The following is a presentation of TFNN Trade what you see with Larry Pezzavento Call now toll free at 1-877-927-6648 or internationally at<PHONE_NUMBER> Now Larry Pezzavento Okay, looking good Billy Ray feeling good. We're going to take a look at the Dow Jones industrial average folks So we've been talking about this big ABCD pattern for quite a few weeks now. It is in place We made the D point. We've rallied five days now folks This is a five-day rally and no one thought it could happen a few days ago by by golly. Here it is Let's review one thing because I think this is Indicative of everything that I've seen in all of these charts for stocks futures the stock indices and stuff They all look pretty much exactly the same and that is by looking at the chart of Tesla You're going to get a pretty good idea of the harmony that we had here in the stock market Over the past few months. That is a giant ABCD pattern folks It's just like the one in the stock market except for one thing and that is the time sequence between A and B and C&D is absolutely perfect. In other words the time in price comes in Exactly as it's supposed to come in now You can see on the far right here that you also had an ABCD here coming off of the 3a2 This was a 1 3 5 pattern right at the 3a2 that led to the big move down And of course now we're seeing the market start to rally, but it's interesting Because you know everything I do folks is a B equal CD I live and die by it and I live more than I die by it, but that's the way it goes sometimes. Sometimes it's good Sometimes it isn't but here's what we were looking at this morning coming in early I posted this real early in the morning. Hold on just a second. I updated it just a second ago Well, not a second ago about an hour or so ago because we were looking this is a ABCD over a five-day period and that target comes in above the 786 at 91 excuse me 90 47 the high so far has been 90 49 that completes that a BCD pattern It's also if you look at the red swing that you can see here when we were still in the bear market We had this huge rally and guess what this one measures to folks Right to that rally right there. These rallies are exactly equal the market repeats itself Over and over again and speaking of repeating ourselves over and over again We have a special treat for you today folks Shane Smollion will be on the air at 1130 to give us his call and what he sees happening in the market And I think we're going to have some fun things to talk about when we visit with Shane Now let's move over to one other market that is really really exciting folks This is what I was looking at yesterday in the hold on one second here. This is the natural gas this thing is It swings five thousand dollars like the S&P moves five points folks this thing really swings There was the 382 retracement On the daily chart that we had back here matching the low that we had here three weeks previous Then we went up and you can see we're making another high or high folks I missed this yesterday. I was not feeling Too good because of the old the pollen and stuff but by golly if you take a look at this I looked at it early this morning and then I saw some of the things that were happening in it I said oh my god the swings it's already it's already moved ten thousand dollars a day folks and it's still gone nowhere Look at this. This is a perfect three drive to a top pattern folks. There's drive one. There's drive two There's drive three look at the time distance between the highs Absolutely, perfectly. I mean you just can't make it up. It's just right on the money 1.27 expansion up there at nine point five four and it dropped $5,000 and then rallied back four thousand dollars and then down three thousand dollars It's had a twelve thousand dollar move today folks and it's quarter after eight in Tucson time. Hello operator Get on board that puppy that is the pork bellies of the futures market Let me tell you that thing really swings. I I've been trading it for several years I know very little about it the participants in the market But they must be really really folks that love the risk because by golly that thing really really moves around a lot And that's what you like to see when we're seeing some of these things, you know unfold here today So it's a it's quite important that we remember when you're trading these things It's about how much money you don't lose not about how much money you make and that's The real key to what we're watching here This morning now, let's get back to one of the markets that we've been in for quite some time It's holding its own hasn't made a lot of money. In fact, it's trading. What's interesting here This is the euro folks. We've been short the euro here for just about hold on one second here We've been short the euro here for about three days now now the difference is is that we've not gone to a loss We're still in a small profitable position of a couple hundred dollars But what we've done is we've raised our stop over the previous day high up there at 1 7 0 6 0 because we sold it at 1 7 oh 3 7 every can't remember somewhere in that bucket It's just a really small risk and if we get above that we want to exit because the market staying at this level and Not going down. It should have broken badly. It did it broke about it broke about nine hundred dollars But it came right back and that's why we have to be really really careful in here We don't want this to turn into a big loss So we keep our loss really small by putting our stop in and if it's hip and if it's hip We go on and not worry about it That's the the main thing that we're doing is we're looking at these charts here each day now Let's let's move over to the gold market here folks because we've had some big moves here in gold If you like a bcd and golly gee, we like a bcd get this up here so we can take a look at it This is the gold market as you can see here over the past eight days beautiful a bcd patterns all ending up here 1868 the short was due to come on at 1868 and we've had a pretty good break in it today We broke out we broke all we broke thirty dollars, which is one half the heart well It is the harmonic number of gold is 32 and 64 and it went exactly to the 38 to retracement folks I just want to bring this to you to your attention because hold on that's not the one I want to see the attention one That's not that one either. I've got a lot of charts here And I'm hopefully able to get them to see it to see everybody can see them to there It is it's over here on this side of the page here. We come now. Here's gold Using the same chart. All I did was I put in the 38 to retracement. Well our target on this is right here folks at 1825 So we've still got 20 more dollars to go. We're in about we're up about 22 dollars right now We've locked in a thousand dollars So what we're looking at is that we want to be able to get down to 1825 that would be ideal right here We're having a little bit of a counter trend move here That may lead to an ABCD to the downside But that's what we're waiting waiting for is 1825 in the gold if we can get there The risk on this was relatively small about eight dollars and as I said, we're up quite a bit Now we had one other one this morning that was looked like it was going to be a good trade but it didn't last longer than Hector who's about 12 years old that little pup hold on just a second here. We'll get this up here so you can see if this is a For our chart, I believe in the Yes, it's a for our excuse me. It's a daily chart in the Crudall We were looking at the 78 percent level here at 212 and you know I said, you know, put a stop in here because if it goes through there by much, you know We could easily get up here to the 618 which is up to the 786 is way up here at 115 That trade lasted about five minutes mainly but when we see these patterns folks We got it taken. Let's take a break eight seven seven nine two seven six six four eight Of booming inflation. We are purchasing powers eroded There's no better place to protect your hard-earned money than ain't gold This the gold flagship asset is the Monk Todd gold project in the northern territory of Australia This is Australia's largest unveloped gold project. We are talking a world-class gold project in a tail one mining district This is a large-scale low-cost project with significant existing infrastructure in a politically safe and friendly mining jurisdiction This the gold just completed the Mount Todd feasibility study Which resulted in a seven million ounce gold reserve in a 16-year mine life All of this combined with the approvals of all major operational as well as environmental permits This this thing which is Mount Todd is an attractive dearest partner ready development stage gold project This the gold trades on the New York Stock Exchange under the symbol VGZ You might think that if you want to be successful at trading in a stock market You're going to need a crystal ball after all it's impossible to predict the future, right? Like any endeavor in life before you decide it's impossible get some advice from the experts You might find that it's not so impossible after all for daily market overviews that give you direction on the key indices Selective stocks and commodities subscribe to the opening call newsletter at tfnn.com The opening call newsletter is written by Basil Chapman creator of the trading methodology known as the Chapman Wave The Chapman Wave up-down sequence gives you an edge in identifying price turns finding the peaks and valleys and stock prices Get the opening call newsletter by Basil Chapman and your inbox every day first time subscribers also get a 30-day money back guarantee If you're not satisfied, let us know and you'll get a full refund within 30 days of signing up tfnn.com educating investors Steve Rhodes started his trading career as a student almost 20 years ago and the student has now become the master Steve won the prestigious timer of the year award in 2018 and barely missed that mark again in 2019 finishing at number two for the year an Amazing accomplishment Steve Rhodes is committed to sharing his techniques and knowledge with anyone who wants to learn And he shares his vast amount of trading knowledge every day in his mastering probability newsletter Steve's award-winning newsletter Mastering probability is delivered every trading day with updates throughout the afternoon sign up for Steve's market newsletter Mastering probability and you'll receive access to seven of Steve's educational webinars Absolutely free at tfnn all our newsletters come with a 30-day money back guarantee So you have absolutely nothing to worry about visit tfnn.com and try mastering probability 30 days risk-free today tfnn educating investors all now toll-free at one eight seven seven nine two seven six six four eight internationally at seven two seven eight seven three seven six one eight Okay, folks. I'm gonna change focus here for just a moment here to talk about the grain markets There's a lot of stuff in the news. Don't watch the news very much, but in the early morning I'd like to see what's going on just to see that there's not been any regime changes across the world or The devaluation or something crazy and they're talking about a fact that you know, Dessa Ukraine there is huge stockpiles of wheat and corn supply. I know it's wheat, but I'm not sure it's corn But they said wheat enough to feed 400 million people. Well, that's a lot of people folks That's a whole that's more than the US of a one-third of China one-third of India But they are concerned that possibly that the Russians will bomb that Grain facility and make it inoperative. I don't believe that will happen But even while that's happening I posted this wheat chart here folks Now you'll see here that we've had incredibly bullish Stuff in wheat and corn and beans as you as you well know But we were in the midst of a correction now and this is a very very important correction We're coming in to the end of May, which is one of the strongest seasonals for grain Especially in soybeans. That's one of the really big ones by the way tomorrow I have I have a special meeting that I'm going to have to go to and I'm going to be meeting someone very famous in our business Peter Brant Lives here in Scottsdale and a couple of us are getting together with him Early in the morning to do something and so I won't be able to be in the show Tomorrow, but I will be back on Monday Hopefully we'll have Jim Bartolioni on on that day. He's been swamped, of course Anyway, as you can see here where I marked the key time. That's a 61 percent retracement folks That watch that very closely because that is a perfect one three five pattern one three five If it lines up perfectly just like that. Oh dear That's that's really a low risk trade in wheat and remember these grains We're we're in the midst of some hyper inflation stuff. There's no doubt about it We see it in gold and we see it in we even though gold's selling awful It's rallying Down a little bit from the hide at me, but still doing pretty good. But let's take a look here. This is a December corn. This is new cop corn. Let me get it up here So we can take a look at it. This is another one that is Very very bullish And we have to have bumper crops just to keep the world from you can see we've been at the 382 here one two three times now so Somewhere in this area here just like in the wheat We're going to be looking for a place to get long the corn We might get all the way down to the 61 percent retracement But you know, we have to wait to see what the trading gods are going to give us There's also that possibility of an a b c d move Down to this level right here, but the wheat is the one that really really looks Looks ready. I mean it really does and the last one, of course I'm going to take a look at here is the soybean market. Just give me one second and we'll get up here to take a look at it Oh, I have a memory about this this trade right here. Okay. Here is the soybeans. This is uh, November, this is the new crop soybeans You can see here. We made this beautiful garlic down in here And there's this really strong seasonal coming in here on the 31st of May I will tell you this story of one of my My favorite well It's one of my favorite to to tell but not to remember if you know what I mean Now this was a we had a friday. We had a crop report coming in. It was on the 27th of May 1983 I was trading on the floor of the exchange And I happened to be over in the board of trade building in the morning to see that report came out And I wanted to see You know what the action was going to be like and I put my order in At lin wall dock about an hour before I went over to the board of trade byron And I went over there to see what the reaction to the report was going to be in the soybean pit itself If you remember of ether exchanges, you could go to the other exchange You couldn't trade on the floor but you could walk onto the floor with your board of trade vads I just wouldn't take any orders because you were a different exchange So we were watching from the gallery after going down and visiting a couple of people in the bond pit And the report came out and I had an order setting in to buy november beans I believe the price was something like 680 680 and a quarter And the market hit 6 79 And it took off and went limit up the limit was 30 cents. It was down about 10 cents So I went down 10 cents to up the limit and I you know, I had a couple contracts on So I I knew I had made $2,000. Well, I get back to the lindall lindall dock office And I checked it, you know the the runs to see where the trade was no fill And I went down and you know, I said you check this out for me And they said that there was just nothing there the broker couldn't get it filled fast enough because it wasn't electronic You know, he had to have his hand up and you know bid on the four contracts And I didn't get filled and folks they went limit up a couple more days Right after that that was the day that rick barns who was trading with Rosenthal Collins And he was in a debit balance In in the bean in the bean market and he came out and he started bidding for a million beans He didn't have enough money to his count, but those brokers out there They didn't know that only the rosenthal people did upstairs and by the time it happened It was already over So he got that nickname bid a million barns because he started bidding and that took the market up up up up And he went limit up he got him out of debit Then it went two or three more limits and he ended up making four hundred million dollars over the next I think it was the next seven or eight years as I recall jim 20 men knows the figures, but I didn't know that I knew rick was one of the brokers that worked for roy facile In the county commodity office out there in los angeles when I first started trading And uh, he was uh, he was a very flamboyant fellow very handsome fellow and incredibly good traded gosh, did he have He had nerves of steel and uh, the real kahoonis folks so but anyway, that's his story his son is still trading and I think rick is as retired down in florida on his fishing boat He doesn't trade much from what jim told me but he does occasionally do something but uh, he loves He loves fishing and that's what he really likes to do Okay, two more minutes before the shane man the wolf trader comes on I wanted to bring in and uh talk about another one here That is very very important because these markets are you know, really screaming and we'd like to see Everybody make a couple of bucks and this this is why I thought this was going to be such a big bottom here in the stock market Let's get this up here. This shows you the Amount of pessimism that we had here right now Was almost half of what it was in 08 and 09 a march of 09 when we were making the bottom That's how bearish it got folks So these markets can go a heck of a lot higher and they most probably will so This is just a five day run and it could be a 10 day run a 15 day run or it could stop today We don't know but that's what we're watching as we're looking at some of these Markets, you know unfolding today We had a sell signal to come in at 40 50 for excuse me 40 47 and a half in the e-mini s and p And that's what we've uh, we're maintaining we maintain that we have to put a 20 point stop on that because it's so volatile But that's what we're doing them all. Let's just an abcd scout folks It's uh, it's perfect and when you have when you see those You just have to get in and say well, I live and die by the sword So yogi baro said you have to dance to the girl dance with the girl you brought to the dance and abcd is the girl I bring to the dance and there was a number right up there It's above the 786 but by golly still have to do it. Hey, we'll be right back with shane's poignant wolf trader.com If you want to take advantage of this sector now is the time to subscribe to my gold report The gold report is a comprehensive look at the metal sector as well as the markets that move gold Which is the currency and bond markets new subscribers get a 30 day money back guarantee So you have nothing to lose every monday morning. I published the gold report with coverage of gold silver bonds the xiu hui gdx as well as more than 30 different mining equities To see for yourself the types of profitable trades that are recommended within the gold report sign up now by visiting tfnn.com don't miss out on the next great gold trade sign up today tfnn has just launched their new trading room the tiger's den hosted at discord tfnn has been educating traders for more than 20 years with live programming hosted by a variety of professional traders during market hours And now they are expanding their reach with the tiger's den available to all tigers and tigers for just one dollar for the year There's no cash or added costs when you join our community of traders in the tiger's den You can look over the shoulders of tom o bryan and the other tfnn hosts while they analyze charts during their live tiger tv programs And join an interactive trading community with hundreds of members exchanging ideas Interact with other tigers and tigers as they share trading ideas news analysis and discuss the market action all trading day Even at night and on the weekends the tiger's den at discord is accessible on mobile or tablets as well So it's always at your reach to sign up today and become a part of this educational community of traders Just visit the front page of tfnn.com tfnn is excited about our new software charting program the art of timing the trade chart In collaboration with tom o bryan and using his best-selling book the art of timing the trade your ultimate trading mastery system David white has programmed an outstanding piece of software that will complement any trader's methodology Using this first of its kind program the art of timing the trade charts allows you to scan thousands of stocks for fibonacci formation setups Including guardleaf abc's butterflies and much more the art of timing the trade charts 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 charting software that will even give you a 30 day Uneditional money back guarantee don't miss out on this incredible new piece of software Get your copy of the art of timing the trade charts today by visiting tfnn.com This segment is brought to you by think or swim for more information Just click the think or swim banner on the front page of tfnn.com Okay, we're back folks and I believe we have on the lion's chain small you in the wolf trader dot com Good morning young man. How are you doing today? Good morning larry. How are you today? Still living the dream baby on the green side of the grass That's the way to be Okay pal, what are you looking at today? We're going up forever. I don't think so. I think I think this is a temporary thing that we're seeing So we have been focusing on the s&p for quite a few weeks now because of the substantial decline in equities and In previous weeks, we spoke about the geomagnetic storm and its adverse effect on equities So on march 31st We had this really big storm that came through and it had the effect of halting the the rally in equities So these storms come off the sun and they take a couple of days to travel to the earth And i'm talking about this again today because We have some increased activity coming because actually going to start coming tonight In general these storms harm equity markets And the report that I showed before was published by the federal reserve It actually showed the negative effects of of these geomagnetic storms on the earth And so what does this have to do with equities? Well on march 31st Two storms had merged to create like a super storm and what happened was that this created this Negative effect on markets that coincided exactly with the top In the s&p on that big rally into march 31st The northern lights were visible all the way down to new york city And again this federal reserve of atlanta had written about this and so this solar storm activity Believe it or not. There's a seasonal pattern to this. So we are in may right now at the end of may It's actually starting to decrease into june And this actually correlates with this the the cyclical activity of the s&p 500 So as the solar storms increase the s&p tends to go down as the solar storms go down the s&p kind of rallies up And then in october we get a big burst of these two and of course that's when We get these these typical patterns of the s&p Having crashed type of situations in october there's that's a that's a classical month So it's crucial to monitor these storms as they they cross come across the earth There's a tracking system used by noah that tracks the intensity of these storms called the kp index and so I'm going to go to that right now just to show you this This In a way, this is similar to this the sapper simpsons scale. Are you familiar with that larry the sapper simpsons scale Is it having anything to do with ab equals cd? No, no, but it's one through five. I don't think it's over my pay grade, buddy It's over my pay grade. So go ahead tell us what you're looking at Sure. So this is how they track hurricanes So cat when we hear category five, that's the sapper simpsons scale This is the called the kp index here Over here and what this does is this actually Will monitor the amount of geomagnetic radiation affecting the earth and as this gets up past the level of four We get into what we call storms and these are the storms and you can have a minor storm a moderate storm Severe storm and it goes all the way down here And these are the these g5 storms are the ones that they talk about as potentially blowing out the the electrical grids and destroying all the electronics if we get a really big one But the storm that we saw back in March was relatively strong. It was kind of in this range into here the six to seven range into here And that that was the one that kind of stopped the market. So what's actually happening right now is We're on may 26 right now. There is going to be an increase in activity So we're right here the the kp is about two, but it's going to go up to three and then four It's going to stay at four Tonight and then into may 28th. And so it doesn't quite classify as a storm But it it classifies as active. Okay, so we're not quite to a storm so it's not going to be the same effect as we saw back in march, but I just wanted to point this out because These tend to have negative effects on the market. So this is just about to show up on the market So for those of you who aren't familiar with what I'm talking about Uh, this was a study that was done by the federal reserve that showed the weeks before uh, the the these storms come Compared to the weeks after the week after the market tends to have a depressive effect after so there is an increase in activity coming These geomagnetic storms are more predictable than hurricanes once they come off the sun. We pretty much know they're coming Hurricanes are a little bit tougher because you have that cone of unpredictability So again, there's an increase in activity coming And so I just wanted to point this out to everybody that this is something that we should be on the lookout for With the s and p 500. So we're right here and then the next few hours The activity is going to increase and it tends to have a negative effect on markets Now the s and p 500 has been in this very consistent downtrend here Uh, and this you know, this is coinciding with the fed Um, you know ended qe, uh, the feds in the rate hike cycle now Uh, next month, we're going to be starting with the reduction in the balance sheet or quantitative tightening There was also an interesting phenomenon here too There's been a lot of money leary leaving the system in something called the reverse repo facility Essentially banks are parking money with the fed right now And so that has it that's generally a negative effect on the markets now that money can come back in at some point But that's also kind of adding to this. We saw this recent decline once we hit about this area into here This is when that reverse repo really started to increase and so that I kind of weight that as a that's a negative weight For the fed juice in other words, that's a negative factor. That's money leaving the system So there's a lot of uh strikes against the s and p right now And I think this is only going to get worse As we go forward Uh, so this you know, we have this fed meeting next month june 14th to june 15th And then Apparently according to the fed they're going to start the quantitative tightening now This has had very negative effects on the markets. We saw this in 2010 very briefly in the summer when Bernanke tried this Uh, when he really tried it and then we've had very very light versions of this ever since We had different taper tantrums But the point is this is not a good look for the s and p for sure We had the negative effects of the of the lunar eclipse after those lunar eclipse here And now we're getting this this rally here now typically Going into a a holiday weekend. It's typically positive seasonals But I think we have a few factors coming in That are going to make this probably not as positive as it would be The first one is I think that geomagnetic activity might start to put a damper on this It's again, it's not quite a storm. Uh, but it is an increase in activity. Uh, we have a We are entering a period where the planetary speed index will be in decline So I'm going to get into this into the next slide. Actually, let's go to this slide first This is showing There's a lot of activity going on here, but this is showing this where I have this pointer This is the geomagnetic storm here ending this first rally here On may 31st or sorry march 31st here and then there was a period here where The fed tries to stimulate and the market ignores the fed and continues down And then this is right when those reverse repos really start taking hold. They just pass like 2 trillion So that's kind of money sitting. It's money that got sucked out of the system It's just kind of sitting there at the fed. They're getting a very nominal rate for that money But these are all negative effects on the market. That's that's like an anti-fed juice if you're taking money out of the system That's not a good thing and again That's a negative weight for the system and then the negative Seasonals are here And again, we have this rally today. We have this this, you know, couple day rally here But I think we're in really a full on crash mode here I think We are going to be entering a period now once they start reducing the balance sheet I think that is going to be devastating for equities. I mean if they really go through with this and they start Doing that. I mean that it that is taking things to a whole another level in terms of of negative A negative weight for the market. Let's just say in terms of what the fed is doing Hey, let's take a break here. Shane. We'll be right back with shane smoking wolf trader.com folks Are you in the market for buying or selling real estate in the bay area? Including the surrounding st. Petersburg tampa and clear water markets tiger real estate LLC is a firm that has extensive experience in the tampa bay area Whether you're looking to sell your current property for maximum value or you're in the market for a second home or investment property Tiger realty has the experience across all areas of real estate in the tampa bay area to help buyers and sellers Make the most informed decisions across 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 727 329 83 22 or email us at tiger at tfnn.com. That's 727 329 83 22 call us today The technology around us is changing every day with so much happening. It can seem impossible to keep up with all the information David whites investment newsletter the technology insider is designed to give you all the information You need to understand the technology that shapes today's markets and tomorrow's future David white has made his living staying on the cutting edge of technology His weekly newsletter will give you specific recommendations for value tech stocks As well as entry prices target prices and stops to set for each trade Dave delivers his weekly newsletters every friday with updates throughout the week You can get the technology insider at tfnn.com for only 37 dollars and 50 cents Sign up for david's newsletter the technology insider and get an inside look at everything the technology sector has to offer Try it risk-free today with our 30 day money back guarantee tfnn educating investors Are china a shares hot or not? If you trade china a shares now may be time to take a closer look trade chau or chad Directions daily csi 300 china a share bull and bear etf's china a shares in either direction Visit direction investments.com today an investor should consider the investment objectives risks charges and expenses of the direction shares carefully before investing The prospectus and summary prospectus contain this and other information about direction shares to obtain a prospectus or summary prospectus Please contact direction shares at eight six six four seven six seven five two three The prospectus or summary prospectus should be read carefully before investing an investment in the funds is subject to risk Including the possible loss of principal the funds are designed to be utilized only by sophisticated investors such as traders and active investors distributor four-side fund services LLC Don't forget you can listen to tfnn live on your mobile device 24 hours per day Go to tfnn.com and hit watch tiger tv That's tfnn.com and hit watch tiger tv Come back folks. We're speaking with the wolf trader himself. Shane smolian want to continue young man Absolutely Okay, so we have a chart here of the s&p daily and I This is a chart showing multiple signals. I'm going to kind of go through this to show you what we have here This this line here. This is the solar cycle This is an annual cyclical pattern that you would just think of as market seasonals for the s&p 500 Going all the way back. You can't even see here But the the fed juice and the double lunar cycle have been in a cell since early february and talking about the fed juice down here This I call this the long wave fed juice. These are the internals both of these are still hanging out in the cell They have not come off that course at all and then you can see here on the 31st This is the geomagnetic storm right here. This is what ends this rally here This was a double storm very it was a very strong storm And then we have the black arrows, which are the planetary speed index here. That's in a cell We had the eclipse here, which typically tends to be negative after which it was And then the the steely and peak was here and then the optimized bradley here So everything's really just kind of lining up right now still into a cell pattern On this s&p from a cyclical standpoint now the fed of course is extremely bearish right now with everything that's going on But this is interesting because next week we are coming into the planetary speed index is making a low Probably around Tuesday or Wednesday. We have mercury station coming up, which can be tough for markets too And then the optimized bradley is still headed down. So we have another cyclical push down here That could be pushing this market down In the coming days. So I don't think we are out of the woods anywhere near yet here Even when we do see these bear market rallies, they do they do tend to get retraced relatively quickly here Even as impressive as some of these might look It's just it's a tough road in long term. We really need to pay attention on what's going on with the fed Now the u.s. Dollar I'm going to show this chart here because this has shown tremendous strength and we've been picking this also up with the fed use too Uh, this this really goes into this buyback here on four six on the fed use and tracks this all the way up It just went back into a buy I do think the strength is going to continue here on the u.s. Dollar as long as the fed is Following through on their word and they're continuing to tighten and they continue to reduce this balance sheet The u.s. Dollar should continue to get stronger because the fed is taking a leading role in the world on this So I think that's going to continue and that's going to create probably more headwinds for gold too in bitcoin now I also spoke about the correlation between bitcoin and the s and p 500 I believe that this is still a very strong correlation So we need to look at what is going on with bitcoin in addition to the s and p 500 This is a new link, but I think we need to look at it Bitcoin is entering a very negative cycle that could start to drag the s and p lower It's just now starting to head down on the cycle and it's been diverging negatively into that cycle So when you see a situation where a market diverges ahead of a cycle, that's not good So in other words, bitcoin's been heading lower and this cycle has is just now starting to top here We have multiple cycles on bitcoin now that are starting to turn lower so If we look at Many of the the correlated assets too like rk innovation. They look very very weak right now and so And bitcoin is really the key to all of this and and so I'm very concerned right now about crypto because bitcoin's really the leader and if bitcoin starts heading down you're going to see more more struggles in in this This crypto arena and I think that you know bitcoin like I said is it's going to travel with the s and p here likely to the downside so You know, this is I'm going to show you another chart here This is this is the daily statistics of bitcoin today is the weakest statistical day of the week for bitcoin And it was down early. I think it's up maybe coming up a little bit now But uh, you know bitcoin in terms of this solar cycle It's it's ready to start heading down and so People you need to pay attention to this because it's been it's been struggling into a peak and when a cycle struggles into a peak That's not a good sign And I think a similar thing has been happening to gold. I'm going to talk about that this saturday In the webinar, I'm going to talk about gold like what's wrong with gold. Why isn't gold going higher? Shouldn't gold be higher? I mean people feel like gold is oh, it's going to catch up. It's going to catch up I don't think so. I think I think gold is pretty much faked in now And I think if we get any downturn in inflation Which we probably will A little bit it's probably going to come off that that 8.3 high, but I think gold now Uh, it's going to struggle along with bitcoin. This is our innovation We've had this fed use in a cell since february the 10th We've had this in a cell and it's really showing no signs here That's trying to bottom and this is going to go with bitcoin too. So I think we have to be careful about this You know just These are great concepts for the future. I love tesla. I like bitcoin for the future But right now I don't think this is a very good looking situation again It's been short since 73 79 on february 10th. So it's still just in a pretty clean cell right now It's not really showing any signs as inside from these little tiny bear market rallies We really don't see any sign here. This is going to turn around same thing with the spider biotech I just threw this in here too. This has been in a cell since february the 25th Both of these are looking extremely bearish. So I talked about the bitcoin after the lunar eclipse tends to be negative that's playing out Gold gold is kind of choppy after the lunar eclipse But one thing that I do point out to people is in 2020 all three of these assets went down together So, you know just something to pay attention to something to be careful about Apple again, there's another one the fed use has been in a cell since september the first so Tough tough road here now long-term cycles. Let me talk about it. Lara. Are you familiar with the jupiter cycle? Oh, I know where jupiter is but it's a big one all I know that for a fact Yeah, I so People were asking me about well what you know shame what you talk about the fed you talk about these short-term cycles What about on like a like a decade basis? Where's the s and p like what would that look like? So there is an interesting jupiter cycle occurring on the s and p 500 So the jupiter cycle Is roughly 12 years So it passes through each sign of the zodiac in about 12 years And so what happens is it spends about one year in each zodiac sign And so when we we put this to the s and p 500 we can get roughly a 12 year cycle So i'm going to show you some very interesting slides here This gives I went back on the dow Jones on this because jupiter is a 12 year cycle We need to go back Very far in time. We need to go back to the early 1900s It just made a peak in march of 2022 so This is interesting too because this coincided with the rally that we had in march in march, so Up into here. You can see this is the peak. So i'm going to i'm going to illustrate this so you can see this So this black line here This is the the jupiter cycle. Okay, so you can see it has these dips and and rises But it has a very distinct peak here and this peak was right here in 2022 The red line here. This is the dow Jones. I use the dow Jones because it goes back further But this makes a very clear peak here and this peak was in March of 22 and it heads down mainly through 2026 here So you can see that if we're just looking at a long term cycle here The s and p just hit it the s and p just hits this long term cycle high and These cycles They can tend to do very well if if we're not having a strong fed in the markets So right now the fed is pulling back and these cycles tend to be much more accurate That's why it made such an incredible high Uh in march. I'm going to go to the next slide. It's going to show this actually zoomed in Uh, so you can see this here. This is the jupiter cycle now The one thing I want to point out here is that I I stopped the data here. We'll talk about this when we get We're gonna take a break folks. Shane's moanwolf trader.com would be right back Sharpening your skills as an investor is like getting better at playing a musical instrument You have to practice sure, but you also need excellent instruction from experts at tfnn You'll get advice and guidance from the authority and technical market analysis And it's not just dry tedious text either tfnn airs live financial content streamed live on tfnn.com and tfnn's youtube channel with tiger tv Live every market day from 8 30 a.m. To 4 p.m. Eastern for free Each host is an experienced trader and gives their take on the market while taking calls and questions live from around the world From the moment the market opens until the closing bell sounds tiger tv has eight different shows with expert hosts To help you make the right moves with your money watch online at tfnn.com or on tfnn's youtube channel And become the investor you were born to be tfnn educating investors You might think that if you want to be successful at trading in the stock market You're going to need a crystal ball after all it's impossible to predict the future, right? Like any endeavor in life before you decide it's impossible get some advice from the experts You might find that it's not so impossible after all for daily market overviews that give you direction on the key indices Selective stocks and commodities Subscribe to the opening call newsletter at tfnn.com The opening call newsletter is written by basal chapman creator of the trading methodology known as the chapman wave The chapman wave up down sequence gives you an edge in identifying price turns finding the peaks and valleys and stock prices Get the opening call newsletter by basal chapman in your inbox every day First time subscribers also get a 30 day money back guarantee If you're not satisfied, let us know and you'll get a full refund within 30 days of signing up tfnn.com educating investors Everything in the universe is governed by the fibonacci sequence This mathematical principle is responsible for everything from the most aesthetically pleasing artwork to patterns in the stock market To stay on top of stock patterns You can take advantage of sign up for the fibonacci 24 7 newsletter at tfnn.com When you subscribe you'll get a weekly report from veteran day trader larry pesavento on stocks You need to pay attention to and you can trust larry's analysis after all He's got 45 years experience as a day trader larry will also provide daily charts videos And data on the key markets that he's tracking expect notifications from larry on market movement You need to act on at any time first time subscribers also get a 30 day money back guarantee If you're not satisfied, let us know and you'll get a full refund within 30 days of signing up Subscribe to the fibonacci 24 7 newsletter today tfnn.com educating investors Okay, we're back folks finishing up with shane's mullion wolf trader.com Shane I have a question for myself and that is we have a direct station in mercury coming up shortly in june, don't we? We do we do june 3rd and You know when when markets are falling, uh, this can be trouble for the smp I mean that anytime mercury is making a station, you know It's a it's an important planet and the speed of the planets when they tend to be slow in general all of them It tends to be negative for the markets So we got to look at all the planets But next week is a critical week for the smp and like I said with All of these cycles coming in here. We could see some more downside next week in this market too Very very good. You want to tell the folks about an upcoming webinar or something that they might be interested in? Yeah, uh, so so if if anybody wants to reach me you can Go to respect the fun the slide here. You can go to uh, wolf trader futures.com and we have a webinar every saturday Wolf trader futures is the name of the of the the youtube channel. Okay, so we've been talking about the smp I don't think I want to talk about it anymore. We've been talking about it for like five weeks here Tired of it. It's going down. I can't reestablish that I'm going to talk about gold this weekend because I think gold is an important topic Why what's wrong with gold? Why is it looking so bad relative to the inflation picture? And where can we expect it to go? So I'm going to talk about that What I think's wrong with it what where I think it's going on so we're going to shift gears a little bit here Because I I'm I'm tired of talking about the smp so I'm That makes good sense. I know that feeling every morning when it opens Yeah, absolutely Thanks for joining us and we'll have you on again Really soon and keep up the great work and I know your program's going well and congratulations towards that So we'll see in a couple weeks then or earlier if you see something that's really important Okay, maybe maybe come around or june the third because oh that's next week because uh, uh, I like that mercury thing I've uh, I've lived and died by mercury as a planet for timing and it's really good So we'll have you on maybe the third but that would that work out for you as far as a uh, you just okay I'll be here larry. Yeah, okay. That'll be next friday. So we'll have you on then. Okay Thanks so much larry. Have a great day everybody. You bet folks. See you tomorrow folks By the way, I will be here tomorrow. It's it's a luncheon meeting not a breakfast meeting


What are some benefits you tell a prospect at an appointment? Benefits. Gold. Come on, man. Is that all you got? First one. So I actually write these down. I actually use these and I walk through these. So the first one is whole life. The second, and what I do is I mention it, I describe it, and I ask if they like it, if it fits important to them. Whole life, price lock, double accident, cash value, local agent, and those are my five. I threw in a sixth one yesterday when I was helping a new agent and it was like a immediate payout or no waiting period. The guy was worried about like a two-year wait and stuff. So those are my five. My go-to benefits. You got to build value. I mean with sales, it's all about the relationship piece and the value piece. And if those two things align, nothing else matters as long as they've got more than eight bucks in their checking account. Good question.


Alan Goldhammer is the founder of the True North Health Center in Santa Rosa, California, which has fasted 10,000 people for conditions ranging from diabetes and cardiovascular disease to autoimmune diseases. He noted that conditions that seem to be tied to dietary excess tend to respond predictably to the use of fasting followed by a health-promoting diet, which he describes as a low salt, all plant, high fiber, low fat, low protein, and low sugar diet. This approach offers people an option to eliminate the cause of lifestyle diseases, often to the point where the medication is no longer needed, in contrast to conventional medicine, which is more about the suppression of the symptoms associated with the disease, rather than removing the underlying root cause. Goldhammer put it this way, if you treat high blood pressure, type 2 diabetes, or autoimmune disease medically, they'll tell you you'll be on these medications for the rest of your life.  Preliminary data suggests fasting may benefit metabolic diseases, pain syndromes, high blood pressure, chronic inflammatory diseases, allergic diseases, and psychosomatic disorders. But the highest level of evidence we have for the benefits of fasting are in regards to rheumatic diseases, autoimmune inflammatory joint diseases, like rheumatoid arthritis. Nearly a century ago, it was written that diet treatment is not generally recognized by the medical profession as one of the weapons with which to attack such diseases. This attitude persisted until relatively recently, but a systematic review of controlled trials has since shown a statistically and clinically significant beneficial long-term effect. Rheumatoid arthritis is a well-known genetic component, but the concordance rate, the chance that a pair of identical twins both get it, when one has it, is probably under 30%. Despite having the same genes, leaving 70% to be explained by non-genetic factors. Even if we don't know exactly what those factors are, fasting has been compared to rebooting the hard drive in a computer. Sometimes, a drive gets corrupted and you don't know exactly what the problem is, but if you just turn it off and reboot it, that corruption may get cleared out. The evidence-based started with case reports. Fasting, followed by a plant-based diet, remarkable reports of years of pain and stiffness gone within a week, and more importantly, stayed gone on the healthier diet. One after another like that, but case reports are just glorified anecdotes. I mean, there have been studies going back decades suggesting fasting may represent the most rapid, available way to induce relief of arthritic pain and swelling for patients who have rheumatoid arthritis, but the studies often failed to have control for the placebo effect, which is especially important when it comes to relying on self-reported subjective symptoms, such as pain and general well-being. But there are objective measures, lab tests of inflammation that don't appear to be affected by placebos, and that's what you can see in control trials, starting immediately and remaining down for at least a year. 10 different measures of inflammation significantly decreased after the fasting, subsequent meat, and egg-free diet, whereas none of the parameters budged in those disease victims that continued to eat their regular diets. And the squelching of inflammation translated into a significant reduction in pain, morning stiffness, a loss of grip strength, and a number of tender and swollen joints. Even a year after the trial was over, those who benefited from the diet continued to benefit. In terms of pain, stiffness, tender and swollen joints, presumably because they stuck with it. There's little doubt that while fasting, both inflammation and pain are relieved, but if you go back to the same diet you were on before, the inflammation returns unless, evidently, the fasting period followed by a vegetarian diet. Why might that be? Well, it could be due to the changes in the microbiome, the improvement in symptoms coincided with a significant alteration of the intestinal flora, which may somehow be beneficial, perhaps by strengthening the gut barrier. We know fasting can decrease the leakiness of the gut in rheumatoid arthritis patients, but we don't yet know what role, if any, it plays in the disease process. It could be as simple as icosinol, the mediator of inflammation that are formed from arachidonic acid. Arachidonic acid is a long-chain, inflammatory omega-6 fatty acid found in animal fats. The biggest contributors are chicken and eggs, which together contribute nearly half of American intake. That's been suggested as an explanation of why those eating more plant-based appear to have better mental health. They're not suffering the cascade of neuro-inflammation caused by arachidonic acid. While removing eggs, chicken and other meat were shown in a randomized control trial to improve mood, suggesting the arachidonic acid might be negatively impacting mood states, and may help explain the impact of more plant-based diets on inflammatory diseases like rheumatoid arthritis. So that may help explain why maintaining a plant-based diet appears to be necessary after the fast to prevent the recurrence of symptoms and inflammatory activity. Or as one popular press article put it, fasting may just be a tool to get you to radically kickstart a change in the way you eat.


Hi, my name is Andrea and in this video I will introduce some concepts about the neuroscience of memory and especially memory loss or forgetting. In this first part I would like to talk about how people started thinking about what could be the biological substrate of memory and how ideas developed at the beginning of the discipline. I believe it is extremely important to deliver the message here that ideas and concepts do not come from thin air. All the discoveries in science were primed by the ideas floating in the discipline at the time of the discovery. As a society we define the course of science by defining the questions that we ask and are interested about and this is a very good example of it. I would like to begin with a quote. It's from the Spanish film director Luis Buñuel and it says, you have to begin to lose your memory if only in bits and pieces to realize that memory is what makes our lives. Life without memory is no life at all. Our memory is our coherence, our reason, our feeling, even our action. Without it we are nothing. I think this quote summarizes extremely well the relevance of memory for the sense of self and some of the things that we will discuss in this video. So what is memory? The first dichotomy that interested philosophers was is it something physical, something we can measure or is it something that is out of our reach? Since we cannot really do much for the abstract hypothesis it was soon discarded towards looking for the origin of a physical measure of memory. During some time it was believed that memory was stored all over the body, however scientists soon realized that the brain was somehow crucial to memory and the identity. The most straightforward thought about how does the brain store memory is, well memory must be represented by something that's created and stored there. So the more the memories the bigger the brain. The initial ideas were guided towards the notion that a new memory would require new cells or something new to be created. There is no much growth going on in the brain since a human turns 10 years of age approximately, but this doesn't mean that everything is settled. The brains of differently aged people who had certainly a different amount of memories puzzle the scientists. How could it be that the brain size did not equal brain storage capacity? We do accumulate an increasing number of memories, thus those memories are not stored by creating new cells but by modifying the existing ones. At this point philosophers, neurologists and other scholars started to be very interested in defending how does the brain record a memory. It was so proposed that the brain somehow manages to associate series of events, but it was still unclear how this association could take place in the brain matter. At this point it was still believed that the brain was a continuous web of intricate connections like a ball of wool. It was believed that the neurons, the brain cells, were physically connected to each other, something called the reticular theory. A notable observation was made by the Spanish scientist Santiago Ramon y Cajal around the end of the 19th century. Cajal spent most of his life glued to his chair looked into stained chicken brains and he was amazed at what he saw. What he saw was that the cells in the brain were not all connected to each other as everyone thought, but there were little spaces between them. These spaces meant that the cells did not really touch each other. This was named the neuron doctrine. After this scientists started wondering what could be happening in those spaces between neurons. They started proposing that those connections were the key to identify a memory. A Polish neuropsychologist defined neuronal plasticity as the ability of neurons to be altered by experience. This is a very important concept as it implies that the brain is both very stable to be able to store information for a lifetime, but at the same very malleable to be able to build and change these pieces of information. Not long after, a famous Canadian psychologist Donald Hub set the basis for what is called synaptic theory, which described how these associations could happen at the neuronal level. In a famous book Passets, he describes, when an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic chains takes place in one or both cells, such does age efficiency as one of the cells firing B is increased. This has been lately simplified with the catchy neurons that fire together, while together. Lastly, scientists managed to describe for the first time the phenomenon of long lasting potentiation, neuronal plasticity induced in the laboratory. This opened a new world for scientists which started using these techniques to study in depth this phenomenon and that has led us to today. But why is this discovery so important and what does potentiation mean at all? This is something we will cover in the next part. Thank you for your attention.


Hi guys, welcome back to the channel, it's Max from MaxCretion. We are giving you the updates. Remember we are talking about Kata 2022, the FIFA World Cup Kata and Issa. So we are talking about the latest updates and that's what we need to definitely to get through. We need to know what is happening, what is transferring, what are the records that are being broken in 2022 in the host country which is hosting the FIFA World Cup Kata 2022. Remember today we looked at the 10 world Guinness Book records that are being written in 2022 before we are looking at Kata hosting the FIFA World Cup. Remember even it's hosting the FIFA World Cup Kata. It is the first Arab country, Gulf country to host the FIFA World Cup and it is the second Asian country to host the FIFA World Cup Kata 2022 after 20 years after Japan and Korea that hosted the cup at the same time. What do we have today? A world-largest football boot unveiled at Katara. This is we are looking at a world-largest football boot in the whole world that has been unveiled. These are part of the tourist attractions or what these are what of the most developments that are being introduced in Katara or being invaded or some of the attractions that are being invaded in Katara. Remember the biggest boot in the world has been unveiled at Katara Culture Village this evening and where hundreds of people gathered to have a close look at what a remarkable event. Remember this boot alone it weighs over 500 kilograms. That's what I can tell you. What does it mean? It is another world Guinness records that is going to be made by the host country of the FIFA World Cup Katara 2022 and what does it mean at that time? That's the world-largest football boot is 17 feet long and 17 feet high. It weighs 500 kilograms o kg and it is constructed using the same materials that are used to construct used to manufacture what you call a football boot and this include what you call the fiber, the latex, a clean sheet then also they look at what you call flow form and what you call lexine. Those are some of the materials that are used to make football poo. However, something that we need definitely to understand according to the latest information that we have from the Katara Culture Village it is still under what you call plain white colors with a thin layer sideways which will be customised later after the FIFA World Cup 2022. However, we are waiting to see whether it's one of the actually must be one of the people one of the invasion that will be tempting to making what you call another record in the FIFA in the world book records at the same time. Thank you so much for coming back to this channel. It's always mixed from the next question giving you always the updates around the group Katara and we are looking at the FIFA World Cup Katara 2022 and latest information. See you again in the next video. By the way, don't forget to subscribe to the channel. Remember it's mixed from the next creation.


So, this is again back to non-singularity, so if you recall that if P is a point in X which is an affine variety, it is an affine variety in say An okay then P is called non-singular non-singular called a non-singular point of X okay or we say X is non-singular at P okay. We say X is non-singular at P if for given set of generators for let me not say let me even say for some given set of generators F1 etc f L of the ideal of X okay the rank of the Jacobian matrix of F1 etc f L with respect to the variables X1 etc Xn at the point P is equal to co-dimension of X which is actually which means dimension of the affine space the ambient space minus the dimension of X which means it is n minus dimension of X okay. So, this was the definition of non-singular point a point of an affine variety is called a non-singular point or a smooth point or we say that the variety is non-singular at that point okay if for some given set of generators for the ideal of the variety if you calculate this Jacobian which is given by the partial derivatives of all these with respect to these variables that turns out to be the co-dimension of that turns out to be equal to the co-dimension of X okay and co-dimension is the dimension of X taken away from the bigger space in which X sits which is affine space okay. So and of course this so you know this is just doh fj by doh xi at P it is just this matrix okay and where of course the xi's are all affine coordinates of an so X1 etc Xn if you take their coordinates on an okay. So this is the definition of non-singularity and then you know this generalizes this can be used to generalize to say when a point on any variety is a non-singular point and the definition will be that well given any point on any variety it always lies in an open set which is an affine variety because any of any variety is covered by a finite union of open subsets which are isomorphic to affine varieties. So you take the point on the variety to also to be a point on an affine open set containing that variety and then it is then you define the point to be non-singular if it is non-singular as a point of that affine open set okay and so in a way you know this non-singularity should not depend on the open set in which you are considering it so you know the non-singularity or the smoothness at a point is a very it is a local notion okay you know when you say a curve is smooth at a point it means actually there is a sufficiently small neighborhood of the point where it is smooth okay and similarly you know when you say surface is smooth at a point it means there is a small sufficiently small neighborhood of the surface where it has to be smooth. So you see the smoothness at a point is something that is it is not in fact in classical geometry you know if something is smooth at a point then it is also smooth in a neighborhood of that point okay and this is true also in algebraic geometry okay but it requires more commutative algebra it needs it requires more algebra to be to establish okay the fact is that the something being smooth at a point is something that spreads out to a neighborhood of the point alright therefore so the moral of the story is that when you say x is non-singular at a point it will happen not only at that point but also in an open set containing that point alright in a neighborhood of that point and in that sense you know you know that but you know any open set in the Zariski topology is huge okay therefore what it will tell you is that the moment you have one smooth point okay then there is a huge open set there is a dense open set full of smooth points okay and this is what happens in truth what happens is that the set of points which are singular points which are not non-singular that is only a small closed set okay and that means most of the points on an open all points on a huge open set they are all non-singular they are all smooth points okay but anyway these are all geometric facts and one needs to have sufficient amount of commutative algebra to establish them alright so so at the anyway at the level of this definition itself there are problems in the sense that you know this variety x could sit in some other affine space and if I change the affine space then the ideal the ideal of x in the affine space will change okay and not only so that is one set that is one ambiguity and the other ambiguity is for this ideal I am taking some set of generators if I take another set of generators then it may be different number of generators and this matrix changes but I am just saying that so this is a condition on the rank of this matrix okay so there are lot of ambiguities in this definition why should this definition be a good definition because there are so many choices to be made first of all I have to make a choice of embedding x into some affine space namely I have to think of x as an irreducible closed subset of some affine space okay and variety can be embedded in so many ways okay I can think of the variety is a line of course I can think of it as a line in the plane or a line in the space in space in 3 space or even higher dimensional space so there is this ambiguity in embedding it in some an and then once you embed it if you look at the ideal of x for that embedding that ideal of course already depends on the embedding but then it could have different sets of generators okay the same ideal could have different sets of generators and they could and the number of generators in these sets could also be different okay therefore this Jacobian matrix you know which is a Jacobian of all these generators this matrix itself could change okay but then the definition is that you know whatever it is you calculate its rank if its rank is equal to co-dimension then the point is a smooth point and on singular point so it looks like this definition involves too many ambiguous things and you know it might not be very consistent if you change the choices the various choices but that is not true the point is because this is got to do with the this has got to do geometrically with trying to you know look at the tangent space to the variety x at that point okay and that is the reason it is because of that geometric reason that this definition actually works but then if you want to really verify that one uses of course you know you translate from geometry into commutative algebra and the necessity commutative algebra is given by the given by the following theorem. So here is the theorem the theorem is that a point p of x where a point p of a variety x is a non-singular if and only if the dimension of mp by mp squared over k is a k vector space is equal to dimension of O xx is equal to dimension of x okay. So here is the this is the theorem alright where of course where mp inside O xx is unique maximal ideal okay so this is basically this is due to Zariski Oskar Zariski and it is a fundamental result and here you know that the definition of non-singularity we are using is this definition which is full of ambiguities okay this definition is full of ambiguities alright and whereas this theorem gives a condition the condition is only on the local ring of the variety at that point and you know you can see immediately one thing because I am it is a condition of the local ring I can rest I can assume that this point is on an affine variety because I can go to an affine open subset of this variety and look which contains the given point okay so it really does not so you know it depends only on the local ring alright and if I and you know the beautiful thing is that this is intrinsic to the variety see here nobody is bothered about whether x is affine or quasi affine or if it is affine or quasi affine which affine space it is embedded inside I mean all these things one is not bothered about the condition is completely in terms of things which are intrinsic to the variety okay and which do not depend on you know the variety being seen as a subset either irreducible closed or open subset of irreducible closed in some affine space or some projective space nobody is bothered about these things okay so that is the reason why this theorem is very very important and so you know so the proof is interestingly the proof is linear algebra and but actually it is it has got to it has got to do with geometry because what you are trying to do is you are actually you know if you look at it geometry geometrically you are trying to you know calculate the tangent space at the for the variety at that point okay and you are also trying to look at the normal space okay the space of vectors in the ambient space ambient tangent that the tangent space is there at that point for the ambient object and you are looking at the normal directions also okay so you know so you know the idea is that yeah okay yeah that is very important yeah it should thank you should be o xp because all the time I am used to small x and then yeah that is bad notation thank you so this should be o xp this should be o xp not small x right so so you know the roughly geometrically this is what is happening what happens is that when you think of an object embedded inside a space okay then you take a point on that object okay then it will have a tangent space okay and then the normal space will be the normal vectors in the bigger space and the sum will add up to the dimension of the bigger space provided the point is smooth okay so you know if I take a smooth surface in 3 space if I take a smooth surface in 3 space take a point on it and draw the tangent space I will get a tangent plane I will get a night I will get a neat plane 2 dimensional plane and I will get a unique normal to the surface which is given by the gradient okay if the surface is defined by a single equation it will be given by the gradient and then therefore the normal space will be 1 dimensional the tangent space will be 2 dimensional sum of these spaces will be 3 dimensions which will be the ambient space in which the object is embedded but however if you take a singular point this will not happen the singular point the tangent space itself may be everything you may not have any normal vectors for example if you take the cone in 3 space and you take the vertex of the cone which is a non smooth point if you draw the tangent space then you will get the whole 3 space so you will not be able to find at the vertex there are no normal vectors all vectors are tangent vectors there are no normal vectors so this kind of so if you see that this happens because that point is a singular point okay so if you have a smooth point what will happen is that you will get a tangent space at that point which is equal to the dimension of the object and then the normal the normal space which consists of vectors perpendicular to the tangent vectors okay that will give you a subspace of the tangent space of the point in the bigger space in which it is sitting okay such that the sum of these 2 spaces will be the whole tangent space okay and this will happen for smooth points it will not happen for non smooth points okay and actually it is that whole it is that calculation which is being reflected here but it is being reflected using algebra alright so what you will do so let us do the following thing. So without without loss of generality we assume x is a fine okay and why is this correct this is correct because after all my definition of non-singularity is a point p of a variety is called non-singular if you it is non-singular as a point of an open subset which is affine because I have defined non-singularity only for a point of an affine variety and any variety can be covered by affine varieties open subsets which are affine varieties so without loss of generality I can assume that x is affine alright and that means and what I mean by this is you go to an open subset which is affine okay by going to an open affine subset containing the point p okay and you know by going to an affine open set which contains the point p the local ring is not going to be changed because local ring does not depend on whether you go to a smaller open set which contains the point or not okay. So the conditions of the theorem are both the both both the hypothesis and conclusions for the theorem both ways of the theorem they are not affected if you go to an affine open subset okay so it is enough to go to consider x affine okay so say we are in this situation p is a point of x which is inside affine n space and now it is an affine variety means it is an irreducible closed subset of an alright and then you know now we will do some calculations okay so now first of all let p be the point lambda 1 etc lambda n okay p is a point of n space anyway so take its coordinates okay so the maximal ideal of p will be by the null still and sets you know I mean the point p corresponds to unique maximal ideal in the affine coordinate ring of the affine space which is k x1 through xn this is the affine coordinate ring of an alright and here I will get a maximal ideal which corresponds to this point by the null still and sets that will be this maximal ideal generated by the xi-lambda i okay so this is the maximal ideal that corresponds to this point alright and you see what we will do is see you define you define this map k x1 through xn you define this map psi okay into kn so here is my map the map is very very simple take any polynomial g in n variables simply apply I mean take its gradient just take the gradient at p okay which means take dou g by dou x1 at p dou g by dou xn at p just do this so just take the partial derivatives with respect to each of the variables in this order and then evaluate them at p okay so of course here when I say partial derivative it is a derivative that is in the formal sense you know how to write the derivative polynomial without having to get the derivative from calculus methods which involve epsilons and deltas and limiting processes okay so we just use a standard rules for differentiation formal rules for differentiation of variable and you write out these so each of these dou g by dou xi's are all polynomials again in the xi's and then you just substitute the point p namely you substitute instead of each xi you substitute lambda i you will get some n tuple and that is this n tuple of kn okay. Now the point about this map psi is nice thing about this map psi is that it is k linear and surjective okay see the map psi is k linear because you know if instead of g if I replace g by g1 plus g2 okay then all these all you know all the partial differential operators they are all k linear I mean they are all linear and therefore if I replace g by g1 plus g2 I will get a sum of tuples here and if I multiply this g by a constant that constant will come out there okay therefore it is k linear and it is surjective because you know if you take you know if you you see if you take these generators as a maximal ideal okay if I take x1 minus lambda 1 alright for g then I will get 1 0 0 0 0 which is the first basis vector okay because if I differentiate this with respect to dou with x1 I will get 1 and substituting p has no effect it will still remain 1 if I differentiate with respect to other variables I will get 0. So if I take g equal to x1 minus lambda 1 I will get 1 0 0 0 if I take x2 minus lambda 2 instead of g I will get 0 1 0 etc so in this way I will get a basis for kn okay and since the image contains a basis it is surjective okay. So the moral of the story is that psi is k linear surjective surjective psi of xj minus lambda j is equal to standard jth basis vector so it is a linear surjective map alright and now the point is that the kernel is exactly the square of this maximal ideal okay. So in other words what I am saying is that psi induces an isomorphism of the n dimensional vector space k with m mod mp mod mp squared okay so mp mod mp squared is just the n dimensional vector space k. So you see see if we take an element of mp squared okay then it is of the form you know it is going to be of the form sigma i some gi times xi so I know in fact I can put i comma j xi minus lambda i so I put gi j xi minus lambda i into xj minus lambda j yeah. You see what is an element of the square of an ideal it is a finite sum of products it is a finite sum of products where each term in the product is a product of two terms one from one each from the ideal okay. So if I take an element of mp squared it is a finite sum where each term has to be an element of this ideal but you know any element of this ideal will be generated by the xi minus lambda i with polynomial equations so it will look like this alright and now the point is you know to this if I apply the operator doh by doh xl okay suppose I apply the operator doh by doh xl alright then you know what will I get you see if you know if l is so you know I have to differentiate product of three terms alright and therefore I use the product rule alright which also is valid in this case okay formally alright therefore you know see if you know if l equal to i suppose l is i then what I will get is I will get so let me write it here so what I will get is well sigma i, j I will get doh gi j by doh xl at p and then you know I apply p okay. So this is you know this is the lth component of this map xi the map xi is apply all the operators all the partial differential operators and then substitute the point p so the lth component of this map that is this map followed by lth projection that is this map alright and what is it if you apply the chain rule this is you know this will be xi-lambda i xj-lambda j at p alright this is one term then the other term will you know it will have gi j at p and then I will have doh by doh xl of xi-lambda i into at p into xj-lambda j at p and then I will have one more term I will have xi-lambda i at p into doh by doh xl of xj-lambda j at p okay this is what I will get alright and now if you look at it carefully this is going to vanish because you see the first term will vanish because I have these two fellow surviving if this is 0 then I am not worried okay but even if this is not 0 if I substitute xi equal to lambda i or xj when I substitute p I have to put xi equal to lambda i and xj equal to lambda j so this is gone in this you know this will go and in this this will go so these terms will vanish these underline terms so this is so this is so this is actually 0 okay so the moral of the story is that if you take any element of mp squared this linear map will kill it okay so in other words what it will tell you is that mp squared is contained in the kernel of xi okay mp squared is contained in the kernel of xi but the more important thing is mp squared is exactly equal to the kernel of xi okay conversely let h belonging to mp be in a kernel of xi okay now h is in h is an element of mp so h is h is actually given by sigma g i xi minus lambda i over i this is how an element of m the maximum ideal will look like it is just a combination of all the generators xi minus lambda is multiplied by polynomial coefficients the g i is of polynomial coefficients right this is how maybe okay this is g i and this is g i j so it should not they are different things right so h looks like this alright and I am saying that I have taken my h to be in the kernel of xi so xi of h is 0 okay so xi of h what but what is xi of h xi of h is well I have to apply dou by I have to partially differentiate this with respect to each variable and then substitute the point p then I should get 0 that is what it means to say that xi of h is 0 which is h is in the kernel of xi okay I am trying to show that kernel xi is also contained in mp square so I am trying to show kernel xi is equal to mp square that is what I am trying to show okay so xi of h is what if I differentiate this with respect to if I take xi of h, xi of h equal to 0 so this will tell you that you know if I take dou h by dou xl at p is 0 for all l this is what it means okay and now write that out see dou h by dou xl at p 0 is equal to this but what is see if I differentiate this I will get sigma over i okay I will get dou gi by dou xl at p into xi minus lambda i at p plus I will get g i at p into dou by dou xl of xi minus lambda i at p this is what I get okay and what you must understand is that you see this is this is 0 xi whenever xi minus lambda i comes if I substitute the point p it is going to vanish okay so this term is gone alright the and this term if you look at it if l is not equal to i this is 0 so this term will be killed and this term will only survive when l is equal to i when l equal to i this is 1 okay and I will get gi of p so this crazy thing will tell you that gl of p is 0 for all l this happens for every l so gl of p is 0 but that means what it means that the gl see if a polynomial vanishes at p then it is in the then it is precisely in the maximal ideal of p because mp is exactly the ideal of polynomials which vanish at p so what this will tell you is that it will just tell you that you know gl is in mp okay but you know if gl if and that is for all l so you know all these gi's are in maximal ideal and these terms are also in the maximal ideal therefore the product is in m squared therefore h is in m squared so this implies that h is equal to sigma gi into xi minus lambda i is in mp squared so all these things put together tell you that mp squared is exactly the kernel of xi okay why take h in m no if h is not in mp I cannot write it in this form it has to be generated by the generators of mp so you can write h is in this form if and only if it is in mp because xi minus lambda i are the generators of mp a general h need not be like that any polynomial need not be like that what I forgot to tell you is that you see this psi is from this polynomial ring into this mind you every ideal is also k subspace okay so this psi the psi also gives you a linear map and restricted to a subspace so psi can also be restricted to mp and so in fact what I want to say is that psi restricted to mp itself is also k linear and subjective okay so I come to that so you know note that mp squared is a subspace it is a k subspace of mp which is also a k subspace subspace means sub vector subspace and there is this map psi into kn okay and in fact you see psi restricted to mp is also subjective because you know I have already told you that psi takes all the generators of mp into the standard basis so psi restricted to mp is also subjective okay so psi restricted to mp from mp to kn okay so here of course I am looking at as you said because I am taking h in mp I am looking at the kernel of psi restricted to mp right so if you take psi restricted to mp has induces is a subjective and induces I mean it is subjective because the generators of mp give their images under psi give you the standard basis right and it induces a k linear isomorphism isomorphism from mp mod mp squared to kn and let me call this isomorphism as psi prime okay so you know the first this simple linear algebra in this first step gives the calculation that you know you take a point p in affine space okay take the maximal ideal corresponding to the point then mp mod mp squared is just n dimensional affine space okay that is the calculation alright and you know if you look at it in fact in view of the in retrospect you know in view of the theorem that we are going to prove what you are saying is that every point of affine space is non-singular okay because you know if you take the local ring of affine space at that point is just the polynomial ring localized at mp okay and it is maximal ideal is generated by the image of mp in that localization and if you take and what you are saying is that well if you take this quotient and localize okay you will get mp mod mp squared at the local ring okay for the point in affine space and you are saying that the dimension of that is equal to the dimension of affine space which is n so you know if you take x equal to an you have got this condition you have got this condition and what you are saying according to the theorem is that every affine space is smooth okay so the significance of this calculation is that affine space is smooth is non-singular every point of affine space is non-singular okay affine spaces are smooth right so well anyway I need to go down to this I need to go down to this subset okay so well see for that I do the following thing you see you have see p is in x and that is that is the same as saying that Ix is contained in mp okay this is again you know this is just applying the script I and the z functors to p and x right and using the NUSH transients so you know p see p is in x so you are saying the subset p is subset of x okay you apply i to this so you will get if the point p contains if x okay but what is if what is the ideal of the point the ideal of the point is exactly mp so mp contains if okay so this is just applying the functor I mean it is it is here it is gotten by applying the getting the ideal of a subset okay and and of course the ideal of point is this maximal ideal mp and so you know what will happen is that if you take if you take Ix so Ix is inside mp right and in fact if you take Ix plus mp squared okay that will also be a sub of mp okay because mp squared is a sub of subspace of mp Ix is also a sub of mp the sum of two subspaces is again a subspace alright and in fact I can even divide now by mp squared so I will get I divide by mp squared and I get this this is subspace I say subspace of this k vector space which is isomorphic by psi prime to kn alright the beautiful thing is if I take the image of psi prime and image of this under psi prime you know what I will get what is of course psi prime is an isomorphism and this is subspace so the image of the subspace under psi prime will be a subspace of kn okay and that subspace what is the dimension of the subspace what is the dimension of the image of a linear map it simply you take you simply take a set of generators for the subspace okay and apply the linear map the image of a subspace is just given by taking the span of the image of images of the generators of the subspace okay so if I want to take the if I if I take the image of if I want the image of this I would just take a set of generators for this apply psi prime to that and take the span of that okay in other words of course instead of taking span of a set of vectors you can write those vectors in column form take the matrix and take the rank of that matrix because you know the rank of the matrix will give you the dimension of the image okay this is the standard rank and nullity theorem in you know linear algebra so it is part of that theorem so you know but you see now you know for I X if I take a set of generators F1 through FL of I X okay then those generators will also give me generators here okay and applying psi prime is actually calculating this Jacobian matrix because actually what is happening is when you apply to each generator okay what you are doing is you are taking you are going to get one you are going to get one row or one column of that depending on the way you write it of the Jacobian matrix so if you take the images of all these generators I am so I am just going to get to Jacobian matrix and each rank is precisely going to be the image of this okay that is the connection so moral of the story is dimension over K of I X plus MP squared by MP squared is equal to dimension over K of psi prime applied to that I X plus MP squared over MP squared okay and this is equal to rank of the Jacobian of doh FI by doh XJ at P okay where F1 F2 etc up to FL are a set of generators for the ideal of X as here so this is how you know the you see now if you look at it like this it is very clear that no matter what set of generators I use instead of using F1 through FL suppose I use some G some H1 through H L prime another set of generators no matter how many generators they are I do not care okay but in any case I am only going to get dimension of this subspace and that is the reason why this this the rank of this Jacobian does not depend on what your generators are okay you are always going to get only dimension of this subspace okay that is the reason why even for a fixed embedding for the ideal of the variety in the affine variety in the embedding into affine space even if you change the set of generators you are going to when you calculate the rank of the Jacobian of the generators with respect to the variables you are going to get only the same dimension I mean you are going to get only the same rank because is a dimension of one and only one subspace this subspace under this isomorphism okay fine so alright now it is a matter of just a little bit more of linear algebra alright so what you do is so let me keep this statement here as it is and continue here okay it is only probably a couple of lines more so what will happen is you have see what you should remember is you see mp mod mp squared divided by ix plus mp squared mod mp squared okay I have this this is a space and this is a subspace if I take the quotient my claim is that this is the same as mp mod mp squared where this mp is unique maximized in the local ring of x at p alright so you see we have an isomorphism of k vector spaces in this way okay because how do you get the local ring you get the local ring because the local ring of x at p is gotten how what you do is you take the affine coordinate ring of x and you localize it at the maximal ideal that corresponds to the maximal ideal that corresponds to the point p inside x you know this is the definition of the local this is how you get the local ring of an affine variety at a point you simply take the affine coordinate ring of the variety and you localize at the maximal ideal that corresponds to that point the unique maximal ideal of the affine coordinate ring which corresponds to that point by the Null-Strauss and such okay but what is but what is Ax it is just polynomial ring you go model of the ideal ix and then what is this maximal ideal this is just mp you localize at mp mod ix alright and because of this if you take if you take this quotient mp mod mp squared ix plus mp squared mod mp squared this will be the same as small mp where small mp is the is the unique maximal ideal in this because you see small mp is actually this you take the ideal mpx dot take the ideal generated by this by its image in oxp okay so this quotient is the same as this alright as k vector spaces and therefore if you count dimensions dimension of this minus dimension of this is equal to dimension of this so you will get you will get dimension of mp mod mp squared over k is equal to dimension of capital mp mod mp squared over k minus dimension of ix plus mp squared by mp squared alright and but you know so that will be equal to what is this this is n dimension because you have already proved mp mod mp squared is isomorphic to capital mp by capital mp squared is isomorphic to kn as vector spaces therefore its dimension because of the isomorphism psi prime its dimension is n so you see this is n okay minus this part is just the rank of the Jacobian matrix at p so this is this as we have seen here is dimension of ix plus mp capital mp squared by capital mp squared is actually the image under psi prime dimension of the image under psi prime of that subspace okay and that is a rank of the Jacobian. So I will get n minus here I will get n minus rank of the Jacobian of dou fi by dou xj at p I will get this okay and what is and this is equal to n minus n minus dimension of x if and only if p of in as a point of x is non-singular that is our definition of non-singularity the definition of non-singularity is that the rank of the Jacobian should be equal to the co-dimension for a point which is a smooth point a point which is a non-singular point. So this is equal to n minus n minus of dimension of x which is equal to dimension of x if and only if the point p is non-singular so that proves the theorem so what you have proved is dimension of m mod m squared mp mod mp squared where mp is the local ring mp is unique maximum ideal in the local ring corresponding to the point p on the variety x that is equal to the dimension of x if and only if the point p is a smooth point okay and the importance of the importance of that is that this gives this gives the tangent space at the point this gives you the dimension of the tangent space at that m mod m squared okay dimension of m mod m squared that actually gives you the tangent space at the point okay and therefore you are saying a point is a smooth point if and only if the dimension of the tangent space is equal to the dimension of the variety on which it lies okay in general what will happen is a dimension it is not a smooth point this dimension can go bigger you can get more tangent vectors your tangent space can become bigger if your tangent space becomes bigger then if you calculate the rank of the Jacobian that will become smaller okay and the point will be a non-singular point I mean the point will become a singular point okay so the moral of the story is that this gives you the tangent space okay and this actually calculates the normal space this is a set of normal directions at that point in the ambient space in which this space is this object is sitting inside okay. So if the point is a smooth point and the x is an r dimensional variety in n dimensional space then the dimension of the tangent space will be exactly r the dimension of the normal space all the vectors which are perpendicular to the tangent space tangent vectors that will be n-r and that should be equal to the rank of the Jacobian for us any set of generators and that is what geometrically is happening and that is what it says okay so that finishes the proof of this theorem so in this connection I need to tell you that the set of points where the where the set of singular points that is a close subset okay. So that is also a fact that can be seen immediately from this argument if you look at all those points where you have which are singular points see those are points on the variety where this rank falls rank of this matrix falls okay and you know where the rank of a matrix falls is just given by the locus of the vanishing of the of all the minors okay of all the maximal minors right. So if you have if you take this Jacobian matrix okay it is a matrix having polynomial entries alright and you know if you vary the point p what are the points p which are singular those are the points for which if you evaluate the Jacobian matrix you are going to get rank less than you would not get rank n-r okay but you will get lesser rank okay and what does that correspond to that corresponds to you take all the maximal you take all the maximal minors square minors of the matrix they are determined should vanish if all the maximal square minus mat vanish at that point the rank has to fall and only at such points the rank will fall and therefore that is a close subset okay. So this argument tells you that if you look at all the points p which are singular points that is a close subset of x that will be a close subset of x okay so the set of singular points is a close subset but the more important fact is that this is this close subset is by no means the whole space it can only be a proper close subset which means it will be of smaller dimension and that needs proof and I will prove it in the next lecture.