Hey, folks, in this short tutorial, I'm going to show you how to upload a video as unlisted on YouTube and then submit that to an assignment on Canvas. Let's go ahead and get started. All right. So I am logged on to my YouTube channel here. And one of the things that I will mention that is if you have just set up your YouTube channel for the first time, you do want to make sure that you verify your YouTube channels. YouTube.com forward slash verify link. Usually they have you put your phone number in and it allows you to upload videos that are like over 15 minutes long, which may not be necessary for your needs, but is the number one issue that I see students have when trying to use this method. So what I've got here is I have recorded a speech that I want to turn into my public speaking class. I've got that speech sitting on my desktop. I just need to get it into YouTube, set it as unlisted so that I can submit it on Canvas. Let's go ahead and do that process. So the first step, once you're logged into your channel, is to go ahead and click this create button in the upper right hand corner of the YouTube channel page. This tends to give you two options, which is upload videos or if you are verified, go live. We don't want to go live. We just want to upload a video. So this will bring up the upload videos interface and you can either drag and drop the file here or you can click this blue button to go ahead and select your file. Alright, so I'm going to cruise to my desktop and you can see I've got the sample speech here, a student underscore informative speech. I'm going to go ahead and click open and now YouTube is going to go ahead and do its thing. It'll take you a few minutes to go ahead and upload that. But one of the nice things about YouTube is you can actually kind of get things set up with the settings while it's uploading. So let's go ahead and do that now. So I'm going to make sure that I give my speech a useful name and I think what works well is to go ahead and give your name and then what kind of assignment it is in my case. We'll say that I am a student and it is an informative speech. You don't necessarily need to worry about putting a description in here. You can if you like. But the main thing that we want to want to do is to go ahead and click next verify it's not for children, skip through here, skip through the checks and when you get to visibility, there is a bunch of options here. Now, one of the main mistakes that students make when submitting speeches to a class with YouTube is they set it private. Private can be great if you are just sending a video to one other person and you know their Google account. But for being able to share it with other folks in an online class, what you really want is unlisted and this will allow anyone with a link to view it but it's not going to be publicly searchable on YouTube and you'll still maintain control of that. You can set it to public but I don't recommend doing that. In fact, in classes that I teach, I actually restrict students from doing that because I just want these videos to be something that they choose to share with class and not be out there in the broader world. So unlisted is really the best option for that. And then go ahead and click on save. At this point, it'll give you a little bit of an idea of how much time is left until the upload and processing is complete. So we'll go ahead and let it finish and I'll just speed this up real quick so that we can show the submission process. I am great now. Our video has been uploaded and processed. So we can go ahead and click close here. And then what you're going to want to do is to go into your content, which is this button over here on the left. And you can see that my most recent upload is the speech that I want to share. There's a couple different ways you can share the video. An easy way is to click on the options and then click get shareable link. Now I'll go ahead and copy it to your clipboard. You can also go into the video itself and copy it from here or even pull the video up and then just copy it off of the title bar. All right, fantastic. Now that we've got the video link on our clipboard, we're ready to head into Canvas and turn this assignment in. So let's go there next. All right, I am logged in under a student account now and we can see that I've got an assignment guide for a informative speech up, which is a sample assignment that would require you to submit a video. And I'll go ahead and walk you through the process of turning that YouTube link in. So this is a pretty simple way to go about it. Once you get to this phase, click start assignment, go on down here. And while there might be a bunch of different options, what you're looking for is website URL. And this is going to allow you to go ahead and copy and paste that YouTube link in there. And you can see I got the whole link in and you can add a comment if you like. But once that is done, go ahead and click submit assignment. It'll take it just a second, give you a confetti and you can see that your assignment has now been submitted. And if you like, you can click submission details and you can see that the sample of the speech shows up with the link to go ahead and do it. And it's now ready for your instructor to go ahead and evaluate. All right, well, that wraps up the process of uploading an unlisted YouTube video and submitting it as an assignment on Canvas. I hope this was helpful and thanks for watching.


YouTube team keep it clean. What's going on is engraving here with another video and In this video, we're here to talk about the game that's going down tonight between the Buccaneers and the Patriots, so I believe the game is from Tampa Bay the the Bucs are coming off a win versus the Giants and the Patriots are coming off a loss versus the Panthers now um Those are two games I think I actually picked them right last week because I did pick the The Bucs to beat the Giants and I picked the Panthers to upset the Patriots now in this game It features two teams that can have a high-powered offenses But the deep fences have been a little suspect But the team that I'm going to go with for this game Is going to be one of the two and I'm going to tell you which one of those two is after I introduced myself Now me I'm engraving vids and this is my YouTube channel engraving vids and I'm a Ravens fan But on here we talk about each and every NFL team no matter who it is So if you're a Ravens fan you can subscribe if you're a Bucs or a Patriots fan You can subscribe and if you just like talking football you can subscribe because it's the perfect place for you And I appreciate everybody coming through make sure you leave a like on the video if you haven't already and when you subscribe turn your Notifications on so when we go live or when we put up a regular video You'll always be notified about it. So you know when it goes up And if you want you can follow on Twitter Instagram and snapchat all three are engraving vids Just like the name of the YouTube channel. It's all one word engraving vids now for this this game Patriots defense has been super suspect me. They've been super suspect I think they like lasted and failed but um, I think that this game I really really really really really really really wanted to pick Bucs. I really want to pick the Bucs for this game But I'm gonna have to go with the Patriots in the bounce back game. I just I Feel I know the Bucs can win it I know they can win it but I feel like the Patriots are gonna squeak out a win in Tampa Bay tonight and I feel like they just Just gonna end up winning this game by a small margin maybe like five six points But either way, whether it's a big win or a small win and win is a win And I'm gonna have to go with Patriots in the bounce back game for this one Now I know they um When Calcy when Calcy is a beast as long as he stays healthy. He's a beast But it's like Jordan Howard or the the Bucs Titan He is trying to show that he's a beast too and both like I said both of these teams Their offenses can go off at any single second man both of them. James Winston is a lot more comfortable than he Obviously, he's a lot more comfortable because this is his 30 year But he's been looking good man, James Winston been doing his thing He is at first round draft pick and he has been living up to his first round draft pick Tom Brady, we already know what he does. That's old news. He's been doing this for a while now But the Panthers showed last week I think I said it in the video in the preview video for the game That if you want to mess Tom Brady in them up or it's really goes for any quarterback It really goes for any quarterback if you really want to mess them up You got to hit you got to hit them You got to get a pressure on them because if you don't I mean besides Flacco Flacco Don't even have to have pressure he'll make a bad throw but anyway For for the good quarterbacks if you want to mess up mess them up You have to you got to get in the backfield and be hitting them man Because if they're not getting hit, they're not going to be scared and not going to fear anything So they can be sitting in that pocket and they they'll stay back they'll stay back there forever And they won't have anything to fear because they know you ain't getting any pressure on them But if you can consistently cause pressure Then it'll mess up those quarterbacks and it'll get in it'll it'll put some fear in their hearts And they be like man, I don't know how much time I'm having this pocket I don't know and then if you can bump the receivers to if you can bump the receivers to throw them off of their routes Oh, man, that's a perfect combination get a great pass rushing and you get a good bump on receivers Jam a little bit be physical with them now. That's gonna be tough for Stefan Gilmore and Stefan Gilmore and Malcolm Butler challenge tonight if they do try to bump because they got two big challenges One of them being Mike Evans that dude is a giant that dude is a beast that dude is a monster And he if safe instance Stefan Gilmore or Malcolm try to bump him then They may just get pushed out the way because the dude's so big and strong He's a giant so they may just get pushed out the way and then on the opposite side him You have the Sean Jackson Safe instance Malcolm Butler or Stefan Gilmore tries to bump the Sean Jackson and they'd not successful at it the dude so fast he'll blow right by him so It's it's a tough situation for him But say both of them Malcolm Butler and Stefan Gilmore They would did some extra weights in the weight room this week and they can they can do it And they they end up being successful in bumping those two Receivers so we'll see what happens and of course they got two good safeties back there with um Patrick Chung and uh and McCordy So they got help, but yeah, their pass rush has been lacking. Somebody just said that from a boy flex from jersey I appreciate y'all coming through man. And good morning to everybody that's up in here right now But um, yeah, their pass rush does need some tightening up But I'm I'm I'm still picking a Patriots and this one in a cool closer I feel like it's going to be a closer. But I I do believe it's going to be a really good game I do believe it's going to be a really good game. This is a matchup that um I could it could go either way My underage said he's picking Tampa. I can't be mad at that I I want I want to pick Tampa bad I want to and I know they can win and I won't be of course won't be mad if they do when But because I I like what they're doing it with that team man I like when I like seeing other teams I mean, I hate seeing my own team do bad But I like seeing other teams that haven't had success recently I like seeing them have some success and I know for Tampa Bay It hasn't been a whole lot of success just beginning of the season But I like what they're doing man. I like what James Winston is doing. I like what their team is doing um But so I I won't be mad if they win and I won't be surprised if they win because like I said I know they can they got all the ability in the world They got enough playmakers in order to win But I just feel like the pets will squeak this one out Barely barely But anyway, y'all let me know who you think is going to win in this game again I'm oh, I wanted to go with the bucks But I'm going to pass in this one in a in a close close close close close come back But anyway, I appreciate y'all. Thank you If you're new to this channel, make sure you subscribe leave a like on the video and turn your notifications on Y'all have a really really really really really great day. I appreciate everybody up in here Appreciate it and I'm going man. Bye


Welcome to Access to Trader, the number one community for those who are committed to taking control of their trading in order to achieve success, profitability, and longevity. Thank you for joining us. Here's Dan Shapiro to help you find your edge, master your process, and own your future. Hey guys, good morning everybody. Welcome to another edition of the AccessToTrader.com weekend update show. Hope everybody is having a good start to the weekend. Nothing says Memorial Day weekend like rainy weather and this is kind of where we are in New Jersey in a lot of states in the Northeast. Again, quarantine life, bad weather, naturally the only thing to do is wake up in the morning and look at charts and well record the video at 9 o'clock in the morning. So I've been up now since 6.30 in the morning. It's 9.20 now, recording the video figure, get all this out of the way. And I started thinking about how the trading week has gone and it was some pretty good action this week and we'll get into the individual pivots in a second. But I started thinking about kind of where I started from to where I've been and I've always maintained the idea that I think I'm really one of the biggest idiots on the planet.  So the idea that I'm trying to get all the answers of being a perfect trader or not having flaws is false. I mean we're completely all of us. We're completely faulted as human beings. We're completely faulted as traders, as husbands, as parents, as friends, everything. So I started thinking back to kind of where we were, right? Where we were compared to where we are now. So go back in history, just to kind of a quick history lesson. In 1825, the first railroad was created. This was 195 years ago. And ever since then, you went from literally the first, however they made it, on four little wheels, to kind of like Amtrak and all these crazy jet trains that are flying all across the world. 80, what was it, 130, 134 years ago, the first car was made, right? And you had this little car, this little thing that resembled the car, and now you have two million dollar Bogates. And if you think about how we use right now the personal computer, okay, and everybody looks at IBM and Hewlett-Packer and Dell, but the first computer was actually made in 1936. Think about it, this was 84 years ago. So 1984 was a huge year. If you're listening to this broadcast, if 1984 didn't kind of play out, or maybe it would have played out years later, chances are none of us would have been sitting here. So in 1984, the first individual trader was born. I was 10 years old. I wasn't trading back then. I was 10 years old, and the first individual traders that started trading their money were called the So's Bandits. And for all you guys who don't know the So's Bandits, again you could pretty much do a history lesson, just Google them. But that was the first area that the individual person, not a bank, not a hedge fund, not a pension fund, not a mutual fund, but the first individual can actually get instant execution as long as the market maker represented their quotes, they could get instant execution under a thousand shares. And this was the first time that a person could actually take their own capital from any walks of life and start tackling the day-to-day grind of the stock market. This was 36 years ago. We are right now in literally the first inning of compared to what this is, what trading is, compared to what every other industry, most industries are in the world. And the amazing part is none of us have the answers. I want to be extremely clear on this. I'm doing this almost 21 years. So this was basically 14, 15 years after the first individual trader started trading. By no means am I grandfathered into the conversation of the original traders, of course not. The people who started way before me kind of showed me the ropes a little bit. They were only doing this maybe six, seven years before I was as well. So the idea that if you're starting trading in 2020, 2019, 2015, and you believe that you should have all the answers right now, you're deceiving yourself. Or if you believe you're getting, for example, trading advice from somebody that's been trading for only four or five years, that they have all the answers, again, you're deceiving yourself. And this is the type of business that there is no blueprint. Think about it, 36 years old, the business started literally when I was 10 years old. So the idea that you can have all the answers, have the best trading process, have the greatest money management skills, have completely be omitted, any emotional feelings you have is nonsense. The idea that a trading psychologist or a trading coach or a trading mentor can tell you how you're supposed to feel when you're in a stock that's going against you in a very, very rapid pace is ridiculous.  This is a business. This is not a team sport, folks. Every single person is built completely different. All of us. I've been saying this for years. Everybody's DNA is completely different. Again, I've never been medically diagnosed, but I'm pretty confident to say, just like a lot of people, I'm pretty much bipolar. I go through my mental highs. I go through my mental lows. But again, I always keep my mind and keep my eyes on the prize of the big picture. And I know a lot of people are just like me. And the idea that somebody else should tell us what we're supposed to go through, what we're supposed to feel, how we're supposed to get over our problems is insane, is completely insane. And the idea that all of us should proceed the same way, the one way, trade exactly the same way. It just doesn't make any sense in the world. And you see the stock market kind of where it is right now. And people are trying to flock to other people that believe that they have the answers, that they believe that they have the magic formula. You can't go on social media without somebody using the buzzwords. Easy, right? Three magical patterns. Trade for 15 minutes a day. You don't need any experience. You don't need any money. All you need is a computer.  You don't even need a computer. You don't even need a laptop. These are all buzzwords that again attract the masses. And the problem with people are attracted to nonsense. You're eventually going to be out of trading. You are. And the funny thing is you've never really are going to have a shot, a clean shot to actually succeed. And what you're seeing right now in the modern day market that again the whole George Costanza market that I've been kind of highlighting now for the last three weeks that nothing makes sense. Again, none of us have the answers. None of us. Okay, there's nobody you could turn to right now in the market that's turning on and say, don't worry, I know what I'm talking about. Just listen to me. Follow me. I know you only have an $800 account, right? What do you mean? Why can't you trade Amazon? Not everybody can fit with everybody's process. Not everybody can fit with everybody's lifestyle. Not everybody fit. Everybody has different account sizes. And the most important part is again, this is where I've always maintained the one common denominator that all of us have. It's right in front of us, right guys?  There is no magic pill. There is no magic formula.   The most important part is right in front of your face. It's right over here. You could respect somebody's opinion. You could respect somebody's method to approaching, but it's all right in front of us. And the idea that you need other people to hold your hand, you need 3,000 people's opinion to kind of figure out what's in front of you is laziness, is complacency, and it's self entitlement that you should completely remove right now because again, if you are not waking up incredibly early and putting in that extra manpower, just understand somebody on the other side of your trade is. And believe me, I'm speaking literally in the live webinar for seven hours a day, five days a week. I'm trading all day. I'm answering emails all day. I'm speaking to traders all day. After the close, I do my research, record the video, and rinse repeat, rinse repeat. So the idea that you think that I want to wake up, it's 6.30 in the morning, on a Saturday, okay?  Do you think that this is fun? This is not fun, but this is completely necessary. And again, a lot of people are trading based on the idea that this magical pill, this magical bubble is just going to pop and this magical light bulb is going to set in front of your face. And again, with everything that everybody's going through right now, whether it's mentally, emotionally, financially, okay, and the most irrational market that I could remember in the last 21 years, okay, you have to figure it out. You really do. And it's not going to come for everybody at the same time. You're not going to get that aha moment at the same time. You're not going to get that moment of clarity. But the more time that you put into this business, okay, the more time that you get that screen time, the thousands and thousands of hours, again, it might not benefit you monetary right now or today or tomorrow, but it's setting up a foundation for you subconsciously that eventually your path to having your aha moment of clarity will click. So the idea that somebody, you know, Joe Trader 69 from Spokane, Washington, who's been trading for two and a half years has all the answers. You're delusional.  It might not be obvious because I know how to fix my flaws before they turn into something very, very aggressive. But I'm just like everybody else. So that's why I have to wake up at 6.30 in the morning. I have to put in ridiculous manpower just to get into the next trading day because I understand if I'm slipping for one moment, if I don't, you know, have my A plus game, it's a wrap. Okay, it's a wrap. And you know what happens?  And again, a lot of new traders, for example, you know, that first trade of the day, if they're wrong, okay, and they're not mentally sharp that day, it's a snowball effect. Okay, it really is an aggressive snowball effect and it lingers not only for that trading day, it spills over the next. So again, guys, it's super important. You know, forget about what anybody's talking about, especially on social media. You have to put in the work, guys. Look at the charts. Keep looking at the charts.  It's like shooting free throws. The more free throws you're going to shoot, the better overall eventually you become a free throw shooter. It might not happen tomorrow. It might not happen that next week and next month, but eventually with practice and repetition, again, repetition equals screen time. Repetition doesn't equal putting on trades. It is equal screen time and it equals back testing and research and everything else like that. Eventually you'll become a better free throw shooter. So the idea, so for example, that Shaquille O'Neal was one of the worst free throw shooters of all time. Steadily, he actually got better. Again, shooting 53, 54 percent. Is that better? Well, it's better than shooting 38 percent and that's the whole point of kind of our individual journeys. We have to do whatever is necessary to put our situation to win long term. Again, it's not going to translate into tomorrow. If you open up your computer today and start looking at a chart, for example, on Netflix and say, oh, okay, I get it. I understand why the stock went lower. I understand why this could be a premium setup going through this week. This one chart is not going to do anything for you. But again, if you keep on back testing, you know, Netflix and see exactly why it went from point A to point B, why it went from point Z to point A, so forth and so on, eventually it's going to have, that have that positive effect. So please, next time around, you're asking opinions about somebody in the stock market. Remember, we're only 36 into this. There is no blueprint. 36 years is nothing. You're talking about 195 years that the railroad was built. A hundred, what, 35 years that the car was manufactured. 36 years in. Nobody has the answers. There is no blueprint. Nobody's going to feel exactly the same way. Again, picture this. What trading psychologist can possibly tell me? What can they possibly show me? What can they possibly make me feel better when I'm sitting in a trade, like for example, like on Netflix a couple of days ago, and I'm sitting in a trade and they're spreading the stock out, you know, 50 cents at a time against me and I'm down $3 in a trade in a matter of 45 seconds. What can they comfort me? What words of encouragement can they give me to tell me how to overcome this? Guys, it's all about us. We're relying on us. Even though, for example, I'm not a big golf guy, but I understand golf is an individual sport. You have to fix your swing.  So please, before you open up your computer and start asking 3,000 different questions about your favorite Twitter traders, get to work, guys. I guarantee you there's no more gratifying feeling. Then actually putting in the work and seeing your results play out because you put in the manpower. So this weekend is a long weekend. If you're an options trader, get your ducks in a row. If you trade futures, get your ducks in a row. If you trade pivots, again, back test. We have 10, 11 hours of content breaking down the PS60 theory. Do what you have to do to put yourself in a better situation for tomorrow. The past is the past. We don't live there anymore. Monday is the first trading day for the rest of your career. The most important part is, again, take the necessary steps to get better. So let's talk about the market. Thursday we talked about potential, right? Potential, there was definitely signs. We saw signs of a potential market back test on Friday. A lot of times, again, the indexes are not going to put yourself in a position to turn around and say, it's pretty obvious. Again, I think charting and looking at technical analysis is not a subjective sport. There is no room for debates. If stocks confirm supply, stocks are going to go higher. If stocks confirm demand, stocks are going to go lower. So for Thursday's session, from the Thursday night session, I said, look, there's signs that suggest that we do have a higher probability for the market going lower tomorrow. And again, when I say the market, okay, I'm talking about the individual stocks we trade. I'm talking about weakness in Amazons and Netflix and Roku's and Alibaba. And granted, I totally forgot Alibaba had earnings next day. So it played out that way that it was weak. But obviously, again, I just totally forgot they had earnings. But the most important part is, again, having an opinion, okay? Having an opinion and let it play out. Whether you're wrong and your opinion is completely destroyed based on technical analysis and reclaim the other way, that's fine. Okay, we're allowed to be wrong. We're human beings. We're flawed.  We're schmucks. All those good things. But again, the faster we realize that, the better we'll be. So Thursday night, we did the video, if you watched the video Thursday night, we talked about the realization that there is a similarity, or there was a similarity, that we saw right around here, right? Right around here in this kind of this blow off top area, kind of a reversal the next day. And we got that, right? We got that Thursday and we got that into Friday. I mean, you sort of started seeing some pretty weak market action pretty much through the whole day. We got a little bit of a rally towards the end of the day and the queues actually turned green, which is actually very, very bullish for this week, because the idea that they reclaimed the five-day moving average. But again, we were looking at the point of one day at a time, one trade at a time. And we got some really good value Friday at the open, okay, literally at the open. That first 45 minutes to an hour or so, was very, very aggressive. And then the market completely stopped, like literally stopped. And although there was some good pivots, we really did see what happens when people start losing the mental edge, start losing the mental juice to get really worn down towards the end of the week. Now again, did the idea of a long weekend take some of the steam out of the market? You have to say at some point, yes, just the idea that even though people are not flying and going on vacation, people are driving, renting homes, whatever the case may be. So you did see a lot of the juice being pulled out of the market on Friday, especially like literally after the first candle of the day. And it was complete ghost town. And unless you stayed till after three o'clock, okay, and this is where a lot of these pivots started breaking down, especially on the short side, Amazon started breaking down, Netflix started breaking down, and I kind of like a lot of these names going into Monday on the short side if they start further confirming. But it's very, very important to kind of understand where we are on the landscape. So from the technical point of view, we did get that back test. A lot of names did. A lot of names did not participate. We'll talk about the individual pivots in a second. But what I like what I saw, and this is kind of a 50-50 proposition entering Monday, what I did like what I saw was the bulls and again, we're talking about the queues. We lost the five-day moving average at the open. That's why we saw those aggressive flushes. And then what I like, what I saw towards the end of the day was that the bulls reclaimed the five-day moving average. Again, the five-day moving average is an incredibly important short-term indicator. So if you look at the dynamic structure of the market for the week, and again, it was a pretty aggressive week. Number one, the indexes were up three, all of them, all the major indexes were up 3%. And the idea of a possible global reopening and the idea of a potential vaccine eventually will be available to everybody, kind of trumped, no pun intended, kind of trumped the idea that the China-U.S. trade war tension was back on. Again, spring hopes internal, whatever the hell the terminology is. So there was a lot of optimism. The market continues to kind of negate bad news and that's very, very important. So going into this week, there's two areas. I can make a case for two areas. Market is still very, very strong. Again, very, very big moves all week. Like for example, in names like shop, continue to be strong, and chipotle continue to be strong. And the video who came out with earnings after a big, big run had a chance to fall twice. And we'll talk about again, the individual pivots in a second. Had a chance to fall twice and it didn't. Again, continues very, very strong strength. Apple, for example, again, big strength in Apple. Facebook ever since they came out with that news, ever since they came out with that news, the first headline that they were going to offer, offer their own webinar service versus ZM. They've been on a very, very big run as well. Amazon is on a big run, but again, last couple of days are showing some weakness and I want to kind of address that as well. So the glass half empty side is still saying that everything is fine. Everything is great. Again, I don't trade with rose-colored glasses on. I like to look at things from both sides of the track. I want to make sure again that the idea of everything will be okay, that this was the generational bottom. Again, I don't buy that anymore. I'm not naive. I understand that stocks are very, very strong. There's a lot of value every single day to the long side. But again, the last thing I want to do is say, ah, don't even worry about it. Just buy the dip, everything will be okay.  So you have to look at the sides. So the bull side, the bull argument is very, very clear. Here is, and I don't want to use the word bear argument, but here's this sell argument, okay? So let's look at the high flyers that we've had in the last week. And again, if you've been watching this video, these videos for the last, you know, even the last week, you kind of know my thought process. So Zoom had this big, big run, okay? Big, big run, and just wanted to have a chance to kind of open up, right? Kind of open up the field and go into the go line to the 52 week highs. It's stalled out and rolled over and hit the 10 day moving average. If you look at Friday's session, again, didn't participate in the recovery. So again, we're one day away from confirming this bottom to go lower. The one that started it all was Netflix.  The five day went to the 10. There was a 10 day confirmation. It went to the 20. And again, look what happened on Friday, right? It confirmed the 20, and we'll get, again, we'll get into the individual pivots in a second. And now look how much movement has to the downside, okay? Amazon as well. Again, huge move, right? For all you guys who caught the whole move from the 23, 60 swing pivot all the way up to the 25 hundreds, you know how strong Amazon has been, okay? But again, you saw similarities.  It took out the previous days low. It stopped at the five day moving average. On Friday towards the end of the day, it confirmed the five day. Again, we'll get to the scenario that now it could go lower as well, okay? So you have Roku, for example. Again, let's take the downgrade from Friday out of the equation, okay? We started seeing the previous day how a breakdown was imminent. You saw the pattern play out. You saw the triple bottom of the 111.36 area. 111.36 area, 12.50, right? We saw the 14 break on Thursday session. It was a nice little, nice little scalp. So all this was setting up. And now the idea, again, you start looking at other companies as well. Like a company like Boeing. Had a big, big chance to run. Had a huge pivot on Wednesday. Was it Wednesday or Thursday? Had that huge pivot off that 137. Made its move. But it kind of died out a little bit and didn't confirm. So you can make an argument. Even stock like Alibaba, who in my opinion came out with a really, really good quarter, right? Incredibly good quarter. Again, you can make the argument. The Senate, the whole Senate passing a bill that the Chinese companies could have a harder time keeping compliance being registered with all major exchanges. Again, you can make that argument as well or you can just make that argument while Alibaba had a really, really good run and now it's time to take profits. So you can make an argument on both sides of the equation, what happens next. For me, it's all about technical analysis. Again, it's not a conversational piece. It's like somebody a couple of days ago said, hey Dan, there's no way Tesla's going down. As I was shorting it to 796. And then on the way back up, at 814, 821 level, there is no way Tesla's going up. The stock went to 835. So again, technical analysis is not an area for discussion. It's either going to confirm or it's not. So you can make a case, if you're a long-term investor, that you love the company, that's fantastic. You're talking about two, five, 10, 20 years away. I'm talking about interval to interval, channel to channel, long, short, day by day, trade by trade. So the conversation is completely different. And I think again, please respect. If you're an investor, please respect the trader. If you're a trader, please respect the investor. Again, our worlds don't cross. It's very, very rare that Mike Pivot on Tesla has anything to do with your investment, whether it's long or short. So it's nothing to do with us. Again, all do respect. And I say that in the most humble way. I respect any single person that clicks a mouse, whether you're investor, trader, scalper, option player, future, whatever it is. I give you the ultimate respect. Again, nobody knows what we go through except for other traders. So I want to put it out there. But the idea that you're telling me, I'm wrong on a long pivot or I'm wrong on a short pivot, it just doesn't make sense. Again, it's apples to hand grenades. So again, please respect any traders out there. Again, it doesn't make a difference what they do. It's not going to affect you. Words are just words. If I think Tesla's a long and you think Tesla's a short, how is this going to affect your trade? Is it going to happen or not? So again, all traders, please respect your brothers and sisters. Again, we're a tribe. We're all we got, man. There's nobody else that's going to sympathize what we're going through. So again, we're trying to create a great environment of mentally stable human beings. The only way we could have that is kind of being on the same side. Be very respectful. Again, at the end of the day, nobody really cares about your opinion anyway. So going into this week, I do like some names. I really do. I do like some names to the long side. I've been watching this NLW. Looks really, really good. It's just kind of just sitting here and just waiting, waiting. I like Tesla, right? I like Tesla this week as well. It's just kind of sitting there and waiting is waiting. But again, you could turn around. You could turn around and say, look, Netflix is one day away from getting hit. Roku had that big nasty move on Friday. It looks like it wants to go to a 50-day moving average. Amazon is gassed out, right? If it confirms these two channels, we'll go down to the 10, and then we'll go down to the 20-day support. So again, we want to make sure we're prepared for Monday's session. We want to make sure that we are open-minded to both sides. So again, the queues did remount and reclaim the five-day on a close, but it's very, very important to kind of have open mind and don't be brushed into the corner. So let's talk about quickly Friday's session. Again, here are the pivots. I only did a couple of trades, and then everything else was kind of dead for the rest of the day. 358 continues to be the after-hours high on the video, pre-market supply, and needs to reclaim and then build. So 358, you guys kind of saw what happened off the 358. And actually, this event happened after the initial short. So here was the 358, right? Here's the 358. I actually tweeted about this the night before. It kept on getting rejected here. 358, 358, 358, 358. Finally took out the 358 and went to almost 364. Tesla, again, these are the continues to be the big levels.  That's exactly where we got rejected. There were levels going in for Tesla for next week. Roku downgraded to 1130 if it builds below Conflush. Roku got destroyed. And again, it wasn't a pivot, right? It wasn't like a one-of-sneaky pivot. It was just macro, right? Here's the 1130, right? 1130 was the lows from May the 1st, right? So here's 1130, and it broke 1130. It just got destroyed when all the way down to 107. 60, BY and D. Oh, yeah, yeah. So I took it short also in the video. 351 builds below Conflush experienced traders only. I thought I had a shot to get down to 344, but the stock was incredibly resilient. So I shorted it. It went down to 48.5 very, very quickly. You didn't even have a chance to react. So I wound up making a couple of coffees. I scratched on the trade very, very quickly. If I didn't cover it, I would have got completely destroyed. BY and D, again, not a move at all. I mean BY and D, I liked that 38.5, I liked that 38.5, 39 level again. Only went to 39.40. And again, if you look at the daily chart, and this is my whole point, if you look at the daily chart, right? This thing is one day away for possibly aggressively back-testing. So nothing really doing there on the upside. Amazon, again, this triggered towards the end of the day. So I wasn't even around for this, but 241.40, 240 is a big five-day support. It's the shortest-term sentiment if it builds below can flush. And again, not a huge move yet. That's the word, yet. But it took out the 40, it went down to 24.30. Again, this confirms it could go all the way down to 23.87. Shop continues to be a monster. A-10 needs to build. Again, we've been talking about the shop pivot now every single day. A-10 needs to build. Big move on shop. You know, a big, big move on shop here. So here is the A-10, right? So here is the A-10 and traded right to the highs of the day of 8.27, which was supply. It probably has one more day up, maybe to the 8.38 level. So a big, big move there. Boeing never made it up to the 41.75.42 area. Alibaba got destroyed. 205, huge support if it builds below can flush. Got destroyed, absolutely destroyed. Here is Alibaba, right? So here is Alibaba. Here is the 205. You see this 205 area, right? Rising support. So 205, it broke 205, got just absolutely destroyed, went down to 199 on earnings. Again, Roku take on the way down. I still like this now. Shop take on the way up. Roku just completely destroyed. And not a big move, not a big move on Apple 318. It only went up like 50 cents. Not a big move there. Netflix again towards the end of the day, broke the 4.30 confirmation, went down to like 4.28. But again, I think there's a bigger move coming this week on Netflix of Confirms. Boblin never got up there. And this is the last pivot of the day, 8.25, 8.26. It finally confirmed off that second entry. And again, it wasn't a huge move. But again, it ran up to like 8.32. Excuse me, it ran up to 8.31. So again, this whole channel is super important for Tesla going into this week. So again, going through this weekend, guys, I'm kind of Delta neutral. I am a little bit sell-bys on the high-flying beta names. I do like the overall market because again, the Qs did reclaim the 5.8. The Qs lose the 5.0 again. And the bear started confirming Friday's price action. Obviously, we'll go... I don't want to use the word 100% sell-bys. But again, we are getting very, very close for a pretty aggressive rug pull. So guys, please get into the work better in yourself. It's only about you.  You don't need anybody, guys.  The key is getting proper information and using it wisely. Guys, have a great weekend. Have a great rest, and I'll see you all on... Congratulations for putting in the time to take control of your trading. You're one step closer to owning your future and achieving the success you desire. Want daily trade ideas directly from Dan? Straight off his personal watch list? Unlock our free PS60 vault where you'll get nightly updates on pivot opportunities we're watching for the next day's session. Click the link in the description to get started today.


Hello everyone forgive me for taking a few minutes out of your busy day But I just want to make you aware of my upcoming Mises Academy class on Keynes Krugman and the crisis And this course is going to be eight weeks long the first week. We're going to study the thought of the Pre-Keynesian economists in other words the economics that prevailed before the general theory came out so what we're going to look at in particular is the famous section from JB Sey's work on what's now referred to as Sey's law and we'll see the sense in which Sey meant that Principle and we'll see if Keynes really dealt with that adequately And then we'll also look at a selection from Lionel Robbins book on the Great Depression that came out in 1934 okay, and so we'll see Exactly what the state of the art in terms of free market economists thought about the Great Depression before Keynes came along Then the next two weeks, we're going to look at selections from the general theory itself And I should stress you don't need to actually buy these things are going to be available online So you don't need to order anything if you don't want to and we will be reading it though in the original and So you can see Keynes talk about his system in his own words We're going to focus on the famous buzzwords that I'm sure you've heard about you animal spirits and the socialization of investment And yeah, didn't he in one of the prefaces talk about how the the Nazi German state was more conducive to his system Than a liberal state would be and yeah, we're going to go over all that stuff But the point's not going to be to demonize Keynes. It's going to be to understand exactly how his system worked Okay, we're going to go through that and then we're going to look at Hayek and see what's his response to Keynes okay, so It's not going to be a full in-depth treatment of Austrian economics It's going to be more things you may never have read before interviews that Hayek gave where he talks about Keynes selections from Tugger by the tail, which is largely just scattered remarks that Hayek made into various places collected in one spot talking about the Keynesian system All right, so and also we're going to look at the letters that Keynes and his followers and then Hayek and his Allies wrote to the Times in London in 1932 to you know giving their different views as to what should happen to get rid of get out of the crisis Then the last section of the course as the name suggests is going to be talking about Paul Krugman My of course favorite living economist and there we're just going to go through relying on his Blog entries and also some of his columns for the New York Times going through first of all we're going to look at Krugman's treatment of the situation in Japan Right the the the lost decade as it's called in Japan and see what Krugman's recommendations were for them we're going to look at Krugman's notorious calls for the creation of a housing bubble and we're going to refer read the dispute because Krugman now claims Hey, I never said that they should have a housing bubble I was just making an analysis of an economist and so we'll go and look at that and look at various things He said and wrote over the years to see is it really true that back then Krugman Was or was not claiming that they're the Fed ought to be trying to engineer a housing bubble and then The last thing of course is his recommendations for what the US government the Federal Reserve should be doing now Given that we're in what he thinks is a liquidity trap. All right, so throughout all this material I'm going to of course always present it try to do it fairly try to make you think like Keynes or think like Krugman So you know what the worldview is but then of course present the Austrian response to that particular viewpoint So again, the class starts at the end of June. It's an eight-week class. It's 145 dollars. It's a it's a steal Right, you're not going to be stimulating many expenditures by taking this class But the point is of course to equip those of you who are fans of the Austrian school with a better knowledge of What we consider to be the enemy as it were right that it's important to understand how Keynesians think and this is going to be a Course where we get hip deep into it and read Keynes in the original read Krugman's Work in his own words and then try to provide a systematic response So I hope many of you can join us. We'll see you in a few weeks. Thanks


This lecture is part of an online course on the theory of numbers, and will be about primitive roots. So, first of all, explain what a primitive root is. So suppose you pick some modulus m, so this is a positive integer, then a primitive root of m is a number a, so that all elements of z over mz times, you remember this group is the numbers modulo m that are co-prime to m. Then all elements of this group have to be powers of a. And let's see some examples of this, just to get an idea of what's going on. Suppose you take m equals one, then z over mz, the multiplicative group z over mz just has one element one, and that's obviously a primitive root, that's kind of trivial for m equals two. It's equally trivial as just one element, that's a primitive root. m equals three, there are two elements, and this time we can see that both of them are powers of two. So let's put the primitive root in this fluorescent pink colour. For m equals four, there are just two elements, and again there's an obvious primitive root. For m equals five, we have to stop and think for about a second because there are now four elements, and four isn't a primitive root because it's square is one, so the powers of four are just four and one. But you can easily check that two and three are primitive roots. m equals six, nothing much happens, there are two elements, one and five, and five is the primitive root. For m equals seven, things are now getting a little bit more complicated, so there are six elements in this group. And what we want to do is to find an element of order six so that all its powers are these six elements. And six won't do because six squared is equal to one, and one won't do because its first power is one. And what about two? Well, two won't do because two cubed is equal to one, and similarly four cubed equals one. However, the elements three and five work fine. So if you look at the powers of three, you get one, three, nine is two, then you multiply that by three and you get six, and you multiply that by three and you get four. So you get all the powers. So what are the primitive roots for m equals eight? Well, the elements of zero for mz star are one, three, five and seven, and we see one squared equals one, three squared equals one, five squared equals one, seven squared equals one. So there are no primitive roots. So there may be no primitive roots at all of a number, so this happens for eight. So let's try to go a bit further. For m equals nine, we have one, two, four, five, seven and eight, and you can check the primitive roots. And now two and five for ten, you get the elements one, three, seven and nine, and nine squared is one, so that's not a primitive root, and three and seven are primitive roots. So if we stop and look at this collection of data on primitive roots, you can see it's rather hard to see any patterns going on. The primitive roots seem to be some almost random collection of numbers. So we need to answer the following questions. First of all, which numbers have primitive roots? So all numbers up to ten except eight have primitive roots, and what's so special about eight that prevents this from happening? Well, we also want to do things like find out how many primitive roots there are, and finally, obvious question, what use are primitive roots? Well, to see what use they are, let's stop by just looking at the case m equals eleven, so we get one, two, three, four, five, six, seven, eight, nine, ten, as the elements of z over eleven z, the multiplicative group, and which of these are primitive roots? Well, one isn't obviously, ten isn't because its square is one, and you can see three, four, five and nine are not because their fifth power is equal to one, and we're left with the primitive roots two, six, seven and eight. And now let's suppose a number a is a primitive root of some number m, and we're going to take a to be two and m to be eleven just to show what's going on. Now what I'm going to do is I'm going to write out the number zero, one, two, three, four, five, six, seven, eight, nine, which are the elements of z modulo ten z, and I'm going to write out the elements of z modulo eleven z star. So as you know, the elements of z modulo eleven z are one, two, four, eight, five, ten, nine, seven, three, six. And why have I written them in this rather funny order? Well, I'm writing them in the order where these are the numbers two to the n. So two to the five is thirty two, which is ten modulo eleven and so on. So we have a map from z modulo ten z to z modulo eleven z start taking n to two to the n, where this two is a primitive root. And what we notice is that this map is a homomorphism. Well, so what's a homomorphism? Well, a homomorphism is a map that preserves the group structure.  And you have to be a bit careful because the group structure here is written additively and the group structure here is written multiplicatively. So preserving the group structure, we have to change a plus to a times. And it's also a bijection. And a homomorphism between groups that's also a bijection is called an isomorphism. And an isomorphism is just a fancy way of saying that two things are really the same. So what do I mean by saying they're really the same? Well, they're sort of really the same as groups provided you just relabel all the elements. And so we have to relabel the elements by relabeling eight as three and six as nine. And we have to relabel the group operation from addition to multiplication. But apart from that, these are really the same groups that addition in here just corresponds exactly to multiplication here. And what this means is that any group theoretic property of this group can be turned into a group theoretic property of this group. For example, suppose we want to know in this group what are the solutions of x to the five equals one? Well, they're the solutions of five x equals zero in this group because zero corresponds to one and fifth powers correspond to multiplication by five. And the elements with five x equals one are easy to find. They're just the five multiples of two. And so the elements with x to the five equals one are just the corresponding elements in this group which makes them easy to find. You see, adding two to something is definitely easier than multiplying something by say four. So the advantage of a primitive root is it turns, in some sense, it turns multiplicative problems into additive problems. So next I should explain where the name primitive root comes from. Well, in complex analysis, we have roots of one which are solutions to x to the n equals one. And if you look at, say, the sixth roots of one, remember the sixth roots of one lie nicely on a certain form of sort of regular hexagon. So that we have one and minus one and we've e to the two pi i over six and e to the two times two pi i over six and so on. And if you look at the orders of these roots, this one has ordered one, this one has ordered two, these two have ordered three and these two have ordered six. And these are called primitive sixth roots of one. So there are two primitive sixth roots of one and primitive means all other sixth roots of one are powers of them. So if we take the six powers of this one, we get all of these things here. And this is exactly what happens in say z over 11 z star. We have 10 tenth roots of one by Fermat, because Fermat's theorem says that all elements of this are actually tenth roots of one. And the primitive ones are the ones of order 10 so that every tenth root of one is a power of one of these primitive ones. And this is exactly the definition we gave of a primitive root modulo 11. So a primitive root modulo prime and a primitive root of one in the complex numbers are really more or less the same thing. There are nth root of one that has ordered exactly n. Now we get to the following problem, which numbers m have primitive roots. So we saw earlier that all numbers up to 11 other than 8 have primitive roots. And so let's try and see some properties that numbers with primitive roots have. So suppose if a is a primitive root of m, then we get an isomorphism from z modulo 5 of m of z to z over mz star, which just takes a number n to 8 the n. So remember 5m is the order of z over mz star. And you see this group here has at most two elements of order dividing two. So if this is in general true for z over kz. So if k is even there are two elements of order dividing two. And if k is odd there's only one which is zero. So we get either zero or zero and k over two. So if there's a primitive root this is only two. This is only at most two solutions to x squared equals one. So if there are four elements with x squared equals one or at least four elements there's no primitive root. And this will give us a way to check where the numbers have primitive roots on it. And actually it turns out that conversely if there are most two elements with x squared equals one then there is a primitive root. That's a little bit harder to show. We might more or less show it later. So let's see how this allows us to eliminate some things. Suppose we look at the group z over mnz star with m and n co-prime. Now we apply the Chinese remainder theorem. And we recall this says that this is really isomorphic to z over mz star times z over nz star. You remember there was a one-to-one correspondence between elements of this group and pairs where you pick an element of this group and an element of this group provided m and n a co-prime of course. And now this has two solutions to x squared equals one which are plus or minus one if m is greater than or equal to three. If m is two then one is equal to minus one so these two solutions become the same. And similarly this is two solutions if n is greater than or equal to three. So all together we get when I say two solutions this has at least two solutions. This has at least four solutions to x squared equals one if m and n are greater than or equal to three. So if there's a primitive root of a number we can't write it as the product of two co-prime numbers both of which are at least three. So this gives us the following possibilities. So the only possibilities for a primitive root a number has to be that form p to the k for p prime or two times p to the k. And we're allowed two here because you remember m and n had to be at least three which means we can allow a factor of two that is co-prime to that. So these are the only numbers that can't be written like that. So the question is can all numbers of this form be given primitive roots? And the answer is no there's still one other obstruction because if you look at two to the k for k greater than or equal to three this is four solutions to x squared equals one. And two of these solutions are obvious they're one and minus one and the other two solutions are two to the k over two and minus two to the k over two. So the only numbers which so if m has primitive roots then m is equal to one of the numbers one to four or p to the k for p odd k greater than or equal to one or two p to the k for p odd and greater than or equal to one. And in fact all these numbers turn out to have primitive roots. Well how do we show this? Well the first step is to do the case when k equals one. So we now have the following problem does z over pz star have a primitive root. Here of course p is prime and this was shown by Euler although he actually struggled with it quite a bit. It turns out it's actually rather tricky to show that z over pz star has a primitive root and the point is in general there seems to be no easy way to write down a primitive root of a prime. I mean you can sort of find one in practice by trial and error without too much difficulty but there's no easy way to write down a formula that always gives you a primitive root of a prime. And the proof will be sort of rather indirect we will show that it has a primitive root by counting up all the elements that aren't primitive roots and showing that there are less than p minus one of them. Anyway let's start the proof. We need the following key point which says that a polynomial of degree n with coefficients in z modulo pz has at most n roots in z modulo pz. And you may think well you already know this. There's a theorem in algebra saying that any polynomial of degree n has at most n roots. So what's the big deal about this? Well the point is this is actually false mod m if m is not prime. So for example we've got this degree two polynomial x squared minus one and let's try and solve it in find roots in z modulo eight z. Well there's just four roots. The four roots are one, three, five and seven. So it is not true in general that a degree n polynomial has at most n roots. However Euler discovered that this is still true if we work modulo p. And let's try and see why this still works if we're working modulo a prime. So suppose we've got some polynomial f of x which is x to the n plus a n minus one x to the n minus one and so on plus a zero. And suppose a is a root. I guess I should make it clear that a is a variable not a word. Then we can write f of x equals x minus a times x to the n minus one plus something or other. And let's call this factor b of x. So this means f of a equals zero. And this argument works perfectly fine modulo any integer and we can just copy the usual proof of algebra. You remember you divide this polynomial by x minus a and the quotient is this and the remainder must be zero because f of a equals zero. So this is fine modulo any number. And now suppose c is a root of f. Then c minus a times g of c is equal to common to zero mod p. So c minus a is common to zero or gc is common to zero and this is the key step. The reason for this is because p is prime. So let's put a big orange box around this because this is the key point where we use that p is a prime. That's because if p divides c minus a times g of c it must divide one of these two. That's the sort of almost a defining property of prime. So c equals is common to a or g of c equals naught and by induction there are at most n minus one solutions. So this equation because the degree of g is n minus one. So there are at most n roots of f modulo p. We should point out that this definitely fails if p is not a prime. For instance suppose we work mod eight and we look at the polynomial x squared minus one. Well this is a root x equals one so we can write it as x minus one times x plus one. But now we notice that three and five are roots of x squared minus one but they're not roots of x minus one or of x plus one. So this step really does break down. So you can see if we put x equals three then this number is two and this number is four which are both none zero. Their product is zero because you can get two none zero numbers mod eight whose product is zero. So that works fine for primes but not for arbitrary numbers. Now we notice that z modulo p z star has at most n elements of order dividing n, this is for any n. And this follows because these are just the roots of x to the n minus one is common to zero modulo p. And we just showed that a polynomial has at most n roots. And now we notice that z over p z star has at most five of n elements of order exactly n. So here we're looking at the order dividing n, here we're looking at the order being exactly n. So suppose there is at least one element of order n. So suppose a has order n. If there isn't one element then there are certainly less than five n because there are none of them. Then we find one a squared up to eight to the n minus one are all of order n. So all of order dividing n. And so there are n of these and there are most n elements of order dividing n. So these are all elements of order dividing n. In particular all elements of order n occur among these. And we notice that a i has order n if and only if i is co-prime to n. If i isn't co-prime to n then you can easily see that that a to the i has order less than n. So order is n is equivalent to saying that i is in z sorry that i is co-prime to n. So the number of elements of order n is just five n. Because this is the number of numbers co-prime to n. So we see that in fact we can say that z over pz star has either five n elements of order exactly n or it is none at all. So we can now do some counting to show the existence of a primitive root. So first of all we recall the following formula that the sum of d divides n of five d is equal to n. Now we're going to take the special case n equals p minus one and we get sum over d divides p minus one of five d is equal to p minus one. On the other hand let's count the number of elements in the group. So we know the sum of d divides p minus one of the number of elements of order d is also equal to p minus one. Because this is every element of z over p minus one z has some order d which must divide p minus one by Fermat's theorem. So this is just the order of z over pz star. Every element of order. So that should be z over pz star. It's isomorphic to the first group but I don't want to confuse them. Now we notice that these two sums are the same but if we look at this term here and this term here we notice that this term here is less than or equal to this term here because we just proved it on the previous sheet. Now if two sums are equal and every term in one sum is less than or equal to every term in the other sum all the terms must in fact be equal. So we say in fact equal as the sums are the same. So z over pz times has exactly five of d elements of order d whenever d divides p minus one. So it is five p minus one elements of order p minus one and these elements are the primitive roots. So it has primitive roots and in fact we can now calculate the number of primitive roots modulo p. It's just five p minus one. So let's give an example of this. So let's solve the following problem. How many solutions are there? Two, x cubed is common to one modulo 97 and the second problem is what are they? Well problem one, we want to solve x cubed is common to one mod 97. So we put x equals g to the k where g is a primitive root and at the moment we don't care what the primitive root is. So we want to solve g to the 3k is common to one mod 97 and this is equivalent to solving 3k is common to zero mod 97 minus one by the isomorphism between z modulo 96 and z modulo 97 star. Now solving 3k is zero mod 97 minus one is really easy. We just see that k is equal to 96 over three or zero or two times 96 over three which is zero, 32 or 64. So we can see there are three solutions and we can see there are three solutions with very little calculation. We just had to notice in fact the only thing we use is that 97 is one modulo three and this works for any prime that's one modulo three. There will always be three solutions to this. Now we have the problem. What are the solutions? Well for this we should find a primitive root and the easy way to find them a primitive root is to look them up in my book of primitive roots. So I actually have a book. Here we have the theory of numbers by Vinogradov and in the back of it he has this nice table, tables of primitive root. So for every prime he lists a primitive root and he lists the powers of that primitive root and he also lists the inverse of this. So here for instance for 37 a primitive root is two and two to the 23 for example is going to be five. And on the other hand if you want to know what the power of five, what you need to raise two to the power of to get 23, sorry to get five you look at in this table so you look up five and you see the answer is 23. So this is a sort of table of anti logarithms and this is a table of logarithms. Anyway let's go to the prime number 97. Let me magnify this a bit so you can actually see it. And you see from this that it says that five is a primitive root and here it gives the various powers of five. And we want five to the power of 32 and you see it says here that five to the power of 32 is 35 and five to the power of 64 is 61. So the solutions are five to the 32 equals 35 and five to the 64 which is equal to 61. I should say congruent to 61. So in the days before computers people actually wrote out these tables of primitive roots and used them to do calculations modulo p and you could use them to solve equations like that and so on. Okay so that settles the problem of primitive roots modulo p they always exist. In the next lecture we will discuss primitive roots modulo powers of p and also relate them to a theorem called Wilson's theorem.


Okay, precious and precious. My name is Gollum. I'm sorry. My name is Sam Vakny and I'm the author of Malignancy of Love, Narcissism Revisited, a former visiting professor of psychology, and an actual professor in SEAPS, Commonwealth for International Advanced and Professional Studies, Cambridge United Kingdom, Toronto, Canada, with an outreach program in the thriving Lagos, Nigeria. How can you tell if the abuse you're suffering is narcissistic, psychopathic, or borderline? In the absence of an official diagnosis, diagnosis of your partner, your partner refuses to attend therapy, refuses to be diagnosed, refuses to acknowledge that there's a problem whatsoever. How can you tell what it is that you're going through? What are the differences between these three types of abuse with hints as to how to recover from them? This is the topic of today's video.  But before you do, I suggest that you watch yesterday's video. Yesterday was 4th of July, and many people were offline, good for them, traveling, meeting family, not good for them, and so on and so forth. So the attention span, limited as it is, didn't extend to YouTube.  I recommend that you watch it. It's a second in a series. I want to start by quoting John Donne. John Donne was a metaphysical poet in England in the 16th century. An amazing mind with great psychological insights. He wrote many immortal lines among them, nothing but men of all and venom things Doth work upon itself with inborn sting. It's a great description of self-destructiveness. But oh, self-traitor, I do bring the spider love which transubstantiates all and can convert mana to gold. Be thy own palace or the world's thy jail. Magnificent, absolutely magnificent. Encapsulates most of clinical psychology in fewer than four lines. Back to history, ancient history, in 1995 I coined the phrase Narcissistic Abuse to describe a subtype of abusive behavior that was all pervasive across multiple areas of life and involved a plethora of behaviors and manipulative or coercive techniques. Narcissistic Abuse differed from all other types of abuse in its range, sophistication, duration, versatility, and express and premeditated intention to negate and vitiate the victim's personal autonomy, agency, self-efficacy, and well-being. Now before I proceed and distinguish Narcissistic Abuse from Psychopathic Abuse and these two from Borderline Abuse, let me just say that in all these forms of abuse there is a marginal group, there's a small percentage of sadistic abuse. One Narcissist, Asadis, some Psychopaths, Asadis in some Borderlines, Asadis in these cases, the original template underline type of abuse is overlaid with sadistic abuse. Sadistic abuse is the pleasure of inflicting pain and discomfort and humiliation and shame, public shame upon another person. So some Narcissists derive both Narcissistic Supply and Sadistic Supply, the same applies to Psychopaths and Borderlines. Today I'm not going to discuss sadistic abuse, although scholars are now proposing the construct of Dark Tetrat. Dark Tetrat includes sadism as well as subclinical Narcissism, subclinical psychopathy and Machiavellianism, manipulativeness. So, and I have the videos dedicated of course to the Dark Tetrat and to my proposal of a dark pentagram, so I will not dwell upon these today. Today I will teach you the differences between three types of abuse and how the recovery and the healing from each of these types of abuse is different. So each type of abuse requires a different way to heal and to recover. Let's start with Narcissistic. Narcissistic abuse is all pervasive. In other words, it affects, infects, afflicts every single domain and area of life. It is not limited to any specific aspect or angle or dimension of existence. It is all-consuming, it permeates everything, it informs and it imbues absolutely every circumstance, every decision, every choice, every happenstance. So it's all pervasive, ubiquitous. Point number two, Narcissistic abuse is driven by the various phases of the Narcissist shared fantasy. Now here I'll make a stop and I recommend that you watch my videos on the shared fantasy. There's quite a few of them, but the summary is titled Seven Phases of Shared Fantasy. When you learn about the shared fantasy, you will find that Narcissistic abuse comes in two flavors, two varieties, each one of which is attached to a specific phase, specific stage in the shared fantasy. Each one of which fulfills highly specific functions, psychodynamic functions, behavioral functions, manipulative functions, and so on and so forth, but the Narcissist believes his own fantasy, he is immersed in it, he is identified with it. That's why Narcissists do not gaslight. Narcissists do not future fake. Psychopaths gaslight, psychopaths future fake, and of course, psychopathic Narcissists. Pure Narcissists don't do this because as far as they are concerned, the shared fantasy with the intimate partner is reality. The Narcissist doesn't feel that he's lying or gaslighting or future faking. He would stake his life on the veracity of the shared fantasy and on its ultimate fulfillment and manifestation. He is the shared fantasy, he is co-extant with it. They are one, the Narcissist and his shared fantasy are one and the same. Take away the shared fantasy, the Narcissist falls apart. Narcissism is a fantasy defense, gun or eye. The defense extrapolated and interpolated to the point of consuming the totality of what used to be the Narcissist's true self and personality. Narcissism is nothing but fantasy.  So the second point in Narcissistic abuse, it is functional, instrumental, weaponized and an integral part of the shared fantasy. It is triggered actually by the transitions in between phases of the shared fantasy. Number three, Narcissistic abuse aims to negate the victim, to convert her into the idealized internal object that represents her in the Narcissist's mind. So it is a form of coercive snapshotting. Narcissistic abuse is a form of testing whether the intimate partner could fulfill her maternal role and love the Narcissist unconditionally, for example. So Narcissistic abuse is about making the victim disappear, vanish, annihilate the victim so that she can resurrect and reemerge within the shared fantasy and in the form and shape of the idealized image of her carried inside the Narcissist's mind, the internal object that stands in for her. Point number four has to do with recovery. The only way to recover effectively from Narcissistic abuse, as I've been saying for many years, the only way is to separate, individuate. But the Narcissist does to his victims. He regresses them. And by the way, when I say he, it could be a she, when I say she, it could be a he, okay? Don't start the war with gender pronouns. I'm using the literary forms and the literary form is to use he, okay? So the only way to recover is to separate individually. The Narcissist pushes you back to childhood. The Narcissist infantilizes his targets, his prey, his victims, and then plays or acts a maternal role. This is part of the dual mothership concept. So you have been infantilized. You have been regressed. You have been placed inside a time machine and then teleported back to your early childhood. You need to start from scratch.  You need to acquire personhood by redeveloping a constellated self, resuscitating your ego and ego functions which you have relegated to the Narcissist during the shared fantasy and thus becoming an individual with autonomy, with agency, and with self-efficacy. How to do this exactly? I have a playlist on my YouTube channel titled Healing and Recovery from Narcissistic Abuse. There are quite a few videos there which describe the minutiae and details of how to accomplish this separation individuation. This is the only way to recover from Narcissistic Abuse. Okay, this is Narcissistic Abuse. What about Psychopathic Abuse? You remember that Narcissistic Abuse is ubiquitous, is all pervasive. Psychopathic Abuse is exactly the opposite. It is domain specific. So Psychopathic Abuse would have to do with your money or with sex or with contacts or with access or with a luxurious lifestyle. In short, it will be domain specific. Psychopathic Abuse manifests and is expressed only in that domain, not in other domains which makes it very difficult to convince other people that the psychopath is a psychopath and that the psychopath is an abuser. Because other people never witness the abusive aspect or abusive facet of the psychopath. He is goal oriented and domain driven and criminalized. One major difference between Narcissists and Psychopaths. Narcissists are pro-social. Narcissists depend on other people for narcissistic supply. They need to collaborate and collude with other people in order to extract supply from the environment. Very often you find narcissists in teams, leading teams. So chief executive officers, presidents of countries, politicians, actors, directors, policemen, judges, the preponderance of narcissistic personality disorder among medical doctors and so on and so forth is much higher than in the general population. Yet all these people are essentially communal, pro-social, collaborative and team workers. Not so the psychopath. The psychopath is a loner, lone wolf, solitary and the psychopath is very criminalized. Narcissists actually are not as criminal as self-styled experts would have you believe. Psychopaths are highly criminalized. Actually most of the studies we have about psychopathy, starting with Cleckley and ending with Robert Hare and Babyac and others, most of these studies were conducted in jailhouses and prisons. So point number one, psychopathic abuse is domain specific, the psychopath wants something from you and will abuse you in that direction and it is criminal. Number two, psychopathic abuse is driven by power. It's a power plane. It's about control. The psychopath's aim is to control you. The narcissist's aim is to convert you. The psychopath's aim is to own you, to possess you, to control you and then to leverage you as an asset on his march towards attaining and obtaining his goal. Number three, the psychopath is goal oriented and psychopathic abuse is goal oriented. The psychopath will trample on people, crush them, kill them if necessary without a blink of an eye and then would have great dinner with fava beans and chianti, all this to accomplish an agenda, to realize a goal, to actualize an ideology. So the psychopath is goal oriented. The narcissist's only goal is narcissistic supply and usually the narcissist uses a shared fantasy or imposes a shared fantasy and coerces people around him to participate in the shared fantasy. It's a cult-like setting. Psychopaths rarely lead cults.  Psychopaths are loners. Narcissists are cult leaders and gurus.  Wants you to introduce him to powerful and important people. Wants you to open up markets for him. Wants you to afford or finance his luxurious lifestyle. Wants something for you. The narcissist doesn't want anything from you. The narcissist wants you. Narcissist wants you to become one with him. Not by way of codependent merger fusion, but by way of rendering yourself an abstract internal object. The psychopath wants to control you, wants to have power over you, but not because of you, because of what you can provide him with, because of any goods and services you can bring to the table. So while the narcissist assimilates the supplier, the psychopath monopolizes the supplier. The codependent merges with the supplier. These are three separate, different coping strategies. Recovery in the case of the psychopath revolves around restoring justice. The restoring justice is a highly idiosyncratic individual thing. Some people restore justice by or via retribution, retributive justice, and they seek to punish the psychopath via the legal system directly by naming and shaming the psychopath, exposing him in a variety of ways. This is retributive justice. Simply cut off the psychopath, denying him the potential in the future to benefit from their goods and services and help. That's a punishment in itself, and it is a restoration of justice. And so, each victim of psychopathic abuse must choose a way to somehow restore a sense of justice, order, structure, because what the psychopath does, he destroys the belief in a just, ordered, and structured universe. And so, the restoration of this belief is crucial and essential to the victim's well-being. However, there's no single way about it, and we should not criticize victims for choosing this path or that path. Some victims are much better off by ignoring the psychopath, removing the psychopath from their lives, and denying the psychopath future opportunities which might have been his.  Others don't feel comfortable until they've exacted retribution in public or via the legal system or in a variety of other ways, among the peers of the psychopath, or by isolating and denying the psychopath access by disrupting the psychopath's activities and so on and so forth. There are as many ways to restore and obtain justice as there are people on earth, so we should allow each victim to choose his or her way of doing this. Psychopathic abuse is usually time-limited and it is goal-oriented and domain-specific. It is much easier to cope with than narcissistic abuse, actually, on a psychological level. It's a tit for tat. It's transactional. It's very clear, whereas narcissistic abuse is all pervasive, all consuming, and subsumes the victim and somehow transforms, digests the victim. And borderline abuse, as we shall see, also is much more pernicious and problematic than psychopathic abuse. So the proportion of the justice meted out to the psychopath is, again, a totally individual thing. So I always advocate a limited victimhood period with very clear restorative justice goals. Define to yourself, ask yourself, what would restore my belief in justice, order and structure? What would make me feel that I have received redress and recompense? What would restore in me inner peace and quietude of mind? And then pursue these goals and only these goals. And when you have attained and obtained them, step back, forget your victimhood, and move on. If you don't or if you can't, you may need help to do so, because victimhood can and very frequently does become an obsession. And that applies to all forms of abuse, narcissistic, psychopathic, sadistic borderline. But as I said, ironically, it is strongest with psychopathic abuse because of the implied narcissistic injury. So while in narcissistic abuse, the aim is to silence the narcissist's voice in your mind and to undo the damage by separating from the narcissist and becoming an individual which has nothing to do with the internal object in the narcissist's mind. So the way to recovery from narcissistic abuse is separation, individuation. The way to recovery from psychopathic abuse is simply to punish the psychopath. What about borderline? Borderline abuse and borderlines are very abusive. Most of the time, actually, borderlines are abusive, not because they are evil people. They're not. But because they are dysregulated and they are labile and they are half-baked and they have severe problems like identity disturbance and they lose control very frequently. They are a bit impulsive, they decompensate, the defenses break down, then they act out, they transition to a facto two psychopathic self-state, et cetera, et cetera.  And the characteristics of borderline abuse are again different to narcissistic abuse and to psychopathic abuse. The borderline wants to coerce you into providing external regulation. The narcissist wants to assimilate you by converting you into an internal object. The psychopath wants to control you, to have power over you in order to attain some goal. The borderline wants to coerce you into providing the function of external regulation, stabilizing her moods, shoring up her emotions, providing her with a safe haven, taking over many ego functions like reality testing. So the borderline needs her partner, intimate or otherwise, borderline needs her partner to actually provide external input that would substitute for internal psychodynamic processes. So she outsources her mind to someone. She outsources her emotions. She exports her moods. She offshores her cognitions. And so then the other person becomes the repository of the borderline's soul and psyche. And no wonder the borderline is terrified of abandonment because when abandoned, the other person abscondes with her interiority with her internal landscape. So she coerces, I'm saying she, it could be a he, of course. She coerces the intimate partner to provide these services. That's the first element in borderline abuse. Element number two, borderline abuse is driven by anxieties, a variety of anxieties, existential, generalized anxiety, abandonment anxiety, also known as separation insecurity, engulfment or remission anxiety, etc. The borderline abuse is driven by anxiety. When the anxiety overwhelms the borderline, when she can no longer take it, she takes it out on you. She displaces, she splits, she projects, she deploys the host of primitive infantile defenses in a desperate attempt to resolve the situation, ameliorate and mitigate the anxiety by exerting control over the object that is triggering the anxiety, in her mind, at least. And finally, borderline abuse is a part of repetition compulsions. Borderline has repetition compulsions. For example, approach avoidance repetition compulsion, borderline approaches, loves infinitely, is unboundary, offers her totality, and then suddenly she becomes cold and detached and even aggressive and violent, critical and walks away and could even have sex with a stranger or do something crazy. So this is a repetition compulsion, it's an integral and very painful part of borderline abuse. How to recover? The only way to recover from borderline abuse is via mirroring. You mirror the borderline in a way you become a borderline or an echo of the borderline. You render yourself unfit to serve the needs of the borderline. If you yourself have become dysregulated, if you display modulability, if you are not safe, if you are unsafe, you can no longer provide external regulation, obviously.   She would then avoid you because you could be a source of hurt, a source of pain and above all a source of anxiety. So let's summarize the three ways to recover. You recover from narcissistic abuse by regaining yourself. The narcissist forced you to lose yourself, to become not you, regain yourself by separating and then individuating. Now to do that you have a playlist that I mentioned before. That is recovery from narcissistic abuse, psychopathic abuse. You recover by punishing the psychopath, punitive recovery, borderline abuse, recover by mirroring the borderline, rendering yourself unfit for her purposes, useless to her and above all threatening because you can cause pain, you can cause hurt and you can definitely enhance and amplify her anxiety and there's nothing the borderline dreads more than anxiety. These are the three types of recovery and these are the three types of abuse and I repeat again I did not discuss sadistic abuse because sadistic abuse is overlaid, is like the cream on the cake, it's overlaid on all these three types of abuse. You can find it with narcissistic, psychopaths and with borderlines. So I hope you had fun and see you next time, next video, precious and precious.