And welcome all to another exciting and exceptional edition of the power trading hour with me. You're humble, lovable and squeezibly soft host. As always, we'd like to come to you at this time. So what do we have going on today besides a little bit of a late start because of some technical issues? Nothing seemed to set up correctly, but we're up two points on the S&P cash up. Let's call it 10, 11 on the Dow, Nasdaq's up 22, Russell's off eight last I have. Crude's up 73 at 59.91. Had a lot of news this morning. Of course, Independence Day yesterday for the U.K., not only independence, but like I said, kind of throwing off the shackles of what would have been a long term of slavery and tossing out the extreme far left and the U.K., and putting them back on the back burner, not as pretty much back to the 1930s. So it certainly looks like the U.K. will get its Brexit deal. The Bojo, if you're like the hip kids like me, Boris Johnson, otherwise known as Bojo, is of course setting up for a U.K. exit on January 31st to make things real easy on everyone. I think they already knew weeks ahead of time that it was going to be a massive blowout in the last couple of days. He kind of just decided to make sure and not try to gild the lily and just sit back and let it all run. But that's kind of it at the moment. Of course, we had a lot of people shorting. I mean, this has been, this is kind of like shorting in the way that the market is, you know, biblically going to fail, frogs, blood in the street, in the rivers, all the kind of stuff that you think the apocalypse is coming. And man, they hammered it and hammered it and hammered it. Dow was down close to 100 points at one time when I saw it. But again, back up a little bit. Now, this is the real problem, and that is that you get these markets, they get highly short into kind of the end of the year. Those shorts are going to cover, let me put it this way, they're going to cover. The shorts are always the weakest hand in any card game, most likely because they're probably sitting behind a computer and can click it any second. And once they start clicking and covering, then that makes other people click and cover. But generally one of the worst things you can do, I'd say eight, maybe nine out of ten times, just be short into Christmas, doesn't always work out that way. But massively, a lot of people, one, think that they can wait and sell and pay taxes in the next year.  I am a big fan of South Park, and I had to laugh at this week's episode, where somebody was telling him about yet another apocalyptic prediction.  Got a lot of stuff to talk about today. You give me a call at<PHONE_NUMBER>. Email me at path at TFNN.com. Expertise is essential to successful trading in today's market. You also gain access to the webinar that Steve Dahl and Tom O'Brien just hosted, the best way to use the TAS Profile Scanner to profit. This webinar archive is available for all subscribers immediately upon signing up. All new subscriptions also come with a 30-day money back guarantee, so you have nothing to risk. Start your subscription by visiting the front page of TFNN.com today, and you'll find the TAS Profile Scanner under the services tab. Sign up today. All price levels. From the price you should be paying per square foot in certain up and coming areas, to the type of cash flow investment properties are capable of creating, Tiger Real Estate can help you make the best decision when it comes to all areas of the market. Before you make one of the biggest decisions of your financial future, call Tiger Real Estate LLC today at<PHONE_NUMBER>2, or email us at tiger at TFNN.com. That's<PHONE_NUMBER>. Call us today. Many of our new listeners have heard about the Tiger's Den. The Tiger's Den is a lively community where professional traders and investors can meet, exchange ideas and information in a comfortable, moderated atmosphere, hear all of the TFNN shows, plus see all of the charts as they happen live, and have access to archives of all of those charts. You can test drive the Tiger's Den absolutely free for 30 days, and greatly enrich your knowledge of these markets, and how to make your money work for you. Details on the Tiger's Den are on the front page of TFNN.com. Check out the new TFNN.com now and experience all the upgrades. TFNN.com educating investors. Call now toll-free at 1-877-927-6648, internationally at<PHONE_NUMBER>. And what else do we have? Oh, anyway, we've got technical issues, as they say, but we'll work them out as the show progresses. Well, let's do a little history and then we'll move on. On this day in 1962, NASA launches an active repeater communication satellite, Relay One, from Cape Canaveral. One of the earliest communication satellites to be Relay One's mission was primarily experimental, but nonetheless it was used from notable events. On November 22, 1963, Relay One was the first satellite to broadcast television to the United States or from the United States to Japan, which happened to be the announcement of the assassination of John F. Kennedy. It was used in August of 1964 to broadcast the summer Olympics from Japan to Europe and the United States, relaying the signal with one other satellite. But for a guy, I grew up always watching the news the day after, because in Hawaii there were no satellites or any of that kind of stuff. In fact, it was into the 80s before Hawaii was seeing the news on the same day as the rest of the other 49 states. So we didn't pay a lot of attention to it because the news was pretty much over by the time we got it. But satellites have truly changed a great deal of how fast the news moves around the world. But really this is the start of it in 1962. My mother bored me just two years earlier. What else do we have going on? Okay, let's go ahead and see if I can't get some other stuff up here and going and start looking at some charts. I had some questions about anything going on with the big leaders today. Do I see any signals? And the answer is no. Again, I think the best description about how things are going is exactly as we've been talking about them. I didn't think that we'd move up this fast, this quick. I thought it would take probably the rest of next week to get up there. I would have added a lot more positions if I would have known the market was so froggy. But you never know how the news is going to fall. So I had some good positions that were going to be good, whether the market probably went higher or not. At least those sectors and those stocks looked fairly good. Microsoft, as we've said, very tough to kill stocks this time of year. If they have a good trend. Apple, Microsoft, both up and FLX. Again, those stocks that are already headed back down, not doing a lot today, but certainly not down like Netflix still. And it's just kind of filling its gap down from the 10th. When this thing had some kind of bad news, I guess you could say. So anyway, very light volume up. Again, if I was looking at shorting this, I don't think I would be long. But if I was thinking about shorting this, again, I don't see any reason to be short before the end of the year. That could change. But from everything I see, we're just going to see days like this where you start off and people short, short, short, short, short, short, short, push it, cram it down. And by the end of the day, we're either flat or higher. And again, we don't have to go that much higher. All we have to do is go a little bit higher each day. And eventually these shorts will start buying. And the rest of the market will not just melt up. But generally you get a real sharp interday top. And that shows you where all the shorts are out of the market. But we'll keep a close eye on it. Other questions about it is coming in from via the email. Is anything really changed in gold? And the answer is no, you're still in this trading range. Would I be short? The answer is no. You did get down to the 136.19 on November 12th and really fill that gap. So that's kind of the downside in the market. More than likely you're probably going to go to 141, maybe 142 on the top side. But between now and Christmas, it may do nothing, but go between like 137 and 139. And just to wear you out before the real move comes, generally you want to wait and not anticipate these things that aren't, that are kind of going sideways and wait for something really truly to move. Another question I had is, am I getting bearish now that the VNQ is below 90? And the answer, it would be yes, if there was a lot more volume today. We had some decent volume yesterday. Really didn't break out the low today. You got about 4.4 million shares. And again, if you're going to have a really bad hair day in the market, it generally, the REITs, take the brunt of it. That is one half of the one side of the coin. The other side of the coin is the TLT. And this again, just looks like it could continue to go sideways for a while, maybe even melt up just a little bit, maybe 139, 140. But this one may be one of the most quiet sectors into the end of the year. I don't see a great deal happening. What else do we have out here that I wanted to look at? IBB, kind of flat. There were a couple of stocks out there that really hit yesterday. Today we've got a fairly decent doji pattern when it went to 122. And again, this one, we're starting to see a lot of posturing for the 2020 election. And part of that is going to be going after all the biotechs. And I just think that there's easier money elsewhere without random heart attacks from somebody basically wanting to nationalize and socialize at least the health care manufacturers, to some extent. Can you still make money in that sector? You can. It's had a good move. I just kind of see that the news flow is going to be against it for the rest of the year. After the bill last night, we had Adobe coming out with fairly decent earnings and a nice pop. ADBE, ADBE, if he typed it correctly. Nice pop. And it gets you above the previous high. It gets you above the previous high with twice the volume. So you got a valid breakout in Adobe. Yeah, that's a July 19th eye with a 2.3 million shares at 313. You got to 321.73. Again, into this type of year, a lot of people are going to chase this. I don't think so, but I do think that anybody that was short the stock is going to have a real problem sitting on their hands until next year, i.e., January 3rd before much happens. So again, you got everybody on the wrong side of these things. It's got two gaps now. I suspect you're going to get one more gap out of this before it really sets a high. That's ADBE. We'll be back in a minute. The path of least resistance is David White's daily trading newsletter. And if you're looking for active trading ideas, then now is a perfect time for a 30-day free trial to this powerful daily trading advisory service. David uses his years of trading experience to offer his subscribers his trading ideas each morning in his Path of Lease Resistance newsletter. Using a combination of equity trades along with options, David keeps his subscribers up-to-date with all pertinent market information with intraday afternoon updates when warranted. Don't miss out on this great chance to get a 30-day free trial to David's daily newsletter, The Path of Lease Resistance, with no obligation to pay anything. 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The Art of Timing the Trade Chart is designed to help you when scouring the markets for stocks just beginning to form the trading patterns that many investors spend days, weeks, or even months searching to find. And right now, we're offering licenses available at only $79 a month. We are so confident that you're going to love this new charted software that will even give you a 30-day unconditional money-back guarantee. Don't miss out on this incredible new piece of software. Get your copy of The Art of Timing the Trade Chart today by visiting TFNN.com. The Think or Swim banner on the front page of TFNN.com. And we're back. To see what else do we have? Okay. Oh, we've got... He dropped. He might be listening. I don't know what he wants. Tim wants to know about XOP. First thing I want to do is familiarize myself if I haven't in a little while with what's in the ETF itself. There's a website called etfdb.com. And if you put the... Anyway, I get rid of this horrible thing. There it is, close. You can see all the weightings of all the shares of the different companies. And this one, I kind of vaguely remember that Murphy Oil was the biggest holding in all the XOP. But generally it's these big conglomerate energy companies, Phillips 66, Marathon Petroleum, Valero, Conoco Phillips, Conchito Resources, Marathon Oil, Simrax, Hess. So you've got a little bit of these people that are actually the suppliers, some of them that are just the gas stations themselves. And it's kind of... You got a little bit of both. I'm not exactly sure what's the next page here. The problem I think you've got in this one is there's handful too many of energy exploration companies that kind of take the edge off this. Cabot oil and gas, Matty or Resources, Devin Energy, EOG. A lot of these companies spend, I think too much for what's going on now. Everybody kind of likes the companies that know what they have. But anyway, the question on this one is just that. And you did break the previous low in the XOP on October 21st. That was $20.37. Got down to $19.90 on December 3rd. You did so with about 5 million less shares. Generally, I want to see something like maybe 10, 15 million shares less. And so could you just kind of rotate around in this area, $21.22? I think you can. Again, a lot of these stocks are probably in sectors, they're probably warming up for what's really going to happen next year. And I do like this one. If it would happen that this would pull back on extremely light volume, let's say the last couple of days of the year, this may set up absolutely perfect. Oh, do we have them on? Okay. Thought I heard somebody talking. Okay. So anyway, we've got that. Trying to see if there's anything else. I don't know if you're long or short or whatever. I would like this to pull back to about 20 bucks on very light volume. And again, as we go into the end of the year, this is where a lot of stocks really set up. And that is they go sideways. They kind of lose all their momentum and all the sellers and the people that think it's going to the moon all kind of have to calm down and chill out. And then you come back to the market on the 3rd of January or 4th, whatever. And you actually start seeing the people and what they want to buy. They think about this stuff over Christmas. And as these things do kind of lose a lot of the momentum, they are kind of setting up. And so this is where you want to really find these companies that are at support, that have pulled back with light volume and really get set up for the beginning of the year. If you're thinking bearish, you want to see these things go to their extreme highs with light volume and be anything other than Adobe where it's actually got a valid breakout of the market, you want to see light volume and maybe even pull back into the trading range on light volume. But yeah, again, even to the first of the year, I'm going to have a lot of problem being very bearish in this market. We're basically flat on the S&P and the Dow, NASDAQ's up 20 points that continues to show some strength in that. What else do we have? Question about, what is this? Question about Tesla, TSLA. 365 was the high today. It's really just kind of hanging out here to the beginning of the year. This is where the real resistance is going to come at 365-21. You got a little bit of reversal, very light volume. This one probably wants to come back around the 280 level. That would probably be a fairly decent pull. But again, I think I'm going to have to look at earnings. But I think we looked this up the last week. Let's type it in here. That it's probably not going to break until earnings and that is January 22nd. So I wouldn't want to be, I think that there are enough people that are manic. I think it's probably the best word to say about Tesla. And eventually this thing will come back down to earth. And they'll eventually give up on this because it is nothing more than an automobile company. They have carved out a fairly decent niche. But eventually the rest of the competitors will come over there over the top of the hill. And their armies will follow and the margins will suffer. And it will become the car company that everybody else always knew it would be. Okay, we looked at Netflix trying to see if there's anything else here we want to look at. Okay. Okay. Do you believe the A team will drive through the end of the year? I don't know exactly what you mean on that. But again, I'm not a big fan of thinking that it is time to short. And again, you know, this is probably the last big day we have a lot of news, all that stuff. Volume will probably be light on Monday and it will just get lighter the rest of the week. Thoughts on Costco. We already did Adobe, C-O-S-T from Wayne. Again, a lot of people thinking too much, thinking too hard about Costco and China imports. You got down to $2.89 today, but you're back up at around what? $2.92-ish? What is that? $2.92-32. Again, I think a lot of these things are just going to be trapped. Now, if you're looking for short and short potential, it's probably in the retailers after Christmas. They always get soft. They'll maybe have some good numbers and some good earnings. If you were looking for something to be short, I don't know if Costco is the best thing. I've been wondering when Coles is going to blow out this $44 volume low that's been at $43 and $44. But my guess is if this thing could continue to go up, maybe 52 to 54 bucks. And if this thing would squeeze all the shorts out, you could get that short on this thing, about 54 bucks. I think that's one that I'd want to be short regardless of the way that the market moves next year. We'll be back. 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That's TFNN.com then hit watch Tiger TV for the latest market information. And what else do we have here? A question about P-A-W-N. Is that right? P-A-N-W, excuse me. Of course this blew up on earnings. I was short this thing for a little while. It really looked horrible. It continued going up anyway. Basically you would have been short at the close into earnings and it got down to 214 off 250. But I don't know if there's anything you should sell or say about it. If we were looking for a market that does roll over, you want about 237.50, something like that, maybe 240, that area on a very light volume. But it doesn't look like you're going to get it on this one. Like I said, there's things going sideways on light volume. You want probably a retest of 214.90 to find a low. But if you're looking for a high, 240, and light volume sets up probably a short, they've got problems. To do what else do we have out here? A question about silver. I'll take a quick look on that one. Again, more of an industrial metal than hiding money in your mattress like gold. You're back up against the previous September 24th high at 3124, 340,000 shares. Yesterday you got into it with 230,000 shares. Today you just have 103,000 shares. Could it still, with the trade, at least some of the issues being out of the news probably all through next year now? Could this get up to 3226? I think the answer is yes, and probably moving a lot better than gold. But we've been looking at that for a while, and it's been doing that for a while. We looked at Microsoft already. Okay, let's take a look at Amazon again. And then we'll look at Facebook.  That's really what started hurt it a bit. Again, we're looking at a lot of these retailers, or not retailers, a lot of these big companies that are web services companies having issues, or RCL. Oracle was one of those. It just doesn't, and hasn't done well at attracting those customers, but it's probably the worst of the bunch, down on fairly decent volume. And of course, I always love Oracle for one reason, and that is I get to say the CEO's name, who just, it sings. I wish I had a name that's singed as much as saffricats. It could be one word or one name, or it could be two names, saffricats. In fact, it'd probably be a nice name for a company, wouldn't it? She'd probably sue me, but I think it sings. Anyway, it's back down to support $53.87. They just continue to not be able to buck Amazon web services, Microsoft or Google. And of course, more and more other companies are coming in, like MongoDB and others that make it problematic. It's almost like databases are legacy issue. They are not, but until you start really rigging these things up to go together very well with web services on Amazon and Google and Microsoft's Azure, it's problematic. This one is the end of the world, no. But is it a growth stock anymore? The answer also on that is a big fat no. IYT. Yeah, I have a feeling this one come the end of the year is at least $200 or maybe over. Had a nice move off the low, light volume day to day, but I think from looking at a lot of the stocks in this also, they've been heavily shorted. Again, if you missed the semi-open-open to the show, there are just a ton of people piling in on the short side in the Dow today. If they don't get a market moving lower, they will have to cover by the end of the year. As other people cover, it just makes it more painful to sit on. I don't see any reason for being short in the market right now. Okay, question about WDC. Is it time to short it? Again, I'll think it's time to short it when people quit asking me time to short. Where I'd love for this thing to be to short it is about $60. That would be kind of the perfect. I don't know if you get it. There isn't a lot of juice back here after it blew up on earnings on the 31st of October, but there's just not much to say about it other than that too. Okay, we're taking a look here. Give me a call at<PHONE_NUMBER>. Email me at pathtfnn.com. And of course, what you want to be doing now is going to the front page of TFNN and checking out the tiger dollar sale. Now, never a better time to check out that than today before you forget about it and you wished that you bought the tiger dollars today. So I'm going to go to the front page on that. Okay, what else did I have? Question about all these companies that popped in the last few days on the China news. You're pretty close on Las Vegas Sands. You wanted about 7.7 million shares. You got 6.7 million shares yesterday. Today's fairly light. It certainly does look like you're there. This thing could just go sideways for a while. Again, very tough to see how you could be short this going into the end of the year, but you are. One nice thing about Las Vegas Sands is that there's a real huge resistance level that comes from the gap down going back to, what is that, July 26th of 2018. You need about 8 million shares, 8 million shares to get through that gap. So a lot of overhead resistance at this point. It's probably going to take a while for it consolidate back up these. You do have a decent break of that April 18th high of this year. Again, you go right back into more resistance. You're only talking about 7 bucks to get up to the June 20th of 2018 high. Beyond that, you could have a fairly decent breakout. I just have a feeling eventually, if it's not this year or next year, we're going to have yet another row for trade disputes. What else do we have? We looked at the IYT, question about the TZA. Take a look at that if we have time. Yeah, I don't know that you get saved out of this. Yeah, I mean, the small caps are kind of the weak sisters today, but I don't see any signal yet. If you did get a little pullback, this would probably go to about 42 bucks fairly quickly. So not a bad $6 trade from the low of yesterday, but again, not a lot of follow through today. We'll be back after this. Most wealth managers tell you can't be done, which is how to time the markets. I'm Steve Rhodes, author of Mastering Probability, and for the last 12 months, Timer Digest has been tracking my newsletter signals, which have earned me the ranking as their number one market timer in the nation for the S&P 500 for the last 12, 6, and 3 months. Timer Digest also ranks me as the number one market timer for gold as well. The fact is, markets can be timed, and I'll teach you the exact set of tools that I use that has transformed me into one of the best at what I do. 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Match that with 14 years as a full-time trader, and he's uniquely qualified to guide you through the light-speed world of ever-evolving high tech. If you're ready to ride the next big technology bull market for less than $40 per month, log on to TFNN.com and get your two-week free trial to The Technology Insider. Get in on the ground floor of the next big thing today. Since 1984, Basil Chapman has been using the Chapman Wave methodology to advise traders of his expert market opinion. While originally hand-drawing charts from the late 1970s into the 1980s, Basil noticed that prices under most circumstances virtually always had a certain number of likes to the upside before declining sharply. Later, Basil found that computer software, which included the standard market technical indicators, enhanced the degree of accuracy in calling price turns, as well as market trend calls. Thus was born the Chapman Wave sequence. Using the Chapman Wave methodology, along with other indicators, Basil Chapman advises his subscribers of his expert market opinion each market day with his opening call newsletter. Right now, you can get a two-week free trial to the opening call, Basil's daily trading newsletter, by visiting the front page of TFNN.com. Cancel at any time during that trial and pay absolutely nothing. Get your two-week free trial to Basil's newsletter, the opening call today by visiting TFNN.com. Catch Tom O'Brien, professional trader and educator, founder of TFNN, also a special guest on CNBC. Tom will bisect and dissect the markets. The Tom O'Brien Show, next on TFNN. And we're back. Willie asked about Sonos, S-O-N-O. This is what you would call one of the failed IPOs. August 3rd of 2018, that sounds about right. Is it going out of business? No. Is it ever going to grow? Probably no. The problem is that you've got to get Amazon to really support you and they really haven't to the level that they need. They need to get bought out. But again, is it a good company? Yes, but kind of, are we back there? Kind of a bad time to be wanting to be bought out, especially by somebody like Amazon.  They may have, this is where you really want to separate products or they have good products from the company. But the company's not going to make money if they don't have some kind of integrated system from Amazon or from Microsoft or from some of the other companies. And they're kind of this lone wolf out there making their own products. That was good for 30 years in electronics. But now if you're not part of an ecosystem with apps on all the cell phones and everything that works together, incredibly problematic. And again, no one really wants to play with Sonos. So I'm not a big fan of this. I think it just probably drifts around down to 10 bucks. Maybe someone buys it. Maybe someone doesn't. But I didn't like it when it came out. I think, again, you got to differentiate good products, company like Tesla with what kind of value that it has over time. Both Tesla and Sonos have kind of really poor business models that I don't think stand the best of times. We'll be back with a Tom O'Brien at $330. So when you can, when you have to, see you here Monday, same back channel, same bad time.


Welcome to the Ron Paul Libertary Report. This report is coming from Angleton, Texas at the Mises Symposium. I welcome everybody to the Libertary Report. And for our viewers, our co-host surprisingly enough is Daniel McAdams. How are you this morning, Dr. Paul? Yeah, and Daniel has all kinds of surprises because he hasn't told me what our program is about yet. Didn't you hear your phone ringing during our break? I kept calling you. But you know, there's a lot of days when we do our report that we don't know a whole lot before. He's getting so professional. Now he keeps his computer open. He says, oh, there's a news flash here right in the middle of the program. So he does keep up. There wouldn't be much of a report there if it didn't have Daniel. They're keeping it going. But of course it wouldn't exist if we didn't have viewers tuning in. And I might ask Daniel to do a little bit of reporting on numbers. But you know, our numbers are very, very good. In a way, it's sort of a mixed blessing. The numbers have skyrocketed recently because of the corruption in the country. And they want to hear something about how we're going to get rid of it. But we do have a larger audience right now than ever before. And something that we didn't have at the beginning is we didn't have live streaming. Those were some of the terms I had no idea what they were talking about. But I know what it is now when it started off. I think Daniel, it might be something like, we had 100 or so people tuning in for live streaming. And now Daniel will update us on that because I think our numbers are growing. And I haven't found out that if you live stream, you can communicate with other people who are live streaming. And sometimes they go back and forth. Then there's a little bit of excitement. And we pay attention to it. It's pretty neat that we can get feedback like that. But Daniel, why don't you give us a little update on how long we've been doing this and what are the numbers doing? And how many do we have now? And how many are we going to have next year? Well, we got really excited early on. This was in 2015 in the spring when we had 60 live viewers. And it was amazing. And one of the things, Dr. Paul, as you know, the real measure of success, the main thing we wanted to achieve with the show is that when something happens, people want to turn to us and turn to you for your take on it. And we find that happens over and over again. When President Trump fired a few missiles into Syria, well, we had a big day because people wanted to know what did Ron Paul think about it? What did the Ron Paul Institute think about it? And we've learned from this past week, well, certainly these past few months, our numbers on the coronavirus have skyrocketed. People want to know that they're hungry for an alternative view. But as Professor Rectonwald pointed out, and we should make no, we should make no bones about it. We have had a show yanked temporarily. There was a little bit of an uproar. And we don't know why, but they put it back up. But we operate under the assumption that any show can be canceled by the mainstream media, by the YouTube, by Google, by the CIA, as we now know. And so it does constrain. And we just had a conversation on Thursday, Dr. Paul, when we put out a title and we were looking at it. And we thought, you know, it could get us a lot of viewers, but we might want to soften it. And it's terrible doing this because this is what they did in communism. This is what they did in communist countries, self-censorship. So it's a problem we face because we want to grow our viewership. We want to do it with snappy titles.  But we also realize that there are risks involved with trying to do that. You know, many people know the story that I got interested in politics, not because I was interested in being in politics or in office, but mainly to have a forum talking about things that I thought were important. And that was in the early 1970s. And of course, there was a big issue of money, monetary policy, and the gold standard in Bretton Woods. And that got me motivated. And I spent a lot of time on that issue and continued to spend a lot of time on that issue. And I got on the financial services banking committee very early on and was always on the banking committee. And yet, as time went on, foreign policy became a bigger issue, too, and a big issue. So I think probably my time is split. But we are also directed by current events. And right now, you know, we talk about monetary policy. We talk about the budget. We spend more time on a liberty report on Fridays on economic events. But I remember early on in the debates, presidential debates, it was announced that this week, we were, you know, going to do economics. And then the next week, they said, well, we did economics last week. This week, we're going to talk about foreign policy. And I always thought that's a dumb statement. You know, how do you separate the two? Can you talk about foreign policy over here and talk about sanctions and protectionism and interference and more profiteering and all these things and say it has no economic impact? It has a tremendous amount of impact. Well, current events have driven us here in the last several months, obviously, to talk about our problem with getting people to understand what coronavirus isn't. And we've been working on that. And, of course, that invites other things, that invites, you know, civil liberties. That is a big, big deal because it's a violation. But so does foreign policy involve the violations of civil liberties. So it's a show that we put on and people are interested. I'm delighted that we have some people interested. But when some people say, well, you add $250,000, well, we have 2 million people watching our station. Yeah, I know, but they don't even know what they're talking about. So I argue that we have good numbers and we go for quality. I'm glad to be here today with all of you. Dr. Paul, one of the things that we've been following, and I noticed when I got to your house last night before our dinner that the TV was on and you were watching the numbers come in and you were watching what happened. I know in your talk, you're going to talk about does voting matter isn't even a point. But we haven't talked about this before. But I was going to ask you, I know you were watching the news this morning. I know you were following things this morning. What are the things you're seeing about the election and what are your thoughts at the moment? Same old stuff. Nothing dramatic. The lying continues. And this is all about lying and who are the best liars? Who's the biggest demagogue? But that's been around for a long time. But it's also it's constantly reinforcing this concern. Who are the police? Who's supposed to police solve this stuff? And the police, I remember as a kid, it would be brought to our attention, boy, you don't want a crooked cop, crooked police. They're terrible. They're evil people. But we have a crooked police force in this country. When you think about, you know, how powerful has the mafia been along? They have their police connection and there's bribery. How much abuse of the police departments have occurred with the drug war? And it goes on. And so you have a system now that's very, very much involved like never before involved in our elections. And we have the Justice Department, the CIA, the FBI, and they've been involved in a long time. But it's still there. It's always who are the corruptors and how much power that they have. I want to take a short story about when I first went to Congress, I told somebody that I was interested. And some of you may remember the name of the name of Dan Smoot. And he belonged to the old right, which were very, very libertarian. And I can't remember exactly why I called, but we had a conversation in the subject of the CIA and the FBI came up. And he was, I believed him to be a very honest person. He was pro FBI in the good sense of the word. So after World War II, he was picked to be in charge of finding individuals to be recommended to go to the CIA and start this new CIA out. So he did. He took his job seriously. He had two stacks, went through all the people. Back then, the scare was, is he a communist and what his views were? So he had two stacks of people that he recommended.  And the people who were moving along to establish the CIA, they took the wrong list on purpose. All the people who were corrupt and untrustworthy and security, that's how we got started. So we shouldn't be totally shocked about what we hear and we've heard it today. The CIA is not our friend. And one other thing that Dan Smoot told me at that time we were talking, he says, the point is, if you want to have a republic, you cannot have a CIA. It's impossible to have a republic. You know, Dr. Paul, speaking of the CIA and also speaking of how the U.S. metals in elections overseas and has done so for a lot of our troubles go back to CIA involvement in Iran and 53 as you point out many times. But, you know, trying to look for a silver lining in the fiasco, the worldwide sort of embarrassment of the U.S. elections over the past week, I found a silver, you know, I'm always trying to find a good news story. And sometimes we have to dig deep. But I actually found a good news story about this whole thing. And this is just simply this, Dr. Paul. After this election, the U.S. will never ever again be able to lecture another country on how to hold elections. And listen to this. Some of you may have followed the election in Belarus in August. Of course, the U.S. roundly condemned that election. Terrible, terrible election. In fact, I observed an election in Belarus in 2007, I think it was. It's one of the cleanest elections I've ever seen. But listen to this. This is Mike Pompeo, the great champion of democracy. Here's a statement that Mike Pompeo made about the Belarus elections. The United States is deeply concerned about the conduct of the August 9 presidential election in Belarus, which was not free and fair. So a few restrictions on ballot access for candidates. Now, get this. Prohibition of local independent observers at polling stations. Intimidation tactics employed against opposition candidates. They did, we regret that observers did not receive a timely invitation to monitor the vote. And we've all seen the observers in Pennsylvania were about a half a mile away with binoculars. And get this one. We strongly condemn internet shutdowns to hinder the ability of the Belarusian people to share information about the election and the demonstrations. You can't make this up. They keep reusing the same speeches of the other people. That's exactly what's been happening here over the past week. Yes, and it is true. Daniel and I work real hard at this. And sometimes the hardest job is to find that optimistic point of view, at least to mention it. Because obviously there are points and I'm always amazed and sometimes surprised that with my concentration on trying to warn the people, that has to be a little scary. You know what's coming economically. And all the weaponry buildups and all the crisis that we have that still, it's pretty rough living if you have no thought of a conceivable silver linings on place. Because that's the way the world has worked. And of course, my point has been that in the 20th century, which I remember pretty well, a lot of problems happen. But horrible problem. If you added up, okay, we are 20 years into this century, but I could pick out almost any 20-year period in the 20th century. Our first 20 years here is not as bad as what was going on there when they were killing millions and millions of people. Just think that when the election of 1968 came, which was controversial and had some similarities to what was going on here, but we elected the peace candidate to stop the war. 34,000 Americans died in Vietnam after they elected and said that Johnson, Johnson was run out of town. So we still have a long way to go, but it's been pretty bad. And of course, that's why we have an institute called the Institute for Peace and Prosperity because that's what the people deserve, and that's what you support. And we know that there's a lot more people like you out there that not only would support this program, but those principles as well. So Dr. Paul, one of the things we've touched on here today as well is the rise of the independent media and the travails and the difficulties that we have with one foot in the sort of, I would call the social media, the mainstream media and the alternative, the independent media, looking ahead for shows like ours and others who are trying to challenge the narratives. Are you bullish or bearish on the ability to get a message out in an increasingly restrictive world? I have to remain optimistic because in one way, it's probably my lack of unknowledge and understanding of exactly how the internet works. When I first, they told me when I was running and or announced I was going to run in 0708, they talked about this viral thing and I was like, was that, is that a real virus or is that a medical term or what? No, it's, I believe that there's a lot of smart people out there. There's a lot of smart people in this room that know a whole lot about the internet and spreading out messages. Just think, if our revolution could be carried by just scraps of paper passed around and you know, written paper and they were able to achieve it, word of mouth is still very powerful. It's what the ideas that they have makes the big difference. But if you have an idea whose time is coming, you have people who are ready to repeat it, I remain optimistic. I think the answer to the trash that we get from the social media because that's nothing but an arm of the government. So if we do that, we have to use every tool possible and I think that's available and you know, I read about them, but I don't understand that, you know, how all those computers work. But I believe that the answer has to be in the competition and there's no reason why this should be permanent. You know, they come and go and politicians come and go and they lose credibility and I think hopefully very soon the social media loses this dictatorship that they have. They have total control. But I know a lot of people are sick and tired of it and a lot of people are recognizing it and the numbers keep going up. We're up to probably about 68% of the people now don't believe what the government tells them and that I think is encouraging. Well, Dr. Paul, if you're about ready, I'll close it out as normal. Yes, go ahead. Give him your statement and then I'll tell people come back tomorrow. Well, I think the message, the real message and it's the message to all of you is that despite the restrictions, human ingenuity will ultimately prevail. There'll be a way to get around restrictions. We always try to highlight good news stories, as we said, small victories. Dictator Newsom has gotten smacked down a little bit this past week. There have been small other court cases and things. So regardless, and this is the lesson from the Soviet world, the regardless of what they do, the human spirit will never die, will never give up. We just have to remember that when we feel down in the dumps as I felt a lot this past six months. We have to remember that and reignite. I'll tell you what, Dr. Paul, for me visiting with people today and yesterday has really reignited my human spirit. So I'm thankful to all of you. And I'll close our program for today by saying that ideas whose time have come cannot be stopped. And it's our job to do it. And that is why I'm here. That is why I helped to a degree to get the Mises Institute started and encouraging it very much. And that is why people like you deserve a lot of credit. And the numbers, besides, we have a full room here. If we didn't have the clowns in Washington and tell us where we can go and what we can do, we'd have a beer room. We'd have twice as many people here. But I want to thank, I want to thank everybody for tuning in today to the Liberty Report. Please come back soon.


Well, we have agreed that I don't know what we can do, but anything we can, we want to. And it's a horrible tragic thing. We'll put a detail around the families, and we don't have authority to go and ask the Congress to give us that authority. In the meantime, we're assuming it. We don't want them to think we're snooping, though, and that MPs around there for their any purpose, except to protect them. But I wanted to, I placed a call on all of you, and they haven't. I told them to get Pierre Southerner, get you, or get Steve Smith, or to get Ted, and they got him. And if you'll explain to them here what we are doing so they won't, the Secret Service man will be in charge. Under the President's law, they can just cover Miss Kennedy, Ex-President, and the President. We're extending that to all candidates, by the presidency, and their families. And Secret Service take charge, and they'll use defense and justice people until we get authority, and we're going to try to get it today. It's a terrible thing, and we grieve with you, and I wish there's something we could do, and I don't want to bother you. But when you're talking to your mother, please tell her that I thought you were there, and our parents were with you too, Ted.


Among the many capabilities of the KC-130J, the newest is its ability to provide close combat support in the form of the Harvest Hawk. The Harvest Hawk is a KC-130J aircraft that has been equipped with hellfire and griffin missiles in order to help troops on the ground. Pretty much we do whatever they need us to. We overwatch their patrols. We develop pattern of life on compounds in different areas they might operate in the future and if they do start taking fire from enemy insurgents then we go ahead and we can provide them with missiles for close air support. Pilots and crew chiefs from several different aircraft such as Cobra attack helicopters, Hornet fighter attack aircraft and Harrier aircraft are used to pilot and man the weapons systems on the Harvest Hawk. Reporting from Kandahar Airfield, I'm Corporal Daniel Wolves.


Today's class, we're going to, you remember we started our discussion, okay, today's class is going to be a brief class, but unfortunately it's week 15 and I have to go somewhere, okay, but anyway, we're going to six o'clock. And the other thing is, next week, all of next week, I apologize for this, there won't be no class. For this reason, I'm going to propose we have three classes of you for the next few weeks, okay. So before we do anything else, let's fix some of the time we have left for the class. So part of Monday's and Thursday's, I need one more slot. Regular basis, can you suggest one? Is this slot okay? Tuesday. Tuesday? Tuesday. Tuesday? Tuesday. Tuesday or Wednesday? Tuesday or Wednesday? Tuesday. I'll just check which of the days, if I need the classes. Okay, Tuesday is fine. So shall we fix that? Monday's, Tuesday's and Thursday's. At least four weeks. Yes, but this is four weeks left. If you don't mind, we just take three classes. Okay, so we'll fix our Tuesdays to 30. Same class. Monday, Tuesday, Thursday. Okay, so we've begun a discussion of cosmology. We discussed that our universe, we're going to make a model of our universe according to the following metric. And we talked about the idea that the metric in the three-dimensional space, the metric in the three-dimensional space was going to be special. Today I want to make that notion of something being special in the model. So, firstly, let me make a couple of definitions. The model has seen before that definition of isometry is a coordinate change, such that the metric in the new coordinates takes the same functional form as the metric in the new. Okay, so let's look at an example. X i is equal to r i j x j plus e to the metric here. This is an orthogonal rotation.  So you get d x i prime d x i a mixed matrix. This is the full set of isometry isometries. Isometries are defined as finite code. But as usual in the study of symmetries, as you probably can probably see in the video, it's much easier to deal with infinitesimal things than the finite. So an infinitesimal isometry is an infinitesimal coordinate transformation. That does not change the metric. But we can write down a simple equation for what's in the form of an infinitesimal isometry. An infinitesimal isometry is patterned by a vector field that changes under the vector field. We know that del is by 3 mu nu. This equals del mu sin tan mu. So you know by the definition of an isometry, the metric should not change. Okay, so under an infinitesimal, you know, a vector field patterned by an infinitesimal isometry, if at all there is del mu sin tan mu plus del mu sin tan mu, isn't it? A vector field that satisfies this equation is called a killing field. And parametrize is infinitesimal isometry. We work with infinitesimals because those are convenient. Well, of course, infinitesimals can be explanations. You can make the coordinate change smaller than another to generate the finite coordinate change. It's just you know lack of information. No. If they are the general matrix, there's no isometry. There are no coordinate transformations that leave its initial form unchanged. And no killing vectors. There's only special space values that admit killing vectors or admit isometry. Okay. This is the isometry. Are these the words that could be defined all over the history? This is our definition. Yes. They generalize these with a partial isometry. What happens in the rest of it? You know, if it may be useful for you, if you're only interested in physics, that's it. But this is not our definition. Okay. Now. I solute the equation looking for solutions of theta. You could think of it that way. If you want to know whether the space time has any isometry, you can look at this equation and check to see if there are any questions. That in general, there are no solutions. Or are there multiple solutions? Could have multiple solutions. But if you arbitrate, I hope there are no solutions. Okay. Why am I start talking about isometrities and the killing vectors? I start talking about that because I now want to tell you more precisely, I mean, by the statement that the space time is homogeneous and etc. Okay. So, let's consider a little batch around the ideal point. What does it intuitively mean that space is isotropic at least about that point? It means that all that if you set up a little local coordinate axis, it doesn't matter what, how you orient it. What does it doesn't matter? I mean, it means that rotation of your loading local coordinate axis can be generated by symmetry. What are the symmetries of our theories? The symmetries of our theories are the isometrics. The field in the theory is the metric. The metric doesn't change. Okay. So, the space is isotropic. It's said to me, isotropic is what I need to find. If all rotations of the local frame at that point are generated by the symmetries. How many parameters are there? Suppose we're in d-spatial dimensions. d-spatial dimensions. Since I don't want this cosmologically possible, context and problems, the spatial matrix. Okay. Suppose we're in d-spatial dimensions. If the a10 is even one, if the space is isotropic of only one point, there must be a certain minimum number of k. What's the number? p, p-1 by q, because that is the number of rotations. So, if the space is isotropic around a given point, then we don't know what number of k is in this. Next question. What does it mean for the space to be homogenous? What means for the space to be homogenous is that in the local fashion and by extension everywhere. There is, okay, so I should speak more precisely about what I said about the isometrics. But there is a killing vector that vanishes at the point. So, what are the isometrics?  So, we would like killing vectors that vanish at that point, but whose derivatives, you know, in the neighborhood of that point, generate all rotations. And so, the example of this is rotations in that space. Okay. So, of course, we had the origin of that space is rotation in that, but the killing vectors that generate these rotations are x mu and mu minus x. They vanish at the point, but they rotate things in the neighborhood. But this is what I mean by a space being isotropic at a given point. And if it's isotropic at that point, then it has at least p into p minus 1 by 2 killing vectors. Well, I mean by homogeneity. Well, I mean by homogeneity is that there is a killing vector that takes you from a given, from any point to any other point. Infinite, infinite, infinite. They would have that by extension of that space. Okay. So, there is a coordinate change. So, it takes one point, then another. The tropic can be defined about a point. Homogeneity is a, if a manifold is homogenous, it has at least p killing vectors. So, that's the dimension of the matter for me. I'm going to quote some results for you without just proving them. But these results are very nicely explained in Weinberg's book on the chapter of Symmetric Spaces. I'm not going to go through the proofs basically because we're running out of time. A killing vector field need not vanish at a point, at least. But if a killing vector is an isometry, then it does. That's part of a definition. So, an isometry is like a local rotation. So, the translational killing vector doesn't vanish. First result. Okay. Okay.   Then, from using the killing equation, you can prove that del sigma del rho of zeta mu is equal to minus r lambda. This is a general identity. You can prove the identity. Just using actually. I will try to prove. I will try to prove. I will prove for you. But it's a general identity very nicely explained in Weinberg's book. Okay. Why is this important to me? This is important because, look, what we've done with this equation is express two derivatives of the killing vector in terms of the killing vector. So, how do we take this equation to differentiate? So, we'll get an expression which is called three derivatives of the killing vector in terms of derivatives of the derivative and derivatives of the killing vector. But we've already expressed two derivatives of the killing vector in terms of the killing vector. So, what this means is that once you know that the killing vector itself and its first derivative, then you know what the sum of it is. That's the big kind of the killing vector field is contained entirely in the value of the killing vector and the value of its first derivative at a point. At one point, that determines the whole vector field. You can construct the whole field by telling us is this clear? Okay, how are we going to do a few more lines? So, this is, you can show this in a simple idea till you get its consequences. Okay? So, that tells you that the number of possible killing vectors let's look at a point. The number of possible killing vectors is entirely determined by the number of pieces of data in the vector field at that point. And it's derivatives. Moro's derivatives are all free because they represent this equation. So, now can you somebody help me do the counting? How many pieces of data are there because the value of the derivative at a point in this equation? How many pieces of data are derivative of a field at a point? Wait, which question? Suppose we didn't impose this condition, how many pieces of data are derivative of that at a point? Peace. Peace, quiet. Now, with this condition, how many? P and 2? Now, there's something in this constant, something by 2, what's this? You're moving the symmetric part. You're counting all the answers in vector field. That's P minus 1 vector. This is the number of pieces of data at the derivative point. There's also data is the value of the killing vector. How many pieces of data are in the value of the killing vector at the point? P. This is the maximum number of killing vectors killing vector fields are a matter for data because these are the independent pieces of data which completely reconstruct the killing vector field. The maximum number of killing vector fields you can have in a manifold is P into P plus 1 by 2. Now, let's look at this P into P plus 1 by 2. It happens to be the number that you get by adding P into P minus 1 by 2, local rotations. And P, the local translations. So, from just this counting numerology, it might suggest to you that, and it's true, that a space type or a space that is both isotropic and homogenous. See, it's isotropic of a one point and homogenous that is isotropic of every point. The homogenous is the vector that goes one every point to every other. So, that space type that is isotropic of one point and homogenous manifold has the maximum number of killing vectors, possibly, which is P into P plus 1 by 2. And then there's the name of what it's called, it's maximally symmetric space. Such a space is also isotropic of every point. Another bit of algebra you can do to show, again, nicely given by the worksbook, is that if a space is isotropic about every point, then it must also be homogenous. So, all these are the same thing. So, when I talk about maximally symmetric space, there are many characterizations of it, all of which I wrote. A, that it has P into P plus 1 by 2 killing vectors. B, that it is isotropic of every one point and homogenous. See, that is isotropic of every point. All of these three completely say the same thing and define maximally symmetric spaces or homogenous and isotropic spaces. So, all that I've said now, I've now explained the algebra that I could have in a total of 15 minutes. Then the result in that way, it takes a little more time. It's a unique landscape for maximally symmetric space. See, suppose you've got some symmetric space, you can of course take it at this scale, take the metric and multiply it and then overall do the problem. That will also be maximally symmetric. That's a trivial question. Clearly, if symmetric spaces are, you've got one symmetric space, you can generate one binary because I have symmetric spaces by scale. Now, the scale will change the coverage. It's something that is strongly covered because it's small, but completely covered because it's big. So, symmetric spaces can't be completely unique because there's the scale coverage. It's like for the scale. Big, small, small. However, you might wonder why the symmetric spaces are unique up to this scale. The answer is yes. So, more precisely, given the signature of the space time, everything at the top of the space, but everything at the space time, given the signature of the space time and the value of its Richie scale, Richie coverage, which is a measure of how big it is, the scale of the space, the size. By the way, can somebody tell me if I scale the metric, G goes to lambda, G. How is the Richie scale? It's different. G goes to lambda, G. That same distance goes to lambda. The radius goes to it. So, G is a radius square. Let me argue. The coverage of, the coverage of has terms that go like gamma, gamma. Remember, gamma was like G first, DG. So, gamma and coverage also, things like gamma. So, gamma and radius. So, our new loop scales like gamma because it's gamma, that's gamma. And this is independent of the overall scale of the metric. You take G to lambda, G. Our new loop distance won't change. But, our new loop is equal to G first. Our new loop. So, our scales like G first. So, you multiply metric by lambda, the Richie scale is equal to what? Big space and small coverage. It's interesting, right? Okay. So, So, So, just get back. Yeah. So, the uniqueness there. The uniqueness there is that, given the value of the Richie scale, that's just setting the scale. And given the signature of space back, there's a unique, there is a unique, completely symmetric. Okay. This takes a little more proving because it's also nicely proven. All of this information. Okay. It is very easy to construct the metric. All maximum spaces. And I'm not going to, but actually the metric space that we constructed of already last class was history. How did you know there was maximum space? Well, it's intuitively obvious that it's homogeneous and isotropic. But, can you count the number of killing vectors in S3? What is the set of coordinate changes that leaves the metric? S3 can change. Think of S3 being better. Rotations. Four dimensional rotations. Four dimensional rotations. How many four dimensional rotations are there? Six. Six. What is three into three plus one by two? Six. So, S3 has the number of isometrics in S3. It's six. Therefore, it's a maximally symmetric space. So, we're searching for a space of homogeneous space time. So, what we need to do is to search for spaces of space times as many isometrics as we can have. So, now the example S3 has given us has shown us how to think. So, but firstly, all equals zero clearly the unique manifold is flat space. Flat space has been to be plus one isometric, obviously. Speed of P max one by two rotations plus P translations. So, flat space is maximally symmetric. The sphere of maximum is symmetric. Now, let me try to find other examples of metaphors that are maximally symmetric. Now, this matter this is close to our output this is sort of what I said. Suppose I you can do this matter. Suppose I look at the manifold minus x zero squared plus x one squared plus x two squared is equal to what you suggested last time minus x one is equal to minus x two. Let's think of this as embedded in our one column. One time like language. In like ordinary processes. As a manifold, the manifold is left embedded by all the range transformation. Because the expression is the range. So, every range transformation match once in this manifold plot the points on the same manifold. You don't leave the cycles out of this by the range. So, now, where is the number of ison entries of this manifold? Six. Because there are six in range. Now, let's think more about this manifold. What's the signature of this manifold? It's something that we have to understand. Firstly, what is the dimension of this manifold? Three dimensions. Now, what is the signature? Public use. You see, we want to know what is this good set of coordinates of this manifold. You can see it by doing equations. You see it by by the following. This equation can be read as x zero squared is equal to e squared plus x one squared plus two squared plus x two squared. So, at every x one, x one, x three, we can solve for x zero. We can solve for x one, x three. So, we can think of the space being parameterized by x one, x two, x three. So, the x one, x one, x two, x three are spatial dimensions. A spatial.  The reason for believing that that this thing will be the signature of the three. I'm going to show it. By the way, this is not the direction. Suppose you try to solve for e x one squared. If you solve for x one squared, you will get is equal to x zero squared minus x squared minus x two squared minus x three squared. And then there will be some values of x two and x three which are large enough. So, that you can solve for x one squared. So, while x one, x two, x three are good coordinates of the mathematical neighborhood. If you try to choose some other set, that would not be good. Again, I guess I'll place an R three, R four. In the last section, we will place a plus plus plus because then you expect that it will always be positive. Any distance in the distance? Because I don't think any distance on R four is R one comma three. Suppose I take this hypersurface in one comma three and look at this. Because it is solving it in R five. It is solving this equation in R five. In R one comma three. We will see exactly what calculation we need to do to check this. But it's not true that every hypersurface will be of the signature. Suppose we think the hypersurface x three equals zero, that would be two plus one direction because this which has signature minus plus minus. So it depends on the hypersurface. You know what I'm saying is very intuitive. There's time and there's space. If you said t equals zero for instance, you've got a spatial hypersurface. If you said x equals zero, you've got a hypersurface that includes that. This is some funny combination of the two. The solutions in alpha x one, x zero, x one, x two, x three. Besides that, the sequence is a bit an R four. Firstly, we now work in R one comma three thing. It's based on the metric of the embedding space there. It's minus, it's dT squared minus x one squared minus x two squared. Okay? Yes. Now I've written down a particular equation for hypersurface. There's a question. Is this hypersurface of signature plus plus plus? Or is this hypersurface of signature minus plus plus? Depending on the equation in question, the answer will be different. So it's not an empty question. What is the signature? Signature means, are you dealing with a space or a space time? Now we'll take the R four to the half more place over the R What? If there is a minus signature, then it's a space time. Yes? They won't all be x zero equal to constant. No, it's just what is the signature of the metric? Yes, that's what I asked. It's not some temporal equation. It's not some x zero equal to constant. So it's not completely space time. Are you making up this? Others? It's just, it will be some space in which there is some action.  Physically, is there some measure of when signature is not in place? It's not constant. How do I find out what the signature is? Okay, so let's do it just a little bit here. You do it by computing the metric of the sectors. Basically, you just take it there. But there are many ways. But let's just do it by computing the metric. Okay, in this particular case. So now, in this case, the coordinate system that we use for the sphere is now, the first coordinate system we use because in this case, it does not have a so-called symmetry. Basically, I have a problem, but there is a 2C. I was supposed to write x1 is equal to r sine theta cos theta. x2 is equal to r sine theta. x3 is equal to r sine theta cos theta. And x4 is equal to a squared plus r squared. This is very natural coordinate system. Let's compute what the metric is. So the original metric was dT squared minus dx1 squared plus dx2 squared plus dx3 squared dx0 squared and it's pluggy. So, I'm just following the calculation we did last class. From here, we get r squared d omega 2 squared. Last we also get dr squared dr squared exactly as we got first time. So from here, we're going to get plus dr divided by squared root of a squared plus r squared r combine these two terms together we get minus r squared d omega 2 squared minus a squared dr squared over a squared. So this was minus but let's see what's the positive and positive and if physically we see a ego on this and always have a positive then it should be a positive it's simpler than that, start on a point move in every direction let's see if it's positive or positive so in some sense by introducing nonpositive definite matrix We are introducing some additional structure on the hypo-surface. Well, you know what we are doing is looking at a hypo-surface in an embedded space which was not possible. This is not possible. We are pretty much by virtue that we have this additional structure on the hypo-surface. Additional possibility. Possibility, namely the signature of the hypo-surface. Yes. Is this here? Okay. So, this space has a name. Okay. This space is called Euclidean Antidecitus Space. Euclidean Adesis. Okay. It's a space as we mutilated last class, just like the sphere has a space of constant positive curvature. This is a space of constant negative curvature. Because, you know, all the formula is following. This is the curvature of the sphere. The rigidity of the sphere was 1 by 8 square. And all the formula is for the space which is lower than the rimless space by 2.6 square. To the curvature of the sphere, the rigidity of the sphere would be minus. So, this is Euclidean Adesis space, the space of constant negative curvature. It's a maximally symmetric space because it's a minimized space. It's 6. It's an R4 version of a hypo-surface. That's right. It's an R4 version of a hypo-surface. Yes. But you know what we do? Cleverly, it's a hyperbola rarely in R1, overall it's a spacelink. We do it cleverly so as to get such a large amount of symmetry. You wouldn't get such a large amount of symmetry for a hyperbola in R1. The linear manner holds a symmetric space, it's a completely symmetric space itself. Signatures with a space with a signature plus plus plus. That's completely classical by the energy scale. When we produce the manifold with every value in which it's set. So it's completely produced all symmetry, the Euclidean symmetric spaces. So they are the sphere of every radius, Euclidean area has a boundary, and it is the spacelink of every radius. And plus this. These are all three dimensions and the proof would be proof of every dimension. These are all Euclidean maximally symmetric spaces. Is this clear? Since we've all done this exercise, now there's a little exercise in which one could do. And one could ask the following question. Where would we have for minus x 0 square, minus x 1 square, minus x 2 square, minus x 3 square, minus x 0 square, minus x 2 square in R2R. Because this is a hyperbola, this is R2R. This also has six killing vectors. It's SO 2 comma 2. Same number as XO4. Okay? What is the signature of this space? What are the two possibilities? Could be one type of two-space or two types of one-space? Where is it? One type of two-space. Same kind of ideal. Just solve for x 0 square plus x 1 square. What are the time dimensions? What are the space dimensions? This space is what's called anti-discipline space. Okay? This space was called completely anti-discipline space. This space is called anti-iscipline. One of the spaces of other maximally symmetric spaces with signature one type of two-space. There's another maximally symmetric space with signature one type of two-space, which is called DC to space. That space is defined by the equation and is similar to this. We will come to the study of DC just when we start on the word space times with the conglotary constants. So I'll postpone the discussion of that. But just to see from this general construction, that it is very easy given a signature, given any signature, it's very easy to produce maximally symmetric spaces. Just by starting from such type of surfaces in RM comma H. Basically, this idea completely classifies, gives you a construction over all the symmetric spaces in a symmetric space. Anti-discipline space is of no normal importance in the real world. But it's very important in this kind of study of strip theory. You could, just mathematically though, you could produce spaces like this of signature M comma N. By starting with something that's signature M comma N plus one. Yes, sir? Sir, let's see if we can do some free theory on the strip theory. It's possible that boundary conditions put on one surface of one type of signature in the other side. Are you working on a hypersite or the whole space time? You're working on the whole space time. The whole space time is this hypersite or just R in problem? No, no, it's the... No sir, let's say I'm working on a solution of IH times. Sir, this is a different question. It's not separate, it's a related question mainly of particular IH times. Our initial conditions would be on some IH spaces. Yes. Which would be space time. Yes. I'm asking, can we solve, ideally, on one space time IH and other spaces time? You're asking, can you put initial conditions on hyperservices which have a time? It's going to be normal euphesies. It's going to be called an initial equation. Still at the mathematical level, you can ask. You see, the equation del squared equals here is solved. You want to know what is sufficient data for solving del squared. Alright, the answer is in this paper. It's focused on... Moving where? After it was conditions on the time like that. Yes. You see, if you have a bump, it's just a box. The wall of a box has a time lag. So it's certainly permissible to impose. It's permissible to impose. Absolutely. It's certainly permissible to impose. But I thought Harshan's question was, in our format set, could you, you know, what surfaces can you put initial data? Okay, whatever it is, let's postpone it after class. I'm going to stop the class and do it. Fine. Okay, great. So, now... Okay, I think maybe we should just actually stop. So, let's see. So, where have we got? Okay, understand our maximally symmetric spaces. These will be the building blocks we'll just focus on the gene. There's something I wanted to say. So, okay, so let's get the difficulty. Sorry. I'm done. I'm done. Okay.


Good morning, everyone. On this Thursday, this is June 2nd, we're looking at the Dow down 180 points at 32,637. Had an absolutely fantastic move from the 30,635 level over the 20th of May, went straight up, this is the leg A, I believe today should be a peak A, and that's the first leg up, and we're going to see where we stop down at the 32,632 level. 32,580 should be really good support. It must be good support, otherwise it can go even lower. S&P is trading right now down 14 at 4,087. I should mention Microsoft is involved. It did pull back after a little bit of a disappointment. I think it might try to come back later in the day, but in the meantime, it is impacting the Dow, it's impacting the S&P, which is down at 4,089, down 12 points, making that leg B, probably a peak B today, the QQQ also impacted by Microsoft, but in fact, it's moving up 19, it's up 46 cents. At 306.30, this is going to be a test because within the next three sessions, by early next week, if it could be up in the 316 level, rather than sliding below the 302s, that's going to be really important. Looking at the IWM, the Russell 2000, trading right now at 185.42 up a dollar, and this is a pretty nice action considering how deep it pulled back. Looking at the, let's go to gold, gold at this point is up nice, it's up $20 at 1868. It's right at that 200-period moving average. We've been talking about this for three weeks now, actually four weeks. Is it going to turn that resistance into support? This is going to be really important. Why? Because the dollar is pulling back after a very nice session, or two sessions actually in the last two days. Now it's down 44 ticks at 102.10. I think the dollars in this consolidation phase, as I said to subscribers, we might see that gold actually can move higher under these circumstances, of course it's got a lot of resistance. Looking at the TLT, the TLT at this particular moment is down sharply, it's down 69 cents again at 115.62 after that peak. The yields are going higher, and if you're looking at Crude oil, Crude oil finally pulled back. Oh, that was too soon. It was down two and a half points earlier. Now it's up $1.1624. I'll be back with the Tiger technicians hour. Hope you can stay for that. It should be a very exciting show because I've got a lot to cover. I'll see you soon.


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