Today we're going to talk about our most popular recipe on our website, our creamy vegan wild rice soup. It has five stars and 150 plus comments and it is distinctly minnesotan. The soup used to be served at Byerley's, a fancy specialty grocery store that neither Lenny or I could afford growing up. It was their chicken wild rice soup. So we decided to recreate it, make it a comfort food for our plant-based lifestyle. So the first thing you're going to do is soak one cup of cashews. If you can overnight, great, if not as soon as you can, then you're going to chop your veggies. This is the hardest part by far, but it's strangely cathartic if you think of it. So you're going to chop one cup of carrots, four ribs of celery, a half an onion, four to six cloves of garlic, and eight ounces of mushrooms. We're going to be using 64 ounces of veggie broth, but you're going to want to reserve one cup on the side. And then you're going to heat up your broth. Add one cup of wild rice, but make sure that you rinse it off a couple of times first. Reserve your mushrooms on the side, but add all the rest of the veggies.  And then if you run out of time like I did here, you can always do a garlic cheat, which is to use the pre-chopped instead of using fresh cloves. And then you're going to add in your spices. So you're going to use one tablespoon of thyme, two bay leaves, and then two teaspoons of salt. You can add more later. While your soup is heating up, you're going to start making your cashew cream. So you're going to dump a 15 ounce can of cannellini beans. You're going to drain those cashews that you soaked, add those to the Vitamix, and then add the cup of broth that you reserved. You're going to blend that up for one minute and you can see how creamy and thick and decadent this soup base is going to become. Then take your lid off carefully.  And you're going to add this cream as well as your mushrooms. So once you've got the broth and veggies, the mushrooms and the cream all in your pot, put the lid back on, lower the heat and cook it for another 15 minutes or so. You'll know that your soup is done when you try the wild rice and it's a little bit chewy. Serve the soup piping hot to your vegan, whole food plant-based, vegetarian, pescetarian, whatever, omnivore friends. If you peruse the comments, it's unquestionably enjoyed by everyone and it's already made it into several families' heavy rotations. So you should add it to yours. Thanks so much for watching. Hit that like button if you appreciate recipe videos like this. And you guys, leave a comment. Let us know what you want us to make next. Subscribe if you haven't already and we'll see you in our next one. Thanks so much. Bye.


Hi, beautiful. Today we're watching season 12 of America's Next Top Model makeovers. I'm excited. I cannot believe I haven't watched every single season yet. Surprisingly enough, I still have several more to go. I don't know how that's possible. It's been so damn long since I started this journey of America's Next Top Model reaction videos.  I don't recognize any of the girls from this season when I looked at the promos for it. I'm interested to see if any of these makeovers jog my memory at all and let's see what happens today. Hopefully we get some good stuff going on, but you know what happens. Most of the time these girls get some weird f***ing makeovers. Let's do it. All right, let's dive into the episode. Oh, I love saying dive in. It's a good phrase, don't you think? Diving in. Oh yes, Bradford, it's a great phrase. Now on to you, Sully. Thank you. All right, America's Next Top Model season 12. Let's begin. It's Hyrule Man. Whether it's on the streets or the sidewalk, you'll be turned in pink. It smells like a makeover to me. Oh my God. Remember how popular limousines were back then? It's so Barbie dog. Cute, it's pink with like blue stripes on. Yes, I need this in my life. Next time I go to an event, I want this pink limo, Emma. Okay. You missed it. I did. Show it to me again. No, no, it's like the most tacky thing.  I need it. You're gonna forget. Okay, fine. I want it now. Yes, Baruchas, sweetheart. It will get you the pink limo. Thank you, Dating. I'm walking out and we see this stretch limo. Honestly, such goals. Ah! Our tire mill said that we were gonna turn heads, and now I know why she's talking about it. Are they in Brooklyn? Whoa! It's so girly. Yeah! It's so fun. They're in Manhattan at John Barrett. My God. Oh! Mr. J, Ms. J. Look at the phone! If you choose to accept it, in your hands are 12 dossiers of 12 busted up models. Wait, this is iconic. I need you to transform these wannabe. Wow, J's hair looks so good. It is so white. Italian models. And yes, I know this mission is going to be difficult. There will be tears. There will be begging. There will be, oh no, no. Care. Cut it, slice it, dice it. Copy that, T. Good luck. Tyra just gets more and more iconic every time I see her. This is scary.  Ooh! Dorf Goodman. Ow! And you're standing in the john. Look at the purple walls. That was such a thing back then. Surprised that she's getting makeover. I'm feeling her. He's absolutely amazing. People wait for two months for an appointment for him. I love when they have to recite these lines like in their confessionals. This girl has no idea who John Barrett is. Like there's no way. She's like, people have to wait two months to get an appointment with him. Like girl, you've never once heard of John Barrett. Don't lie. And all of your looks are right here in these dossiers. For fierce eyes only, that means I can look. And your makeover is complete. I remember this girl. Oh my God, she's so pretty. She looks like a doll, a living doll. We've got some extensions going on. We've got some color. Here's the top secret plan for Jessica. She's the prettiest girl in her high school, but she needs to be edged out to be a true top model. So we're gonna chop it shorter, add a little wave, and a little red. I wasn't nervous at all. And oh! She looks exactly the same. However, still we're on season 12 and they still can't get the before picture right. They still can't show you what the person looks like beforehand. I don't understand that at all. Put her hair down. Let me see what's going on beforehand and let me see what's gone on after. So we can do a little comparison moment. She looks exactly the same. I think they like tinctured her hair red and added extensions, which she did not need at all.  Good luck to her. And I would have loved to see her platinum blonde. You live up to see everyone kind of blonde. Why does everybody say that? I don't know. Because I kind of like stands true though. You love blonde. No, I love blond. I love it. I think every hairstyle has like a preference of like what they enjoy doing the most. And I like blonding. And that's a very, very, very, very common thing with hairdressers. Yeah, blonding. It's a thing. I like redding. No, that's not it. I like browning. I do always compliment brown hair and tell people that they should have brown hair when they have blonde hairs. Everybody ignores when I say that. And then every time I say anything about blonde hair everybody's like, only like blondes. And I don't care. I'm over it.   God, I need to get that off my chest. No tears. No tears. I'll just keep moving on.  She looks like a serious top model. So I'm cutting off that mohawk thing and making the hair that remains a lot. Oh. Mm, wow. I didn't really notice that I look good. Here's a prime example where I liked the girl better with brown hair. Like way, way, way, way, way, way, way, way better. I don't like the blonde in her. She looked so much more like a model beforehand with the natural hair color. I do like the haircuts, but not a fan of the color. Allison, those eyes, those eyes, those eyes. She's so pretty. And they deserve to have big. Ooh, they said Bolly-odd. Hair. Oh my God. They made it look like Dolly Parton and like no offense to Dolly Parton. She's gorgeous. Like it ain't the vibe for this. It's so upsetting. It looked so much cuter before. I would have just liked if they gave her a really edgy haircut, like a chin length blunt bob and just straighten the f*** out of it and had like no bend to it and was just like super architectural and it was kept brown and like we didn't do anything else. I think that would have been way better for her. This highlighted blonde with the teasing and the curls and the extensions. It's like all too much. Nia's hair is nice. She's so pretty too. We're gonna exaggerate that weed. All right, let's go. Ooh. I mean, listen, she didn't need much change. I actually like that they didn't do a lot on her because I think the dark brown hair color she came in with was gorgeous. I love the length and she just has incredibly beautiful hair. I don't know how she gets it so silky and soft and so shiny. It works for her and her face says it all. I don't think she needs anything else. When I look at foe, I see cuteness. Cute. She is so cute. Don't cut it in top model world.  Be fat. Ooh. She was not expecting it. Okay, aw. Whoa. That was really, really, really, really pretty. I'm obsessed with that makeover. That haircut was beautifully done. It was like an edgy pixie cut and I love it. I love the color. I love the cut. I loved the styling. I think it made her look like a serious model and she looked incredible. Celia. Oh, I hope I cut all of her hair off. Such beautiful hair. But it gets in the way of those gorgeous cheekbones. So I'm cutting it off. Every girl out there has long, stringy hair. Her hair was long. Literally. Hey, sandal. Celia's. Yes, they're cutting it off. Oh my God, she already looks. Right next time, thinking it's gonna happen. 20 times better. Honestly enough, I feel liberated and I think that'll translate better in photoshoes. Okay, here's the thing. It was the styling for me that did not work with this one. I love the haircut. Like it looked really, really nice but then they did that weird like push back faux-hawk thing. But, you know, this was filmed a very long time ago. You just called it a faux-hawk. That's what you call it. Oh, because I think you're gonna do a certain hair name as faux. No, I'm not a different girl now. I'm not a different girl now. A faux-hawk. This is what I deal with every day. Every day. I mean, this weave afro is absolutely beautiful but limiting. So we're gonna take those weave tracks out that are the fro, cause they have to go. We're gonna add- I liked it. Campbell waves. Oh, of course, J has to always do the most. This is the best way to do behavior. Oh, I mean, honestly, this is kind of a look. I actually saw a shirt from I think it's Balenciaga that they made with hair extensions. And I'm considering buying it. Can we put a picture of it up here? What do you guys think? Should I get this? I love my new hair. It's definitely different from the fro. But it's long, it's beautiful, and it's been fabulous. It was equally as good before and after I think. I mean, the fro, it just looks a little more natural and I don't know, I just think it looks a little bit better on her as a model. But I do really like the straight on hair on her also. So I wish they did more than that, not really. Like I feel like it was the perfect amount of a makeover for her. But I don't know, the fro was really pretty. I don't know if I love the straight hair. Courtney. Gosh, she's tan. And there's not much I can do about that. Courtney. Change the color of her hair. Oh. She will be co- Is this one of my top favorites? It may just be today. Courtney, it made her skin so much more glowy and vibrant after the more copper color. Wow. I mean, I really love the styling of it. I love the haircut. I think it really changed her look up. She actually kind of looks younger after and I really, really love this color. It's amazing. Chatur London's bone structure. Bone structure like that needs shorter hair. That's a lot. Oh my God. T-shirt. This has to drastically change, but I do believe that change is good. Definitely pretty. I wish they cut it shorter. I love that they did a good amount of a change and they did a great job at lifting her hair from that really dark color to that really blonde color. But I don't know, the haircut was just lacking for me in the media styling. It's cute. Not my favorite though. I need two J's. I need a water spray. Oh no, here it comes. Just your sheet. Natalie. I did not think I would say scissors. No, wait, wait, wait, wait, wait. I know it's gonna be extra. Oh, she's gonna be so dramatic. Not only John, he's gonna wait to tie her.  Cut her hair. Oh wait. No, I can't, dude, I can't. Just put your head down, please. I can't do this. Oh my God. It's actually so funny to me how, not funny, I guess I shouldn't say funny, but it's so interesting how dependent these girls are on their hair sometimes. And like, it means everything to them. This girl is about to have a panic attack because they're cutting off her hair. It's sad, like, you're more than your hair. Hair is amazing and you can have fun with it, but you're more than it. I can't, dude, I can't. I can't do this. Just a second, John. It's literally Emma getting her hair done. Like, I'm cutting off a half an inch. She's like, you can't. Nothing's happening to your hair. Natalie. She looks fine like she is. First time you're in casting, we went model head to toe. We don't need to do anything. The real thing is you gotta trust the people you work with. We're not making decisions for shock value. Have a nice makeover. Psych. You kids are horrible. They're not changing her hair. They think her hair was perfect. It was just unnecessarily long. It was just really boring and she should have at least got a haircut. That's it. Great, great. I'm so flattered because I don't think Tyra has ever just left somebody's hair alone. Oh. Flattered? I'd be bored. Wind tunnel. So I'm gonna have Tiana's hair slicked back and juicy like a chair. One wave of hair, that's something that can blow in the wind. They screwed you over with that weave, first of all. I didn't even give you a part.    My God, I can barely see. Whoa, that's a lot of plastic.  I don't think it looks bad. It was a little bit too warm for her. I would have liked to see a more cool tone neutral blonde on her rather than a very warm blonde but you don't know, maybe they couldn't lighten it enough to make it a neutral cool. It was just like, to me, like, eh. It was cute. I like the change. It wasn't like anything like, ugh. Like, maybe I could do more. Okay, so I only had two top favorites today and they were Courtney and Foe. I think the person that takes the cake is Foe. It is sort of a more simple makeover but I just think it really works for her. I don't know, it really transformed her into a serious looking model. It was just so high fashion and pretty and I just, I don't know. She just looked amazing in my opinion. You may disagree with me and that's totally fine but let me know who your favorite was. If you would like to let me know or not. They may not let me know. But they could let me know. They could let me know. I'll let you know if they let you know. Thank you. So that was Cycle 12 of America's Next Top Model Makeovers and wow, I feel like they were more current than the other episodes we've seen and they looked fabulous. There was nothing that really stood out that was actually terrible, terrible, terrible. So I'm happy about that. But you guys, make sure you follow me everywhere else. These are all my social media handles and every single different platform. I'm everywhere at all times. This is my phone number. Yes, it's really my number. Yes, I can really see all your texts and yes, I will be picking up a few of you to respond to. So text me now. Make sure you guys check out my haircare brand, Xmodo Hair, link down below and check out our new shampoo and conditioners available on 1022. Ooh, I'm so excited. We finally have all kinds of shampoo and conditioners for you guys and they're stunning. Also, you can follow us at Xmodo Hair to learn more about all of our new releases coming up. Make sure you guys subscribe if you're not already or right down below. Click the like button and the bell icon if you would like. No pressure, but it'd be nice.  Thank you, Cassandra. I've been thinking about cutting my hair and possibly changing the top color of my hair. I've done green, blue, purple. That's it so far. I also want a haircut because it's super long. Any advice on a color and cut to me? Oh my God, I find your color right now very intriguing and very interesting. I like what's going on a lot. Honestly, if you're gonna change anything, maybe do like orange root and yellow ends but in the same variation of what you're working with now. Like I think they'd be a fun change. And then also, I definitely think you should chop it and do like collarbone length. It would look unbelievable on you. If you end up doing that, I would love to see a photo. So make sure you send one to me. That's all for today guys. Thank you so much for watching. Don't forget to live your extra life and I'll see you next time. Bye guys.


What is going on everybody? It's Stas here. Welcome back to another video. So in this video, we're going to be doing an overall market update, taking a look at the Dow Jones, the S&P 500 and the NASDAQ. We're going to be doing a quick little trading update as well as talking about a couple of stocks and ETFs that I'm personally keeping an eye on here for the rest of April in 2019. So before we do get into the topics of today's video, all I ask from you is if you find value in these videos, you enjoy the content here on YouTube, feel free to go down below and hit that like button. It really supports me and supports the channel in general. And if you're new to the channel, I have two links down below in the description box for you, one of them being the Discord group chat and the other one being the Facebook group. Both of these are 100% free of charge. And I guarantee you guys, you will find value in those two communities. So without further ado, let's just hop into what ended up happening today on the 22nd of April in the overall stock market. And it was another pretty boring day to be quite honest with you guys. The S&P 500 here ended up closing up $2.94, nothing much at all, up about 0.1% here. The Dow Jones industrial average ended up closing red down about $48.49 down 0.18%. And the NASDAQ composite here, guys, after hours, it's currently up about $4 right now, up 0.05%. But if we look and see exactly where it ended up closing, roughly about, yeah, roughly about where we are right now. So pretty much a very minimal green day in the NASDAQ as well. So guys, the market is just quite frankly, to be quite honest with you all, they've been pretty boring here over the past couple of days in terms of the indexes, right? But in terms of stocks and ETFs, there have been nice movers like there always is. Doesn't mean since the indexes are boring, it doesn't mean there's no stocks to play. But overall, the markets have been boring. So let's hop back over here to the S&P 500 very quickly and break down what I am personally seeing. So if we're just taking a look here at the five day five minute chart to kind of get an understanding of what's been going on on a closer term basis here, we can see the two levels that we've been talking about, 29.05% and 29.15%. These levels have been pretty much resistance levels for the S&P 500, right? Over the past week, we've been struggling to get out of 29.05%. We finally gapped up, got rejected twice at 29.15%, that general area. We sold off last week on Wednesday and Thursday, ended up closing the day on Thursday, roughly at around 29.05%. And today, guys, we're seeing a bit of a reversal pattern to the upside here in the S&P 500. And let me explain what I mean by that, right? We've been noticing, again, over the past week, Tuesday, Wednesday, Thursday, these three trading days, we were kind of down trending, right? Lower lows, lower highs, we ended up gapping up here, but it was still a lower high from the previous that was kind of bearish, right? We were talking about that in last week's videos. But today, take a look at what ended up happening, guys. The low here is at 28.91%. We ended up gapping up or rather popping up rather to a higher low at about 28.96% here, and another one at about 29.00 flat, which is a good sign that we're reversing to the upside. We also ended up finally breaking out of that 29.05 level of resistance. We're now maintaining it as a new support. And we actually bounced off of that support, and we closed up to 29.07, which just happens to be roughly a higher high from the previous, right? Very briefly, a higher high here, but it's still, technically speaking, here is a higher high. So let me show you guys here with this little trend line what we're seeing, right? It's kind of like, you can say, a little cup pattern now, like a little V pattern, right? We were going down for those past three days last week, right? The last three days. And now we're slowly starting to pop back up. So for the S&P 500, just keep an eye tomorrow. Are we going to maybe retest 29.15? If we do, that's a good sign that we slowly want to push to higher highs. And of course, if we break 29.15, guys, that is a one-stop shop to the all-time highs. And just judging off this 184 hour, we're looking at a couple of green candlesticks here. That's a pretty good sign that we're pretty bullish right now in the S&P. So just keep an eye on that pop tomorrow potentially above 29.15. So let's go to the Dow Jones very quickly here. Not much to say to be quite honest, guys. We're still just trading in between this level of support at 26.400 and the level of resistance at about $26,800. So what I would watch for tomorrow is, are we going to retest 26.400 possibly if we continue this little red movement that we've had from today? Or are we going to pop up, let's say the markets do well tomorrow, the S&P pushes up? Likely the Dow will follow. Let's say we end up popping up and retesting or testing rather that resistance at 26.800. That is what I'm watching. But as of now, we're just simply trading in between old support levels, right? Well, now they're new support levels at 26.400 from back in September of 2018. And we're trading at or under rather a resistance from back in the middle of September in 2018. So this general area and if we break out of the 26.800 level, that is really the one-stop shop to the all-time highs. And for fun, let's just see how far we are right now roughly from these all-time highs on the Dow. We're about 1.6% off. If we're going back to the S&P 500 very quickly, we can see from about 2907 roughly up to about 2940, we're roughly about a 1.1% off from the S&P 500. And you all know by now the NASDAQ actually ended up hitting, was it today? Actually, we hit an all-time high again today, but we broke the all-time highs from back in October on the NASDAQ. A couple of days ago, it was last week. So pretty much guys on the NASDAQ now, we're at all-time highs, right? So we're not fighting to get to that all-time high resistance. We're just continuing the uptrend pattern here, right? We're looking to maintain the previous all-time high at about 77.30-ish, which was a resistance. Obviously, we broke the all-time high. Now it's a support. We're looking to maintain that level as a new support. So everything is looking pretty solid right here, right? We got the little pullback, the retest on the support on the 50-simple moving average here. We bounced on that. We pushed to a higher high. Everything in terms of an uptrend is looking juicy right now in the NASDAQ. And let me just hop here. Let me make sure we hit that all-time high today, because I'm actually not too sure with you all. We actually hit it after hours here, guys. Take a look at that. 4.22, which is today, 4.30 pm Eastern Standard, about 30 minutes after the market. This ended up trending up. And again, this is the future. And it's at about 77.46. So yet again, guys, another all-time high was set today, 30 minutes after market hours in the NASDAQ composite. We're trending down a bit. So just keep an eye on it. Are we going to continue to push to all-time highs? That is what I'm watching in terms of the NASDAQ. So what did I end up doing today in terms of my trading, guys? Day trading? I didn't make any day trades today, to be completely honest with you guys. But I have a bunch of stocks on my watch list right now that I'm honestly looking to swing trade and day trade, depending on how the overall market ends up performing these next couple of days. But what I did do today is I actually re-entered into Apple. So for those of you all that watched my video earlier today and if you didn't watch that video after this one, it's extremely valuable. I talked about trading during earning season, a warning to trading during earning season, what you should be cautious about. That is what that video is about. But in that video, I actually mentioned how I already got back into Apple today, guys. Apple saw a pretty solid dip in its price this morning. We sold off pretty rapidly, actually, down to about 20247. And at this point, we tested that simple moving average of the 50 SMA here on the 20-day one-hour chart, right? We sold off aggressively. And I mentioned last week that if Apple were to pull back this week, which it did, I was going to re-enter. That's exactly what ended up happening. I re-entered on the pop-up to about 203.25 or something like that. It was a very quick move here. But I did end up building a little position on this pump-up here. So I got into Apple, and I do plan on swing trading this one with the goal of selling it sometime this week, to be completely honest with you guys, because earnings is coming up on the 30th for Apple. And like I mentioned in that video that you guys again should watch after this one, I don't really like swinging stocks through earnings. So the goal here is to hop out hopefully with about a 2-3% profit this week on ticker symbol AAPL. And honestly, guys, that's all I'm doing right now in terms of my trading. Again, the markets are near all-time highs, right? I'm being very cautious at this point in terms of my swing trading because the markets are at all time highs. It's earning season. The big companies are reporting earnings. Who knows? Things can go sour very quickly, especially if some of the big names like Apple, Google, Amazon, right? If they report poor numbers, their stocks go down. They have a heavy weight on the market. They have a lot of influence on investors and traders out there on the market in general. You know, this could send down the market. Who knows, guys, right? So I'm being very, very cautious here and I would love to know what you guys think about that, right? Are you being cautious right now since we are itching to all-time highs, inching to all-time highs in the stock market right now? Drop a comment down below and let me know what your thoughts on that are. I would love to know. So let's just talk about a couple of stocks here that I'm watching and ETFs that I'm watching here for this upcoming, really the next coming days here towards the end of April. There's a couple that come to mind, right? So Square is one that we talked about in yesterday's video. We talked about how it was trading or it is trading rather in this range, this horizontal channel from about $70 up to about $78 to $80. What do we see today, guys? We got the perfect bounce right at that support level, nice 2.6% a dollar and 84 cent a day today in terms of Square. And this is what we needed to see, right? So this is definitely one I'm watching tomorrow for the potential continuation up to maybe the 50 Simple Moving Average Resistance that's been a resistance here over the past couple of days and the 180 SMA resistance, which again, has been a resistance over the past couple of days. But what I want to warn you guys, just because we bounce on the support, you should still be approaching this one with caution because A, there's an earnings report coming up. What date is this one on? I think it's the 1st of May, right? Earnings report on the 1st of May. And we're seeing overall, it's still kind of a bearish trend right now on the 184 hour, right? The 50 SMA is crossing below the 180 SMA. We're at technically right here a lower low from the previous. So if we do end up getting rejected here at a lower high from the previous, that's just going to push us in my opinion below the $70 level of support. And at that point, we're going to be free following in square unless the earnings report ends up popping it back up, which who knows if that's going to happen. That's just what I'm watching and being cautious and mindful about in terms of squares. So another one, what's that other one guys? Oh my God, I'm blanking out right now. JNUG. JNUG. Oh my goodness, JNUG. This one has been getting absolutely pummeled guys, right? Absolutely pummeled. Where is it? Here it is. JNUG is a gold bull ETF, right? Whenever goal is going up, JNUG is going up in price. And what do we notice here guys? JNUG has been hitting supports and smashing through those supports day after day here over the past couple of trading weeks, right? We were holding above $9. We had some hope at this point for JNUG. It broke that level, right? We were holding $820, $830. We were talking about that one in a couple of videos. In the group chat, we broke that one very, very quickly. And now we struggled to even hold above the $8 level of support. And we had another 6% down day today guys. Now we're just hovering around the $730 level. And notice we're getting to levels that we haven't been towards in JNUG since November, the October, September days. So this price, although it's a falling knife, right? That's very obvious to see here. Although there's no confirmation that it's finding support and reversing to the upside, it's still one that I am heavily considering trading and one that I'm heavily watching. Because stocks that get battered like this, or ETFs that get battered like this day in and day out, there's going to come a day. It's just inevitable, right? Where they're going to bounce back up aggressively. And it's likely there's going to be a couple of days in a row when it bounces back up aggressively, right? Just take a look at JNUG's stock, the price action over the past couple of months, right? It's not really predictable. It's not a beautiful chart by any means. But what do we notice here, guys? Take a look. This stock got battered, or ETF rather, I always mix those up. But this one got battered $11 back in August, down to $9. And then we had a couple of rebound days back up to actually, no, $7 got battered down to then we rebounded back to $9. And we got battered down again to $660. And we rebounded back up to $950. We got battered down again to $6. And then we doubled our price, or rather we rebounded back up to $10. We got battered down again to what price was this, $8. Then we rebounded back up to $12. So typically, guys, every single time, there hasn't been a time where it's just gone down nonstop without having a rebound. So just keep an eye on the rebound, guys, and keep an eye on gold. Once gold does show a nice strong rebound, Jnug is going to follow. And at this point in time, gold is out of support at about $12.75, $12.76, roughly. And over the past couple of trading days, it's been holding that level quite nicely. So keep an eye, if we do end up popping up here, Jnug is going to reverse pretty strongly. And I can bet, honestly, that we're going to see at least a 10-20% move in Jnug over the span of a couple of days once gold does end up reversing, because it's judging off the price action, guys. That's what historically has happened, right? So that is one, probably, in terms of ETFs, the number one that I am personally watching here. Let's take a look. I saw Facebook did very well today. This is what I want to talk about. We ended up bouncing on the 180 level of support. Finally, guys, we're trending in the middle, roughly, of this channel from 180 up to about 185. So tomorrow, if we get a pullback here on Facebook, this one's going to be interesting, although we do have earnings in two days. Most likely, I'm going to be waiting until after earnings. And I'm a long-term investor in Facebook, so if I miss the move on a swing trade, that doesn't bother me, because let's say the earnings push it up 10%, that's probably not going to happen. But let's say hypothetically, that does happen. I'm making money on my long-term position, right? And I wouldn't be that mad about missing out on the swing trade, right? So I'm just keeping an eye on it, right? Looking to enter on a potential pullback. If the earnings, the guidance, everything's looking good, right? I'm looking to enter into Facebook stock. So let's take a look at some other ones. Oh my God, I'm blanking out right now, guys. I had a couple in my head before recording this video. Let's talk about AMD very quickly. AMD has been one of those stocks that we've been talking about that's been trading in between this channel here, if we go to the 20-day one hour, this channel between $27.15, roughly, and $28.09. And we've struggled, guys, over the past week and a half now to hold that $28 level and advance to the next resistance, which at this point is around $30. So until we see that slow pop up into the mid-28s, I'm staying away from AMD because I'm scared it's just going to sell back off to $27 and just continue this repeating pattern of up and down, up and down. So until we pop up, that is one that I'm not really going to be playing here, but it has honestly been offering some nice day trade potential. If we look on the one day, one minute, this would have been an amazing day trade today. I know a lot of people in our group did end up day trading this one. So if you did, let me know down below in the comment section and congrats to you because, hey, it did very well today. But we are noticing a resistance again, but it is just simply maintaining that level of support, but an overall resistance around the $28 level as well. This is just really maintaining or really containing the price of AMD around this general area here. So guys, I'm watching AMD, Apple, Facebook. Those are probably my three main stocks here, Square as well. Those are the four main ones that I'm watching here heading into tomorrow. And Jnug as well as D-Gas and U-Gas. Those are three ETFs that I'm watching. And what's the other one off the top of my head now? I think that's all we talked about in today's video, guys. So keep an eye on those as well as Tesla might as well throw this one in because they are reporting earnings on the 24th. Tesla stock actually did very poorly today, down about 4%. It's testing the support here at around 262.263. Can we maintain that? After earnings, what's going to happen? A lot of people think Tesla stock is going to crash through the roof. Others think it might not do anything, right? But I'm waiting, of course, till after earnings to see what ends up happening.  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So I'll catch you all in tomorrow's video. Good luck tomorrow. Enjoy the rest of your night. Peace out.


Hello everybody hooded Cobra Commander 788 here. It's time for another vintage G.I. Joe toy review and we are going to do a toy review in this video but a large part of this video is going to be a rant so I'm warning you now. We're going to look at the 1987 G.I. Joe 3 pack Cobra Law. In last week's video we looked at the 1986 Cobra Emperor Serpentor and as I said in that video that character really represented the line for how much fantasy I was willing to accept in the G.I. Joe universe. The characters we're going to look at this time not only crossed that line they blew by that line at Mach 3. I've read the message boards and I've read the Facebook discussion groups and I know there are some of you out there that just love Cobra Law and love Serpentor and if that's you that's great. I don't want to change your mind if you found something in this world that you enjoy fantastic keep it but I'm warning you right now this video is about my opinion and it may strongly disagree with yours so maybe you accepted all the weird stuff in G.I. Joe they introduced in the later years maybe none of that stuff crossed any line for you you thought it was all great and if that's the case that's fantastic but every fan still has a line even if it's only a theoretical line every fan has a line at which if it's crossed they're going to say no this doesn't fit in this group so even if you accepted all the weird stuff they introduced in later G.I. Joe the aliens the spaceships and all of that I'll just bet if Hasbro had presented a G.I. Joe Smurfs crossover every single one of you probably would have said no that doesn't make any sense and I don't like it so wherever you draw your line which is probably somewhere short of G.I. Joe versus Smurfs I respect that I completely respect your line and your right to draw your line wherever you choose it's a free country this video however is about my line so if you love Cobra Law and you can't stand to watch a video of someone who strongly disagrees you might want to stop this video now no more warnings after this we're moving forward we've got a lot to say about Cobra Law so let's look at the toys here they are this is Cobra Law they were sold in 1987 and 1988 as a three-pack it included all three of these figures this is Galobulus the Cobra Law leader this is Nemesis enforcer he's sort of like a second-in-command I guess he is the Will Riker to Galobulus's Captain Picard or perhaps he is the Igor to his Frankenstein and then we have the Royal Guard and they were like Cobra Law troopers let's look at some accessories Galobulus came with a weird little laser pistol that I don't have and I don't care Nemesis enforcer came with bat wings because he's a vampire or something they're kind of small bat wings not big enough to help him actually fly you can just imagine them as larger wings I guess they pegged into his back he also came with a set of tentacles which I don't have and I don't care these bat wings are made out of kind of a rubbery material and I bet if you tried really hard you could rip them right in half the Royal Guard came with this big size thing odd shaped bladed weapon he also came with a pistol and an antenna that stuck on the side of his head I don't have either of those and I don't care let's look at me individually now starting with Galobulus and wow he has an unusual piece of anatomy this top part of the figure is like a normal action figure it's put together and articulated like any other normal GI Joe action figure the bottom half however is well this long female pleasuring device you can see it is ribbed for her pleasure it is a bendy snake tail and it does bend somewhat it actually doesn't bend as much as you'd want it to it does not bend enough to like coil around and create a stand for the action figure so you can kind of stand up on a snake leg so it really kind of is more of an impediment than an awesome feature how you are supposed to stand this figure up I'm not sure I guess you can kind of do it that way behold the mighty Galobulus pay no attention to the highly suggestive tail that is pointing directly at you the sculpting has some detail to it you can see he has this kind of red thing that goes around his head and covers an eye looks like a pretty grotesque eyeball there and he has some veins on the top of his head looks kind of like an old school Hollywood horror monster he has this red body armor which is file card says is actually crustaceans these are living creatures that he's using as body armor and they are bred for their super strong shells so this is supposed to protect him it looks extremely ridiculous we've got like some details of crab legs on here it looks like you know he stumbled into the buffet at Red Lobster alright so just imagining this is extremely strong armor made up of crustaceans and suppose this really works alright let's just imagine that this armor makes sense even if this armor is great he missed a few spots so he's gone through the trouble of creating this living armor but he's left a lot of his body parts completely vulnerable his right arm continues the red crustacean armor theme with these armor plates and up here I can't tell if this is just the paint worn off or if this is an unpainted detail but it looks unpainted and it looks terrible he's got whatever that is I don't really care what it is this figure has a crack in the torso and I do not care and his left arm for some reason is green with red veins and I don't know why and I don't care okay let's look at Nemesis and Forcer and this guy is super purple and he's got a lot of textured pattern all over his body the figure itself is really not all that detailed in place of detail we have texture his whole body has this sort of grainy texture all over it really from head to toe having the texture is kind of cool we didn't normally get this sort of texture on regular action figures but it doesn't really correspond to a more detailed action figure we have a little bit of detail we have this whatever it is and I don't know maybe this is more crustacean armor I don't know on his legs we have what looked like they should be either holsters or sheaths for some kind of weapons but when I checked the weapons and accessories that he came with I didn't see anything that would fit these so what these are for I don't really know on his elbows we have these spikes these spikes come out of his elbows and that's kind of cool that might have been a nice feature on a better action figure so that's not bad then he has these shoulder pads that look like they should be part of the shirt that he's wearing they look like they're armored and they have that same texture pattern but they are unpainted this is an unpainted detail and honestly this looks terrible unpainted details are a problem on any figure but on a figure like this where they're trying to introduce a very outlandish fantasy element to G.I. Joe this figure all of these figures really need to be done well and this is not done well this is it just looks bad it looks cheap look at this his zipper it's under a big W that's a movie reference all you young kids can Google it that's Nemesis enforcer now let's look at the Royal Guard he is a bug face and he has this weird asymmetrical pattern on his head he has this collar on here doesn't hinder the head movement all that much if you care about that sort of thing some really high shoulder pads that's really bizarre-looking got more red armor maybe this is more crustaceans I don't know he's got gray pants he also has some pads on his elbows but these pads are just bizarre-looking the shape looks more like the armrest on your grandma's old chair elbow pads should be cool that should be a really cool feature but they managed to find a way to make them uncool he's wearing a gray belt and keep in mind that according to the file cards all of Cobra Laws technology is based on living organisms so apparently this belt and his clothes this is not like modern technology this is supposed to all be based on living organisms even though it looks like he's wearing a belt he picked up from Target he has some barnacles on his legs and he has some red boots and there you go that is the Royal Guard let's take a look at the file cards that also came with the figures they each had one let's look at them quickly here's Galobulus's file card read that quickly there's nemesis enforcers file card you got that and there's Royal Guard that's his file card there we go I have to confess though these file cards are not badly written I don't know who wrote them but whoever did really made an effort to try to make them sound interesting and cool it doesn't work it still doesn't make a whole lot of sense but somebody really did try to make chicken salad out of something that wasn't chicken salad all of these characters were introduced in the much-maligned 1987 G.I. Joe animated movie and according to that movie Cobra Law facilitated the creation of the Cobra Emperor Serpentor so they took Serpentor a character I only barely accepted as a part of G.I. Joe and was just this side of nonsense and decided that no it needed to be complete nonsense so they added this Cobra Law element to it which was totally unnecessary and totally screwed up a barely acceptable character Cobra Law was not included in the origin story of Serpentor and the G.I. Joe comic books because Cobra Law was not in the G.I. Joe comic books because the comic books at least tried a little bit to make some sense so why doesn't Cobra Law fit in G.I. Joe to understand that you really have to look at the cultural context in which G.I. Joe was introduced the new G.I. Joe line was introduced in 1982 this is the early 80s and America was kind of coming out of the hangover that was the 70s of the Vietnam War had really kind of scarred the national psyche and by the 1980s Americans were really ready to feel better about themselves they wanted to feel strong again they wanted to feel powerful I wanted to feel righteous and just so that was the 1980s we were entering into a new phase of the Cold War it was an era in which we felt like we had the upper hand and a lot of our media and our toys for children reflected that the movies were great because in the movies America could always win these movies made us feel better about ourselves and made us feel powerful a lot of the movies were about the Vietnam War Hollywood fought the Vietnam War for years after it ended and you know what in the movies we tended to win more often than we lost so along comes G.I. Joe in 1982 and it really feeds on that national mood I honestly think if G.I. Joe had come along a little bit earlier or maybe even a little bit later it would not have been nearly as successful as it was but it hit at exactly the right time and it gave us a lot of toys that were symbols of American might we got Jeeps we got tanks we got jets but we didn't just get the toys we got something more one thing that sets the toy lines of the 1980s apart is that they didn't just give us pieces of plastic they gave us entire universes a lot of them had media tie-ins so we didn't just get the toys we got universes we got characters that we had grown to know and care about through cartoons and comic books so this is the world in which I was introduced to G.I. Joe I used to get these things with with the pages books I had these books that I would look things up in I had an encyclopedia of world military weapons whenever I would get a new G.I. Joe toy he had a new gun I'd look it up I'd try to find out what real world thing was this representing I loved it it was educational and it built this fantasy that was very appealing to me because the fantasy drew upon things that I was seeing in the real world it made the fantasy feel more real so I did a figure like grunt and I'd see okay he comes with an m16 rifle so I'd look that up in a book and I'd see okay this looks like a 20-round magazine he's only gonna have a couple seconds of sustained automatic fire so I'm gonna have him firing this weapon on semi-automatic so he doesn't run out of ammunition too soon there are no bullets it's just a piece of plastic I could have pretended that he had infinity bullets but that's just not how I played I wanted to integrate some real-world elements into my playtime and that enhanced the enjoyment for me there are always right from the very beginning science fiction elements in G.I. Joe but they were never so far out there that I couldn't sort of just kind of bring them home and make them a part of the G.I. Joe that I loved so that's the kind of G.I. Joe fan that I was and everything was pretty good between me and G.I. Joe up through 1986 when things started to get a little bit weird they introduced the cobra emperor Serpentor which was a character I didn't really like I didn't think he fit within G.I. Joe but I reluctantly accepted him but then in 1987 the G.I. Joe animated movie hit my memory of that time is a little bit fuzzy but the best I can kind of reconstruct it is I don't think I saw the animated movie in 1987 because I remember after seeing the animated movie I had a very immediate strong negative reaction and I essentially stopped buying G.I. Joe figures but I know that I had some 1988 G.I. Joe figures in my collection so I think I saw the 87 movie in 1988 I may have rented the tape or I may have seen it on TV I can't really remember the first time I saw it but I think it was in 1988 always had an uneasy relationship with G.I. Joe in the animated form it seemed like the G.I. Joe cartoon series was written for younger kids or maybe not younger kids but definitely kids who had a different vision of G.I. Joe than I did definitely not for the type of fan that I was the G.I. Joe comic book I think more closely resembled what I envisioned for G.I. Joe and I understood that you couldn't show a lot of violence and death and injury on children's television and it's not that I wanted to see a bunch of violence on TV it's not that but even at that age I understood that war has a human cost so when you're showing me these laser battles with people shooting laser guns all over the place and nobody ever gets hit and nobody ever gets hurt I knew you were bullshitting me but in a movie they're not constrained by that so I was hoping that in the G.I. Joe animated movie we would get a form of G.I. Joe that's animated but that's more honest and more mature instead what we got was snake people snake people or bug people or flying bat people I'm not really sure what they were supposed to be the concept is a little bit on incoherent but some kind of mutants from prehistory there were some good moments in the G.I. Joe animated movie and I don't want to imply that there weren't there were absolutely some good moments in that movie but the good moments are far outweighed by things that don't make any sense things that are just weird and things that that trash everything about G.I. Joe that they had been building up over the last several years they just took it in a completely different direction to me it seems like some executive somewhere looked at he man and saw that hey he man is making a lot of money kids are buying a lot of he man so instead of coming up with their own sort of knock off of he man or something like that they shoehorned these he man villains into G.I. Joe one of the worst things about that movie is what it did to Cobra commander when I was a kid and my friends who are not G.I. Joe fans saw Cobra commander in the cartoon or the toy or whatever they always wanted to know is he a snake man does he have a snake face behind that mask and I would always explain no he's not a snake man he's a regular person and that is something that's a lot scarier snake people are not real that's therefore not all that scary but what Cobra commander represented was something more tangible something that was evil in the real world at the time we were playing with G.I. Joe there were real terrorists hiding behind masks and doing horrific things high hijacking jets and blowing things up and so what Cobra commander represented was something more real and more terrifying than any snake man so what did the animated movie do it turned him into a snake man and then it turned him into an actual snake so on the one hand the movie completely trashed everything I liked about G.I. Joe and then it gave us Cobra law which was a purely fantasy element it was this ancient civilization of mutant people things and their society their technology was completely built on living organisms they didn't like human technology even though they were trying to steal a piece of human technology to carry out their nefarious plans which doesn't make any sense the whole thing's just nonsense I could talk more about what was good about the G.I. Joe animated movie more but that's not what this video was about when I first saw the movie I was crushed it wasn't just that the movie was not written for the type of fan that I was it almost seemed like it was written to reject the type of fan that I was it's almost like they intentionally wrote this thing to be repulsive to the type of fan that I was it's like they were trying to get rid of me when I saw the G.I. Joe animated movie I got one clear message and that message was this so G.I. Joe wasn't for me anymore they took it in a completely different direction maybe the people at Hasbro figured that fans like me we're getting a little bit too old we weren't buying enough toys so they were just gonna completely gear it in a totally different direction to attract different types of kids and as far as they were concerned I could just go jump in the lake I don't know if that's the message they were trying to send but that's the message I received and I received it loud and clear there's an interview out there on the internet of Buzz Dickson who was involved in producing and writing the G.I. Joe animated series in which he essentially disclaims the creation of Serpentor and Cobra Law the decision to take G.I. Joe in that direction came from Hasbro came from Hasbro executives the name Cobra Law was supposed to be a placeholder name and it was a takeoff of Shangri-La they were supposed to come up with a better name for it before the movie actually you know reached production but Hasbro decided they love the name so we're sticking with it we're gonna call it Cobra Law even though it's a ridiculous sounding name and that of course led to the battle cry that Cobra Law used in the movie I do not blame the creators for any of this the way G.I. Joe was developed there was one group of people that designed the characters and then there was a separate group of people that created the universes that these characters existed in in the cartoon and the comic book and then there was yet a third group of people the marketers at Hasbro that decided what was going to be in and what was going to be out now throughout the history of G.I. Joe in the 1980s most of the time those relationships worked really well to produce a really great product that kids loved but sometimes the ideas just did not mesh I want to be clear I don't just mean Cobra Law doesn't fit very well in the G.I. Joe universe it's not a very good concept all on its own it's incoherent the characters look a little bit goofy I would not have been interested in it even if it hadn't been shoehorned into G.I. Joe but a lot of kids liked it and that doesn't make it good a lot of people like those real housewives shows that doesn't make them good a lot of kids liking it doesn't make the concept anymore coherent it doesn't fix the unpainted details on the action figures it doesn't improve anything that's bad about them it just means a lot of people like something that wasn't very good that happens every day and if you liked it that's fine you don't even have to have a reason for liking it you can just like it because you like it you can like Nemesis enforcer because your favorite color is purple it doesn't matter you just like what you like and that's fine but one thing that really bugs me is all the excuses I hear for Cobra Law at least they were trying something new to give them a break trying something new you get no points for trying something new zero points the fact that it's new doesn't make it good every idea whether good or bad has been new at some point so you can't judge ideas based on that you have to judge ideas on their own merits G.I. Joe is not a documentary it doesn't have to be realistic it didn't have to be perfectly real lighten up well of course it doesn't have to be perfectly real in fact if you think about it it's entirely a fantasy even the somewhat realistic military stuff isn't completely realistic it's not how the military really works it's all a fantasy that's not the point the point is the fantasy world that was built for G.I. Joe looked very much like the real world so yes there were these fantasy elements from G.I. Joe but the characters walked around a world that looked very much like ours so when you throw in this entirely fantasy element that's totally out of the blue totally doesn't match anything else it does not enhance the fantasy it breaks it and it's not that I didn't like science fiction and fantasy I liked a lot of these other toy lines like Star Wars and Transformers and all of these and those each had their own fantasy world built for them so for instance if you were watching Star Wars and in the background you saw an F-14 fighter jet even if Star Wars is awesome even if the F-14 fighter jet is awesome if you put those things together it totally breaks the fantasy it pulls you right out of that fantasy world like if you had tried to put Smurfs in G.I. Joe it doesn't fit and neither does Cobra Law it's it's a children's toy got to look at it from a child's perspective it's for the children children children's toy children when this stuff came out I was one of the children and as a child I was a lot less merciful on these toys than I am now I'm all sunshine and rainbows now compared to how I saw these toys at the time I was really bitter at the time I'm not bitter anymore can't you tell I hate how this excuse is trotted out to explain away crap toys I don't know of any kid that likes playing with crap toys so I gave you a snake man that's half a snake and his tail is bendy but not enough so you can't stand him up you can't call him around it's a crap toy so looking at it from a child's perspective does not make a crap toy any better well it is shit but kids like playing with shit so it's for the kids when I was thinking about what I was going to put in this video there was one question that kind of stumped me and that is why did it matter to me the G.I. Joe animated series never defined the G.I. Joe universe for me the comic book did the G.I. Joe animated series always had weird things in it that I just thought were dumb and I just kind of ignored so why couldn't I ignore Cobra Law just like I ignore ignored everything else in the G.I. Joe cartoon the best answer I could come up with is by the time I saw this movie in 1988 I would have been 12 years old and that's getting a little bit old to be buying toys a lot of my friends had transitioned from buying and playing with toys to starting to be interested in girls and sports and things like that and I was still buying G.I. Joe toys because I really liked them at that age you're starting to get concerned about being cool and G.I. Joe just isn't cool anymore but I could still point to the fact that G.I. Joe was a lot more sophisticated than a lot of the other toys and things out there at the time for kids so there was still that there was still something more to G.I. Joe than just a children's toy but then when I saw this movie and when I saw what they did to G.I. Joe and when I knew that when my friends saw this I knew what they would think about it it was very disheartening I knew I couldn't make that claim anymore G.I. Joe was just for children what that meant for me is I was officially too old for this stuff the phase of my childhood in which I spent countless hours building these fantasy universes with these toys and watching cartoons and playing that was coming to an end and I knew it G.I. Joe was the last thing that I gave up from my early childhood but it was time for G.I. Joe to go it was time for me to transition into the teenage years and that was not an easy transition for me for other reasons not because of G.I. Joe but that break from G.I. Joe was a symbolic one it sticks with me in my mind as the beginning of not a very easy phase in my life so despite the fact that I got years of enjoyment out of G.I. Joe my last experience with G.I. Joe was a very negative one when I look at yojo.com and I look at which figures came out which years you can I can really tell when I watched that movie because anything that came out after I saw that movie in 1988 I didn't have any of it I didn't want any of it no that's not exactly true that's not exactly true there was one thing that I know I got from the 1989 G.I. Joe series and that was version two of rock and roll and I got it for nostalgic purposes I liked rock and roll way back in 1982 and they gave us a pretty cool update of rock and roll and I thought that was pretty neat I enjoyed that I got it for nostalgic purposes but not to play with it wasn't playing with toys at the time I just wanted to own rock and roll one more time that makes me wonder what might have happened if there hadn't been a Kogrelaw if there had not been a G.I. Joe animated movie or if it had been done differently if it had been geared more toward the type of fan that I was I know there are some G.I. Joe collectors that didn't stop collecting as a child and then like I did later pick it up again as an adult they made the transition from collecting as a child for the purpose of playing to collecting as a young adult and as an adult for the purpose of owning and collecting and displaying and I may have made that transition I was on that trajectory I was still enjoying these toys at the time I saw this movie so I might have made that transition it wasn't so much me that left G.I. Joe it was G.I. Joe that left me it was G.I. Joe that filed for divorce I just had to accept it when I got back into collecting as an adult I was going through a very difficult time in my life and I was looking for something that represented an earlier time when I was completely happy I was wanting to go back to a time in my life when I didn't have anything to worry about when life was good and G.I. Joe is what fit that bill nothing else really even came close transformers Star Wars weren't even considered it had to be G.I. Joe that's how important G.I. Joe was to my childhood but we have to look at all things with our eyes open nothing no matter how good it is is ever purely good there are good and bad things about everything and so I wanted to make this video to talk about something that I didn't love about G.I. Joe I might even say I hated it about G.I. Joe because I thought it needed to be said but and because I wanted to be honest about my feelings regarding this particular aspect of my hobby so now that I've said my piece I think it's time to go to something else I think it's time to look at something that I loved about G.I. Joe let's get back to the fun and we're gonna do that in next week's video I hope you'll join me I'll see you then thousand years ago the glory of Cobra la dominated this planet but an age of ice destroyed much of what we had built and with it began the time of the barbarians surprisingly they evolved if you ask me some of them did not evolve and gradually they master the technology


Now, if I put here a parameter t, which runs between 0 and 1, so for t, I can also put t in front of here. This will be a homotopy through for whole maps between, you know, for t equals 1, I have exactly the complex that I have, but for t equals 0, I will have just the terms that I have written down on the blackboard. So what we have actually for t equals 0 is a sum of two complexes, which we have already seen before. So what was that? So the first complex was 0 goes to 0, goes to gamma s plus, gamma s minus 0, and here is dA plus, and the other complex was 0 goes to omega 0, omega 1, omega 2 plus, 0, and we have just d and d plus. Now what you can easily see is that the determinant of dA plus, so what is that? This is the determinant of the kernel of dA plus, well, you know, lambda top, tensor, lambda top, the core kernel of dA plus, but we can identify this with the, you know, the kernel of dA minus. Now the point is that both dA plus and dA minus are complex linear operators, so in particular the kernels are complex linear vector spaces, and they always have a preferred orientation, at least if you fix your convention, right? So conventions are not really uniform, you have to be aware of that, but once we fix the convention, this is always R, okay? Now it's also easy to handle this complex, right? So the corresponding operator here is d plus plus d star, and if you take the, if you want to consider the determinant, so we have the kernel of this is just h1mR, well, we have this always purely imaginary, and the core kernel is also easy to compute, this is just h0. Let me just write h0 plus h2 plus, and these are spaces which are defined, which are determined by the topology of your form manifold, so you may ask to, or you may orient these spaces, and this doesn't depend on the smooth structure. So the upshot of this discussion is that an orientation of those homology spaces actually determines you an orientation, or a trivialization of the determinant line bundle. So let me write this down, so very good. So we now have all the ingredients that we need, and let me state this formally, so we have a right at our main theorem, and the theorem is this, so assume v2 plus of m is at least 2, then mg eta is a smooth compact oriented. So I write oriented, but I should have written probably orientable, and with choice of orientations of homology groups we have oriented manifold of dimension d, and d is a number which already disappeared from the blackboard, but you remember. And this holds for generic g and eta. So any two choices, g0, eta0, g1, eta1, m, g0, eta0, and m, g1, eta1 are oriented. So by now you actually know already the proof of the theorem, maybe the only thing what I need to say is, why do we require v2 plus at least 2? This is something that we have already discussed. This is because if you choose g0 eta, so two pairs of parameters, we want to connect them by a path, and we want to consider the module as a parameterized modular space, and we will avoid reducibles whenever v2 plus is at least 2. This is where it appears. Okay. Now let me come to the point. So this hybrid variant, here is what we have. So I will pick any m0 in my base manifold m, then what I have, I can take any map as values in u1, and I can evaluate this at the point m0. So I have a map into u1. This is clearly surjective. And the kernel of this is denoted by g0. So this is just the subset of all those gauge transformations which are identity at the point m0, and we have the following exact sequence. Okay. Now what we have is I can take m hat eta to be the space of all solutions psi eta such that sw eta psi eta is 0, but I will divide this by the base gauge group g0. And now what you see here is the rest of the actions. So we have an action here by u1. And if I quotient by u1, I will get my original modular space back. In other words, what I have is m eta hat fibers over m eta, and the fiber of that is u1. In other words, we have a principle u1 bundle over the modular space. So this is principle u1 bundle. And let me denote by mu its first 10 class. Okay. Now, so it was not explicit in the notations here, but implicitly just to define those modular spaces, we have chosen a spin C structure. So I have here made a choice of sigma in S m. And this is the set of all spin C structures. Okay. Now I can define the cyberquidding variant relative to this choice of a spin C structure. So sw of sigma is defined to be an integral over m eta of mu to the power d by 2 whenever d is even, or it's zero otherwise. And so with the work that we have done so far, you know that this number that I have defined does not really depend on the choices, so that we have an orient, we have a number. Well, if you want to be strict here, this the cyberquidding variant is only the absolute value of the cyberquidding variant is well defined, right? Because we have made here the choice of orientation, but if you can fix your underlying topological form manifold, then you can make sense of this as an integer. So if you combine all this, this is just a map from S of m into Z. And the basic property that, so this is the cyberquidding variant. The basic property that this variant have is the following, sw vanishes on all, but finally spin C structures. And the proof is not really hard. This follows from the prior estimates that we have had already before, but this is an exercise for you, so you will solve this today in the afternoon. Okay, so let me finish this lecture with a sort of collection of results that you can obtain with the help of the cyberquidding variant. So there is no time left for proofs anymore, but I thought it may be interesting to see where this could be applied to. In any case, one of the first theorems in this area was by Witton. So if m admits a metric of positive scalar curvature and b to plus of m is at least two, then the cyberquidding variant vanishes identically for any spin C structure. And again, the proof is sort of, just follows from the Weissenberg formula. So that's something that you can prove on your own. Now the next result, this would be all sort of, the whole theory could be absolutely boring. It could have happened that we would end it up with a very complicated description of the zeroes map, right? And that would be very disappointing. But Taub's proved very general statement which tells you the following. So assume m is symplactic, and as always we assume that b to plus is at least two, then the claim is that the cyberquidding invariant of m does not vanish. The statement is a little more precise, but I don't want to go into details here. Should I explain what a symplactic manifold is? Okay, now, so this gives you lots and lots of examples where the cyberquidding invariant doesn't vanish, so you know that your invariant is an interesting one. Now, so by the way, you can play here and you can combine those two results. So if you know that b to plus of your manifold is at least two, then either, so if it admits a symplactic structure, it doesn't admit a metric of positive scalar curvature and vice versa. This is the only way I know, which shows you that a priori there is no reason to expect that symplactic structure is related in any way to metrics of positive curvature, but this actually tells you there is set in relation. Okay, so yes, and CP2 is also not a count example. So another result is the following theorem, usually attributed to Whitton. So who gave us a sketch of the proof is, the statement is as follows. So assume M1 and M2 have both b to plus at least one, then the cyberquidding invariant of the connected sum M1 with M2 vanishes. Do I need to explain what the connected sum is? Okay, so what this result tells you is that you can interpret this in the following way. So assume you know that the cyberquidding invariant is nonzero and you try to decompose your manifold into simpler building blocks, but here simpler building blocks would mean manifolds with b to plus at least one and you will establish this as impossible. And one more result, so I wanted to show you is the theorem of Donaldson, originally proved by Donaldson much earlier by other methods, but you can prove this with the help of the cyberquidding theory is that there are many topological closed four manifold which do not admit a smooth structure. So I don't want to specify what many means, but this is really a huge sort of family of four manifolds which are, you know, where you have an atlas where transition functions are continuous but can't be made smooth or, you know, ck for k say two or something. Okay, and one more result which is sort of complementary to the last theorem is the following. So again the results that I will state in a minute was proven earlier by other means but still it's interesting to state I think. So what I mean by fintechel and Stern is that there are infinitely many manifolds over here I should say well let me just say manifolds of dimension four say parameterized by some number which are homeomorphic pairwise non-defilmorphic. So in other words what so what you can say is that if you take four manifolds and there may be a sort of topological four manifold then there may or may not be a smooth structure and if there is one it may happen that there are infinitely many of those smooth structures. Okay, thank you very much for your attention it was pleasure for me and if you wish please give me the evaluation forms back.


4 Activities for Teaching Future Tenses in the ESL Classroom In a previous post, we looked at various teaching ideas for future simple, and here we are going to describe some fun ideas for teaching three other future tenses. There are a wide variety of usages for future tenses, and it's always important to make sure your activities focus on the usages that you've taught in your lesson. For example, future continuous can be used to talk about an ongoing action at a point in the future. A fixed future event, polite enquiries are to predict the future or the present. Predicting the present is one that students often have trouble conceptualizing, so we might as well start from there. Predicting the present. When someone we care about is going on a long journey we often think about what they might be doing at any given time. When we do this, we typically use the future continuous tense, such as Rosie will probably be getting on the plane about now or don't call her now, she'll be cooking dinner. A nice activity for this is a guess who came where by the teacher prepares a list of celebrities that the students are likely to know, these will normally be world famous people such as the Queen of England, David Beckham, George Clooney, Elton John etc. It's well worth checking with some other members of staff or friends beforehand, though as people we think of as world famous may be unknown in some parts of the world. The idea is for the class to be divided into teams and each team is allocated a name by the teacher and they have to create clues using future continuous for others to guess the person. An example could be this person will probably be practicing the piano right now. You could think about ways to make this competitive as students tend to enjoy this and consider handing out a name bank for each team to guess from if they struggle with guessing. A great way to end this game is to have students think of famous people themselves and continue the game. It really doesn't matter if the teacher doesn't know the celebrity because students can tell you about them in English once they've been correctly guessed. ongoing action at a point in the future Another way we use the future continuous is to talk about what we will be doing at some point in the future, such as this time next week I'll be sitting on a beach. We can use future continuous to talk about arrangements when we want to give some kind of reminder or warning, such as I'll be leaving for work at eight o'clock if you want me to give you a lift. We can also use it to make excuses if we don't want to do something such as go out on a date that someone you don't like has invited you on. There's a classic TEFL game called a date from hell which can be used to practice this. Half the students in the class are given a page representing a diary and they mingle speaking to each other trying to make dates with other people in the room. The aim is for respondents to create amusing reasons for not going on a date and the students asking the question make a note of them to report back at the end of the activity. Examples are Sue can't go to the cinema with me on Saturday because she'll be washing her hair and Mark can't go bowling with me on Sunday because he'll be tidy in his room. Expected achievements at a point in the future Moving on from something we will be doing at some point in the future, we can also talk about what we will have done by a point in the future by using the future perfect tense. This is often used when planning careers or life achievements, by this time next year I will have finished all my exams. It's also acceptable to use other modal auxiliary verbs here instead of will, such as should, might, may. An enjoyable activity that works well with this is to set students up in small groups to invent an extremely successful future career for themselves. For example as musicians, politicians or travelers. Examples of what to aim for could be musicians. By this time next year we'd have signed a contract with a recording company. In two years' time we will have performed in many countries around the world. A good way to use this is for each group of students to have exactly the same role and get them to describe their future career to the class in the most optimistic and ambitious way. Something that will have been continuing up to a point in the future. The future perfect continuous describes actions that will continue up until a point in the future. The activity will have begun sometime in the past, present or in the future, relative to now and is expected to continue in the future. When we use this we're projecting ourselves forward in time and looking back. This is certainly challenging to teach and you're unlikely to teach it to any students below intermediate level as an EFL teacher. This isn't a blog to teach grammar but an example that you might relate to is. I will ill have been teaching EFL for four months by the time I move to Vietnam. This doesn't tell us when the action of teaching started in relation to now. When combined with still, the future continuous refers to events that are already happening now and that we expect to continue some time into the future. For example I'll still be paying for my house when I'm 60 years as old. As so often is the case, the simplest activities are the most effective even with the more difficult teaching points. Set students up in small groups and give them two stacks of cards with prompts, time markers, next July in 2 years as time. And verbs, work, live, learn, wear dot dot. Alternatively, you could make some cardboard dice and put the same information on the faces. Students either pick up a card from each stack or rolled the two dice and make sentences using the prompts. This can be made more fun by setting it up as a tennis relay game whereby the last student to speak is the winner of each round as long as they haven't repeated something that has already been said or made an inaccurate sentence. For example, this time next year live, I will ill have been living with my partner for 18 months by this time next year. Are you ready to teach English abroad? These activities for teaching future tenses will help you create fun lessons your students will most certainly enjoy and benefit from. Apply now for your TEFL TESOL certification course and start teaching in a matter of months. Speak with an ITTT advisor today to put together your personal plan for teaching English abroad. Send us an email or call us toll-free at 1-800-490-0531 to speak with an ITTT advisor today.