Okay, traders, welcome to this week's live analysis session with me, Patrick Munley. If you can see a Tick Mill welcome screen and you can hear me, if you could type a Y in the chat box just to let me know that the audio and the visuals are working. Very much. Okay, let's go here. Before we do obviously, as always, it's incredibly important that we adhere to the risk disclaimer and that you're aware of the inherent risk in trading any financial instruments and also that any of the views expressed by me here today are expressly my own. They are not those of Tick Mill. For those who are joining us for the first time, a quick introduction with respect to who I am. My name is Patrick Munley. I've been involved in the markets now for 15 years. I wasn't always in the financial markets after I graduated. I went into the world of consulting. I then did a consulting startup that experienced some pretty rapid growth and I cashed in my shares in that business in 2004 and then started to explore my passion for markets. Really, in 2004, what I was ostensibly doing was gambling.  I started trading, loosely described as trading, the S&P 500 day trading markets would not be trending north and I caught some lucky early breaks and started to make some decent and then some quite significant gains. However, as is often the case, my beginner's luck ran out. I'm not just gained back the gains I made. I further to that, I would actually experience a six-figure loss. It was at that point that I decided I either stop gambling or I get serious about trading in the markets and go about this as a commercial endeavor. I sought out a mentor, worked exclusively with him for 18 months, two years, really learning not just the technical skills but also the mental skills that are required to be successful in the markets. During that period, I developed and back tested, extensively back tested my trading plan, forward tested it and actually came back into the markets in 2008 in conditions similar to, not quite the same as we're currently experiencing, and since 2008 on an annual basis, I've been profitable. The performance you can see on the screen at the moment references from 2013. That's when I actually started and managed the account service initially for friends and family and that's grown organically. Again, on an annual basis, the accounts have been profitable and that's really how I look at performance. I'm not concerned about the outcomes of individual trades or even a string of trades. For me, what I'm focused on is the next 100 trades because I know that if I adhere to my process and my plan and I execute that to the best of my ability, then that's where I'll see the returns. I'm perfectly comfortable with the idea that I could easily go through a period of 10 or more losing trades but because I've got a laser focus on risk reward with respect to my trading, I know that over the next 100 trades I should see positive returns based on the strategy's efficiency. Predominantly now, my trading is end of day. It's an end of day strategy and there's some interesting stuff but mainly it's end of day and it's an automated trade management setup that I have now. I've got a quite a bit of time in my hands and I have some additional projects that I work on. I'm one of the resident market experts at Tickmill providing a daily market outlook and a chart setup that's of interest. You can subscribe to get those updates in your inbox through the Tickmill blog site. Also the head of trading and trader education at a leading FX trading education firm called FX CareerSwap whereby we offer emerging retail trading talents the opportunity to enhance their developments and ultimately trade a larger capital base through our funded account offering which really helps retail traders to overcome the major issue that tends to hinder their development and that's capitalisation because you can have an excellent plan and strategy and if you adhere to professional risk management so keeping your risk low, ultimately if you experience 30 to 50% returns in a year which are fantastic, if you're trading a thousand dollar account or less then that isn't going to add up to a financial return that's going to move the needle for anyone and so what tends to happen with retail traders is that they risk more than they should do and end up blowing up accounts when they experience a small drawdown and so what we do at FX CareerSwap is we help with your development as a trader, we have a team of over 80 traders now that we're working with at various stages of development and through our courses and our education modules and our weekly webinars we develop you to the point that you can then go on to manage and grow an account with a significant capital base and so for anyone who wants to learn more about that you can contact me through LinkedIn or through the site FXcareerswap.com. Okay so that gives you a flavour of where I'm coming from and what I want to do now is start to think about some of the markets that I'm tracking and some of the opportunities I see that potentially develop. As a general note with respect to the market at the moment certainly in the majors we've seen this grinding action over the past week or so and predominantly driven by some big options flows that we've seen that are pinning the market so to speak. By the end of today we'll have had 10 billion dollars worth of euro USD options expiring between this 108 and 109 level and that's kind of been pinning the market and creating this grinding heavy rotation action that we're seeing that's frustrating but those are predominantly rolling off like I say today and so that should actually allow us to see some more decent flow action in the markets. We've seen the implied volatility curves come off since we experienced the height of the crisis that initial panic phase and you can see they're starting to tick up again notably in the Australian dollar so this means that we should start to be starting to see more trading opportunities developing. These are those options that are rolling off today we've got 1.2 billion down at 10750 and the euro I think that's close to where we see the lows today. You can see the cluster of about 10 billion here between 10750 and 10950 and that's really been been pinning the market. With respect to where I've seen decent opportunities developing and we'll talk about it when I move into the charts in a minute but this is a study of the Canadian dollar from a seasonality perspective and what this shows is that the second quarter over the past 20 years has had a tendency to see or we've had a tendency to witness Canadian dollar strength and you can see that in terms of the last 20 years 13 times so about 65 percent of the time we've seen a decline in the Canadian dollar and on average you can see that we get you know somewhere between 300 and anywhere up to 1100 pips to the downside but when we've seen upside it's been between 100 and so 450 pips so you can see from a set up perspective here just using the seasonality that the declines that we see 65 percent of the time are more than two to one the advances we see in the other 35 percent of the time. So if you're thinking just about obviously it's a relatively small sample but from a statistical perspective that gives us a bit of an edge there in terms of a set up with respect to the the seasonality and if we then think about that in terms of what we've seen with oil we're moving to take a look at the oil chart now let's just bring this that so I posted I did a chart of the day earlier in the week with respect to oil and what we've seen with oil basically is obviously that we've seen this historic decline we saw the the May contract trades at negative levels you know historic historic reprints in terms of the your contract but in the continuous contract here what I've highlighted to the guys in the trade team is that we've seen a pretty nice from a cycle perspective we've seen some nice symmetry in terms of this ending pattern here if we think about this as an impulsive decline and if we you know just from an Elliott Wave perspective for those who are who are Elliott Wave enthusiasts you can see that we've got the one two then we've had our three four then we've had an equality leg five complete here and I talked to the guys in the room about this 12 to $12.50 area as potentially being significant for oil certainly for a tradeable low and it looks like potentially tonight for my strategy anyway we could get a long signal here if we get a green clothes on oil somewhere around well somewhere above the $14 level and what could we reasonably expect in terms of upside here well what I use again is is these symmetry swings so if we look back to the last advance we saw prior to the decline and we overlay that versus our current low then that would give us a target about the $25 level so if we think about risk reward here for the trades if we're going to get long let's you know choose at or current levels so you know probably looking at that $15 level you've got a stop at the lows here everywhere you could use to stop the low today's low to enhance the risk reward but given the volatility you probably want to use the low so we can even if we just if we replicated the price actually we saw prior to the down draft then we could see that we could drift higher here you know this I'm not expecting this to happen in in any short order so it's certainly with the you know the current economic environment but that said we could drift higher here over the next couple of months and you get a three to one nearly risk reward on the trade there and if we do get a first leg of recovery here then then there's a chance or or technically certainly we could see a three-way bounce at a minimum and and if we think in terms of some type of move like this where we test let's just bring in the fibrotrosons so if we fit the entire decline you know we he's certainly into even the 38.2 here let's actually let's see where that comes in so yeah I mean even if we just thought in terms of making a 38.2 percent retracement which you know technically could well be on the cars then we'd be up at $30 a barrel and you know if we get a if we get a signal or in terms of a setup to add to add to a long trade here well then you're looking at you know a risk reward scenario of closer to to 4.5 to 1 so again always thinking you know all the analysis in the world is fantastic but at the end of the day what we're looking at is returns in our account so we need to think about risk reward so that this the risk reward of this trade stacks up certainly if we if we can see a corrected move play out here so I'll be watching the crude oil on the clothes tonight now if we think about crude oil if this is the view in terms of crude oil well then if we think back if we think again about the Canadian dollar obviously it trades as a proxy for crude oil well then if we go to the the Canadian dollar we'll see if we've got a setup developing there and we have what we've done here with the Canadian dollar basically is we've we have this spike high during the crisis and we've drifted low made another leg lower and so we've run into some symmetry swing resistance now in in the Canadian dollar we tested the level we haven't been able to close above this 142 level for two days so we've got a clear area where we're seeing some supply in the market between 142 and this 142 80 area so there's the supply we've got those you can see there's two tails there we're testing the volatility resistance bands and what I've been looking for now is a breakthrough this 141 area to open up a deeper correction again notes I'm using the term correction here a lot you know I'm not suggesting at this stage that we've seen the absolute high here but certainly what we could think to ourselves if we just look just these settings bringing the 61.8 so again in terms of targets here what we have is we have a symmetry swing objective that comes in an equality level at 136 we've got the 61.8 percent retracement of this advance at at 36 level so if we can get if I certainly what I've been looking at tonight if we get a close that closes below the near-term VWAP so somewhere below 141 let's see where it is somewhere below 141.30 let's say that's going to flip this daily chart bearish we'll have a bearish inside candle these tails at the 142 is giving us our resistance level so what we could be again if we think in terms of risk reward what we'll be looking at is you know selling the area here we're looking at stop above this 142 area but we've seen the resistance and then we've got a downside target well initially what we'd look at is for a move certainly to test the the 50 percent retracement we came close we didn't do it so we're seeing more complex correction develop here but if we can get this bearish close we could certainly look for a move down initially to retest these prior lows where you'd have 2.5 to 1 your risk reward then into the 50 percent retracement obviously in the volatility sport bands we'd have to watch how we trade there but you know then you're looking at three times the risk reward and if the equality move plays out and we trade into that 61.8 percent retracement well then you're looking at a potential five to one risk reward so again you'd have to be thinking about that in terms of the the potential for a move in crude oil but again thinking about the seasonality we know that statistically there's a 65 percent chance that that the canadian dollar can can see some strength in this second quarter so that's just how I'm you know thinking in terms of my trade thesis for getting long crude and I'm short this canadian dollar I posted today the cad yen also could give a bullish signal if we got a close above the near-term VWAP here we've tested the volatility support bands and that will then set up a move to certainly to test this 7847 in terms of the first resistance area these prior highs as well but through there what I've been looking for is actually the equality move and the 50 percent retracement of the decline which will bring us into that 80 level so again let's just look at how we could position this from a trade perspective so looking long have to get the close at the the VWAP to go bullish but again what we've got there in terms of risk reward on that trade we probably need to widen stop here to account for intraday volatility but again you get a three to one risk reward on that trade in the cad yen the other one that's broken out here I've noticed this morning as well as the cad swiss so again similar story you can see what I'm getting at here we're seeing this cad strength premised on the fact that we're seeing a little an uptick in crude oil we've broken out of a channel here or a potential bull flag and then the objective here is again the equality move for obviously we'd watch how we trade at this initial equality level at the 70 handle the 50 percent retracement again so but by this stage you know you'd have the trade running as a risk-free position if we get up here and then the next target is going to be the bigger equality objective and the 161 extension of this structure so you know there's move there with the potential to trade up to towards the 72 handle so that's one of the core opportunities that I'm looking at at the moment let's let's take a look through some of the major markets now looking at the dollar index dollar well I'll just take a sip of water so the dollar index could be grinding higher and what we're looking at at the moment is the potential now for the dollar index to test this equality objective and what I've been looking for is by the time we get up there that my my momentum indicator here the site indicator would actually be testing this descending trend line that's potentially in place now so as prices grind up into this 101 40 to 102 area I'll be watching for bearish reversal patterns on the daily chart obviously that's my time frame to actually set short positions especially if we're at or near testing this this descending trend line resistance so what we've been looking for there would be then obviously prices to decline and then we should see a pullback in terms of the psychic indicator as well obviously further confirmation would be the RSI stochastic trading above the 80 level and rolling over so I'm watching this dollar index very carefully as you'll know from previous weeks I see the potential for for a dollar decline to develop obviously potential is the is the keyword focused on there you know any we can't talk in definitive in terms of the market we're always dealing in probabilities here but I see a higher probability opportunity so I'm going to be watching how we trade when we test this area if we break higher then we could see the potential for a big double top here that's the one six one extension of this structure but for now my area of focus is going to be on this 78.6% 102 to 101 40 area I certainly want to see how we're trading in terms of the psychic indicator when we get up there into that that's sending trend line resistance the other major markets the S&P 500 so we spiked up into the the resistance area this is the equality objective versus this initial reaction high and initial reaction low here and we got bearish reversal and a short signal since then we haven't really made too much headway in terms of the downside and what we could be potentially setting up for here is is another yeah another leg higher as we know the Federal Reserve and the US government have are throwing everything they've got at these markets in terms of stimulus stimulus both monetary policy and fiscal stimulus packages and so what we could be looking at here certainly whilst we trade above the 2690 area is another leg higher now obviously if we if we do push higher here I'll be watching for the potential of a double top to develop here but more likely than not what I think we'll see is another leg higher into the the 161 extension of our initial reaction high and reaction low here and the 78.6% of the tracement of the entire decline now from there I would anticipate or I certainly I'll be watching for the potential to set short positions with bearish reversal patterns the you could easily see or the the technical target for that trade would actually be the equality move which could take us back down to this 1900 area and again as I've talked about in prior sessions do I anticipate that that's going to happen with the same force that we saw in terms of the initial decline now I would expect more grinding trade but certainly that's where I see the potential but again watching for a retest of the highest double top potential if we break through there then we've got a target to watch very carefully for short setups so that's what I'm looking at in terms of this 500 gold so gold looks like it's about to retest these prior highs which are again is an equality objective versus this structure so what we're seeing is the equality move played out we tested held it to the tick now we're seeing the pullback and in terms of the support area we are looking at this symmetry swing support so we're seeing an equality unit again equality in the markets as a recurring theme so we've held there now what I look for is the potential that we retest these highs and we've got one two seven two extension of this last leg here watching for bearish reversal patterns here to set short positions but again we'll be looking at symmetry swing support as the initial area of concern for any short positions because we could be setting up then if we hold the symmetry swing for yet another spike higher up towards 1850 would be the equality objective before we see a more significant decline but if we do get a short signal here there is the potential again we're just thinking in terms of equality that that we don't find symmetry swing support and and we see actually a deeper decline let's remove that before again thinking about the next leg higher in terms of gold so really what I'm watching is the retest here of 1750 to 1770 looking for potential reversal patterns to set short positions is the plan for me in gold crude we've just talked about let's see where we get if we get the clothes tonight to do something on the long side there in crude the euro similar to the idea that I've just talked about in terms of the dollar index we'll have to see where where we close today we'd be cognizant of the fact we've got this ECB meeting we've got these huge options pinning pinning in the the market at the moment there's work with I'm seeing on the wires talk about two trillion euro stimulus package which which is pretty much the bare minimum for what they need and we'll see how that's delivered to the market but for now I think whilst we're holding these 10990 highs then I'm looking for a retest of this 10630 area and then the potential for a you know a significant double bottom to develop as we complete the equality move and then maybe the opportunity to trade higher in the euro so really watching price action as we test into this area looking for bullish reversal patterns to do something on the long side in the euro and obviously that that's versus the idea that that the dollar index would trade up in and hold this resistance area because obviously they trade inversely sterling sterling is pulled back into symmetry swing support and if we hold here and we get get a bullish reversal then I think long long positions should work at least for a test of this 127 area and again that we bring in our retracement tools so if we look at the climb so that brings us broadly into that 78.6 percent area I think from there we would probably then see a more sustained pullback probably looking into the 50 percent retracement area of this move if it plays out before we can potentially then build for another leg higher in terms of cable. Dolly Yen going nowhere sideways in the market at the moment technically what we're what we're looking at is whilst we hold this resistance at 109 then we can see the downside target here at 104.50 but we're going nowhere fast at the moment in terms of the Yen. Suisse's broken out of its triangle and now looked poised again to test the equality objective and potential here for a significant double top and that again broadly coincides with the idea of the euro putting in a double bottom here so you can see the synchronicity in these some of these dollar pairs so got some key levels we'll be watching so I'll be watching for a retest of this 98.90 area again bearish reversal patterns to potentially do something on the short side looking to see if we got watching this this resistance area trend line in terms of the psych indicator as well it's keeping an eye on that the loony you know what I'm looking to do there so we'll see if we get back to the close to confirm the trade tonight the Aussie it's held its symmetry swing support and and if we get a bullish close here then it looks set for the Aussie to to trade up and test this this is the equality objective version versus this structure and it's the 78.60% retracement and we've got these prior lows over here so this will be a very interesting area if it plays out in terms of the Aussie testing up here from here I would expect a more sustainable back in terms of the Aussie so the level that I'm going to be you know from get a bullish close and I think we've got the potential for a breakout but ultimately what I'm looking for is a test of this 67 area where I'd be looking to set short positions with the price confirmation a similar story in the Kiwi whilst we hold the symmetry swing support we can see we can see this grind higher let's just bring in this here so if we can get a bullish close there that initially would target move up to 62 but ultimately as with most of these pairs and if you think in terms of the S&P 500 I'm really focused on these 78.6% retracement areas that you can see across these major markets that they're all looking to sync up and I've talked about Caddy M and Caddy Swiss already Euro yen watching this test of this big double bottom in the Euro yen and we've got this contracting price pattern here obviously what we would need to see if this thing is going to reverse is that you know there would have to be some very positive news out of this this Eurozone area but I've been looking for a bullish reversal if that news does come out later today or tomorrow back through the 117 area could could see us trade up and and test retest this 119 range high but we have seen no price confirmation as of yet so with respect to the markets and the opportunities I see at the moment I'm really focused on the Canadian dollar and again thinking in terms of the seasonality aspect of that as well so that's that's it from me for for this week guys does anyone have any questions or any chart you'd like we take a look at that I haven't covered and I can give you give you a view yeah I mean at this stage wait it's it's really just it's a positioning squeeze a short squeeze where you know we've been heavily oversold and what would really drive like you say what would actually drive a significant recovery would be would be a vaccine certainly but it would appear at the moment well we've got UK in the UK we've got human trials starting with the Oxford's research lab so I don't you know nobody knows at this stage but at the moment what we're just seeing is a repositioning and actually allow a correction to take place and that's all we're thinking in terms of at the moment I'm not looking to pick bottoms here but you know we kept technically we've been very oversold and could witness a correction but in the long term from an economic perspective then you know it really is all about a vaccine at this stage to to really deliver some positivity to the markets on an extended basis any other questions okay if there aren't any other questions I'll wrap this one up here you can follow me through the through TradingView at fxcareerswap and you can reach through the site fxcareerswap.com or you can contact me personally on LinkedIn and I can point you in the right direction for those who want information on that and if there aren't any other questions we'll wrap this up here for this week and I'll see you all again at the same time next week safe trading guys


If you've never been to this conference, I mean this is an exciting place. It's so awesome to come. You'll be super welcome. Everyone will be so excited that you're here and you'll have a real chance to just enter in to a relationship with God on the weekend. You just let God love you for a weekend. I mean, it's not hard. It's very easy. When you come to the Power and Purpose Conference, you can't help being moved and just empowered by the Holy Spirit to be launched out, to really love as God's calling us to. One of the most powerful aspects of the conference is that the Holy Spirit dwells here at Franciscan University. Like, this is God's footstool. And so when the people come here with expectant faith and the leaders come who are seeking to help you, a witness and a vessel of God's grace, power happens. This place is soaked in prayer. It's soaked in the power of the Holy Spirit. Great things happen at Franciscan when the conferences happen because God dwells here in a mighty way. To know He's that close.  I mean, Jesus calls you to do everything. You don't have to say anything.   When we drive up that hill with the bus and you enter the campus, it's like the atmosphere changes completely. You know that the Holy Spirit is here. I think I witnessed some healing as the Father was holding the monstrance over certain individuals. I mean, I could just tell that they were being healed and as a convert to never have experienced anything like that before, it was just beautiful. Everything that we believe as men and women of faith is being challenged. So the devil is busy. He's real and he's busy. But John says that greater is he that lives in us and he that is in the world. So this is decision time. Where do you stand? Why wouldn't you want to come or how come you can't come because there's so much love there and wouldn't you want to be where there's a lot of love instead of out in this crazy world? I think I'd say to someone who's never come to a conference like this, like Power and Purpose, give it a shot, right? This beautiful episode in the Gospels where Peter recognized Jesus walking on the shore and Jesus reaches out to him and Peter says, Lord, could you bid me to come to you on the water? I love what Jesus says. He says, come. Just come. You know, there's a risk involved there. So I would say to anybody who's thinking about it, just come.  That's okay. Just come and experience the grace and the mercy and the love of God.


Bob Euker has called the fourth most games on radio and baseball history. He's trailing the retired Ben Scully. Ben did it 67 years. Another Dodger icon, Jamie Jaron, 62 years and running. I should say Jaime Jaron. Kansas City's Denny Matthews, 52 years and counting. And Bob is ready for his 50th year calling Brewers Games in Bob Euker. Mr. Baseball joining us on the program. Hi, Bob, how are you? And you son, how you doing? I'm doing OK. No pressure on you other than I wanted to have some fun with baseball and there hasn't been anything fun with baseballs of late. So how are you doing? How's your morale? I'm doing OK. I'm glad we're going back to work. And it'll be my 60-50 year overall in baseball. You know, as a player, if you want to say that. And of course, calling the games here in Milwaukee, I worked a couple of... I worked a couple of seasons with the Braves, with Milo Hamilton and Ernie Johnson before Bud brought me back to... Bud Saley brought me back to Milwaukee. But other than that, I'm hanging around and I'm waiting to go back to work. I just saw where your official batting average in your career was $199.7. I, you know, that I couldn't... A lot of my sponsors would be upset if they dropped below $200. Because at that time, it tied me with another sports grade averaging $200 or better for a 10-year period. And that was all came over Don Carter.  But were you the Mendoza line before the Mendoza line, Bob? Well, yeah, but she's got a job in baseball now. I think she works for the Mets, doesn't she? That's a different Mendoza. Oh, OK. And tell me if this is right. Did you get traded? Did your baseball career get extended because you were a good clubhouse guy? Yeah, I mean, laundry has got to be done, man. There's, I mean, for a couple of extra bucks a month, I was making I was making below the minimum, you know that. And and selling other players equipment got me a couple of bucks doing laundry. There's a lot of things that you can do without playing. I actually thought it was an infringement when they asked me to play a game. But but I thought you got traded to the Cardinals because you were going to back up Macarver and you might have had a better arm, but they liked your personality. Is that and and I think armwise, I had one on each side, which was fine, but yeah, to back up, Timmy, who's remained a great friend. And of course, you know, we win a World Series that year when I got traded to St. Louis and I'm not I'm not going to say anything. They didn't win one before when I got there. So something had to be working right when you when you were first went on on Carson, first time you were on there, were you still playing baseball? No, I was I was done. And as a matter of fact, the first show I did with Johnny was in New York. They had moved to the West Coast yet. I think it was in 1970, maybe 69 or 70. How'd you end up on the show? I had been friends with a great trumpeter, one of the legendary Trumpeters of all time, Al Hurt, and I did a couple of jobs with him. I was traveling. Alex Karris was a guy that I worked with. He was there because he was a great player. And I was I was the wind up speaker. But I did a couple of jobs with Al Hurt and he told me he was going to get me on a tonight show. And I said, oh, yeah, sure. Well, I got a call from the tonight show about two weeks later. And I went to New York. I had a I had auditioned with a talent guy and he I went to his office and he said, what do you do? I said, nothing. I'm here to let me see some of your stuff or let me hear what you're going to talk about. So I did a couple of things.  They called me back to New York and I did the show with Johnny. And I remember the one thing that was funny about it, Dan, was at the end of the show when, you know, the same good night and everything, I heard Johnny say to Ed, after we we said, good night, did that guy really play baseball? Ed said, I think so. I went back two weeks later and did another one. And then I got to be kind of a pretty regular, you know, with with Johnny, we had a great relationship. And I did what I still do with Doc Severington. And, you know, a lot of the guys in the band, I would go over and do a tonight show when we were playing in Anaheim, when the Brewers were playing in Anaheim, I would go over and do a tonight show and then come back. I'd get back maybe in the third inning. And some of the bad guys would come up and sit in the booth at the ballpark. So it was, I had a great time with the night shows all the time. How did that change your life? Well, it raised my salary by $220 a month. That was the big thing. But I had a pension, you know, the Screen Actors Guild. So I wasn't worried about baseball anymore. But I did, you know, I stuck around baseball for six years, I guess. Had a great time doing it, made great, you know, really great friendships, including yourself. And your crew there, but all of those, you know, if I ever had a good year, it would really screw me up later. I couldn't, there were a couple of times I got off to good starts, I had to go in the tank. Well, yeah, nobody, there's nothing funny about getting off to a good start. You know, like batting 225 is not funny, but 197, that's funny. Exactly, exactly. And, you know, sitting in the other team's dugout was not always all that pleasant, but I was still at the game. Wearing a road uniform at home. And Carson introduced you one time, when you think of great baseball players, a lot of names come to mind. Bob Euker is not one of them. Right. And he called you Mr. Baseball. Yeah, and that kind of stuck around. He, I have a great picture at home here of him, Elston Howard and Roger Merris in New York and Mickey, all with Johnny. And he, he's got a Yankee uniform on and it looks awful on him, the way he's wearing it, the socks are, you know, down on the ground.  I think he tried to throw batting practice to those guys at Yankee Stadium. Really? Yeah, oh yeah. He was a great guy to work with. Dan, and like I said before, I always had a great time with him. He treated me, I never got bumped off the show. You know, I always stayed on and somebody else got bumped. But we had a good relationship. Matter of fact, I went out to the University of Nebraska. He built a, he built a studio and a really nice building out there for, you know, people who want to get involved in movies, television, whatever it may be. And I went out there as part of the opening with that with our owner, Mark Attenasi, was a matter of fact. And had a great time. They did a lot of shows, you know, tonight's show is that Johnny, I could break his chops, man. I could make him laugh. I just saw one on, somebody just sent me one of me in, it was a picture of me and Bob Gibson holding hands. I love that picture. So that's the team picture. So Gibson was in on the joke, the team picture with the Hall of Fame picture. You're holding hands with Bob Gibson, who seemed like a very serious guy. He was really good. He was a great friend. As the guy was getting ready to shoot the photo, I just reached over and grabbed his hand and we both started laughing and they took a picture. It was really good. I love it. We're talking to Bob Euker, his 50th year with the Brewers. And people should know, like you did have some legitimate moments there. You homered off Sandy Kofax. Yeah. I mean, that's real at Dodger Stadium, right? Yeah, but I, you know, every time I see him, I apologize. I always thought that was gonna keep him out of the Hall of Fame. I was really worried about that. Is that why Sandy doesn't do interviews is because he gave up the homerun to you? That's part of it, yeah. I don't know why I hit him fairly well. I really don't. Maybe it was, I don't know, probably 530 instead of 8 o'clock. Well, you didn't want those shadows if Kofax was on the mound. That'd be trouble. Did you, did you have to audition for the role of Harry Doyle and Major League? No, you know, I was doing a game in Chicago against the White Sox with the Brewers and a security guy came in and said there's two guys outside want to talk to you. So when I got off from my innings off, I went out in the hallway at Olkomiski Park and Chris Chester and David Ward were there and they had this script for the movie and asked me if I would consider doing it. So I said, I'll look at it, which I was gonna do it anyway, whether it was good or bad. But I looked at it and read it and they told me, you know, you do whatever you want.  And I did and I had a good time. You know, I met a lot of good people and the movie did good and Major League II, Major League III was on airplanes the day after we finished, it was terrible. Yeah, did you know at the time when you did the first Major League that it was gonna be good? You know, it had some really funny stuff in it and watching, I met Charlie Sheen the first night, the Brewers came back from a road trip and they had already set up County Stadium for the movie and David asked me if I'd go in and say hello to Charlie Sheen, he wanted to say hello. So I went in his trailer and talked to him for a while and then when I watched him throw, I mean, he threw pretty good, he really did. And watching Tom Berenger work behind the plate and Stevie Eger deserved a lot of credit for that too because he really worked with Tom. But you know, the script was kind of funny. I didn't use any big time curse words, I was kind of shocked when I heard the first one, but other than that, you know, they kind of let me do what I wanted. I did their stuff and then they made the picks. Yeah, there's great stuff in there. But just a bit outside was a natural man.  Were you ever a beer guy on the air like Harry Carey was? No, not really. I was into Jack Daniels. The team was, it depended on how bad the team was that year, what you were drinking. Oh, the team was at the airport a lot of times. I was still doing the game. But I remember listening to Joe Nuxall. And Joe Nuxall, you know, God rest his soul, he'd always say the old left hand a rounding third heading for home. He spilled his beer on his scorecard one night when I was listening to him and Marty Brenman. And it was just so funny. Cause we don't, we're listening on the radio and Joe spills it. He's not, he's not describing what he just did. And you just hear him like he's mad. And it's, you know, Marty Brenman's trying to call the game. And then they eventually got around to, you know, Joe had spilled his beer on his scorecard there. Oh, they were, they were, they were a great team, Dan. I, I, you know what his name for me was Blatsy. Remember, remember Blats beer? Blats beer? That's what he drank. Oh God, my dad drank Blats. Yeah, I called him Blats. I never called him.  He's a great friend too, man, what a guy. Great team. Great team. I'm going to miss Marty this year. Yeah, Hall of Famer. On a serious note, you know, this, this virus here, Bob. Yep. How concerned, how concerned are you? Well, I am, I'm, I, you know, I feel bad, Dan, for all the people that got furloughed. I don't care if it's baseball or anything else. People that I've worked around here at the ballpark for a, for a lot of years and, and got furloughed. And I, I, you know, I got furloughed when I was in the army. Um, that was, that was about it for me. And I was on our side too. I want that out. But, but it's, it's sad when I, when I see what's happening. We're going back to work on a very limited basis. Um, my partner, Jeff Levering and Lane Grindel will be totally separated.  And you know what our boot looks like in Milwaukee. So, and the engineer will be separated from us. Um, it's, I have to go in a whole, there's a whole different set of rules to do this stuff.  Matter of fact, I'm going to get tested tonight. Um, my wife and I and, and, um, our trainer, Roger Kaplinger is going to do that. Um, but, you know, I get, I get a second look a lot of times because I, I go into a store once in a while and I'm, I'm wearing my catcher's mask. I don't know if that's approved by the, uh, CDC there. Well, it, it saves the pain from a punch because there's a lot of people still living that saw me play. Uh, do you think you would have done steroids if they were around? Um, I, I, maybe, I don't think so. I don't think so. Suppositories, maybe, uh, no, not steroid. No. Does your wife, do, do people get straight answers out of you? Sometimes. I feel okay. That's what I figured. You've never been arrested. Oh, yes, I have. Really? Yeah, I got two hits in a game. Uh, well, it'd be great to have you back and, uh, thanks for, uh, just putting a smile on some people's faces today. You kids. Great to talk to you. I appreciate it.  Thank you, buddy. Bob Uker. Mr. Baseball there.


Couple wins $60 million, five years later ask police to destroy home.  She hears the sound of high-pitched squeaks and a terrible smell lingers in the air. Like rotting flesh, Casey can taste it now on the tip of her tongue as she walks through her new seven-bedroom mansion. Casey and her boyfriend Matt thought all their problems would have been solved by winning the lottery. But they were so wrong. You see, their problems had only just begun. Lovebirds Matt Topham and Cassie Carrington were an ordinary couple from a small town in England. Although the couple was deeply and madly in love, nothing exciting ever really happened in their lives. Every day seemed the same. So when these two lovebirds entered a jackpot for $60 million at their local town, never in their wildest dreams did they think they would get so lucky. To make ends meet, Matt worked as a carpenter and Casey worked at her local supermarket. The two were more than content with their lives in their one-bedroom apartment just outside of the town. It was small but cozy. But little did these two lovebirds know that fate had something else in store for them. It was a brand new week and both Matt and Casey went to their local shop. After picking up some bread and milk, Casey noticed that this week's lottery was for $60 million. She looked at Matt and quickly she filled in a lottery card with their lucky numbers. Casey and Matt didn't do the lottery every week, just when they felt like it. They had never won anything big before either, merely a crisp $10 bill. But Casey had a gut feeling that was telling her to enter the lottery. Casey filled in her numbers and handed them to the cashier. She didn't think anything of it if she was going to win anything it would probably just be $10, maybe even $20. It was only later that night when the lottery numbers were announced that Casey and Matt's biggest dream had come true. Later that night, Casey and Matt were sat around her television waiting for the jackpot numbers to be announced. Casey's eyes were fixated on the screen and her ears perked up when she heard the winning numbers. 7, 28, 25, 5, and 17. Casey couldn't speak. Her mouth dropped wide open and her heart began to race. Those were her numbers. She and Matt had won. Casey and Matt ran into each other's arms with happy tears streaming down their face. $60 million was all theirs. It wasn't hard for them to come up with things to spend the money on. They would obviously take care of their family and go on vacation, probably get a new car, definitely a new house. This couple thought all their problems had been solved. But they had no idea that this was the start of something truly unimaginable. The first thing that the happy couple did with their winnings was buy a seven bedroom mansion for about $1.6 million. The mansion was everything they were looking for. For many people in their town, this seven bedroom mansion would be a dream come true, but for Matt and Casey, it was only the start of a horrific nightmare. Although the mansion was all theirs, when Matt and Casey bought it, they didn't move in straight away. You see, they planned to do work to it, to renovate and customize it. The total cost for this project would be just over $6 million. But with still around $60 million in the bank, a mere $6 million looked like nothing. They had no idea what was coming. Matt and Casey called their new mansion serenity, but their plans and projects for the mansion were far from calming and peaceful. They had goals of adding a second house to the property, building a 10-car garage as well as a swimming pool. Their plans were foolproof. Or so they thought. Even though Matt and Casey's plans for the mansion were big and bold, they were confident they would be able to accomplish them. After all, with millions of dollars in the bank what could go wrong? Matt and Casey soon got to work on their big and grand project, but their renovations soon came to an abrupt halt. With so much money in their bank, this was such a strange yet incredible experience for the young couple. Not only did they purchase the mansion, but they also bought another home, specifically for their closest friends and family. They also went on numerous luxurious vacations to New York, Japan and France. Then, a year after they first won the lottery, Casey had some news that would change everything. Just when Casey and Matt thought life couldn't get any better, Casey found out she was pregnant. The two soon-to-be parents swiftly tied the knot and finally, this family felt complete. While Casey and Matt were having the times of their lives with their new fortune, the couple had completely neglected their dream mansion. They had no idea what state it was in.  Trespassers were constantly breaking into it, and police from the town often made trips to the mansion to keep vandals and criminals away. The mansion itself was originally built in the 1930s. Throughout the town, it was known as the Rainbow House. But after Casey and Matt bought it, it soon became a house of horrors. Neighbors of the mansion were constantly complaining about the property. From the untidy and unkempt garden to the offensive graffiti that covered the mansion's exterior. But criminals and vandals were not the only unwanted guests at this perfect mansion. When Casey and Matt went back to the mansion to see what all the uproar was about, they were disgusted to see it in such a state. Toilets were smashed up, dead animals were scattered everywhere and rats and other creatures were running wild. The entire house was a death trap, and a serious health and safety hazard. Neighbors were angry at Casey and Matt for letting it get this bad. But things were about to get even worse. You see, many children and teens in the area had called the mansion the scariest place to take a selfie in all of the town. Casey and Matt knew they couldn't carry on like this anymore. They both knew what they had to do, but neither of them would admit it. Casey rang her local police station and asked them to come and demolish the entire mansion and property before it got even worse. Inevitably, Casey and Matt were heartbroken knowing that would never get to transform their dream mansion. But this didn't mean their dreams of living a luxurious and celebrity-style life was over. You see, the couple still own the land so they planned to build a brand-new home on the site. Casey and Matt presented the council with their updated plans for their new home. As of now, they're still waiting for permission, but they're confident it'll go through. When it comes to their new home this time, the lucky couple has promised to keep an eye on their property every single step of the journey.


productive weekend for Dickinson is they get a couple of wins here at the Mustang Classic with head coach David Webster. Let's talk about the global view here real quick to come here two ranked opponents and walk away with two wins. What does it do here for you guys this weekend? It was fantastic. Our guys are playing with a lot of passion and enthusiasm and that helped us through the fatigue today just that energy and we kind of went in waves today and Denison was really tough and resilient and they kept coming back but at the end we were able to make some plays and finish it. Sometimes your best defender's got to be your goalkeeper and in that third quarter I mean Denison brought everything but the kitchen sink at you guys in the third quarter and Patrick just stood incredibly tall in the net and talk about his play and what that meant to keep the lead and really keep it at a comfortable distance for you there. Right he sure did he made some tremendous plays where they had some real opportunities and he stole some today. Great weekend for Patrick and so excited for him and his hometown to have his first start and just do an amazing job. You guys really showed a lot of balance on the offensive side. Is that kind of by design what you're looking for because you through the weekend you had a ton of contributors for you guys. Yeah we sure do. We try to spread it out. I thought today we got our spacing wasn't necessarily great. You saw some fatigue in our dodging but we're able to keep moving the ball and find the open man and that's that's certainly by design. Obviously somewhere later on during the course of the season you're going to play in a scenario like this to be able to simulate this against this type of competition in this classic. You guys keep coming back here and playing. What does this event do for you. It's amazing. I said this yesterday it's the premier event in Kyle's across and it's just so much fun. So we're here because it's fun. We love the competition. We love the opportunity to compete and learn from this atmosphere and we just have tremendous fun doing it. A challenge now maybe the maturity factor of handling winning a couple of games like this and maintain that focus going forward. Right. So now we have finished our non conference slate. Now we're into our conference and our conference and 10 year conference is an absolute grind. Some tremendous coaches and strong players on every team and we got to be up for everyone and we've got a young team not a lot of experience. So those are challenges we have to deal with every week. Congratulations on the victory and safe travels back to Carlisle. Thank you. Great event. Thanks. David Webster joining us here as Dickinson gets the victory here by count of 14 to 10.


reason why Islamophobia is spreading is, first of all, new sources emphasizing incidents which have in place where people of Islamic origin are involved. This is essentially the already present fear of Muslims in people, which results in people feeling as if all terror attacks are due to Muslims. Another big problem is the film industry, as most of the times, whenever they show a play hijacking, a suicide bombing, or a mass shooting, they show people dressed in stereotypical Muslim attire, clearly showing their origin as a form. This then rather makes people associate all terror attacks or violent attacks with Muslims.


I really like you to put a shirt on. It's now our naked reactions. Demonitized. Josh!  I'm Naked. And you can follow us on Instagram, Twitter for more juice at gondank. Thank you to every sports on Patreon, follow us on official Twitter, and subscribe if you haven't and hit the like button. I have a shirt over there, but I'm not gonna get up to get it because if I get up, you will see the uncut version on Patreon. I don't know. Gross. Whoever doesn't have a shirt on, shot Tupac. If you haven't heard. Where were you in 1996? I was not in Las Vegas. Actually in 96. Ooh, I was still, I was in LA, I was close. You shot Tupac. Anyways, today, the reason we're on Skype is we weren't planning on filming today, but something dropped and we don't really film, we don't really live that close, especially with traffic. With traffic. And so we were just gonna do this instead of just coming over for one trailer reaction. But the new trailer for a Hindi film called Gunnapath. Yep. Which is probably the Agnapath sequel. I agree, probably. But it's with Amitabh Bachchan, Tiger Shroft and Creedie are in it. It's awesome. Pretty good cast. I think it, and it comes out October 20th, and I think it's sci-fi a little bit. This is maybe... Speaking of sci-fi, I just watched, it's way overdue. I had promised Kuber said I would do it. I watched the first episode of season one of Foundation on Apple TV. How was it? About as good of a kickoff episode for a sci-fi series as you could want. The writing, the acting, the visual effects, I'm in instantly. I can't wait to watch the next episode. So I don't know what else other than that. I guess we'll let the trailer tell us what this is about. And let me record the screen here. And ready? I am ready grizzly. Make sure this doesn't do the thing. And... Bring it on. Three. Three. Two. One. Ooh, my back looks the exact same. Ooh, 2017. I was gonna say, yeah, it reminds me of you. A lot happened in the past 25 years. 40. 40, yeah. Must be tough it again. Clearly this is Texas.  Oh! Jektokamoru yutanaja. Of course, martial arts. Nice, look at pretty using nunchucks. How often do they just wrap the box shut up? Nice. That was Ganesh in the sky. It does the name kind of mean Ganesh. It's Ganapath. My wife would know, as with all of you commenting in the comments below. Ganapath. Oh, that was pretty cool. It was. I love the fact that they're doing sci-fi. We've talked about it many times that... We have. It's not a genre, at least in the past that has been kind of explored very much in Indian cinema, right? When it has, it's been done in more quirky ways than just either pure action or even seriously. And we know why that obviously it usually to do sci-fi, at least modern day sci-fi. It usually means VFX heavy. It doesn't have to because there's like old school, like real sci-fi, old school. It actually wasn't very VFX heavy at all. Star Trek, it's part of the lead. Like there's no VFX of that. It's just human stories in space. Right. That's basically what it is. Yeah. And that's one of the things my wife loves about sci-fi. It's just the humans. It was basically like human political stories. Yes. With aliens. Have you guys watched it all or has she watched Foundation? No, no, we haven't. Yeah, but I can't wait. I'm gonna be watching it just every morning right now for each episode. The first episode is as good an episode. Forget sci-fi, just everything about it. The writing, the acting, the visual effects obviously for sci-fi and it has exactly that. And it's this beautiful combination of feeling both very specific to sci-fi in space but also feel Shakespearean and even a little game of Throne. I love it so far. But yeah, it looks pretty cool. The thing I would worry about because it looks like it could have some cool action. Tiger Shroff, you're gonna get great fight scenes. All my stars, yeah. Especially MMA, that's kind of where his specialty is. Yeah. So that's pretty cool. But the thing I would worry about is the VFX being not up to snuff. I saw it many times in the trailer. Yes. And just the past year when we were in a Comic-Con with Prabhas and that sci-fi, that VFX was flawless. And so I think people are now expecting Hollywood level VFX. As they should. Because Indian films are now spending enough money to have that same level. Not that they couldn't obviously do it with the talent. They had the talent. It's just we spent a billion times more on films than they did in the past. Still do, but India is now spending a lot more. And so you saw VFX in this. Like it was like, that looks like it was probably made in 2010 VFX instead of... So that would be my biggest concern. I guess obviously going for big commercial sci-fi which is cool. I love that they're exploring it. Tiger Shroff, Creedie, looks awesome. They seem to be wrapping up Amatuck Bakshan a lot. And I feel like we've seen that a lot recently in his curd films is them wrapping him up. Wasn't he like that or was that Kamal San or was it just thinking of Patan? I thought that we saw it in the Comic-Con thing. I thought... We did, he's in it. He's wrapped up, isn't he? Narrating and wrapped up. I thought he was wrapped up. They always wrap up. Everybody protects from STDs and pregnancy. That's right. Good on you Amatuck Bakshan for wrapping up. But yeah, it looks cool, but that would be my biggest concern. Is that the VFX are just not gonna be up to snuff and it's gonna take everybody out of it. Yeah, me too. And then in addition to that, it may be all bite and no bark. It may be all action and not really strong on story or acting. Although I will say the difference between Tiger Shroff and say the old school Jean-Claude Van Damme is that Tiger Shroff can act.  And it was really cool, Creedie. I think that was her.  So with him, you know, you're gonna get an entertainer and my hope is that it's just the story is gonna be strong enough to keep you engaged and that's gonna be a good time. Yeah. I'm interested. Yeah. It's just the VFX would probably be the biggest concern for me. Which have to be good for, if you're doing sci-fi. I mean, like you said, it's kind of inexcusable now. Yeah. I mean, even with like, what's the last sci-fi, I guess that, I mean, technically that Tamil film would be sci-fi but it wasn't very VFX heavy at all. The Mavidhan, right? Right, yeah. Technically be, would it be sci-fi? Ah, fantasy, I think. It would lean more fantasy than sci-fi, probably. And it did have some VFX issues in that film but it was like 1% VFX. That was really. This looks like there's actually heavy VFX. Cities are built. Well, and again, I didn't see, did you see a release date? If it was there. 28th of October. Oh boy. That's probably the end. They're done. That's probably your end result. Yeah, they're done. That's one of my biggest concerns with big VFX heavy films. We like, audiences can forgive some stuff like in a Patan, there was some stuff that, you know, wasn't up to snuff but not all of those. Or the one shot in theater that we just saw the train shot where it looked like there was an overlay of CGI on the train. Oh, yeah, yeah, yeah, yeah. Small things like that are completely forgivable. But if it's like through the entire film, it's gonna get exhausting looking at bad VFX. It will, it will. So yeah. You don't want that, which is why I say if you don't have the money, don't do it. Simplify your story so you don't have to rely on VFX as much if you do not have the money. Cause that's one thing that it just takes money. It does. But you have the talent. But in order to get it where you need it to be, it takes money. Money and time. Because most sci-fi things, whether it's a TV series or it's a film, you're gonna spend as much time if not more time. A more usual. Months, months at a time on your post-production. So yeah, it's if you're gonna do it and you're gonna visualize it. Yeah. Especially if you have a name as big. I mean, Tiger Shroth. Tiger. Big star. Creedie and Amatob. Yeah. So I mean, there was a lot of stuff that I thought looked really cool. And me too. Hopefully it could come together and do well, but those would be my biggest concerns. You guys let us know what you think about the trailer. Are you excited for it? Do you have concerns? What have you? We need to see obviously more of Tiger. So let us know what other Tiger films we can watch down below and what were your thoughts on the trailer? Let us know down below. Josh!


In this video, we're going to prove what one might call the analog of Lagrange's theorem for field theory. Because remember what Lagrange's theorem tells us is that every subgroup of a finite group divides the order of the group. And then from that, you can infer this statement about indices of a group. Where if the index of a subgroup measures the number of cosets, then you can factor indices, right? So if you have some subgroup K, the number of cosets of K inside of G is equal to the number of cosets of some other group H inside of G times the number of cosets of K inside of G, where here we have K as a subgroup of H, which is a subgroup of G. So when it comes to counting cosets, we get this property, the index factors, okay, between some intermediate subgroup. Now, the same is also true for field extensions when we look at their degree. Some people call it the index of the field extension. We generally call it the degree here. So imagine we have three fields. We have the field F, which sits inside the field E, which sits inside the field K. So K is a field extension of F. It's also a field extension of E. E is this intermediate field that sits in between F and K, excuse me. And so we can then talk about the degrees of these extensions in all the cases. And so what we claim is that the degree of the extension K over F is equal to the degree of the extension K over E times the degree of the extension E over F. So you can factor degrees of field extensions analogous to how you could with coset, the number of cosets for groups. And so that's why we call this the field theory version of Lagrange's theorem. And this will be very important because we're going to see as we study Galois theory that these degrees of field extensions actually have something to do with indices of subgroups when we look at the Galois group. But we get a little ahead of ourselves there. So let's prove this identity here. This is a counting argument here for which let A be a basis of E when we view E as an F vector space. And let B be a basis of K when we view K as an E vector space. Now, it makes sense to view K as both an E vector space and an F vector space. The basis, when we look at it as an F vector space, will be much larger than when we look at it as an E vector space. So be aware that this basis B is viewing K as an E vector space right now. Now, in particular, since E is a subset, it's a subfield of K, the elements of A, which belong to E, can also be viewed as elements of K. And so in particular, we can add to track, multiply, and divide these things. And so consider the set C, which is going to be the set of products between elements from A and B. In particular, C is the set of all possible products where all the possible products alpha times beta where alpha is an arbitrary element of the basis A and beta is an arbitrary element of the basis B. And so we claim that this set C forms a basis for K viewed as an F vector space. Okay, so let's first make sure we know how many elements are in C in the first place. So for the sake of simplicity, well, not not simplicity, just for the sake of clarification, right? Thus, cardinality of the set alpha is the, since it's a basis of E over F, it's going to be the dimension of E as an F vector space. That by definition is the degree E over F. And likewise, the cardinality of B is the dimension of K as an E vector space. And that by definition is the degree of the extension K over E. So is the set C, does it, is its cardinality equal to the cardinality of A times the cardinality of B? That seems likely. And that's what we want to prove here. But what we have to, in order to do that, we have to prove that each of these possible products alpha times beta are distinct, because if any of them overlap with each other, we might not get the full, the full amount of elements there. And so let's consider the possibility that alpha beta equals alpha prime beta prime, where alpha and alpha prime are potentially different elements of A and beta beta prime are potentially different elements of B. Now, when you look at that equation, alpha beta equals alpha prime beta prime, I'm going to move, I'm going to set the right hand side equal to zero, so we're going to get alpha beta minus alpha prime beta prime. This is equal to zero. Now, the significance here is that when you look at that, it's like, I have some linear combination of elements from a field that adds up to be zero. Could I make some argument about linear independence or something? That's exactly what we're going to try to make the argument right here. Because notice the elements of alpha, excuse me, the elements of A, including here alpha and alpha prime, these are elements of E. And when we look at B here, B is a basis of K as an E vector space. So B is this E basis of K. So what we claim here, what does it mean to be an E basis? We mean that every element of K can be written as a linear combination of things from B, but your coefficients can range over elements of E. Well, the things inside of A come from E. So when you look at this equation right here, you can think of the alphas, alpha and alpha prime here. These are our coefficients in a linear combination because they belong to the set E, like so. But beta and beta prime, they came from B. And B is a linear independent set. So the only way that this linear combination can add up to be zero is that the coefficients have to all be zero. So alpha and alpha prime have to all be zero in that situation. So the only way you get agreement that alpha, beta equals alpha prime, beta prime was that the alphas, alpha and alpha prime had to be zero. But wait a second, alpha was, excuse me, A was also a basis for E over F. And alpha prime came from A. If alpha was equal to zero, that would mean zero belongs to the basis, but no basis can contain zero because it's linearly dependent. That gives us a contradiction. So it turns out that there is no possibility that alpha, beta equals alpha prime, beta prime. The only other possibility is that these elements were in fact the same thing. That is, you would have to have that beta equals beta prime. And then in that situation, you can divide beta from both sides. So since you got alpha, beta equals alpha prime beta, you can divide beta from both sides inside of K. You'd get that alpha equals alpha prime. So the only way you can get those things to be the same thing, the same product, is if you have the same factors. So this tells us that we can identify in a natural way C with the set A cross B. There's this bijection between the two sets for which honestly the map makes sense to go the other way around. If you have an ordered pair of alpha, beta, you can identify without the product alpha, beta, like so. This map will be one to one and clearly onto by the definition of set C. So there's a bijection between those. So this gives us that the cardinality of the set C is equal to the cardinality of A times B. For which this is the Cartesian product. As sets, this is equal to the cardinality of A times the cardinality of B. And as we observed earlier, the cardinality of A is the degree of K over E. And the cardinality of B is the degree E over F. Therefore, because of this statement right here, the cardinality of C equals this factor degree. To prove our equation here, we have to prove that C is a basis for K over F. Because if C was a basis, then that's the dimension of the vector space K over F. And that's exactly what this degree is measuring. So we now will proceed to show that C is in fact a basis for K over F. So take an arbitrary element gamma inside of K. Well, by what we've observed earlier, since B is an E basis for K over E. That means every element gamma can be written as a linear combination of the betas. So you have some beta 0, beta 1, beta 2, beta 3, whatever. But the coefficients in that linear combination are going to come from E. But A, the set A is a basis for E over F. So each of those AIs can be written uniquely as a linear combination of some C's times the alphas, like so. So the element AI that you say right here, it can be written as some combination of using alpha ij's and coefficients Cij's, like so. Where now the coefficient Cij comes from the base field F. And the alpha ij's of course belong to, they belong to the set A, like so. Now taking M to be the maximum here of all of these MIs, for which MI here, this is some finite number in this combination, right? Like how many of the alphas do you need? You potentially can use all of them if you have to, right? Setting some of these coefficients to be 0 if they're not already defined is the idea here. We can then come up with a single M and a single N that takes care of everything here. So look at the combination of gamma again. If we look at it as an element in an E vector space, we have this coordinate vector right there. But each of those AIs can be written in the following sum. You have a sum where j ranges from 0 to M of Cij alpha ij, where again we might have to throw a couple of zero coefficients in there so that all of the sums are consistent in this situation. But then this is a combination inside the field K. We could distribute the beta i's throughout this. So we get the double sum where i ranges from 0 to N, j ranges from 0 to M, and you get Cij times alpha ij beta i. For which as the alpha ij's range over the elements of A, the beta i's range over the elements of B, you have all these possible products. These are what the elements of C looks like. So this shows that gamma can be expressed as a linear combination of things from C. That is, gamma belongs to the span of C. And since gamma was an arbitrary element, this indicates that C is a spanning set for K viewed as a F vector space. Alright, so that's a good start. We have a spanning set. Is it a basis? Is it linearly independent? So consider that we have some combination of the alphas and betas that adds up to be zero in this situation here. Alright, so can this combination give you a non-trivial combination of zero? Now since B is a basis for K over E, then it has to be the only way, because you can factor this sum like we did above, the only way that a sum of the betas can add up to be zero, that happens if and only if each and every one of the coefficients is zero. So the coefficients of an individual beta i is the sum of the Cij alpha ij's. So each of those combinations has to equal zero, which remember alpha ij comes from capital A and Cij comes from F. But A itself is a basis for E over F. So the only way that you can take this combination to equal zero is that if each of those coefficients were equal to zero for each of the alpha ij's. And so each of the Cij's has to equal zero, but the Cij's are the coefficients of this original linear combination. This shows in fact that C is a linearly independent set and therefore is then a basis for our field extension K over F. This then proves Lagrange's theorem for fields that finite extensions can be factored in the way that we've seen here. And in fact the proof that we just went through never actually requires that things be finite dimensional. This would also be true for infinite dimensional field extensions. Now cardinalities, these infinite cardinals, multiplication might not mean as much as you might think. And for our lecture series we're really good at both to be concerned with finite extensions. But be aware that our theorem actually is perfectly applicable for infinite extensions well that the commonatorics we made in this argument applies to infinite cardinals as well. And so that the theorem doesn't need to be modified for the infinite case as well. Let's look at an important corollary of this result here. So imagine we have the field extension E over F and suppose this is a finite extension and as we observed earlier if it's a finite extension it must necessarily be an algebraic extension. Take some element beta inside of the extension field E. Then we know by what we've just observed that the degree of the minimal polynomial of beta over F has to divide the degree of E over F and why is that? Well that's because if we have the field F and we have the extension field E then the simple extension F a joint beta would have to be an intermediate field between those two. So applying the previous statement right there we then get the degree of the extension E over F. It has to factor as E over F a joint beta times F a joint beta over F for which this second one right here is equal to the degree of this minimal polynomial of beta over F like so. And so that gives us the divisibility condition we want. In particular if E itself is a simple algebraic extension this tells us that the degree of the minimal polynomial beta must actually divide the degree of the minimal polynomial of alpha here. In fact we even get better that the polynomials in fact divide one another. Okay let's look at an example of these principles in practice here. Let's consider the element alpha which looks like the square root of 3 plus the square root of 5. Now this is an element which we can produce by radicals and so as we saw earlier in this lecture we will be able to construct a minimal polynomial utilizing the fact that we have radicals here. So if you move one of these square roots to the other side I'm going to take the square root of 3. We get x minus the square root of 3 that's equal to the square root of 5. Squaring both sides we see the following. x minus the square root of 3 squared that will give you x squared minus 2x times the square root of 3 plus 3. When you square root the right hand side the square root of 5 squared is 5. So attracting 5 from both sides we can move that over here. You can end up with x squared minus 2x times the square root of 3 plus minus 2 in that situation. So we get that. Now what we can do next is we can move this square root to the right hand side so we get the following equation. x squared minus 2 equals 2x times the square root of 3. If we square both sides again so we square this side we square this side. On the right hand side we're going to have to foil it again. x squared minus 2 squared that will give you x to the fourth minus 4x squared plus 4. On the right hand side when you square things you're going to get x squared clearly. You'll get 2 squared which is 4, square root of 3 squared which is 3, 4 times 3 is 12. You end up with 12x squared for which then when you move that to the other side you'll get the following polynomial. p of x equals x to the fourth minus 16x squared plus 4. This would then be the minimal polynomial of alpha over the rational number. So you get this degree 4 polynomial. This will be our minimal polynomial. You might recognize this polynomial if you've been paying attention in this lecture series. It's like I feel like I've seen this somewhere before. Actually the very first video of this lecture 26 we talked about this exact same polynomial. x to the fourth minus 16x squared plus 4. Now you might recall in that situation it's like, huh, I thought you said the roots in that situation were plus or minus the square root of, oh boy, what was it, 8 plus the 2 times the square root of 15. But now you produce this other number, the square root of 2 plus the square root of 5. No, that wasn't what it was. Sorry, the square root of 3 plus the square root of 5. So do we have a fifth root of this polynomial? It's degree 4, it should only have 4. Let's investigate this thing a little bit further. Now this is an irreducible polynomial. So if you take Q adjoin alpha, look at that field over Q, the degree of the extension will in fact be the degree of this, if it's irreducible minimal polynomial. In which case that gives you that this field is degree 4, okay? And clearly on the other hand though, alpha belongs to the field Q adjoin the square root of 3, square root of 5. Clearly these two elements would add together, give you alpha. So alpha belongs to that. And so we look at this field extension. This field extension would factor, okay? It's going to factor as Q adjoin the square root of 3, square root of 5, over Q adjoin the square root of 3, and then Q adjoin the square root of 3 over Q here. And so let's compute these things. This one, Q adjoin the square root of 3 over Q is clearly going to be degree 2 because this is a simple extension and your irreducible polynomial there would be X squared minus 3, okay? What about this one? Q adjoin the square root of 3, join the square root of 5 over Q adjoin the square root of 3. This is also a simple extension because that field Q adjoin the square root of 3 times the square root of 5. You can think of that as Q adjoin the square root of 3, adjoin the square root of 5, like so. You've added one new element. I mean, I know of its algebraic consequences, of course, but you've added a new element to Q adjoin the square root of 3. So over this base field, this is a simple extension right here. And so the degree of this extension is going to come from the degree of the minimal polynomial, which the minimal polynomial here will be X squared minus 5. You can take the exact same rational polynomial, which is still a polynomial over Q adjoin the square root of 3. That would still be irreducible. And its root is going to be the square root of 5, negative square root of 5 as well. So this is also a degree 2 extension. So you get degree 2 times degree 2, which is equal to 4. So look at that. Because alpha belongs to Q adjoin the square root of 3 times the square root of 5, it has to be the case that Q adjoin the square root of alpha is actually a subfield of Q adjoin the square root of 2, excuse me, square root of 3, square root of 5, like so. But this is a degree 4 extension over Q. This is a degree 4 extension over Q. And so because these degrees divide each other, or even better than that, if you have a four-dimensional subspace of a four-dimensional vector space, they actually have to be one and the same thing. So these vector spaces are equal to each other, which means these fields are actually one and the same thing. Interesting enough, this field Q adjoin the square root of 3, square root of 5 is actually the same thing here as just adjoining a simple element. This happens a lot. It turns out that adjoining two elements, two algebraic elements, you can often replace it with a single element that takes care of it. So a double extension can actually be turned into a simple extension. We'll explore more of this in the future. Now, before we go to the next example, I'm sure many of us are curious about what's happening here, right? How do you have this, right? Is this a new root of this polynomial? The answer is no, it's not. I do want you to consider what happens when we square this element here. If you take the square root of 3 plus the square root of 5 and you square it, well, you square the square root of 3, you're going to get 3, then you're going to get 2 times the square root of 3 times the square root of 5, like so, and then you'll get the square root of 5 squared, which gives you 5, which this gives you 8 plus 2 times, well, the square root of 3 times the square root of 5, that's the same thing as the square root of 15. So I want you to be aware that the square root of 3 plus the square root of 5, when you square it, it gives you 8 plus 2 root 15. 15. So the square root of three plus the square root of five is a square root of eight plus two root 15, for which there's two of these of course, you have the positive one and the negative one. So I want you to be aware that we've just argued that the square root of three plus the square of five is actually equal to the square root of eight plus two root 15. So we are calling these two different elements alpha, they actually are the one and the same element. This is what can get a little bit tricky about radical elements is that different radicals can actually be equal to each other. They look different, but they're actually one of the same alpha, one of the same. Yeah, in this case, they're both this element alpha, these two different radicals gave you the same thing. One way that you could try to determine whether these things are equal to each other, well, you could try some type of numerical analysis. But of course, that only gives you that they're probably equal. We can actually look at their minimal polynomials, that if these two different radical elements have the same minimal polynomial, so at the very least they have the same minimal polynomial, you can make an argument from there that they're actually one of the same thing. Because notice that both of these elements, the square root of three plus the square root of five and the square root of eight plus two root square root of 15, they are both square roots of eight plus two root 15, which is forcing them to be the same thing, because there's the positive and negative case. All right, let's look at another example here. Let's look at this one. Take the field where we're going to adjoin the cube root of five and the square root of negative five. Consider this field extension. Well, look at the field F, which will define to be the field Q adjoin the cube root of five. Notice that this F is a subfield of the real numbers, because the cube root of five is by definition a real number. And so taking rational numbers and throwing in a real number, you can only produce real numbers in that situation. Since F is a subfield of the real numbers, clearly the square root of negative five is an imaginary number, purely imaginary number. It doesn't belong to F. And so since the square root of negative five doesn't belong to, excuse me, the square root of negative five doesn't belong to the real numbers because it's purely imaginary. And since F is a real subfield, that means the square root of four i, excuse me, square root of five i doesn't belong to F. This is a trick that we're going to use a lot, that if you have a real subfield, you can use that to eliminate imaginary numbers or complex numbers that have non-trivial imaginary components. All right, so that's an important thing to see here. The square root of negative five does not belong to F. On the other hand, the minimum polynomial of the square root of negative five is going to be x squared plus five. This is a polynomial over the rational field, but it's also a polynomial, a irreducible polynomial in F a joint x. Because if this polynomial was reducible, we'd have to have a root, which means the square root of negative five would be an element of F, which is not. So we get that the degree of E over F is degree two. So that's a nice calculation there. And again, that's because the minimum polynomial is x squared plus five. But then if we look at the cube root of five, its minimal polynomial as a rational polynomial is x cubed minus five. So this tells us that the degree of the extension F over Q is equal to three. Now, because of the factorization, we have E over F, we have F over Q, we then can compute the degree of E over Q, which by factorization, it'll be the degree of E over F and F over Q. So you get two times three, which is six. And so this factorization principle can be very helpful in computing degrees of extensions, field extensions. And if we know the degree of a field extension, we can often utilize that to show that certain fields are equal to each other, certain algebraic elements are one and the same thing. So this is a very, very important property. Let me end this lecture with a theorem that I'm actually going to leave as an exercise to the viewer here. Given a field extension E over F, then the following are equivalent. E is a finite extension of F, that's condition one. There exist algebraic elements alpha one, alpha two, up to alpha N that belong to E such that E is equal to the extension F, a joint alpha one, alpha two, alpha three, up to alpha N. So you do have this finite number of elements you can join to F to create this extension E. And that condition two is equivalent to the last condition here. There exist elements alpha one, alpha two, alpha N, that belong to the field E for some number N, of course, such that E equals the field extension F of joint alpha one all the way through alpha N. And that then contains the proper subfield F of joint alpha one all the way to alpha N minus one, which that contains the proper subfield F of joint alpha one all the way up to alpha N minus two, all the way down to F of joint alpha one, all the way down to F here. And in each of these situations, these are proper containments that adjoining the next element makes the field get bigger. And each of these elements were algebraic along the way. That is, this field is algebraic over that field. This field is algebraic over that field. And then all the way down to this is algebraic over that. And so like I said, I leave this as an exercise to the viewer here. It's a consequence of the properties we've already proven already. That's where we're going to end lecture 26 for now. Thanks for watching. If you learned anything about algebraic or finite extensions, please like these videos, subscribe to the channel to see more videos like this in the future. And if you have any questions, please post them in the comments below. And I'll be glad to answer them as soon as I can.


OK, so let's continue talking about lattice models and see what we can learn from them. And it turns out that lattice models are not only useful for modeling gases, but we can also use them to model liquids as well, or fluids. So let's consider what it might look like if we use a lattice model to describe a liquid. So a liquid, as you know, is something that occupies the entire volume, rather than expanding to fill its volume like a gas, it occupies the lower portion of the gas, and molecules are not separated from one another. So let's say we have a lattice model for a fluid. If I'm going to take eight molecules, then they're going to occupy, in this small example, they're going to occupy all the eight lattice sites in this model. And I don't want to include vacant sites down at the bottom. So the fluid's going to fill the container from the bottom up. So if I want to talk about fluids mixing, which is what I do want to talk about, then I need to be able to describe, let's say, I put that beaker of a fluid next to a different beaker with the same size. But in this beaker, I'll put a different fluid. I'll put molecules of a different type in this beaker. And let's say I've got an equal size beaker with eight of these molecules that I'm calling b, molecules of b, rather than molecules of a. So these green molecules. So now what I want to do to understand what happens when the fluid's mixed or don't mix is, let's say, pour those molecules into the same container. So now I have a total of volume of 16. And really what I've got is, if I want to describe, so here's the microstate of the system. I've told you where every individual molecule is in that combined volume. The macrostate of the system, the way I've described it, is I've still got eight molecules on the left side of type A. And on the right side, I've got eight molecules of type B. So the macrostate would be eight of these on the left and none of them on the right. So that's enough for you to put the molecules down the same way I have here. The multiplicity, how many ways are there that I could have drawn microstates consistent with this macrostate? There's only a way to put eight molecules of the red molecules on the left, orange molecules on the left, and eight green ones on the right. But mathematically, that's like saying, how many ways are there to choose which eight of the spots to occupy with eight molecules on the left? And so I'm multiplying how many ways are there to choose which zero of the states on the right to occupy with the orange molecules. So eight choose eight is one. Eight choose zero is one. That product just comes out to one. There's only one way of drawing a microstate, this one, that is consistent with that description. So what we want to understand is what this lattice muzzle has to say about whether fluids mix or don't. So I can draw other configurations that show the fluids mixing partially or fully. And the multiplicity, the probabilities will tell us how likely those particular outcomes are. So let's consider a state. So I've still got this combined volume of 16 grid positions. And let's say I want to let the molecules partially mix. I want to find out how likely it is that most of the molecules have stayed separated, but one molecule has moved over to the other side of the box. So my macrostate would be seven of these on the left and one of them on the right. So that's, again, my macrostate. I can draw an individual microstate just so it's clear what I'm talking about. I still have eight of each type of particles, so I'm gonna fill every grid position in the box. And I can ask, how likely is it that this, or what's the multiplicity? How many different microstates could I have drawn that are consistent with this macrostate? How many ways do I have of choosing which seven spots on the left to occupy with orange molecules and which one spot on the right to occupy with green molecules? You might ask why I don't also include a binomial coefficient here for describing how the green molecules behave, but once I've told you which seven spots are occupied by orange molecules on the left, there's no more choices to be made. All the green molecules are specified. Same thing on the right. If I've told you which one spot is occupied, all the other ones have to be occupied by green molecules. So eight to seven is eight. Eight to one is also eight, so the product there is 64. So it turns out that the multiplicity for this partially mixed system where one molecule is crossed over to the other side is 64 times more likely. There's 64 ways to draw this. There's only one way to draw this. So it's 64 times more likely that the fluids mix at least a little bit. But of course that's not the most probable thing that will happen. I can ask questions about any degree of mixing I want, but it turns out not surprisingly at this point perhaps. If I ask the question, how many microstates are there that can be described by four orange molecules on the left and four of them on the right? So if that's my microstate, I want to put four molecules down on the left somehow and then four of them on the right somehow, the rest of them green molecules, four on the left and four on the right for the green molecules, then the multiplicity will be how do I choose which four of eight spots to occupy with orange molecules on the left and how do I choose which four of eight spots to occupy with orange molecules on the right? Eight choose four is 70. So 70 times 70, 4,900 is the numerical answer we get here. So even for this small system of only eight molecules in each beaker that I've mixed together, turns out that the mixed system, where they're fully mixed half and half, that is almost 5,000 times more likely than having the system remain completely unmixed. So that tells us two things. Tells us an answer to the question, why it is that fluids mixed together? When I mix two fluids together, why do they not stay separated? Why do they mix together? The real answer to that question is because it's much more probable that they'll find a mixed configuration than they'll find this rare configuration where the fluids are separated. The other thing it tells us is, excuse me, that again, it's not just, it is only overwhelmingly likely that the fluids will mix together. It's not guaranteed that the fluids will mix together. That it is possible to find a configuration that represents a separated configuration. But again, the larger the system gets, the larger these values of n that I'm taking factorials of, the larger this number will get and the more overwhelmingly likely it will be that the fluids mix. And it's also worth pointing out that, again, because we haven't built any chemistry into this model, we haven't said whether these are molecules or water molecules or methanol molecules or oil molecules or so on. For this simple case, we get the same answer for every pair of fluids. We don't have the ability yet to distinguish why water and methanol mix together fairly well, but water and oil don't mix together. So once we start building chemistry into the problem, then we'll begin to see some nuances in these answers.


Welcome to the ITU Telecom World 2018 here in Durban, South Africa. I'm very pleased to be joining the studio today, Mr. Cesar Alieta Ithuel, who is the chairman of the Fundación Telefónica. Mr. Alieta Ithuel, welcome to the studio. Thank you. Now, I'd like to start off by asking you about digital education. Why do you think digital education is important to meaningful connectivity? Well, because connectivity is used in instrument, all right? And it's a part of the digital world, which started with connectivity, but now covers many, many other fields, okay? Fortunately enough, we have nothing to do with connectivity, but digital education gives people know how in digital skills to use connectivity and many other things. So the basic thing is to develop knowledge about digital skills in all the young people in the world, okay? And in terms of digital education initiatives to bridge the gap in vulnerable and underserved communities, how do you think that they can help? That would be easy. I mean, digital education has to change completely. The education we have around the world now is the education of the 80s. In the 80s, the world was not digital, and now we are in 2018, so we need all the boys and girls from primary and secondary education to have digital skills, because 65% of them are going to work in professions that do not exist now and only have in common one thing, which is digital skills. How important do you think multi-stakeholder partnerships are in accelerating inclusive digital education? Well, it's important, but they have to be partners and contribute to improve the digital education, all right? Traditional education is no longer valid, so we have to use partners that know the importance of digital education and have the means to work on that, all right? And they require a few, and so if we work together with them, it will go faster. And finally, how important are events such as ITU Telecom World to Telefonica? To Telefonica, but these are very important, because at the end, in these events, we talk about everything, and you see the points of view of other people, which are interesting, and you tell our point of view, and we have a framework to collaborate in a better world. Now, we've got a very wide and diverse audience watching these videos, and I wanted to ask you, do you have a message that you might like to convey to them from the Fundación Telefonica? Oh, yeah. We prepare the world for digital, with digital education and digital development, we are going to have a much better world. And for the first time in mankind history, this is possible to do it in one generation. Well, thank you very much indeed for being with us. Thanks a lot. Thank you. Thank you.