In the late 1800s, a man named Heinrich Hertz, the person after whom we have named the unit of frequency, Hertz, right? This person accidentally discovered that when you shine, sometimes when you shine light on metals, they eject electrons. And we called this phenomena the photoelectric effect because light is photo and electric means electrons coming out, so photoelectric effect. And this experiment revolutionized physics. It changed the way we thought about this world. And when I first learned about this, I was like, what? I mean, this is such an innocent looking experiment. Like what's so special about, what's so surprising about this? You shine light with energy and you get electrons. So what's the big deal? And so the goal of this video is actually to understand what was the big deal about this experiment and why it shook physics and why we had to come up with a completely new theory of light. Now the answer to this lies in the details of this experiment. And a fun fact is this effect was discovered even before electrons were discovered, which means it took about 10 to 15 years for, you know, and a lot of experiments for us to realize what was going on. But in all these experiments, people were trying to figure out how does changing the properties of light affect the electrons? To be more precise, there are two things that you can change about light. You can change its brightness, brightness, or more technically, you can say the intensity. So that's one thing you can change about the light. You can make it more bright. You can make it dim. The second thing you can change about light is its color. Or again, more technically, we can say its frequency. All right? So you can change these two things. And people wanted to know how does changing these two things affect the photoelectric effect? And the question is now, what are the things that can change in these electrons? Well, again, there are two things that can change in these electrons. So in the photoelectric effect, there are two things that can change. One is it could affect the speed of the electrons. Electrons could either come out faster or they could go slower. So it could affect the kinetic energy of the ejected electrons. The second thing it could affect is the number, I'm just gonna use hash for number, number of electrons. So you could have a lot of electrons coming out per second or you can have a little amount of electrons coming out per second. And so now the stage is set. People wanted to figure out how does changing these two things about the light affected these two things about the electrons? That was what people were trying to figure out. And of course, some of you might be curious and you may be wondering, well, how did we measure these things? I mean, electrons are so tiny. How do you measure their speed or their energy? How do you measure how many electrons are coming out per second? What kind of experiments did people perform? There are some clever experiments and we will talk about all the fun stuff in some other videos, the experiments and all of that. But in this video, let's focus on what the experimental results were and how it shocked everyone. So let's start with the brightness of the light. My question to you is, if you think of light as a wave and if you increase the brightness, increase its intensity, increase the energy of the wave, what would you expect to happen to the kinetic energy of the ejected electrons? Can you pause the video and think a little bit about that? What would you expect to happen? Well, if you're providing more energy to the electrons by increasing the intensity, I would expect electrons coming out with more energy, right? So we would expect more brightness, more kinetic energy, less brightness, less kinetic energy. That kind of makes sense, right? But to everyone's surprise, what they found experimentally is that the kinetic energy of the ejected electrons was independent. This was independent, independent, okay? Off the intensity, off the intensity. And people are like, what? What does that mean?  It doesn't matter. The speed at which electrons come out doesn't change. And I was like, what? How does that make any sense? To understand better, let's think of an example. Instead of thinking about light waves and electrons, let's think about water waves and boats. I'm sure over here you would agree that because you have a huge wave when this comes and hits the boat, it's gonna launch that boat into orbit. And over here, nothing's gonna happen, right? So you see, with the speed at which the boat gets launched should depend on the height of the wave or the intensity of the wave, right? And that's why it was so weird when we found that the kinetic energy of the ejected electrons was independent of the intensity. We're like, how does that make any sense? But we did find that increasing intensity, if you increase the intensity, we did find that the number of electrons that increases. That was our experimental finding. So that increases. But kinetic energy doesn't increase and that's the point, like why? Okay, time for a second shock or something even more weird. They changed the frequency or the color of the light keeping the brightness or keeping the intensity exactly the same. You know what they found? They found that increasing the frequency increases the kinetic energy. What? Let me write that. They found that if you change the frequency, if you increase the frequency, they found that now the kinetic energy increases. If you decrease the frequency, the kinetic energy decreases. And again, people were baffled like, why does the frequency matter? Why if you increase the number of waves per second? For some reason, electrons are getting more energy. I've kept the intensity the same but somehow they're getting now more energy. This was even more weird. And let me tell you what this means. This means if you keep decreasing the frequency, even though you have enough intensity, very bright light, you keep decreasing the frequency, electrons will come out slower and slower and slower. And after one point, electrons won't come out at all.  And this frequency, this minimum frequency, even name to it, we call it the threshold frequency. That's just a name, threshold frequency. And what this means is no photoelectric effect below this frequency. Which is so weird. And let me give you an example. If you take copper, its threshold frequency is 10 to the power of 15 hertz. This means even if you shine blindingly bright light below this frequency, you get nothing. All of that energy, nothing. And even if you shine very dim light above this frequency, you get photoelectric effect. Electrons will keep coming out. You increase the frequency, not the intensity, but frequency, you get electrons coming out faster. It's kind of like saying in this case, if you increase the number of waves, that will start increasing the energy with which the boat launches, which makes no sense at all. It's kind of like saying, hey, nothing's gonna happen over here because you only have one wave per second. You need minimum five waves per second to launch the boat. That makes no sense. You would say, why would the frequency matter? Frequency shouldn't have mattered. What should have mattered is just the intensity. So why is there a threshold frequency? Why frequency matters? There should have been a threshold intensity. That's what people were saying. And so that's why this did not make any sense. Physicists were completely baffled at this point. So it's the frequency that decides the kinetic energy and people have no idea why. And brightness does not decide the kinetic energy and people have no idea why. All right, the last one, there's another one, there's a third shocker. This has something to do with the time delay between the incident light and the electrons coming out. See, we thought light was a wave back then and when you're shining this wave of energy, there are billions and trillions of electrons inside over here, right? So we thought that all of that energy will be distributed among all these electrons and each electron will get a very tiny, tiny fraction of the energy, which means for it to gather enough energy, it would take time. It would take some time to gather all the energy needed to finally eject itself from the metal, to gain enough energy to eject itself from the metal. And calculations showed that if you have very dim light, it could take days before the first electron is able to get enough energy to eject out. If you shine very bright light, maybe it would take few hours and maybe if you shine even brighter light, maybe it would take few minutes. But you know what we found? We found that regardless of the brightness, regardless of the frequency, photoelectric effect was always instantaneous. You shine light, you immediately get electrons. You stop shining, no electrons. Doesn't matter whether it's bright light or dim light, doesn't matter if it's high frequency light or low frequency light, you either get photoelectric effect instantly or you won't get it at all. So we found instantaneous effect. This was an instantaneous effect and this also confused people because according to wave theory, the theory back then, we predicted that there should be a time delay, right? So why didn't that happen? And so now you know why this is such an important experiment in the history, one of the most important experiments in the history of physics because it was at a time where we thought physics was complete. We celebrated saying that, light is an electromagnetic wave, we have understood it and then came this experiment which completely shook us. And after this, a few incredible folks like Max Planck, Niels Bohr, Werner Heisenberg and of course our beloved Albert Einstein came along and came up with completely revolutionary ideas of light which you probably know why now as the quantum nature of light to explain this and of course many other phenomena we discovered later. And that's how this is one of the experiments that led to the quantum revolution. We'll talk about all the fun stuff in the future videos.


and you're doing press for Fargo season four and also you're learning disability you seem to be doing I wasn't really you know you know things come out now I like it the public me I'm just you know and it's easier than apologizing to a lot of people individually so you just I was doing over the airwaves yeah okay I guess I can get a little of that it was very satisfying for me for you to have a learning disability because careful careful that was very satisfying for me because we would argue about your our different styles basically I feel like I made you less cynical and you made me more cynical meaning I have I have that effect on people on the world in some way I have that effect on people and I would argue that I made you slightly I made you realize that there is value to feelings it's not I never didn't think there were value to feelings Neil maybe there's value to my feelings maybe there's value to there's like your sort of gruff old exterior well I'm you know I'm you know I'm always like okay I'm the head of the family right right so you know me and my kids and you know sometimes I'm the boss at work more times than not so my feelings don't matter in the overall pantheon of moving things forward right you know we can't slow down for my feelings would you say that you found out that you kind of need to though I need to slow down individually yes but I will never inflict my feelings on others but no no I think but I think you do I think you inflict you inflicted your feelings on others by not addressing your feelings so then I bet that the next time you run a thing or you run an organization yeah you'll be your management style will be different than it was would have been five years ago probably probably a little bit from being like softer no I mean it's weird there's a bunch of jobs I won't even take just because just producing things and directing things because some of them especially like like a nightly show or you know certain certain things just required an urgency yeah yeah and you know sometimes you have to raise your voice when things get urgent yeah but raising your voices against the law now so I will not take the job I will politely passing them okay yeah you know and and then you got to assess what piece of talent you're working with so some people don't need to be pushed you know Jimmy Butler of the Miami Heat does not need to be pushed yeah but Tyler Hero might need a foot in his ass you know what I mean right yeah well that's the thing where Riley is he's apparently like a real hard ass like and practice I didn't realize there's a Lakers book right called Showtime about the 80s Lakers and he would practice the fuck out of them which it would I didn't know that well he the Miami Heat or the LA Pat Riley's teams are always the best conditioned teams in the league they it's very rare those guys get tired like they are not fat I guess Shaq was fat they're like track stars right Shaq was the one okay yeah yeah yeah he can have a donut but the rest of you motherfuckers yeah that to get this salad um and that's exact that's how you like my Pat Riley that's a good Pat right yeah


That's a good looking noodle. I'd love to play this. There's a lot of stuff in sauce. Do that all right, yeah. I'm just trying to update my Instagram. Just don't get no pics. Yeah, yeah. What have you got to do? See! I've got the screen, Tav, and I'm here. Quick, quick, quick. Are we going now? Yeah, I think so. What was it? Yeah. Ask, yeah. Ask, um, See what, great stuff. Great stuff to find about somewhere. No, serious, nice to know. Good first week. Yeah, I'm enjoying it so far. Been, um, very productive. Got a lot of running, got a lot of base fitness in there, so. Been a while. That's my first couple weeks. Yeah. You've snapped back in to get it quickly, though. Exactly, that's the plan. I just need to, obviously, get more training with the boys and start that kind of fitness area. Running wise, I can't scratch. Just in case I'm not getting that match, I'm just getting that kind of game show and stuff. Yeah, excited to do it. Hello, welcome. Yeah, I can't wait, man. So, yeah, four to the west. Happy days, all of us. I'm a misfit. Red light, risk it. Big goosebark. Oh, my God. Oh, you stopped video on that, didn't you? Oh! Can't move, can't you? I'm swimming a little, I'm a drama. Shook on the driver. He bought that. He just blew off a bridge. And they expressed it. Right, to go out and do jazz, he fetched it. Had fire. Oh, no, man. No, man. Yes. On the top of the market, I'm not a misfit. Oh, no. I'm a misfit. I'm a misfit. I'm a misfit. You could have had memory loom. Right, I'm a misfit. I'm a misfit. No, man. Too easy. I've got to know your players. Give them chances, but the dogs had a chance as well. First win this year. The league was not quite there, then who is there as an opponent? Oh, for God's sake, anyone can challenge me, really. I knew he wouldn't like that one. He wouldn't like that one, did he, Kean? If you're on to it, I'll give it a go. If that wasn't a tough session, then we had Tuesday's training session was a little bit tough. Yeah, Tuesday was tough. Not nice. So I'm going to tank and go again tomorrow. Just a bit of recovery now at the moment, throughout the weekend, though. If you've got recovery then, yeah. Some sort of recovery day today, but that was tough stuff. Give it a go. Some shot. Don't pop the wire. That's got to be a fine map. Five minutes. Who started diesel? He started it, just to go for our turn. I thought I was off to a terrible start. This is our turn, up now. I wish you showed a bit of this when we were players together, mate. I'll say it. I thought that was down on the ball. What's the Thomas down there for? First touch. Let me go, I'm not seeing this. I've never seen anyone as if I sleep on it. You're seeing that man on 28, why would you say that? Why, man? 28. 29. 26, there we go. Round the world as well. I've been in the lock and all time, didn't you? You just wanted to add to the drama. They've come out, they've had a drive today. I'll make it worth it. No. Firstly doing that ball. I've got the flyer, but you've got the numbers. Thank you.


The Marines and sailors of 2nd Marine Aircraft Wing may call the Carolinas home, but their impact is felt around the world. The Marines and sailors prepared and trained around the clock to be ready, capable, and successful as the aviation combat element for 2nd Marine Expeditionary Force. For 80 years, the Wing has participated in major battles and campaigns that defined our nation. 2nd Marine Aircraft Wing has continued to generate, deploy, and sustain expeditionary combat-ready units to support mission requirements, allies, and partners worldwide. Since its activation on July 10, 1941, with squadrons in San Diego and Hawaii, 2nd Marine Aircraft Wing contributed mindlessly to the successful execution of operations and campaigns in the South Pacific. Relocating to North Carolina in 1946, the Airwings presence has since been felt across the globe in support and defense of the United States and its allies from East Asia, the Middle East, the Balkans, and the Americas. 2nd Marine Aircraft Wing has dominated land, sea, and air by providing close air support to the Marines and sailors on the ground, reimagining electronic warfare, and reinforcing air defenses and advanced aerial reconnaissance. When natural disasters occurred, 2nd Marine Aircraft Wing provided humanitarian assistance and disaster relief efforts to countries in need. Every Marine, sailor, and civilian who make up America's air wing will continue to write chapters in its illustrious legacy and will always remain committed to excellence. Marine, sailor, civilians, and families of 2nd Ma, this has been an historically successful and rewarding year, and we thank each and every one of you for your efforts. As we prepare for 2022, one thing is certain, we're continuing our predecessor's legacy of being the most ready when our nation is least ready. This year, you accomplished many significant and groundbreaking tasks, training events, and deployments. You built these accomplishments on the foundation of your continued flexibility, competency, and readiness. You also provided humanitarian assistance and disaster relief to the people and government of Haiti after a tragic earthquake, and you did that within 96 hours of notification to deploy. You strengthened relationships with our allies and partners, flying and operating in places like Japan, Canada, Finland, Spain, Italy, Peru, and the training ranges of the continental United States. Finally, you supported multiple Marine Expeditionary Units' global deployments to include supporting the evacuation of Afghanistan. Your tempo never wavered, yet today you continue to perform, improve, and adapt the new challenges across the aviation enterprise. Behind every operation, aircraft, and mission lies our true strength, our people. Our blue-collar mentality and work ethic coupled with this wing's strong culture and obsessive drive to win at everything we do, our hallmarks passed down from the giants who came before us. As a result of your determination and efforts, we achieved more than 80,000 flight hours, far exceeding our fiscal year requirements. We tested new aircraft platforms that will serve our corps for years to come, like the CH-53 Kilo. Furthermore, we made significant contributions to our corps' ability to develop new operating concepts through training events like the first F-35 Bravo operations at Bogue Field, executing concepts that support Expeditionary Advanced Base Operations. We pushed the limits in training to prepare for the next challenge in the future fight, carrying our Commandant's vision, all the while focusing on operational excellence in warfighting, as we have for the 80 years of our MAW's existence. The sun never sets on second MAW, and I'm proud of all you accomplished this year and in the 79 years preceding this. We'll take a short operational pause over the holidays to close out our wings' 80th year of existence and come back ready to set the pace for Marine Corps aviation once again in 2022. Thank you. Thank you for a job well done and a year to remember. And be ready to come back in 2022 for the 81st year of continued excellence. Seper Fidel, second MAW.


Haunted back straight, big braking for that corner that's going to be 4 or 5. Here's a bit of the kerb. Braking onto the crest, car always gets super light here. Don't use that kerb on exit, it's very not friendly. If you can do that right, change that out. Amazing, that's going to give you a lot of lap time. Here, big braking. A few possibilities using the side kerb. I don't really like using the outside kerb, but you can. And then that's the corner called the kao zal. You do want to stay on the inside. There's no real grip on the outside. There's no point in opening the corner. On the back straight, into the kink. A lot of corners, not easy on full cars, car bottoms a lot. Big top speed here.


This 2019 Ford F-250 Crew Cab Short Box XLT is stock number 21J177A. We are here at Summit Automotive in Fondlac, Wisconsin. You're new and used heavy-duty truck headquarters. This 2019 Ford F-250 has the 6.2 liter V8 engine. This truck has been fully-safetyed and inspected by our service shop per the state of Wisconsin inspection process. It has a fresh oil and filter change. All the fluids have been checked and topped off, and this truck is 100% ready to go. Magnetic gray metallic is the color we shoot all of our videos in 1080p, 60 frames per second, so if you have HD capabilities on your computer, tablet, smartphone, or television, I highly recommend turning them on right now because it is your best way to check out the quality and condition and options of the truck before seeing it in person. And if you like the video and want to subscribe to our YouTube channel to see videos we do each and every day of our new and used inventory here at Summit Auto, in the bottom right-hand part of the screen is a subscribe button. Click that and then click the bell notifications, you'll get updates on the videos that we do each and every day here at Summit Auto. This one has Goodyear Wrangler LT27570R18 all-terrain adventure tires, and it has the chromed 18-inch rims. These tires have right around 50% to 60% of the tread left. Frame and underbody on this truck is in excellent shape, didn't see any corrosion on there. Front fender is in excellent condition as well. No major dents or dings, the headlight lenses are nice and clear. It comes with the factory fog lights, and the front bumper and lower valance are in excellent shape as well. This one does have the chrome appearance group, which gives you the chrome toe hooks, chrome trim grille, and chrome trimmed mirrors. The hood is in very nice condition as well, and it does come with the clearance lights up top. Passenger side front fender, absolutely perfect. And the passenger side rim, no scuffs or scrapes on there. Looks really good. I always like showing off these metallic paint jobs so you can see the metal flake, kind of simulated sun experience, if you will. Lots of metal flake in that magnetic metallic paint. As you go down this side, the truck, take note of how clean the body is, how reflective and mirror like that paint is. And we take these HD videos, so if you are far away or even if you're close by, just cannot make the trip down, but you're still interested in purchasing the vehicle, you can see the truck, hear the truck, and have confidence in the vehicle that you're looking at before you even get here. So when you do get here, there's absolutely no surprises, and you can make a smart and informed buying decision from wherever you may be watching this video or checking out our ad. Very nice down that side, this back rim is in excellent shape as well, and the back tires have just as much tread as the front tires. Frame and underbody is in excellent shape, very little to no corrosion, as all the remainder factory exhaust, and allure rockers and cab corners look really good. Factory chrome step bars, as we come around to the back of the vehicle. Very nice back here, rear bumper, no dents or dings on there, it does have the back up parking sensors, full towing package, which includes a receiver hitch, four pin and seven pin wiring, and the tailgate is in absolutely perfect condition as well. It does have a Ford factory soft roll up tonneau cover, no rips or tears on that. Comes with fifth wheel bed rails, bed is in nice shape, and it also has seven pin wiring back here, part of a bed mat. And as you come around to this side of the vehicle, just as clean as a passenger side, no dents or dings on the box, and for full disclosure this back rim is in excellent shape as well. Down the rest of this side of the truck looks really good. This one does have the door code entry, we do have the code, and if you ever wanted to find out where your personal 17 to 21 super duty code is, we have a video on how to find that, it's in the upper right hand part of the screen, click that, check us out there, heated mirrors, built in directional signals, these power telescope out, they power fold in as well. Inside the XLT package gives you the gray cloth interior, 40-20-40 split bench seating inside, no rips or tears on the seats, really nice condition. These front seats are heated and power. Weather tech floor mats throughout, power pedals, auto headlamps, and tilt and telescopic steering wheel. That's for the LED side lights on the mirrors, power windows, power locks, power mirrors, they do power fold in. I was showing both sides so you can see that both sides are working properly, and they do power telescope out and in. Once again, both sides working really good. We'll hop inside, take a look at the instrument cluster and the radio. Check out everything that this one has to offer on the interior. As you can see, this one has 17,458 miles, you get the digital speedometer, compass display, instrument cluster is very nice and clean. Steering wheel is a multi-function steering wheel cruise controls and information center controls on left, no excessive wear or scratches on that steering wheel, Bluetooth and information center controls on, I'm sorry, volume controls on the right. Six speed automatic transmission with the optional tap shift. This one has the sync eight inch radio. This particular one has AMFMN series, it does have the factory navigation system on it. You can also get all your different apps on here, including Android Auto and Apple CarPlay where you can project your cell phone to the screen, use a different navigation system perhaps or listen to music or just control your phone from the radio, cool systems there.  There are two USB's down there, 12 volt power point and 110 volt 400 watt plug-in as well. Dual glove boxes, passenger side format and seat are in excellent condition as well, no rips or tears on there. Smells very clean inside this truck, I don't think it's ever been smoked in and it does have the panoramic vista roof, so second row fixed glass front power sunroof. This one has six auxiliary up-fit switches on it, power sliding rear window button, headlights and sunroof controls. We'll take a quick look at the back seats and then we'll start it up and take a look under the hood. Back seats are just as clean as front seats, no rips or tears back here, it does have the latch, child safety system for any child car seats you may have, power sliding rear window with the built-in rear defrost, that headliner is in nice shape as well. These seats do fold up for extra storage, there is a collapsible floor back here as well and the factory floor mats and carpeting back here all look really good. These seats come back down like so and you do get child safety locks on the back doors, bottoms of the doors look really good too. And we'll start it up, starts right up, no check engine lights or anything like that. I would personally like to thank you for checking out the video today and hopefully from this HD video you will have been able to tell just how clean this truck is all the way around, verify the quality and condition on it to make a smart buying decision or just learn a little bit about the 2019 Ford F-250. Under the hood we have the 6.2 liter V8 engine, engine bay is very clean, runs very smooth, once again this truck has been fully safe and inspected by our service shop, has a fresh oil and filter change, all the fluids have been checked and topped off and this truck is 100% ready to go, there is your emission sticker. I would highly recommend this truck from a quality and condition standpoint and to see more pictures of this truck or one of our other 450 new and used cars, trucks, SUVs, minivans, wranglers, halftons, three quarter tons, one tons, you name it we got to go to that website right there www.summitauto.com, full pictures and descriptions of every single vehicle from two locations all at www.summitauto.com and if you like to check out more HD videos you can go to www.youtube.com slash www.summitauto.com, remember to like, subscribe and share on this video and all the videos that you see there, click the bell notifications you'll get updates on the videos that we do each and every day here at Summit Auto, in fact in a second you will see a link to subscribe to our YouTube channel in the upper left, a link to more F-250 videos like this one in the upper right, a link to this vehicle on our website in the lower left and a link to one of our latest YouTube videos in the lower right, click those check us out and we're super excited to help you with this ultra clean 2019 Ford F-250 Crew Cab Short Box XLT and Magnetic Gray Metallic, thanks again for checking out the video.


So a martial arts instructor, also known as MAI, is an 0-9-16 in the United States Marine Corps. They're responsible for training Marines in the Marine Corps martial arts program and advancing them through the 5-tier belt system that we have. My name is Gunner Sergeant Isaac and I am the lead instructor trainer for the Martial Martial Arts Instructor Course 124-TAC-20. The P-6 signifies being on the battlefield with that bayonet in hand attacking the aggressor, the enemy. The O-Course is a series of obstacles that requires the Marines to be physically fit to go through the obstacle course. We also give them a lot of time and have them put on their flag jacket and a little bit of weight. The E-Course is a test of Marines in Durris. The first half of the E-Course is a run, it's about a 3-mile run through the woods. The second half of the E-Course is a 2-mile run that includes several different obstacles that the Marines are required to navigate. The beginning of the course, the Marines have been given what we call discipline. It's a sandbag that they're required to carry with them everywhere they go. They realize at the end of the course that the discipline, the weight that the burden that they were carrying is now inside of them. It's a challenge, a challenge, weight, success. The whole thing right here is a straggler strike, right? Yes, it's going to strike. So this is your mental, your physical and your character discipline, is it not? Yes, it's going to strike. So essentially this is what you are, is it not? Yes, it's going to strike. I'm going to ask for reward. Here, I have to go away. Oh yeah. So once the Marines graduate, they leave with a 10 straggler they add to their MiGMAP belt, and they're known as a martial arts instructor. Their sole responsibility is going to be training of the Marines, instead of the same three disciplines that they have learned and instilled in themselves in the past three weeks. The ultimate goal for them is to just battle Marines and make better war fighters throughout the course.


What was the biggest difference with cold stuff tonight? He was just executing pitches around the zone. Not made a mistake from him tonight. He seemed like you guys moved away from the cutter a little bit at this evening. What went into that part of the game plan? I mean, nothing really. We just didn't really get to it. He was executing more pitches than the cutter. I thought his fastball command was really good and slider command was really good. What did you notice from him in the sixth inning when he had to bear down a little bit with some traffic on the bases? He did what he's supposed to do, go out there and make pitches. That's the good thing about Garrett. You get him in that position. He's not going to back down.  What did you think of some of the defensive plays in that inning in particular? Really good. Really good.  That was pretty impressive. I had that guy 1,000% safe. I couldn't believe it, but Webby did an awesome job there. How significant are you looking at this series? You now have a 10 game lead on the raise for Garrett in middle of June. Just coming every day, handle our business, do our job. We win a game. We move forward, but I mean, we're not thinking we'd think one day at a time.


Hello, welcome to tomorrow. In this special space pod, we're entering some of your space questions that were submitted with the hashtag AMA Superpod, submitted to our subreddit r slash tmro, or sent to us through email via spacepods at tomorrow.tv. Both myself, Lisa Stojanowski and Jared Head are going to be answering some of your questions for this very special Ask Us Anything Superpod for August 31st, 2016. So first up from our email account, Jan Strom asks, I believe his name is Jan, it might be Jan, so please correct me if I'm wrong. For any name case, Mr. Strom asks, will SpaceX ever make a crew dragon full orbital reentry landing on solid ground without parachutes? We know that NASA do not like that, but asking anyway. Good question. So the short answer is yes, eventually. The long answer is that NASA is going to require them to prove themselves and is going to want SpaceX to land the dragon capsule successfully under rocket propulsion multiple times before they'll ever let a living crew member step inside that thing to land on ground with it. That being said, they might do a lot of landings with maybe some sensitive experiments or maybe even living animals on board first as kind of a step-by-step approach to being safe enough in order to land crews via rocket propulsion, but I mean, this is something that they're going to need to do anyway. If SpaceX is seriously going to do the red dragon mission, sending a dragon capsule to Mars and landing it under rocket propulsion, then they're going to need to do this at least once here on Earth to prove that they can do it. I mean, it looks like so far that everything looks like they could do it, but they haven't actually done it yet, so I think that they'll do it here on Earth at least once. Whether or not we'll ever see crews on board just depends on whether or not NASA will be satisfied with the safety requirements, but in any case they will at least land a dragon capsule with rocket propulsion at least once. The next question comes to us from Reddit user Brandon Mark who asked, if you had money to fund two specific missions, crafts or experiments, what would they be? So the first experiment that I'd like to fund is really cool, but it's also really important for helping humanity to expand their presence across the cosmos. The Mars plant experiment is a proposal to send a cube-sat-sized box on the Mars 2020 rover. Now the Mars 2020 rover is based on the construction of the Curiosity rover, and the plan is to put the cube-sat-sized box on the spot where the sundial currently sits on Curiosity but on the 2020 rover. The box will contain over 100 seeds of the plant Arabidopsis thaliana, including cameras and sensors to see whether the seeds can germinate and grow on Mars. The inside of the box will be very earth-like containing earth-like air and water as well. The water will be taken with the spacecraft, so the only thing the experiment is testing is whether plants can grow in the conditions of Martian gravity and radiation. The problem is, however, that the Mars plant experiment hasn't been confirmed as a payload for Mars 2020. In my last spaceport I was talking to the program scientist for Mars 2020, Mitch Schulte, and he didn't even know the proposal existed. Anyway, I think it's still really important to fund this experiment because growing plants on Mars is essential if we're ever going to be sending humans there to live permanently. In fact, I love this experiment so much that my second experiment coming back to the original question would be to fund a successor to a Mars plant experiment where we tested the conditions of Martian atmosphere as well, perhaps with a little bit of modification like pressurizing the atmosphere. Anyway, thank you so much for your question, Brandon The first question that I'll be answering comes from Twitter user Albertina. What could the weather of a tidally locked planet look like? Assuming that this planet has an atmosphere, shout out to Proxima B. The weather on a tidally locked planet would be quite interesting. And just so that everybody knows what a tidally locked planet is, that means that it goes around its star and it rotates at the same rate as it orbits. Basically, one side of that planet is always facing the star as it goes around it. Now, that would obviously lead to some really weird weather patterns. Obviously, the side closest to the sun would be a lot warmer than the side opposite of the sun, where it would be a lot cooler. But if you have an atmosphere, you can actually distribute heat through the atmosphere. That means that it's somewhere like Proxima B. You may actually be able to have heat from that side closest to the star distributed on the far side of that planet. So that may end up meaning that the life on a hypothetical planet like Proxima B may actually be found on the nighttime side as opposed to the daytime side. This next question comes from Twitter from the user Ross Trower, who is also one of our patrons. Thank you very much, Ross. And his question is, should we consider the Venusian atmosphere over Mars for colonization? Very interesting. In my opinion, I don't think that we should consider Venus colonization over Mars colonization. I think that we should do both. And the whole idea of colonizing the Venusian atmosphere is super interesting, because most of the atmosphere in Venus has the same density as water. And there's a particular layer that is actually kind of cool. It's not as hot as the rest of the Venusian atmosphere. And we could easily send stuff to float on that layer. And with the temperature being pretty nice compared to the rest of Venus and us being able to send stuff to float on that level without having to worry about sinking, it actually might be pretty cool. We could have like cloud cities on Venus, but without that giant pole that holds up the city in the Star Wars movies, they would actually just be floating on the atmosphere. So I think that we should be looking at Venusian colonization. But whether or not we should look at it over Mars, I don't think so. I think Mars still might be the easier target. But I think that we should do both. And my final question for the Superpod AMA comes from J.C. Warp on Reddit. Proxima B makes me wonder about the habitable zone of our sun, especially considering radiation and sunbursts. How far does it reach? Well, J.C. Warp, that is an excellent question and one that most people assume with Earth being the only planet inside of our sun's habitable zone. But actually there are technically three planets inside of our own sun's habitable zone. Venus, Earth, and Mars. Now Venus is on the inner edge of the sun's habitable zone. That means that if there was liquid water there would be a very warm place to be. In fact, when people were initially studying Venus, they thought it would be a tropical paradise. Turns out it's actually sort of these very hot volcanic lands. So not exactly the best place for life. Now Earth isn't necessarily smack dab in the middle of the habitable zone. It's a little bit further out in the middle of the habitable zone itself. And then finally at the very, very edge we have Mars. And Mars is right on that edge of the habitable zone. So liquid water actually did exist on Mars. We have direct evidence of that thanks to our surveys from orbit and our rovers that we have landed on the planet. So Venus, Earth, and Mars, they're within the sun's habitable zone. And that's about the extent at which it is in our solar system. Now the habitable zone will change. As our sun gets older, that habitable zone will actually move out. And within about a billion years Earth will be out of the habitable zone. It will continue outwards into the outer solar system. So we've really only got liquid water oceans here on Earth for about another billion years. Which I think is enough time to leave the planet. So in closing, thanks to everyone who submitted your questions for our AMA Superpod today. We hope you learned a little bit more today than you did yesterday, thanks to tomorrow. Keep submitting your questions and maybe we'll be answering them on our next Superpod. But until then, keep moving onwards and upwards. Keep on discovering and keep exploring. Now Venus is on the inner edge of the habitable zone. So if Venus didn't have that wild atmosphere at 860 degrees, ooh, I used imperial units. That's bad.


Speak, Speak, Daddy, Daddy, Park, Park, School, Laundromat, Laundromat, Machine, Machine, Realized, Realized, Fussy, Fussy, Home, Mommy, Mommy, Found.


Hi everybody. Welcome. I'm Lisa Larson. We're here with podcast Pete. Hello Pete. Hello Lisa. How are we doing today? Good. How are you doing? Pretty good. We've got the cats here. We may have some visitors. So we've got kind of a thing going on. Everybody wants to be in front of the one open window. So we've got a lot of crawling. So you hear things knocking, being knocked over and all of that stuff. That's what's happening. I have to tell you a friend of mine's description of the word nervous.  Little bit of cornpone there for you. It is. Oh my. Okay. Well let's hope that they will let me be because we're doing this later on in the day and they're probably getting hungry. So let's let's try and get through this. For those of you who have been following us, you'll know that right now we are doing a series on euthanasia and this is our second in the series. And last week we spoke about the benefits of euthanasia and why to choose euthanasia. Today we're going to talk about once we've made that choice and we know that understanding, when is it that we call the vet? When do we make that decision? So that's the genesis of what we're talking about today. Well these are going to require emotional steps. I guess my question is when do we even consider making this decision? Yeah you know I mean one of the hardest things about making this decision is and when to make the decision is that you have to marry what's in your heart and what's in your head. You know in your head you can understand that it is the right thing to do to call the vet. Of course then we have the when do we call the vet but it's the right thing to do to call the vet. But we have to marry that with what's in our heart because we really really don't want to let our loved ones go. No we don't. And as we talked about in the last one it's the altruism of it. And you know it's it's very very difficult because what I find with a lot of people is that they will tell me maybe I'm on a conversation with them they've called me to ask me is it time is my animal ready to go. And they say well I've told them they can go on their own. And the problem with that is is it's usually the case that they have told their animal that because they don't want to have to make the decision. Sure it's easy way out. Yeah it's the easy way out and wouldn't it be the easy way out if they would just all have a nice peaceful passing on their own. And as we talked about last week it doesn't always happen that way. So we do have to make that decision. So you know I think what's one of the most important things is planning ahead. And you can do that in a number of ways for one thing you can call an animal communicator. Yeah that's why people call me. They will call me to say where are they in this process how are they feeling how are they feeling physically and how are they feeling about leaving their body because some animals know that they're leaving their body and other animals don't I may have to explain it to them. Interesting. Yeah and this is something that is in the book extended in the book about where you know everybody being on the same page. But that's part of the process is trying to get your head and your heart in the same place and planning ahead and knowing who to call. So we talked last time about home euthanasia. So one of the things when I'm talking to an animal and let's say somebody's called me and the animal isn't saying oh my god oh my god let me go let me go. So it's not quite that time there's they're saying I can go on for a few maybe another day maybe another week they're not quite there yet. But I'm still going to tell the person plan ahead think about who it is you're going to call if you're going to be doing a home euthanasia find that place now call them talk to them set everything up answer all the questions fill out all the forms because on that day that you wake up and you say oh my god it's time and you realize that it's time you have to call the vet and it has to be that day then you don't want to have to be overwhelmed with oh my god who do I call what do I do what do I do you want to plan so part of that is yes talking to a communicator is certainly an option it's not required but it's an option and it certainly helps but also thinking ahead of what you're going to need to do so thinking ahead on who you're going to call who you're going to have do the procedure and and where is it going to be done and and it's just a matter of when do you make that call now you know granted this is a big decision but as far as knowing when to start this process I mean a vet's got to be involved right yes yeah oh yes yes yes yes and that's and that's a very unfortunate thing in some cases people say there are some people there are some people who say well I don't want to pay a vet to do that so they just take matters into their own hands and and that is killing your animal because that is inhumane and cruel and no a vet needs to be involved you need to call a qualified licensed veterinarian who knows how to do this absolutely that's a great question and they can expect certain things to be discussed and brought up if they do call a vet like like what um so you know a lot of it is timing we're going to do a whole episode on the procedure itself once the vet comes over to your house or once you're at the at the vet's office and what that will go through so we'll we'll do a whole episode on that but yeah that that will generally tell you especially if you've never had it done before they'll they'll kind of go through what the procedure is the shots that they give them and a good vet will give you the time that you need like I I called when I had to lift Makana up some people say put them down that I heard somebody say it's better to say lift them up so I'm I'm I'm choosing to go that route yes when I held I when I chose to lift Makana up we called a place called pause into grace and I mentioned this the last time that I talked to the woman who started that and um oh my god I'm gonna I have to try to say this without crying but she was so good she was so um empathetic because I was not ready you know I mean I was holding him and who really ever is ready no one is no you know but sometimes people will come in they'll just do it and it's all part you know it all takes place and maybe you know half an hour or 45 minutes this woman was so wonderful to me because I just I was not there and to the point where she gave him the first shot because there's usually two shots that help him relax and then there's the shot that stops his heart and she actually after she gave him the second shot and he was gone I just couldn't let him go she actually went out and she would she took a long walk and she just let me have my time with him gave you time and certainly there are signs that you look for to be sure when it's time yeah with Makana you know it was we just both of us he was sleeping in between us and both of us just woke up and realized today is the day and ultimately that is going to be it now there are other signs like you know maybe they will stop eating and it's not going to be for every animal you know I mean this is this is just very very general because every animal is going to be different but you know maybe they will stop eating maybe they can't walk anymore or they're peeing on themselves because they can't get up and they can't use the bathroom anymore they or they can't eliminate anymore cat sometimes will will lie in that what I call the meatloaf position they just kind of lie like you know with with their arms tucked under them and their head tucked under so there are signs that are very very clear but but then not every animal does that sign so ultimately if you know certainly if you see those signs it's important but ultimately it's waking up and looking at them and you know your animal better than anybody else you know your animal better than anybody else and it's just knowing and can I share an experience there's one one client called me and she said everybody is telling me that my dog is ready everybody is telling me that I need to to euthanize him now and I need and I need you to talk to him and I talked to him and he said to me no I'm not quite ready I need I need to finish out a few more things first and I told her that and this is something that she's brought back to me many many times because she's a longtime client and she's a student of mine and she said given that right after that conversation he had this turnaround and for a week he just felt really good and we did everything that we always you know that we hadn't done for a while but that we knew he loved to do we took him to the beach we did this we went to the park we did every for about seven days we did everything he wanted to do and then I just woke up that last day and I just knew it was then all of a sudden it was time and I could tell it was time and she said you know I never would have had that last week with him if I hadn't had that conversation with you and and those animals they may be hanging on for a reason maybe it's hanging on because the person is not ready to let go or maybe it's hanging on for this reason because there's something they feel they have left to do yes so as a communicator then you have a role when someone is faced with making this decision or you have many roles don't you yeah and and it's I mean I always look at myself as part of the team you know by this time maybe an animal has has been ill for a while they have their chiropractor they have their vet they have their acupuncturist well I I like to think of myself as part of the care team or part of the sometimes it's hospice sometimes it's making the animal feel as as comfortable as possible but a lot of times they will call me animal parents paw rents will call me when they are really kind of on the precipice and they say I don't know how how close are they to being ready you know more times than not they're calling me in enough time so that I can say yes either either they've got a couple of more days maybe or something like that or there's a few times when they might I might say oh my god they're ready to go they're ready to go please just let me go you know they're telling me but what I do find is that animals will hang on for their people so more often than not what will happen is somebody will call me they'll say I'm not sure if it's time I'm not sure where we are should I be calling the vet today should I be calling the vet tomorrow should I have called the vet yesterday and I find that the animal might say well I'm not quite ready but I'm I will be ready when my mom is ready and what that tells me is that that the mom or the pet parent is is not has not married that head and heart struggling is struggling and so what I will do is I will have a conversation I will have the talk with the pet parent the animal parent and I will explain what we talked about in the last episode as well the you know why it's so important to to to consider euthanasia and to make that decision and to make it a day too early or a day rather than a day too late and and with it it's very interesting that because once I've had that conversation I will find that people will a couple of days later say you know my my cat just two days after our conversation my cat I just knew and it was time and what I find it is is that cat just let's go when they realize that their mom has married their head in their heart so it's almost a body language um no it's an energetic feel interesting it's an energetic feel and you know one of the things that I didn't mention earlier is is I've got something called the 3070 rule or the 7030 rule and in making a decision on when to call the vet this was something that a vet had shared with me before I ever did this work and I found it really useful and then he said if it's 70 percent that your animal is enjoying life eating the foods that he's like that they like even if it's a little less enjoying being with you being in the sun doing the things that they like to do and only 30 percent that their quality of life is not that good then maybe it's not time to call the vet yeah but if it's the other way around if it's only 30 percent that they're enjoying life then maybe it's time to consider making that call and I think that's a lot of times around that time when people end up calling me when they're not sure where that where that lays in that 3070 rule and that's a lot that's one of those things that I usually tell those those people so maybe the pain and the ability or inability to continue is a factor here percentage wise in this decision yeah because as we talked about before we don't want our animals to suffer yeah and it is the most altruistic thing that we can do in making that decision to lift them up and relieve them release them from their suffering so that they don't have to feel that suffering anymore yeah and we need to know that once they're there their spirit is still with us their spirit is always going to be with us they may not be the confined by their body anymore they're not wearing their clothes anymore but their spirit is still always around us and that's a really important thing for people to understand and even when I talk to animals I tell the animals that when I'm preparing them so that they can understand that once they go over on the other side they can be around they can go with their people all over the place that places that they never were able to go with their people before yes so on both sides of the aisle people need to know that their animals will be their in spirit and their animals need to know that they will be with their people in spirit so as far as people finding you and and and utilizing your gifts and services the best way is what your website yeah best way is my website pausetalk.net so tell everybody where to get this book because it's wonderful thank you very much it's pause talking a course in communicating with animals and it's on amazon and it's on apple as an ebook it's actually on barnes and noble as ebook but nobody seems to use apple apple is a good one um and amazon is great okay well this is a series on euthanasia the next podcast will be on the process itself and what to expect for those of you who have never gone through the process and i know there's some of you there who have not or those of you who have and just need to to know that you're not alone in the in in going through the process we'll go we'll go through it step by step and and the things to expect and then we'll be talking later on about grief and signs and all of that stuff but i thank you guys for joining us i thank you pete for joining me and you guys if you are enjoying this please hit that like button and the subscribe in the bell to be notified so i thank you so much and uh we will see you again soon have a good weekend see you soon thank you pete bye bye thank you lisa


Hello and welcome to another video in the February Scary Campaign series.  And in this video, we're going to uncover something you may not have ever thought about. The weird ways we sexually exploit fish and other little creatures. That's right, not even the fish are safe from humans in their lust to dominate, control and commodify through the exploitation of the reproductive organs of every animal on earth. According to the UN Food and Agricultural Organization 2018 Fishery and Aquaculture Stats, the contribution of farm fish to total fish use has risen over the years reaching 46.8% in 2016 up from 25.7% in 2000. This figure amounts to about 80 million tons of farmed food fish annually compared to about 90 million tons of wild-captured fish. Farm fish have recently superseded wild-captured fisheries as the main source of seafood for human consumption. While almost all farm fish production is destined for human consumption, the proportion from wild-captured fisheries now stands at around 78%. Today we're going to look at the bizarre ways some of the most popularly consumed farm sea animals have bred. Salmon consumption worldwide is three times higher than it was in 1980. Salmon aquaculture is the fastest growing food production system in the world, accounting for 70%. That's 2.5 million metric tons of the market. It is scientific consensus that fish are sentient beings who feel pain and suffer. I understand that this process, although may not look like it to you as we all express pain differently, I can assure you these fish are suffering. Salmon are removed from the water where they will immediately begin to suffocate and are thrust onto a conveyor belt into a factory-like setting. These animals are sorted and the female is stunned via an automated percussive system which is the predominant method used for stunning commercially whereby an air-powered hammer-shaped cylinder delivers a forceful blow to the head of each female salmon. Salmon is then sacrificed in a brutal fashion. Her stomach is sliced open and her eggs are removed. When they're ready to spawn, we'll kill that fish and then, which sounds really rough. Male salmon who are ready for spawn are then milked or essentially masturbated into the container of salmon roe which is then mixed ready for incubating. Catfish is the leading aquaculture produced seafood product in the US. The annual harvest of farm-raised catfish in the US is at least twice as much as the annual aquaculture production of all other species of fish and shellfish combined. Annual production over the last decade has ranged from about 500 to 650 million pounds. The stripping of female catfish is a procedure where the animal is taken out of the water and dried with a towel with the cloaca exposed. A finger is then runned down the underbelly to push eggs out of her into a bucket. The male spawner has to be sacrificed an hour prior to the stripping of the female eggs to obtain the milked, which in catfish cannot be gotten through the same stripping process. The procedure on the male fish is carried out by cutting open the abdominal area to expose the testes for easy dissection. The milked or fish semen is then extracted and mixed in with the eggs to fertilize them ready for incubation. Now that was absolutely awful. Global farmed shrimp production in 2016 was more than 5.7 million tons. The top importers of shrimp, both farmed and wild caught, are the European Union and the United States. Now one of the weirdest things I've ever seen since I've been looking into the ways humans sexually exploit animals is seeing a shrimp being jacked off by a human. Although it's uncertain at how common this practice actually is, the fact that it's even practiced at all was just weird. Apparently the procedure for artificial insemination in shrimp goes as follows. A female shrimp with mature eggs or ovaries is selected. The male shrimp is essentially jacked off to extract the sperm mass from the spermatophore and the prawn semen is then inserted into the female. Now come on, this is just getting out of control. The last animal or more like insect I'd like to feature in this series is the small but significant honeybee. And I'll let my friend Sonya say explain this part. Hi everyone, bees will only produce honey if they have a queen. Queen bees are often artificially inseminated, which means that the honey industry per scales by crushing and squeezing a male bee to take out his semen and then they forcibly inserted in the queen bees vagina. Wow, is there an animal on earth we haven't sexually exploited for our own gain? This is just getting creepier as the weeks go on. Please share this video far and wide with the hashtag February Scary to those who need to see exactly the type of sexual abuse of non-consenting animals they are paying for when they purchase animal products. Let's all oppose and boycott the sexual exploitation of sentient beings no matter the species. Thank you.


Let us make connections between connections so these two notions obviously are very closely related as a name suggests so in fact we can even provide Dictionary so on the one hand we have Vector bundles on the other hand we have principle bundles now So as we have discussed already if I have a vector bundle I can construct a principle bundle So let's do a name. So e I can construct a principle bundle of frames of e and In the other direction if I have a principle G bundle P I can construct an associated bundle P times G row Say Rk this is e so this gives Way ways to go back and forth between principle and vector bundles but Let us perhaps go a little further. So if you have a section s So this is a section What does this correspond on the right-hand side? So it turns out that this corresponds to a equivariant map from P into a Representation say Rk and this is required to be G Equivariant and so the the correspondence is very explicit right, so if if you have an and a G equivalent map as hats and you can define as head of the class say P X just to be So I can define s of P X to be as head of P If you wish the class This guy now if you have a connection Nubla On a vector bundle this gives us a connection on the principle bundle. So let me denote this by a in omega 1 P G in the standard way, so something that I've already mentioned if you have a Local trivialization of your vector bundle the connection becomes a one form with values in the Lie algebra And this is exactly what you have if you look at this globally What you get is a one form on the total space of P rather than just a bunch of local one forms and As we discuss here, we have the gauge group Of a vector bundle and we have the corresponding notion of the gauge group on the right-hand side So what is that? G of P Let's just say Set if you wish of bundle automorphins. These are the maps from pi from P to P such that pi P times G is She by times G But in other words what we see from here is that the value of phi at the point P must be in the same Orbit of the Lie group action so that they say can represent any map phi as a map Psi from P to G and the condition is that Psi of P times G is Psi of P G G inverse Okay Since we have we have here also discuss the notion of the curvature. So for a connection nublar. I have the curvature F nublar Which was defined as a composition you remember of the differentials the nublar and you have a corresponding notion of the curvature here For a connection a so now F a becomes Da plus one-half a wedge a Well here the brackets together with wedge means simultaneous Brackets in the Lie algebra and taking the wedge product in the space of one forms. And so what you have is That of course these notions are related so you know if If you have a connection nublar which induces your connection A on the principle bundle you take its curvature And this is more or less the same as a curvature of this connection F nublar. All right now the most important property of the curvature is the so-called Pianchi identity the theorem is That if you take the nublar and apply this to the curvature So the curvature is a two form if you apply the nublar to this you will get a three form on a manifold There was values in the endomorphism bundle. This stands out to be zero Or if you think of the connection in terms of the principle bundle or Locally, this is the same as saying that D of F a equals a wedge F a up to a sign So here is a minus sign. Okay. Maybe let me give you One example of that So here is an example. So let me assume that P over M is a principle U1 bundle So a particular feature is that you one is an abliently group. All right. So what we have is the following so the gauge group of P as we have discussed earlier. It's just a set of maps psi from P to U1 So I said in this case G P times G is just Psi of P Right. In other words psi is an invariant map with respect to the U1 action That is this is just the same as the space of maps from the base manifold Into U1 Now if you have a connection A on P The gauge equivalent connection to that. So let us pick also a gauge transformation. So this is a smooth map Right. It's just an element in this space So then the corresponding One form of G is a plus G minus 1 DG Let us try to compute the curvature of this connection. So F a G is Because of a Lee Algebra is ablient This term over here is trivial. So we have we have just the differential of a and this is D a plus T of G inverse DG But this is close. So this vanishes and we have F a Yes, you do. Yeah, so what I mean is that they cover Indeed the identity map here on the base manifold M Okay, so in other words What we see is that the in the ablient case a curvature actually It's independent of the gauge transformation. Okay, are there any questions to that? All right, then Let us move a little bit so Let me consider now elements of the Tran wild theory So first we consider the notion of an invariant polynomial. So what we have is We take a map P from the lee algebra G into Say R or C. So let me take to the complex numbers and I Say that P is an invariant Or maybe G invariant polynomial If the following whole so P is G invariant as a map that is P Had G XI is P XI right for any G and then XI in the lee algebra of G and P is a polynomial. So P is Polynomial meanings that you know if you choose Say a basis XI one up to XI n so basis Full G then P of X1 XI one plus X and XI and is a Polynomial in X1 Xn and Sometimes it will be convenient to write this homogeneous polynomials, which just means so piece homogeneous Of degrees a D F P of lambda XI as lambda to the power D P of XI so Here are Some examples So we will take Here as an example we take G to be UK and So the corresponding D algebra is UK and we could take Say P of XI to be Trace of XI to the power D and this is obviously a homogeneous polynomial of degree D more importantly we can take so P of XI to be the determinant of lambda one plus I over to pi XI and so Now we have a parameter lambda here. So if we expand this in lambda you will get an expression like lambda to the power K Plus C1 of XI lambda to the power K minus one plus and so on CK of XI Now these are homogeneous. So each CJ is a homogeneous polynomial of degree J Now so we can compute easily certain terms right if you put if you put lambda equals zero what we get is CK of XI is a determinant of XI essentially. So C K XI yes, and for instance C1 of XI is just I over to pi Trace of XI Alright now if you have a principle bundle together with a connection So P M is a Principle bundle If you pick a connection nabla on P We have the character of nabla, right? This is now a two-form We can think of this at least as a two-form on the total space of G with values in the Lie algebra G We can apply P to F nabla And this will give us some form on the total space of P was values Say in complex numbers But now it's easy to check that this form is actually G invariant and basic so basic here means that whenever you take you know Particle so V is a Particle tangent Factor to the principle bundle P is that that is it is tangent to the fiber of the projection map if you Inserts this into P of F nabla you will have zero and This implies that actually there is a unique form Maybe F nabla So I would just you know by the same symbol but when saying is that this is a form Essentially on the base manifold M was values in C so let me Temporarily denotes this with Twiddle Such that the pullback of this form nabla Twiddle is by Nubble so it drops a symbol Twiddle in the sequel and now the Yankee identity Tells us actually that this form Whatever way you think either this form on the Total space of the principle bundle or the the form on the base is closed. So P Nubla Twiddle is zero In other words, this means that we can Consider the the Ramko homology class of P F nabla So this is H The Ram see and this is Well defined Independent of the choice of connection now In other words would be a constant is an invariant of a vector bundle or a principle bundle itself Now here is an Example which will be of Importance to us So if you have a you want a UK bundle as we have had over there then C J of P. So, you know P is a K bundle then C J of P So this is now an element in the two J's in the Ramko homology group of M Was values in C. So this is called the J's turn class maybe Let me just finish by saying that for the Classes for the polynomial C K that we have constructed here. They have the properties that If you take C J bar, this is C J So in fact, they are real polynomials and this means that we have constructed classes in the Real co homology group rather than the complex one Okay, let me stop here and we will continue our discussion today in the afternoon


President Mohammed Buhari is calling on religious leaders of all faiths to unite in support of the fight against terrorism, kidnapping, banditry and the novel coronavirus. Presidential spokesman Garbashir, who says the president made the call when the Sultan of Sokoto said Abu Bakr III called to celebrate Id with him. The president also commended the Sultan for his leadership of the Muslim Ummah.