even the mattress pad landed on the floor after a good shaking. No bugs, thank goodness, Gert said. Two pairs of hands made short work of putting the bed back together. The couple lay down. Their fears calmed to enjoy a peaceful night's sleep. They got no such thing. The invisible entity tickled them unmercifully. The plumbers giggled, cried, moaned, squirmed, pleaded. Eventually the entity relented and allowed the exhausted couple a few hours of sleep. At four o'clock in the morning, a thump rattled the bed frame, jerking Billy and Gert from an uneasy dose. Billy slapped the light switch, but no one was in the room with them. At least no one they could see. A symphony of taps, rattles and bangs played up and down the bed frame. For months the strange nocturnal noises continued. One night in February, a deep voice came from somewhere underneath the bed. Is the baby asleep? Gert shot from the bed and into the baby's room. To her immense relief, their infant son was sound asleep. In mid-March, Billy decided to try an experiment. He twisted a copper wire onto one of the bed springs and ran it to a gas pipe in the kitchen. That night, for the first time in months, the plumbers slept peacefully. They woke the next morning refreshed and rested. The next night, the tickling and thumping was back in full force. Billy had had enough. So had Gert. On the first warm spring day, Billy took the bed apart and hauled it off to the Wichita dump. A new bed was a small price to pay for a good night's sleep. If you enjoyed this episode, consider sharing it with others and help build the Weird Darkness community by converting your friends and family into weirdos as well. This special episode is part of my 12 Nightmares of Christmas series, a collaboration with paranormal blogger and author Sylvia Schultz. The stories I used in this episode are from her book The Spirits of Christmas, the Dark Side of the Holidays, and you can find a link to that book in the show notes. Do you have a dark tale to tell? Share your story at WeirdDarkness.com and I might use it in a future episode. Music in this episode is provided by Midnight Syndicate. You can find a link to purchase and download this dark, creepy Christmas music in the show notes. I'm your creator and host, Darren Marlar. Merry Christmas and thank you for joining me in the Weird Darkness. Hey Weirdos, be sure to click the like button and subscribe to this channel and click the notification bell so you don't miss future videos. I post videos seven days a week, and while you're at it, spread the darkness by sharing this video with someone you know who loves all things strange and macabre. If you want to listen to the podcast, you can find it at WeirdDarkness.com slash listen.


The Drake Curse is back, and it appears his latest victim is none other than the superhuman Shohei Otani. Since Drake was seen wearing Shohei's jersey, August 3rd Shohei left with a hand cramp. August 13th, he felt arm fatigue and he missed his start. August 23rd left to start early with arm fatigue, and the worst was yesterday. Diagnosed with a torn UCL, won't pitch again this season, likely won't pitch next year. Tommy John surgery. The Drake Curse might be the most powerful curse we've ever seen in sports.


So this lecture will continue the overview of complex projective surfaces by talking about the surfaces with cadera dimension equal to one or two. So in previous talks we talked about the cadera dimension minus infinity, which we saw with the ruled surfaces, and cadera dimension zero, where we found there were four different classes of surfaces. And cadera dimension one surfaces all turn out to be elliptic surfaces. Here an elliptic surface is a surface S with a map to a curve C such that the fibres are mostly elliptic curves. I will explain what mostly means later, some of the fibres aren't elliptic curves. A typical example of an elliptic surface is just a map from E times C to a curve C, and obviously the fibres are all copies of this elliptic curve E. Actually not all elliptic surfaces have cadera dimension one. We can have elliptic surfaces with cadera dimension minus infinity or zero. Some examples of these are E times P1 for E elliptic, which maps to P1. So this is cadera dimension minus infinity. Or we could just take a product of two elliptic curves mapping to an elliptic curve and this would have cadera dimension zero. So the reason why cadera dimension one give you elliptic surfaces is that for any surface we have a map to some projective space, which is the projective space corresponding to the graded ring, where you take some of, sorry that should be a gamma, global sections of nth powers of the chronicle bundle. So this is always some projective variety or empty. And if the cadera dimension is one, this space is a curve and you can then check that the fibres are mostly elliptic curves and this gives you the vibration making it into an elliptic surface. So the examples where you just take a product E times C to C are the sort of trivial examples. There are more complicated examples as follows. So first of all, it may be a non-trivial bundle. So we see that this map here is a trivial bundle over C because it's just a product but you could put in some sort of twisting in where E is sort of bent round a bit. In particular, the fibres can vary. So instead of just having one elliptic curve as the same fibre, the elliptic curve could vary from one point of C to another. Moreover, the fibres may be singular. So they need not just be elliptic curves but they can sometimes be sort of degenerate elliptic curves with singularities. In fact, you can sort of classify elliptic surfaces by using this data. So to specify an elliptic surface, you have to specify a curve C. You have to specify what the singular fibres are and which points their fibres over. And then you sort of have to describe the bundle over the other points of C. For example, you get a map from the fundamental group of C minus the singular points to the first homology of an elliptic curve and so on. So that gives you some sort of invariant for getting hold of the surface. I should remind you that if you've got a map from a surface to a curve, even if the surface and the curve are non-singular, some of the fibres can be singular. So a very simple example of this is if you just take the surface z equals x, y and you map it to the affine line by mapping x, y, z to z, then the fibre at naught is x, y equals naught which is singular, whereas the fibre at z not equals zero is some sort of hyperbola. So it's non-singular. So the hyperbola, you've got a family of hyperbolas which sort of degenerate to a singular curve at one particular point. You can do the same thing with the fibres being elliptic curves. For example, suppose we take y squared equals x cubed plus ax and map this to the a line by... So this is a surface in three-dimensional space and we're looking at the fibres for various values of A and for A not equals zero, this gives you an elliptic curve, but for A equals zero, we get y squared equals x cubed, which is a cusp. So here we've got a family of elliptic curves except that one of them degenerates into a cusp and this is a fairly typical example of what a singular fibre looks like. Of course, these should really be projective varieties and here we've just done the affine case for simplicity but should give you the idea of what goes on. So the next case you can ask is, what are the possible singular fibres? So these were actually classified by Cadiara. First of all, the fibre can be irreducible and if it's irreducible, it can be an elliptic curve, obviously. Or it can be a cusp and we saw an example of this with the family y squared equals x squared plus Ax at A equals naught, it becomes a cusp. Or it can be a node looking something like that and here we can, for example, take y squared equals x cubed plus x squared plus A and as A goes to zero, we get an elliptic curve with a node. And the other ones, I can just list the other ones that Cadiara found. If we just describe the ones without multiple fibres which I won't worry about we can also get ones that look like that. So these can be two or three copies of P1 intersecting the following way. Here they touch in a double point and here they all intersect in a single point. You can also get copies of P1 arranged in a sort of cycle like that. So here I've drawn a cycle with one, two, three, four, five, seven of them. You can also get them all arranged along the line like this except that you get the sort of double ones on the end. And you can also get them arranged like this. Sorry, that should be a... This should both be separate. Or you can get them arranged like this. Two, three, four. Or they can be arranged like this. It's very difficult getting the number right. And that's all. Well, where does this funny collection of diagrams come from? Well, it may look much easier if you swap lines with points. So here I've drawn a line for each copy of P1. It's a point where any two copies of P1 intersect. But if instead I draw a point for each copy of P1 and draw lines between them when they intersect, the diagrams end up looking like this. So first of all, we've got cycles with any number of points. Secondly, we've got something that's looking like this with any number of points. And then these three become these diagrams. Not one. It should be there. And now you recognize these. These are just the Dink and Diagrams A, N, D, N, E6, E7 and E8. That turn up in the classification of compactly groups and also turn up in the classification of lots and lots of other things. I should say if you think I put too many points on these Dink and Diagrams, these are actually the affine Dink and Diagrams, which are the usual Dink and Diagram together with one extra point. So if you delete these points, you get the usual non affine Dink and Diagram. So in other words, the classification of singular fibers of an elliptic surface turns out to be more or less the same as the classification of compactly groups. Well, there's another classification that's very similar to the classification of elliptic surfaces, which is the classification of elliptic curves over Z and the integers. Now, you remember, a speck of Z has dimension equal to 1, so it's a sort of curve. And an elliptic curve over Z is really a sort of surface. I mean, its spectrum is actually two-dimensional. You know, we have a map from the spectrum of the elliptic curve over Z to the spectrum of Z. And you can think of this as being not a curve but a surface, and of this as being a curve. So this is really a sort of very similar to an elliptic surface. So the fibers are elliptic curves over points of Z, which are really over the spectrum of various finite fields, except that sometimes they are degenerate elliptic curves. And again, some of the fibers may be singular. For example, let's just look at the following elliptic curve over the integers y squared equals x cubed plus x plus 1. And so you have a map from the spectrum of this elliptic curve to the spectrum of Z. And if we try and draw it, well, the spectrum of Z looks like this. And we've got a generic point nought. And if we look at the fibers, the fibers you should mostly draw them as some sort of elliptic curve. So here we've got elliptic curves. And there's one point where it's not an elliptic curve because if you work out the discriminant of this, it's minus 31. So x cubed plus x plus 1 becomes x minus 3 by x plus 17 squared if I've worked it out right. So this is no longer an elliptic curve, but a curve with a cusp. So over the point 31 of spectrum of Z, you should actually picture it as looking something like this. So you can picture this elliptic curve over Z as being some sort of family of elliptic curves that degenerate into a curve with a node over the point 31. Well, the degenerate fibers for elliptic curves over Z were in fact classified by NERON independently of Kadara. And I think it was noticed a little bit later that both of them had really... Kadara and NERON's classifications were both really the same. Unfortunately, this left us with two completely incompatible sorts of notation for the singular fibers. Okay, well now I'll say a little bit about the surfaces with Kadara dimension 2, which are those of general type. So examples where we might have a product of two curves with genus of C1 is greater than 2 and the genus of C2 is greater than 2. Greater than 1, I guess, is enough. Or a non-singular hypersurface in P3 of degree greater than 4. So there are masses of these. And there are huge numbers of other examples. For instance, instead of hypersurfaces, you could take complete intersections in some high-dimensional projective space that are surfaces. Nearly all of these are of general type. And it turns out there are, you know, dozens or hundreds of constructions of surfaces of general type that people have come up with. I'll just give one example of the many, many constructions people have come up with. So typical example, this is one of the easiest ones, might be the Goddow surfaces. And for this, what you do is you take the surface S given by w to the 5 plus x to the 5 plus y to the 5 plus c to the 5 equals 0 in three-dimensional projective space. And this isn't the Goddow surface. I haven't finished the construction yet. What you do is you take this surface, you take an automorphism sigma of order 5, which takes w to w, x to zeta times x, y to zeta squared times y, and z to zeta cubed z, where zeta to the 5 equals 1 as a fifth root of unity. And S modulo, the action of sigma, is then a Goddow surface. And these are kind of a bit interesting because they turn out to have geometric genus and irregularity both equal to 0. So you remember Castle Novo at one point asked whether this condition implied the surface was rational. Enriquez gave the Enriquez surface as a counter-example. And it turns out that Goddow surfaces are also counter-examples to this question. So in the last slide, I'll try and draw a picture of a sort of ball surfaces. So this is a sort of map of surfaces. And what I'm going to do is I'm going to classify surfaces Well, it's sort of traditional to use the churn numbers, which is the self-interception number of the canonical class. And the second churn number is just the Euler class, which is the usual topological Euler characteristic of the surface. And you can just draw all the surfaces in general type by plotting them on this diagram where you use c1 squared and c2 as the two axes. So for surfaces of general type, c1 squared and c2 satisfy the following inequalities. First of all, c1 is greater than 0 and c2 is greater than 0. Next, c1 squared plus c2 equals 12 times the holomorphic Euler characteristic. This is a Notar's formula. And Notar also found an inequality, which says 5c1 squared minus c2 plus 36 is at least 0. And there's a much more subtle inequality that was only found much later, found by Bogomolov, Mier, Ochre and Yao, which says that c1 squared is less than or equal to 3c2. So Bogomolov proved this with a 10 here. He reduced it to 4 and Yao found the best possible number of 3. So if you add all these conditions into the graph, you find all surfaces must lie on these lines where the sum of c1 squared and c2 is a multiple of 12. So you get various lines like this. And if we put in these inequalities, well, the Bogomolov, Mier, Ochre, Yao inequality sort of looks like this. I'll mark this as bm y, not bm w. And notice inequality sort of looks like this. So we find that the surfaces of general type must lie inside this funny shaped region here and they must lie on these lines here and most of the points on these lines inside this orange region are known to be churn numbers of a surface of general type. So you can also look at this in a bit more detail. For instance, we can look at the points on the boundary. So there should be 10 points here. This one isn't actually a churn number of a surface of general type because c1 squared has to be positive but we have all these other numbers here. And the Godot surfaces actually live here. So they're almost the simplest possible churn numbers of a surface. The ones here are called fake projective planes and you can understand this if I mark on the churn numbers of surfaces not of general type. So you find that the ruled surfaces all lie on this line here and most of them are kind of down there off this diagram and the projective plane has these churn numbers. And the projective plane has the same churn numbers as certain surfaces of general type called fake projective planes. These are quite hard to find and the first one was only found by Mumford and quite late on. For example, if you take a surface of degree 5 in p3 it's somewhere just off to the right here. I can't quite leave myself enough room to draw it. You can also ask where do things like Enrique's and K3 surfaces live? Well, these are the Enrique surfaces, these churn numbers. These ones turn out to be K3 surfaces and these ones are where you find the abelian and hyper elliptic that they're all at the origin. The surfaces of Kaderid Dimension 0 just live down here. The surfaces of Kaderid Dimension 1 all lie on this line here and more generally all elliptic surfaces lie on this axis here. So there's been a certain amount of work trying to classify the surfaces of general type and the answer is they're incredibly complicated to classify. Gazika showed that for any fixed values of C1 squared and C2 there's a scheme, a quasi-projective scheme whose points classify the surfaces of general type with given churn numbers. So for any given values of the churn numbers you can in principle classify all surfaces of general type with those numbers. There's been a lot of work studying these Gazika schemes. Mostly they aren't known except for a very few cases around the edge where it's just about possible to find them and all indications are in that in the middle these schemes are incredibly complicated. They have wild singularities and can be reduced at every point and things like that. Okay, so that's a summary of what we know about surfaces. Surfaces of Kaderid Dimension less than two, we sort of more or less know most of them at least if they're projective. Surfaces of Kaderid Dimension two, it's wide open for further exploration.


What's up everybody, Jay-Z here for jayspeakscasebrakes.com. This is our last filler guys This sold out the last 10 spots and immaculate first we do the break randomize the customer names and teams to strip the hits out then Randomize the customer names after at the end to see you guys the last 10 spots and of course this is a 1920 panini mosaic cello pack break number seven seventy four So let's do the break first roll it four to five nine times one two three four five six seven eight nine Nick Smith down to Dylan Dylan nine times one two three four five six seven Eight you taught jazz out of the New York Knicks. All right, so again stick to what you got guys Let me actually pop it paste this title for the list All right, so there's a quick line to your teams break hero LeBron Switch scenes now guys and let's do the giveaway now. So again top ten get in guys ten roll One or two three times one two three Boom three times Number 20 sad people from Logan down to Nick. There you go Fortunately not in guys, but after three times top ten are in though Aaron last bomb. Oh Joe Nick Aaron Nick Michael Carl Carl Nick Carl and Carl. There you go. Oh Couple of names double tripled and there you go So let's place your guys names into the list randomizer and that officially does sell out the break guys and Coming up next is immaculate. Appreciate it. Good luck


Do you remember the last time the Tennessee Titans blocked a field goal and returned it for a touchdown? Well, it was 297 games ago, nearly 18 years to the day. It happened on October 21, 2001. Detroit kicker Jason Hansen set to attempt a field goal with his team ahead 14-9 in the third quarter. Titans defensive tackle Henry Ford with the block and the ball is scooped up by Tennessee defensive back Donald Mitchell. Mitchell rambles 69 yards for a score that will propel the Titans to a 27-24 win over the Lions. That's the last time the Titans have returned a block field goal for a touchdown.


Welcome back everyone. Today I'm going to show you how to get emotive data into basically Weka for analysis. And what we have here are two emotive data files. We have this baseline CSV and we have cat.csv. And essentially this was a person looking at a cat and we recorded their responses. And the baseline is a person basically just looking at a white screen. So if we open up baseline CSV we can see what we have here. Out of the emotive we have the channel that it was recording on. The emotive has quite a few channels and then we have theta, alpha, low beta, high beta, and gamma waves. And what we found of course is we're going to have the most the most interesting data let's say is going to be in this low beta and high beta area. We can use all of this but basically it's in the low beta, high beta area. So we have these two files baseline CSV that I just opened up and I'm opening up again. Okay so channel theta, alpha, low beta, high beta, gamma. And then in the same in the same file format we have the same data just for the cat. And we've recorded this over time. So we have all of these entries and these are all of the channels. I forget what the sample rate was but I think it's every second or something like that. Okay, so we have this measurement out of every few seconds or second for these different things. So basically what we want to find out is is there a difference or can we differentiate between the baseline and cat actually looking at or detecting the cat game. So I have this both CSV and I'll talk about that in a second. But what we want to do first, the first thing to do is essentially open up Weka. So Weka you can get, let me see if I can pull it up here. Weka is data mining software. You can get it free from this website. Just go to download. This is cs.wadako.ac.nz. Go ahead and download whatever version is suitable for your operating system. I'm currently using it in Linux but it works the same in basically all of them. Okay, so let me just open it up here. Okay, so once Weka opens up, you'll have this Weka GUI chooser. And one of the first things you might want to do possibly, especially if you're dealing with emotive data or any brainwave analysis of data is go to tools and package manager. And then that pulls up your package manager here. And these are all the different packages that you can install. There's a bunch of extra algorithms, for example, Lib linear is an interesting one, Lib SVM. If we want to install more algorithms or just more basically features, we can install it from the package manager. Package manager makes everything very easy. What you should search for is what was it called time series. Time series. And what should show up if we look at time series, I already have them installed. I think it's not going to show me again. But if we look for time or time series, then you should see time series packages, and there'll be two of them. And time series packages let you analyze this time series data directly, we won't be doing time series analysis today, we'll just be doing clustering today. But definitely look into Weka's time series packages. Okay. So next, once we have Weka open, we have all the packages or all of the algorithms that we want to use installed. Next, we need to go to explore. And that will open up basically a menu where you can open your data and also start to clean it. So I have my data files in CSV format. Okay, so my data is already in CSV. And it is in desktop data. Okay, desktop data. And I click CSV. And then I have my baseline in my cat. And the first thing I want to do is understand a little bit about about my data. So I'm going to just load in the baseline first click open. And everything loaded up. Okay, it looks like we didn't get any errors immediately. If I click on each of the settings, I don't get an error inside of these. These are just descriptive statistics about basically the levels that it sees. We can see here, the different values that each of the that each of the basically wavelengths or frequency values are giving us down here, it gives us a little bit of an idea about what's going on, but not a lot. Okay, so we can also something else that's potentially interesting is, for example, if we click on, like I said, we want to focus on low beta and high beta. So if we click on low beta, then we can see the mean is 38.7. Okay, if we click on high beta, then we can see the mean is 37. So I'm going to make a note of that. Okay, opening up just a text text document, high beta, I'll say high and 37 low, high 37 low of 38. Okay, and that might be interesting. We need to one of our one of our analyzing some other information that might be interesting. Now just with the baseline data. Basically, that's what I was interested in. What is our mean here? What is for at least low beta and high beta? Okay, and I'll show you what we can do with that in a second. Okay, so now I want to open up my open up another file and I have this cat CSV. And this file is where the user was actually looking at a cat and I want to differentiate between not doing anything and looking at a cat. So I open that up. And because it's in the same format, we get hopefully everything loads up again, we can see all of the instances we have. I'm going to focus again on low beta. And we see that our mean for low beta is 42. So I have my mean low beta for 42. And I have my mean for high beta 123. Okay. Now, this is already somewhat important because whenever we're looking at the cat, I mean, just between the baseline and between the cat, I have a high beta average, a high beta, a high beta average or the mean high beta is actually much, much greater. Now, what what exactly is this? If we look back in our data, we look at it. Okay, so we have low beta, high beta, and then we have all of these channels. Now, what exactly are we looking at here? Well, we are actually looking at all of this column for low beta, all of this low beta column combined, the average overall out of all of these channels, right, we didn't actually filter out based on channel, we're just looking at only the channel at what we're looking at all channels, all data from all the channels. If we wanted to focus on a particular channel, for example, I think PZ was the back of the head, right? So whenever we're doing image pattern recognition, PZ might be the most interesting. So we might need to remove or somehow filter out all of these other channels and just focus on PZ. Okay, but right now, we're just loading in all of this data, and including all of the channels, low beta and high beta together, we're averaging all of these different things. Okay, now from that average, we are getting a relatively high mean for low beta, no, for high beta, sorry, for high beta, whenever we are looking at a cat. So the average for high beta is much greater whenever we're looking at the cat than whenever we're not looking at the cat. Okay, so this means that we might actually have a pattern we can detect. So it's already looking somewhat interesting, actually. Okay, so I'm going to focus then on only high beta. Okay, and what I want to do is see if I can make a classifier, see if I can make a classifier that will be able to differentiate between not looking at a cat, just looking at nothing, basically looking at the baseline, which we can just call nothing, or looking at the cat. Okay, I want to try to figure out if I can differentiate that using machine learning or just find it automatically, essentially. So one of the things we're going to try to do today is clustering to see if we can detect the differences. Okay, so using just the means I've already figured out I want to focus on high beta because I see a difference, a big difference in the mean. For low beta, I see a little bit of a difference, but not much, right? So it could just be noise, it could be who knows what it could be, but with high, it looks like it's actually quite a bit of a difference. Okay, now, whenever I want to start clustering, whenever I want to automatically detect or pull out these things, I need to combine cat and baseline together into one file, obviously. Okay, so before I forget, which I already forgot, before I forget, looking at all this data, once we've actually loaded this in, we can do this in this visualized tab, you might be interested to look at it. So what I tend to do first, one of the first things I do, not only looking at the mean, but also looking at the actual graphs of all of these different patterns, essentially. So here we have, for example, high beta. I can see that I have kind of a cluster here and some extra data at higher values. I have a cluster relatively low, and then I have some a little bit of data spread out a little bit higher and same for versus low beta. So I have some kind of interesting patterns here. Now, if we go back to prepossess, open up the baseline, and then go back to visualize, then I look at it again. And if we look through high beta, well, this high beta versus theta is maybe almost the same. High beta versus alpha is almost the same. Low beta looks a little bit different. So I just basically go through and visualize all the data. Initially to get an idea of where is the data falling for the baseline? Where is the data falling for looking at the cat? Okay, so just think about this visualized tab. Just go through both of your data sets and see if anything kind of jumps out at you. That's that's one way that I start. Okay, so I'm going to go back. And right now we need to combine our cat data with our baseline data. And I've put both of these into the both category. In Linux, what we can do, you can do cat, which just means concatenate baseline baseline.csv and then one greater than sign into both.csv. And this basically takes everything that's inside baseline.csv and puts it into both.csv. Okay, then I'm going to do echo and echo a blank space into both.csv. And here I'm using two greater than signs. The first one overwrites all the data in the file basically makes a new file and puts data inside of it. The second one appends. So I've appended an empty line into both.csv or I'm appending it. Okay, so now this both.csv has baseline, everything that was in baseline plus an empty line. Okay, so the next thing I want to do is cat cat.csv. So basically take all the data inside cat.csv. And we need to do something special with it. I need to do tail dash in and plus two, I think it was. And what this does is actually I'll check to make sure it's working. Okay, yeah, so what this does is let me let me remove it. cat csv head. Okay, so here at the beginning, we have this channel theta alpha, low beta, high beta gamma, we want to remove this before we put it into the file. So we need to use tail dash in plus two. And basically it lists out all of the data without this heading, we want to remove that heading. Okay, so I'm going to go ahead and put that into my both file. So here we have both CSV. So I have cat cat.csv and then pipe that to tail dash in plus two, greater than greater than both.csv. Okay, hit enter. And then if we do cat baseline.csv and then WC dash L, we can see how many lines are in baseline, we have 4359. Now if we do instead of baseline, we do cat both.csv, then we have a lot more. So it should be cat plus baseline. Yeah, so that that should be it. So we know that we actually have all of the data inside both.csv. Okay, so now I can go back to Weka, open up my file both.csv open. Okay, now we have as many records as we expect to find, right, we still have all of the same attributes. But we're not really interested in anything else except high beta, I'm really looking at pulling out patterns specifically with high beta. So I'm going to remove everything else, just select everything you don't want to include and click this remove button. Okay, so then I have high beta only and this is all of my data, I can already see that there's, you know, quite a few entries here. And then there's something going on here. I don't know what that is. But, you know, it's something's happening. Okay. Right.  Simple k means k means is an interesting, a very simple type of clustering. And, yeah, I mean, it's a relatively effective way. It's a very interesting algorithm. I won't talk about it here. But I recommend you read up on it because it is pretty, pretty interesting. We do want to use a training sets. Right. And that's pretty much it just select simple k means with your data, your combined data. And then we click start. Okay, now it's going through and it found two clusters with about 5369 entries each, just with high beta, yeah, high beta. So we only have high beta. And it found two different clusters. Okay, so that's actually pretty good. We were expecting two different clusters. Let's see what we got here. Cluster one 99 cluster 283. Okay. Yeah, so basically, we have high beta, whenever the value is relatively large, it's cluster zero, whenever the value is relatively small, it's cluster one. Okay, now if we right click on simple k means, then we can visualize cluster assignments. Okay. And then that pulls up this box. Okay. And we have cluster zero is this top cluster here. And cluster one is the bottom cluster. Now, if we go back and look at our mean, let's just focus on high for now. Okay, we have high of 123. And 123 is about here, right for the mean. And then we have, or sorry, the the cat, the cat is about 123. And it's about here. So all everything kind of above 123 was clustered as the cat. And then everything around 37, which is probably about here, more or less, was clustered as the kind of baseline, essentially. So we have this information. Well, basically, what this tells us is that we seem, we seem to be able to differentiate automatically between the baseline and someone looking at the cat, right? Now, with this information, we could basically go in and start to do some categorization, try to detect specifically when this is happening. Or if we saw some data that looked like this, would it be a cat or would it be something else? So essentially, what we're just looking at here is can we automatically differentiate between this baseline and looking at something else through brainwaves. And it looks like we're getting a, you know, it seems like we're probably getting a pretty good cluster here about where we would expect. Okay, so the next thing I would probably do now is go to classifiers and try to make a classifier, I would have to change the data slightly. But using a classifier, I might be able to classify or detect new data coming in, or we can potentially just keep using clusters depending on what your data actually looks like. So I thought this was pretty interesting, we're using just very basic data to kind of go through and say, you know, can we differentiate between two, two different things? And it looks like our clusters were pretty accurate between our high data for looking at the cat and low data for not looking at the cat. So that's it for how we can do simple k-means over emote of data. Thank you very much.


حالیت ہے سلامہ الرحمن الرحيم اور حالیت ہم پاکستان musimy گیا۔ کیونکہ ہمارے مانتاہے ہمارے دوری ہمارے موعدیت اور حلیت ہمارے ساتھ ہوتی ہے۔ اور ہمارے حالیت ہمارے انہاز ہونے کبھی بھی کنی بھی بھی بہت چاہول ہمیں RM مدیشت دیکھے۔ اور اپنے در دو بہت نوٹا رہا ہے کہ ہم میں ناقل کے ساتھ بھی کسی نہیں ہوئی تو کسی ہر احترارتیی کو بات کرتے ہیں ہمیں اپنے تقریوں کر دیکھنا ہونے کیا ہے اور اپنے اپنے انہوں کو بہتا نہیں ہوگا اور اسی بڑی میں بہت سے بہتا ہے کہ پر اپنے اپنے رہے ہیں today we going to be looking at another one and that is the bystander effect and we going to talk about a case study also and we going to see that how it has different implications especially in the context of good governance or bad governance because why is it that when people know that there is bad governance people just stay quiet and are just onlookers just like bystanders like they are watching a maybe a game of football and they just quietly just watching it just being amused with what is going wrong. and actually the bystander effect is 180 degrees opposite to what is called whistle blowing because actually now by law in a country like Pakistan many countries around the world it is mandatory that if something wrong is happening or if there is any element of corruption it is mandatory on the other person knowing in the organization to blow the whistle to inform the authorities that something wrong is happening and this is mandatory and if we do not inform the higher authorities of whatever wrong doing is happening then we become an accomplice to the whole act and being an accomplice by law basically means that the person who is the bystander or who is just staying quiet not informing the authority can also be punished for being quiet. so by law by morality and by humanity it is our duty to specify and call out something wrong a corruption or a malpractice which is taking place and if we don't do it then we ourselves are becoming an accomplice to the crime and we are only a little bit different from the real criminal because the real criminal is doing everything and we are just simple bystanders looking at what is happening so whistle blowing ladies and gentlemen something which is mandatory upon you and mandatory upon me also and that is the essence of good governance and corporate governance so the bystander effect is having a sense that the responsibility is entirely on the shoulders of an authority figure can relieve us from the unpleasantries of guilt making it easier for people to act in ways that one would regret if one had a chance to sit back and reflect on our actions so just like I was mentioning ladies and gentlemen because we are not doing it being done by someone else is a person with some authority is abusing his or her authority and doing their election of duty and corruption but we are going to stay quiet because we don't want to create unpleasantries we don't want to create an enmity with that person we want to have a cordial relationship we want to maintain good relations with everyone but that's not how the cookie crumbles it's very important that we do not do such a thing because it tends to reflect our lack of responsibility and also our lack of principles our lack of values and our lack of allegiance to the organization whereby we should be doing everything correct as per the law as per rule and regulations without doing any hanky panky or without doing any corruption that is extremely important so ladies and gentlemen what we do is we often pass on the responsibility groups feeling that if everyone else is doing it then why can't I so this common corruption syndrome if the majority of people are corrupt in Pakistan then why can't I be corrupt why should I be corrupt why can't I take gifts why can't I take a commission why can't I take speed money well look at others they are in a similar position to me and they are living a judicious life why can't I live a little judicious why can't I take care of my children why can't I give them the luxuries of life but then there's no end so the bystander effect basically is something which we should not indulge in we should not fall prey to we should not go into that dal dal that marsh which would suck us down into the system of despondency and corruption we should be able to stand up so that we can change all of this so this statement that if everyone is doing it then why can't I is absurd is abhorrent and should be condemned and done away with rather than being followed that's the bystander effect now the phenomenon of diffusion of responsibility is punctured when someone takes the lead and helps so what do we see is that there can be a diffusion responsibility but someone has to take the lead and someone has to raise his or her voice to ensure that something wrong does not happen now we have a very big example in that example many years ago two boys and it reflects unacceptable behavior so these boys were suspected to be thieves not proven to be thieves so the local people got together and they basically picked up 17 year old movies and 15 year old movie but and they were lynched publicly they were put up on a tree and they were lynched they were whipped they were stoned they were beaten up by all of these crowd they were policemen in it they were double one double two members in it they were businessmen in it they were students in it they were teachers in them they were professionals in them all of them got together and started lynching these two boys and after lynching them and killing them they dragged their bodies with a tractor and everyone was having fun everyone was a bystander everyone was clapping and everyone was enjoying all of those atrocities of inhumanity taking place and no one realized that I should raise my voice I should try to save the lives of these two kids but everyone was a bystander that oh we are not doing it or we are not the main people behind it they are going to be responsible but we are responsible because we encouraged them because we stood there and in an implied context gave our consent to what was happening which basically instilled confidence in the other people basically enabling them to do something abhorrent gross something inconceivable in broad daylight in front of hundreds of people um actually one of those hundreds of people was the criminal was the culprit and was the one who contributed into such a painful and tragic incident unfolded لہذا اُن 2017 گرم تک ببارت کے بردان میں بارت کے پاس انسان میں کھان دیتے ہیںTHW because بھی تیزیز ہوتا ہے۔iseen جانتے ہوں، کیونکہ ایمان میں بسکل کر دیا کہ ایمان ایمان کی لنے کے لئے ، ایک ایمان کی طرح ایمان Senator سینے کیا ، جب جانتے ہیںگی کے لئے ، مجھے ذنگ ہوں اور جو جانتے ہوں گے بارٹنے کانooooo تھوڈے دن ہے جس کے ذنگ مدامت کیا ہے۔ اس کی Tulیلی گریا ب leider تھفسہ ہے۔ یہ بتراوش andila rental انہوں کے نظر حاضر انہوں کی 수اوش جازی ت Wasn't ابو ، لیکن یہ م Development항buch لی LDہل으�ی ہوا لہذا ، اِس بارت لے لی بارت کے بارت کے لئے ملیک س fascin آقا ہوتے ہیں جب کا نقوس ہے، ہمارے آپ کو درسیار کرنا چاہتے ہیں۔ ہمیں درسیار کرنا، ہمارے آپ کو درسیار کرنا چاہتے ہیں۔ جہاد میں جہاد نفس آئے سے، امامید سورت توہلیہ کے جانتے ہیں۔ یہ پر وہ بہت ساری جہاد ہے۔ جہاد میں کہا جو اہمارا ہے، مجھے اہمارا ہے۔ اپنی بہت ایسا ہے وصولت پر قرآنast اور اینہوں کو تھا۔ تو جو ایک مجھاےку اور حکم بہتر آجا ہوتی ہے ایک طرف کہ یہ ساری حسوم ہے بہئی مجھے جانتا ہی بھائی ہے ویسی جو سیریہ اور میں جو many اوشید انسانی کو رفلکتا ہے واقی طرح پر مجموح و اگر اس کے حلیہ ار μια مدوہ جاتا ہے اور ایک مدوہ جاتا ہے اور بہت حقیAUDIENCE شروعوں میں مقالی گیا جاتا ہے اس لڑکائی و جلی کوئی از بہت ارامی فائرہ جاتا ہےContolation ایک بیدیت should be obedient but only for what is rightful and if something is wrong then one should be able to stand up and say that it is wrong and not do it. And yes conformity can be good but not conforming so what is bad and we should abstain from peer pressure or grow pressure to accept all the bad or all the wrong because others are doing it. We should not indulge in such excuses, we should be able to move forward with confidence, with courage, with truth, with honesty, with Esther the Queen, with this strong desire to make a powerful positive impact at home, in the community, in the society, in the institution. At a national level globally, one should not compromise, one should not sacrilege one's principles and values but one should stand up, accept reality and call out the truth, thank you so much.


Hello everyone this is Ahmed Dan of Ahmeddan.com Today is my second day in New Zealand in the last video I took you to the geothermal valley in Tipuya and in today's video I'll show you some random roadside scenes from a New Zealand mountain village in Rotorua. New Zealand is a country in the southwestern Pacific Ocean made of two main islands North and South Island. In the next video you'll be seeing the white tumor globeworm capes from the outside. Thank you for watching this video. Forget about subscribing to this channel, forget about liking this video. There will be more videos coming up so I'll see you shortly. At the park you're just the weather's precluding a decent view of the cutting, cutting. It's by poor attempt at rendering their song but there's a special, special melody. The Māori are famous for their singing voices. They have a beautiful harmony. To the mountain this goes up to a lookout at the top of the mountain. It's a pretty good lookout over the lake. What it does have is you get up to the top and there are various things you can do from the top. You can do there's a luge of the canopy of the forest behind. And this is sort of you can see there's a lot of people here taking advantage of that. And this is one of the, this is Fairy Springs amusement park here. There's lots of things for people to do.