This is about an Afghan farmer and his family who is living on the edge of starvation like many people in Afghanistan his only income that he earns does come from crops and He borrows two thousand dollars from a local trafficker so that he can plant his next Harvest for the crops and of course he chooses Poppy because Poppy is very resistant both to disease and drought and Poppy is by far the most profit profitable crop That you can grow in this part of the world and where there's a huge demand And he does that Chooses Poppy that not only he can Support his family but also pay back the debt and the interest that's being charged on and so shortly before the harvest a government eradication team comes with an I guess equally good intention you can say and eradicates his Entire crop in one go leaving the farmer not only was nothing but also was a burden of Debt that he owes to the local strongman and so what does he do he flees? His family and he flees the region where he is but he's found and caught and by the way This is a true story that was reported in the news He's caught is put in front of a local tribal Council that rules that the farmer must compensate the local strongman and given that he has no money It is being ruled that he has to compensate the local strongman with his own daughter a nine-year-old girl That gets married off to the trafficker and I'm sure all of you have heard about the term poppy brides This is only one story But I think it shows what the impact of current policies on the development agenda is and I'd like to quote from a UN odc and World Bank report that writes about the strategy of Vacation I quote is felt most by the weakest and the poorest actors involved in the opium economy Poor world households who lack political support are unable to pay prides and cannot otherwise protect themselves before 1979 Afghanistan produced small amounts of opium for local consumption traditional opium smoking Which is less harmful than injecting heroin by great margin and maybe some small regional trade But very small then after the war started Cultivation was increased and was used as a means for financing the war against the Soviet Union And then later it also was used for financing civil war. So I Think it clearly made things worse, but how it started was in this kind of situation where without governance without a functioning state that can control the countryside and also conflict and Displacement and that's what's led to Afghanistan's. That's the background what you do about it now. It's a much more complicated Situation, but I think we should be clear and I think other countries often are that and in the ungoverned spaces where There's no alternatives in terms of livelihoods or and where the government is weak and there are strong men let's say who benefit from the Cultivation that's how it develops. I Think it's estimated that there's something in the region of four million men women and children who are engaged in the cultivation of illicit narcotic crops And what we do know is that drug crop cultivation is actually a sign of poverty rather than a sign of wealth And it's traditionally in communities whether it's Afghanistan, Bolivia, Colombia, Burma Which is obviously Myanmar which is a very important region for us currently with the transition It's where we have this absence of citizenship where we have an absence of security that narcotic crop Cultivation becomes a a key driver of stability and livelihoods So when you go into these communities and you destroy this crop cultivation without Effective citizenship models or states citizenship models being created This has devastating effects on livelihoods and it has devastating effects on development and security first How? It is not easy in the minds of the of the of the people who who are Designing the project the question is very easy We substitute the coca for example in Bolivia with coffee because in the global market the coffee is With the high prices, but who controls the high prices in the of the coffee is the New York birth You know then is that the question? No Till today, we didn't give the possibility for the Pesant organizations or the farmers To show us the way of develop they want we show them the way they love of develop we want That's the problem some of the financing of the Taliban comes from opium production, but I they are not dependent on it The estimates are very rough, but maybe 50 to a hundred million dollars a year So you compare to the international community spending of maybe a hundred billion dollars a year in Afghanistan It's it's pretty tiny and it's the the Taliban also have other sources and I very much object to this kind of Linking the Taliban to the drug industry and sort of using a way to demonize both and the idea somehow that if you Take harsh actions against drugs. You will get rid of the Taliban. No, absolutely not Certainly the dependence of the Afghan government on funds from opium is higher through Corruption patronage bribery and so I think I think you need a balanced approach the the money is Influencing whoever is in power in Afghanistan in some places. It's the government in some places It's the Taliban in some places. It's other strong local strongmen and so So I think it's actually better to to keep a clear mind to separate the Taliban issues from the drug industry And the Taliban actually would love if the international community engaged in heavy eradication or something because the farmers would be very Upset and they would join the Taliban in Colombia, you know six million of hectares were sprayed with the glyphosato and the the Colombian plan will spend till this year one and a half million billion dollars in spraying and We are now Insisting in scientific research about the consequences of the glyphosato spraying We know Empirically the problems are causing the The spraying in Colombia in the Amazonian forest With the people with the persons animals fauna It is a matter of a long study and I hope Sincerely that the international community will punish Monsanto because they are they are really criminals in this question They are profiting with the with the superion of million of people But I think what that also speaks to is the vested interests of the kind of military defense Conglomerations isn't it which is signed so embedded in US foreign policy in US power And I think the key thing really which also goes back to what William said before is that even if we Remove the narcotics, it's not going to remove the key sources of funding for insurgents and rebel groups And now does it address the drivers of that insurgency or conflict in the first place? So even if we take out the cocaine even if we take out opium What we've seen traditionally with insurgent groups is that they will find other means of funding their insurgency So whether this is through kidnapping whether it's through money laundering whether it's through engagement in in other forms of illicit economies It simply has no net effect on our ability to reduce conflict and build more peaceful societies Because we're not addressing that fundamental cause of grievance So the big danger that we have is that we have this elision of the war on drugs and the war on terror Which is really what we've seen in places like Columbia and we've seen in Afghanistan And this is a this is from to my mind really catastrophic merger of security and defense and development policies Which is simply not addressing how we actually deal with these conflicts in the first place simply to eradicate the narcotics Deals with nothing in terms of these insurgencies or how they're funded or as I said how we build these peaceful societies Because the Afghans are very you know, they have a lot of communications both informal They have more cell phones now than a long time in history radio television and they know what's going on and they see that Eradication is going after farmers, but there have been some major cases of direct Allegations and evidence let's say of higher level peoples associated with the government linked with drugs And they are not touched and there is actually a famous case where one of the Afghan Airlines was was blacklisted by the US military for Suspected involvement in transporting drugs and the president of Afghanistan himself got so upset about that that he prevailed on the US to withdraw that allegation and so so what it means, I think is the farmers are the ones who don't have all the political protection and they are They are vulnerable and if so if you crack down on law enforcement you get the small farmers and other small actors and of course you still don't touch the Larger actors who in a country like Afghanistan are politically very Important, I think the kind of whole neoliberal economic reform agenda of the 1990s Also created a wonderful mechanism for the laundering of money because the sale of state assets the privatization Particularly in places like perhaps Mexico and in the Balkans has actually created these wonderful opportunities for laundering cash So there is does seem to be a correlation between the laundering of money and neoliberal economic policy agendas and when that's in a post-conflict context Then it creates a very unhealthy and unfavorable mix the second largest producer of opiates in the world after Afghanistan is a country named Australia and Australia produces large amounts of opiates which are entirely legal Licensed regulated and they go to the pharmaceutical companies now those opiates go into the US And are consumed and many case the abuse of legal opiates is a big problem. So so I'm saying the mix of the legal and illegal For for the poor countries, do you think licensing would be a solution for Afghanistan? No, I think because what Afghanistan now produces 90% of the illicit opiates, let's say about half of total opiates From only 10% of Afghanistan's land. So what would happen if you license that amount of production? They would produce they would be happy to do that and then they would also produce a lot of illegal It's very hard to control the leakages when you have two different markets But my point of view is from a point of view of some of the corporations and things you're mentioning something is entirely legal and leads to Legal opiates being heavily abused in countries like the US lots of people use abuse painkillers and addicted to them and It's completely legal and and the farmers in Australia are treat. They're not criminalized. They're treated well It goes all through the value chain, but the end result is a problem And yet the Afghans then who produce it and also have end abuses at the end Become criminalized and I think it's a an interesting dichotomy and suggest some of the contradictions that are going here, but The short answer to your question is I think If there's a global reform then there would be opportunities for licensing I'm more doubtful if if the global regime doesn't change Then and for one thing Australia would not accept Afghanistan to be a licensed producer just like agriculture Subsidies in the EU and the US why would they let a somebody else come into that market? And there are these examples of success and it's basically long-term rural development It's not like we are saying one magic crop or one substitution It's a comprehensive rural development approach and it will take 10 to 20 years And it will solve the problem like it didn't largely in Thailand and some other countries But it won't affect the global so countries that have a strong enough governance and you know take on the issue There is a way forward on the production side, but it will deal with it at the country level not at the global level because then it just goes to the The other country that has the right conditions, which is insecurity and poor governance and deep poverty and they will produce Opium in the case of Afghanistan so so again I think you're you're pushed into thinking about can you make broader changes or else it will just be Rotating among different countries let one quick point on the on the transit and transfer side This is big a very big problem. You know when you have anti drug measures They change the transit routes each time they change the transit routes. You leave addicts there Because because addiction grows along the transit routes And so if you keep imposing law enforcement, maybe you move the transit somewhere else And then you would create more addict elsewhere, and it just goes on forever and creates Long-standing problems of drug use the other aspects of this which is really important and just developing what William said about Thailand You know 15 20 years. It was the Monarch It was King boomie ball who was head of this program and that was continuity and consistency The challenge that we have today is that the UNODC and also the development community itself with its Millennium Development Goals Works to very tight timetables and schedules which are very narrow in focus and very short termist So you can have countries such as Laos PDR which was actually making some progress in terms of long-term strategy for the reduction of drug crop cultivation But then suddenly Laos felt that it really had to kind of come on board with the UNODC and in regional organizations Such as the ACN and therefore it kind of went through this very horrid process cultivation reductions forced eradication So neither the development community or the current drug policy community actually looks towards a long term Everything is in a very narrow compressed time frame, which really is completely irrelevant And not very helpful in terms of trying to address the issue of drug crop cultivation. Thank you I'm Peter Shariff from the Hungarian Civil Liberties Union And I have two questions and one is about the banking system just a few weeks after the Financial crisis started in 2008 Mr. Antonio Maria Costa the head of the UN agency on drugs and crime said that Several banks were saved virtually saved by the liquid cash coming from the black market Do you think is it is it true or is it an exaggeration? My second question is about Afghanistan and Russia I Attended the Commission on narcotic drugs in Vienna last year and it seemed that Russia has great ambitions in Afghanistan Like Victor Ivanov the head of the anti-narcotic agency made a speech and he said that After NATO is moving out from Afghanistan. They try to take over the role of US and NATO operations and They have they have this rainbow plans to eradicate Corrupts in Afghanistan. So what do you think bill? How how how serious is the threat that that Russia will play a greater role in Afghanistan? I hope that the Russians would have learned the lessons from their occupation and so I so and I also Question whether they have the strength of political will to do too much damage in Afghanistan So that would be my first answer that I I don't think I think they're trying to bluster and They're also trying to put more pressure on others to do their dirty work But I I would be doubtful if if the Russian influence in any way replaces The size of the NATO and the US involvement. I would say that 120 years ago The United States used narco diplomacy And counter-narcotics as a tool of foreign policy and I would say that Russia is probably doing exactly the same thing today I don't believe that drug policy has anything to do with drugs at all I think drug policy is all to do with foreign policy and defense policy and security policy So I'm not really surprised given Russian ambitions that Russia is actually using the war on drugs as a new vehicle for its For its international diplomatic and perceived security efforts on banking again I'm I'm not the most knowledgeable, but you know 10 years ago when I was in the United States There were scandals then about the US banking system being used to launder money from Mexico This isn't a new story and the failures of the first world banking sector particularly after the liberalization of the financial sector To be used as a tool for money laundering is is an old story So I would say that the UN odc is slightly delayed in that That interpretation, but of course the Western banks are fully culpable if not more so It's it's very convincing for us to focus on problems of cultivation when I would argue that the real problem actually lies in the The Western financial systems It takes a focus off there if we just focus on the problems of the Afghan cultivating farmers. I was just wondering I Was intrigued by this discussion and also by the Short movie. I was just a bit puzzled because I don't deny or I don't question the ultimate finding that Irradication was not very productive But the argumentation was not very let's say scientific because obviously everything depends on the counterfactual What would have happened without for instance eradication strategies wouldn't have the market even more exploded so to speak So as I said, it's not it's not necessarily questioning the finding that eradication didn't work but my question would be actually what would be kind of For policy people be a desirable kind of involvement of Academic research. Well, I think if we did not eradicate We would have more cultivation and that would bring down the cost of the end product itself So actually eradication has the counter-intuitive and counterfactual Impacts of actually increasing the prices and therefore further incentivizing people to come into the narcotic drug market So we all I think we already know what the counterfactuals are and we've had the counterfactuals since the end of the Second World War when really The kind of war on drugs was escalated in terms of evidence based on where does academia come in? I think that we already have substantial evidence in terms of the impacts of Countenarkotics activities. I think the challenge is that we don't articulate that evidence in a way that either the development community Or the international diplomatic community can engage with it in a way that can actually affect policy change If there is anywhere where I think it would be very useful to have for the research I think it would be in terms of longitudinal studies Which again goes back to my point that the problem is countenarkotics policies very short-termist I think we need studies which look at you know 15-20 years impact of what a countenarkotic strategy actually does we William and I were at a conference recently in Sausage Where we had a colleague over from the United States who was talking about a Mexican community that he'd been working with He showed us photographs of the children in this community 10 15 years ago And he said I can tell you now these children are narco traffickers For example when you look at the shifts that we've seen in public policy around for example in the UK where I'm from We've just legalized gay marriage. What was it that allowed that big shift in public policy? How do you shift public policy debates which are informed by morality? Which is what the drugs debate is all about and so I think we just need to understand with what are the drivers of public policy change Rather than worrying about bringing any any more empirical evidence to the table There they didn't go in for fumigation But they did do manual eradication and also the most effective things they did was actually just banning poppy And I mean the Taliban at one point banned it all through the country and then after the international Intervention it's been banned in certain provinces at certain times quite effectively in the short run but so you have these policies imposed and over the long run you have no real decline it seems that the the poppy cultivation and especially the production is determined largely by price by by yields by weather factors and things like that so so last year Production went down and it was because there was a cold snap in the in the key time of the season So I think if you looked at Afghanistan the evidence is pretty clear that compared to eradication and and bans did not have Significant impact compared to these other factors the weather the price Start with a major Has anybody done some simulations and studies What the implications would be on the supply side on the economies of the supply side shifting away from from the drug production into other areas Any studies that demonstrate Comprehensive I mean there's a series of you know random very very specific studies But I don't think there has been this kind of comprehensive pulling together of all of the information to track whether we have the same kind of Generic impacts as far as I know that hasn't been done But I'm happy to stand corrected if anybody knows of any universalized studies And as I think Some of the policy reform advocates quite explicitly recognized this just like nothing else will solve all problems The whole licensing and regulation approach also won't solve all problems And if you look at the abuse of legal opiates now, you can see some of the problems that come up But you know I think on particular countries it would be possible It'd be an interesting area to work the feeling on Afghanistan would be that if it's a completely legalized and regulated regime Afghanistan might not produce any opium which would have some Economic costs, but I would argue probably more than offset by the benefits of not having such a major Criminal activity. I know criminals would get into other activities, but I don't think they could be quite so lucrative Please stay tuned on the websites of the open society foundations global drug policy program And also at the CEU School of Public Policy for the next event, which I believe will happen in April and then we will talk about the role of the international drug control system That's that's actually the detail We all should focus when talking about this issue. So thank you very much for your attention and Please have a glass of wine or juice


What's the word y'all be back with some more reacting to Bleach reports lists Eventually I like I said we will get back to doing highlights, but I want to go through this entire series We've done point guards and shooting guards You have not seen those go back a video to but now we're here small forts based on this season is the way this works So we're forgetting resumes and everything just based on the the sample size that we have for the 2019 2020 Seasons this is who the Andy Bailey and Dan for veil believes are the top 15 small forwards throughout the first couple episodes I've agreed with some stuff. I've disagree with a lot of stuff But it's all in the sake of entertainment, right? That's what sports is about now Some of y'all were wild on yesterday's video because Chris Middleton wasn't listed as a top 25 or top 15 shooting guard Which obviously means that Chris Middleton is not a shooting guard So he should be on this list. You know I'm saying if somebody is blatantly Like he was an all-star this year. How can he not be at this position? Then that means he's got to be at another position All right, so he should be here in small forts And I'm curious what they do up top here with Kawai and LeBron, and I'm guessing that Yannis is technically a power forward Okay, anyway, let's get to the top 15 right here Starting off with TJ Warren Duncan Robinson at 14 Ojiata Nobby Kelly Ubre and Joe Ingalls interested stuff here. Okay There's one player that I wish was was in this and that's wheel Barton I think real Barton is great and very underrated But I expected him to be in this range, but he's not so that's kind of trash. TJ Warren I think TJ Warren is also underrated 2015 seems kind of low. It has to be something about his defense He leaves plenty to desire on the defensive side. Yes, it's about his defense not being good But he's one of those few players in the history that went from being unable to hit a three to being pretty nice at the Three-point shot TJ Warren, that's what offseason work does baby He hits a lot of them nowadays Duncan Robinson basically I'm gonna say Duncan Robinson came to the league here because I know he's officially a part of a couple rosters before this But this is the first real taste of Pat Paul's Duncan Robinson. We've ever had in his career So I'm gonna I know he's not Taglia rookie But this is the first year that the world has known the name Duncan Robinson and yesterday I was live streaming And we were talking about players That a high percentage of their shots are assisted on it kind of stemmed from see a Martian gore Tiger spoon fair from John Wall and we determined that like 95% of Duncan Robinson's point this season have been assisted on So he's just coming off screens catching the shooting coming off screen catching the shooting His job is not to create his own shot And he is elite at that catching the shoot and it says Steph Curry and Steve Novak are the only players in league history Who have matched or exceeded Duncan Robinson's 2019-2020 marks for value? 10.2 attempts per 75 possessions and efficiency at 44.8. That is ridiculous for the amount of shots that he's hit So shout out to Duncan Robinson Even if he doesn't dish out a ton of dimes or locked down the opposition's best player The impact is driven from shooting and I believe that Duncan Robbins is not a bad defender either You know I'm saying like some players may not be good, but they give the effort and he he's a high IQ defender as well So I don't think he's a bad defender either He's just ain't very good. Then we have Oh Gianna Nobby, which is great to see because once Kawai Leonard left the team You knew that you needed somebody to take those defensive assignments and we knew it was gonna have to be oh, gee We just waiting to see if you can actually do that thing and he has been Oh Gianna Nobby the secret weapon of the Toronto Raps because he wasn't really playing once they went on that championship run He was injured Toronto ranks in the 84th percentile when he's on the floor defensively all you need to know his defense is elite He knocks down the shots 38% from 3 on 3.4 attempts amazing Kelly Ubrecht I'm ironically I know we make a lot of memes here on my channels about Kelly Ubrecht But I legitimately enjoy watching Kelly Ubrecht play because in my mind when I see him play the only thing that matters to him is to win You know I'm saying he tries to lock in when he when he needs to He wears his heart in the sleeve and I love players like that I think that he is still getting better and better and better every single season So to see him 12th is pretty good for a 24-year-old rising player Who's not looked at to be like the number one number or even number two option this? He's the prototypical 3 and D guy for for the future of the Phoenix Suns So we have Joe Ingalls at 11 We talked to talk about him a lot over here, but it's picking roll really go beard I don't know if that was last season of this year. I'd be getting them mixed up was elite level A good defender even in his 31 32-year-old age and he does everything well So now we have Bogdanovich. Okay, so people always ask Like for for example when we got to point guards We saw Fred Van Vleet and Cal Lauri as point guards and now we're seeing by Donovitch and Joe Ingalls as small forts How is that even possible? But it is I mean let's be honest though by Donovitch has played a lot of minutes at power for it this season He is notoriously known playing small forward and it's good to see him on his list He has hit a couple big shots for them I remember one specifically in the corner against the Bucks He had another one at the top of the key or like the wing area, but I can't remember who he's going against Again a good defender. I remember a few years I know this list is not about a few years ago But it just comes to my mind that you remember that paces series with LeBron He did a pretty good job regarding LeBron. Nobody's got nobody stopped in LeBron But he did a very good job just doing what he can to slow down LeBron in that series By Donovitch is one of the six non-bigs averaging more than 20 points per game with a true shooting above 60% I didn't know he was that efficient But there he is with Yanis Devon Booker James Harden Dame and Chris Middleton That is a great class of players to be in with shout out to by Donovitch. Oh, there's will board it Let's go like I for I really believe that will Barton is one of the most underrated players But now he's at number nine So maybe he's not underrated maybe he's underrated to like the general NBA fair But I love watching will Barton who bro? I love I want to see what he says well They say because it's two people kitchen sig metrics love love Loving will Barton season he grades out of a French top 50 player. We're looking at his average rank across six catch All I don't even know what that means that clearly over estimates his impact, but it also isn't flat out egregious Yes, yeah, I did go to college for a little bit. So I know that where I know you're looking at it like Kenny I'm 12 and I know what that word is line-up composition accounts for more of Barton's advanced stats yadda yadda yadda his thousand check and Opponent have shot just 14 of 37 against him a nice elation That's what I'm talking about. I just love that will Barton. He's like When I see will Barton go to the paint. He's just the king of the acrobat He refused to get a shot block that he going up and under over he doing everything to get the shot up And he's man. He's making them. Um, I Really like will Barnes game. I really really like will Barnes game Barton contribute. I don't I gotta read this because this is an italics Barton contributes at a considerable above average level across a wide variety of categories of both offense and defenses and He's doing yadda yadda on the floor Just know that he's a bucket and when he's on the floor the Denver Nuggets are a lot better But him at nine is so surprising to me But it makes me happy it might be just a tab it's too too hot if we be honest But it still makes me happy that he is on this list number eight Demond the Rose and now the Marder Rose is one of the rare cases We're like we know that he is a good basketball player But the advanced metrics hate Demond the Rosen like the team just seems so much better when he's off the floor But we know he can get his buckets like look at his percentages over the last couple seasons He's been kind of underrated in that in that field So I understand him being at the list eight. I think eight makes sense. I think eight around there makes sense next player is Gordon Hayward Okay, I did not expect to see Gordon Hayward this high on the list. I Could agree that he should be top 15 But seven seems a bit high doesn't it and I know he's having like the most official season of his career But it's also because he's not taking as many shots as he was in Utah. He plays his role very well He's a good defender and everything But seven does steal feel pretty high, right? I can't be the only one it feels that way I Yeah, that seems this seems pretty high. He shouldn't remarkable 55% inside the arc including 53% on pull-up two-pointers. He raised a 95 percent howl of spot-up possessions like we know like again We know he's good, but it feels like this is this is a bit high for me But it is Brandon Ingram at six seems kind of low. Oh That's interesting Brandon Ingram at six seems kind of low. Who's number five Jason Tatum. Oh, that's the conversation I do I would probably have Jason Tatum higher too I would probably have Jason Tatum higher, but that's not taken away from Brandon Ingram amazing season this year Blossom into an all-star caliber player He him and Zion on the court together have looked nice even though he's kind of taking a back seat and It seems like he's cool with that You know, I'm not he's like I'm an all-star this season But I'm okay with letting Zion get this many shots because that ultimately could mean that we can be better And I could finally hit the playoffs. So Brandon Ingram BNS six seems kind of low, but then you got Jason Tatum at five and I'm like, okay six This makes make sense But Jason Tatum man I think you can't go wrong if you like Brandon Ingram more than Jason Tatum That's cool too, but personally I would take Jason Tatum over Brandon Ingram. So that's why I'm cool with this Especially we take a look at like from January to the end until when the season got Terminated or postponed or whatever Jason Tatum was looking ridiculous, bro. He's looking ridiculous. So yeah Jason Tatum at five at four There's Chris Middleton cast money Cast money 50 40 90 basically basically he's he's this close He's got eight games in the bubble to get to 50 40 90 and I don't know if he's gonna do it But he's just got to keep up the efficiency and he's got to hit a little bit more of his free throws I think his free throws are what's holding him back right now at like an 89.2 percent or something crazy like that He's a good defender. His defense hasn't been as as amazing as previous years But they don't really need him to be you know lock in every possession Chris Middleton because they have so so many great defenders around But even then he's still a well above average defender It's just maybe not as great as it was two three years ago. I really love Chris Middleton at the four spot at three Jimmy Butler a I know the statistics of Jimmy Butler don't look amazing He has not been able to hit a jump shot this season But his impact is there think about with Miami. He were before he signed to this organization He fits like if there's any player that fits the culture of the Miami Heat and his Jimmy Butler So when he ended up there, I was like match made in heaven Boy was in the gym at three o'clock in the morning practice started at like eight. I Couldn't even matter why why I feel like that's a little excessive But you get what I'm saying that's the type of player Jimmy Butler is and it makes sense that he's three even though on paper It may not seem like he is as good as he is But there's a reason for that because he is the team leader He is the closer for this team and he is the culture is the culture so Three three makes sense. I would put him over Chris Middleton, too And two they have Kawhi and that one there's LeBron's a's I was interested to see what they would think because I've seen a lot of rankings were Kawhi Leonard was one and LeBron was number two like hey LeBron, you ain't the king of the league no more, but brother I Still agree with LeBron being a number one dog. It's it's hard for me not to I Don't hate this list man again There's some things that I don't agree with like number seven being Gordon Hayward and There's some things I really love I mean I again I love move on but this may be still a little bit too high But there's some things I do agree with and that's what it's all about Let me know what you think in the comment section leave a like on the video subscribe if you're new I don't think I've said that but it's still like 50 50 50 percent of the people that are watching these videos are subscribed and 50% of the people that are watching these videos aren't so let's let's get that to like at least 60 percent subscribe, right? Let y'all I'm out


Now, as gunshots echo across the windswept snow-covered reaches of the wild northwest, Quaker Puff Wheat and Quaker Puff Rice, the breakfast cereal shot from guns, present the challenge of the Yukon. It's Yukon King, swiftest and strongest lead dog of the northwest, placing the trail for Sergeant Preston of the northwest mounted police in his relentless pursuit of lawbreakers. I'm King, one must be. Gold, gold discovered in the Yukon, a stampede to the Klondike in the wild race for riches. Back to the days of the gold rush, with Quaker Puff Wheat and Quaker Puff Rice bringing you the adventures of Sergeant Preston and his wonder dog Yukon King as they meet the challenge of the Yukon. At breakfast tomorrow, try this. Pour out a bowl full of crisp, fresh Quaker Puff Wheat or Quaker Puff Rice. Add milk or cream, top with fruit, and get set. Yep, get set for the keenest, swellest tasting breakfast ever. Now, did I hear you say, look, nothing could be that good? It couldn't, huh? Well, just you try Quaker Puff Wheat or Quaker Puff Rice tomorrow sure. Niku sat on the floor of the igloo facing the sleeping bench and watching the stranger as he talked with his uncle, Kulak. This was the first white man the Eskimo boy had ever seen. Wonder was in his eyes.  Neither had Kulak for that matter. He watched the flashing blade constantly, although he spoke of other things. Travel now. The wind is a whisper, but soon it will change. The storm will come. It will last for many days. After sleep, I must go. One of your dogs is lame. He cannot travel far. Yes, that is true. I must find another dog. The men were silent for a moment and in that moment fear took possession of Niku. This was trading talk. The man was offering the knife for a dog and Niku was afraid he would choose his own dog, the black husky he had named Tonak. They have many dogs. Yes, I've seen them. They sleep in the tunnel with my dogs. They are a good dog. Yes, they are good dogs. This is a good knife. There's no life like this within a thousand miles. The blade is sharp enough to cut a hair. I'll show you. The stranger pulled a hair from his hand. A flick of the blade and it was cut in two. It is a good knife. But it would not be wise to trade a dog for a knife. No, it would not be wise. Buckland does not talk to you. No, Kulak, but there is wisdom in his speech. Man can make knife of whalebone, but without dog he's nothing. A boy is nothing. Hold your tongue. A man can't make such a knife as this from whalebone. And if a man has many dogs, it is a small thing to lose one of them. But it must be a good dog or I will not part with a knife. Oh, Kulak's dogs are good. But there is only one I want. Name the dog. It is the black. No, Kulak. Tonak is mine. He was given to me by my father before he died. The black husky is the one I want. You cannot have him. The black husky shall be yours. No, Kulak. He's not yours to give. He is the price you pay for food you eat. The dog is yours, Buckland. Give me the knife. No, Kulak. Oh, no. Not yet, Kulak. It may be that as we sleep, the boy will turn the black dog loose. This cannot happen.  Shall be it. Tonak. No, Kulak. No. There was nothing that Niku could do when he knew it. But when the others were asleep, he put on his parka and crawled into the tunnel where the dogs were sleeping. Some of them growled at him.  Tonak, the stranger will take you away with him when he goes. There is nothing I can do to stop him.  What would you find food?  No, Tonak. You must go with him because Kulak is greedy for the shining knife. Tonak, someday I will find you. Someday we will be together again. Someday, Tonak, I promise. The stars were still shining as Bucklin prepared to leave the village. For there is no day during the long winter above the Arctic Circle. Tonak was harnessed just in back of Bucklin's lead. But these were strange dogs, and he fought to be free until Bucklin lashed him with his long whip. No, no, don't beat him. Tonak! Tonak! I have told you, you must go with the stranger. Eh, that's better. Now the knife. Here it is. I must warn you, Kulak. There is powerful magic connected with a knife. If men come this way and ask for me, you must tell them nothing. You must hide the knife until they have gone. Tell all the men in the village, Kulak. If anyone speaks of me, the knife will turn against you.   I will tell the men. No one will speak of you. Good. Stay. Kulak was right about the change in weather. The wind from the north became a gale, and no one in the village stirred out of the igloos. But 24 hours later, Kulak's dogs began to bark. There must be someone outside, Kulak. Perhaps the stranger has come back. Oh, shoot. The boy lifted the skin curtain that separated the large living room of the igloo from the tunnel. He crawled through it and out into the storm. Nothing! The travel, but not the men with the beard. My name is Niku. I am nearly a man. Oh, I can see that now, but tell me where the chief lives. This Kulak's house. He is brother of my father, and headman of village since my father died. Good. I want to talk with him. It'd be well for you to unharness your team, bring dogs into the tunnel. It's not possible to travel in this storm. It's possible, all right, but I guess we could use a little rest. I will help with team. Good. What you call your lead dog? Boy, he wishes to be friends with me. He likes to be friends with nearly everyone. But how can he be good lead dog if he is gentle? He isn't always gentle. The other dogs obey him? Yes, well, that question he settled out a long time ago. Oh, all your dogs are good dogs. Yes. Good dog is a fine thing. My dog was called Tonek. Huh? But he is gone now. He died, Niku? No. No, he's gone. You come. I will show you the way. Come on, boys. Inside the tunnel where you can warm up. Your dogs will fight with Kulak's dogs for a little while. Oh, I don't think so, Niku. You stay here, King. Make everybody behave. Oh, it is a wonder. Even Kulak's lead obeys him. King's a pretty big dog. I will lift the curtain. Kulak, here is a traveler. He will rest with us until the storm dies. Give him food. A kind greeting, Kulak. Rest here on the sleeping bench. Just as soon as I take off my parka, it's warm in here. Kulak! What's the matter? All my uniform. Yes, it is red as blood. Yes, haven't you ever seen a Northwestern-Ordered police uniform before? No. And you don't understand? No. Well, you have heard of the great white mother across the waters. I'm her servant, Kulak. My name's Sergeant Preston. Whenever a man has done wrong, it is my duty to find him and bring him before the judges. Kulak has done no wrong. I believe you, but all men are not like Kulak. Let me tell you. A hundred miles to the east, there was a trading post. A trading post? Only a hundred miles? Yes, it was started last spring and many Eskimos went there to trade their furs. There was also a mission where the good father doctored the Eskimos. But now there is no trading post and there is no mission. The white man did not like our country. No, it wasn't that. An evil man came to the trading post one day and killed the trader. The good father tried to stop him and he also was killed. The killer left the post and headed in this direction. I believe he's trying to get to Alaska. His name is Buckland.  If you have seen this man, you must tell me, Kulak. It's the wish of the great white mother across the waters. Have you seen him? No. We have seen no traveler from the east but you. The Kulak. Why do you stare? Give Sarge a food. Yes, Kulak. Here. Here's food. Well, thank you, Niku. I will feed your dogs. That's fine. You will rest here, Sarge. For a few hours and I'll have to be on my way again. An hour later, everyone in the igloo was asleep with the exception of Niku. He crawled close to the sleeping bench and touched the sergeant's shoulder. What is it, Niku? I must speak with you. Come with me outside. All right, Niku. And a moment later, outside the igloo... What is it? The man with beard. He is evil man. He's very bad. I knew that when he beat Tonak. You knew? You've seen him? Yes. He was here a space of summer day ago. You will take him before judges so he cannot beat Tonak. You can depend on that, Niku. What? What's the matter? Kulak. I saw him in the tunnel. He has heard what I told you. You don't have to worry about that. He should have told me himself.  But it does not matter. What are you saying, Niku? It is true.  We'll continue our adventure in just a moment. You know, girls and girls, I was out walking one night. It was a beautiful night, full moon and everything. And well, sir, maybe you won't believe it, but here's what happened. Hello! For a moment, I didn't realize who was talking to me. Hello! Then I saw him. Say, aren't you... Yes, I am the man and the moon. Gee, I've often seen you, but this is the first time I've had the pleasure of talking to you. I don't talk to everyone. But why favor me, Mr. Man and the Moon? I want to compliment you. About what? About giving all the boys and girls such good advice. You mean telling them to eat a good breakfast and that nothing tastes better than delicious Quakerpuffed wheat and Quakerpuffed rice with milk or cream and fruit? Precisely. Well, I don't want to brag, but I must admit that wheat or rice shot from guns exploded up to eight times normal size to make them bigger and better tasting. They're shot through and through with keen nut-like flavor. They're crisp, they're tender. And what's more, I think it's important to tell all the fellas and girls that Quakerpuffed wheat and Quakerpuffed rice are good for them. They furnish added food values of restored natural grain amounts of vitamin B1, niacin and iron. Good advice, Dad. But say, Mr. Man and the Moon, how do you know so much about wheat or rice shot from guns? We don't sell Quakerpuffed wheat and Quakerpuffed rice up there on the Moon. I am old and wise. The Man and the Moon knows many, many things. Well, sir, fellas and girls, what do you know about that? One thing, though, and this is for sure, unlike the Man and the Moon, you can always enjoy nourishing tasty breakfast of Quakerpuffed wheat or Quakerpuffed rice morning after morning. Grocers everywhere down here have crisp, fresh wheat or rice shot from guns. But mind you, it's never sold in bags or bulk. Always look for the famous big red and blue package with the smiling Quakerman on the front. That way, you're sure to get the original, the one and only Quakerpuffed wheat and Quakerpuffed rice. Now to continue. The sergeant looked with concern into Niku's face after the boy announced that Kulak would kill him for what he had said. What are you talking about, Niku? To save himself from the magic of a knife, what knife? Kulak traded my dog for a knife with shining blade. The bearded man said there was great magic in it. And he told Kulak not to tell anyone about his being here. Yes, sergeant. He said if anyone told Kulak would die, the knife would turn against him. I... I do not believe in such magic. You have a lot of sense, Niku. But Kulak believes.  No, he won't.  Take you with me. And Miss Storm? I have traveled in worse storms. I can help you find the man with beard. But this is your home. I won't be coming back here. No, I... I am not wanted here. I have heard there are schools where one can learn the speech and ways of the white man. I would like to go to such a school.  I think you'd do well in a mission school.  That sounds like a good idea. I'll put the fear of the queen in Kulak, but even so I wouldn't feel safe in leaving you here. Superstitions are almost impossible to fight. Well, settled. Come on. We'll tell Kulak. Kulak made no objection to Niku's leaving. In fact, he was glad to be rid of him. The sergeant called the men of the village together and delivered a lecture on cooperating with the law. Then he and Niku started out. Their course lay across the frozen surface of the sea. The wind roared down from the pole, whipping the snow in the air to a height of 30 feet. It was bitter weather, and after traveling many long hours, the huddle of igloos in the icy waste was a welcome sight. Honking! Niku will find the man with the beard here. Oh, yes. Even with Kulak, his team is not as good as yours. He is not strong as you. We will find him here. Look, Niku, men are coming out of their igloos. Sergeant, they carry spears. We are not welcome here. I'll find out why. Hulking! Oh, your husband! We'll stay here, Niku. The sergeant walked toward the village. As the figures of the Eskimos became clear through the whirling snow, he saw one of the men raise his spear. The sergeant whipped out his gun and fired into the air. With wild yells, the Eskimos turned and ran. Up! I come in peace! In spite of the sergeant's shout, the Eskimos disappeared into their igloos. The sergeant started on once more when a volley of shots rang out from one of the snow huts. He dropped to the ground and fired and returned. Hing! Get the team turned around! He began crawling back toward the sled. And as he did so, the wind increased in violence and a curtain of driven snow blotted out the village. He leaped to his feet and ran back to the team. Hing had the team turned around and the sergeant leaped on the runners of the sled. Okay! The great dog leaped forward along his back trail. Sergeant, I'm afraid. All right, Niku. The stick that belts his fire and thunder. We call it a gun. There was another in the village. Yes, it must have been the man with a beard who fired it. I not see him. No, he set the Eskimos out to drive us away. When they turned and ran, he had to shoot. Why do Eskimos raise their spears against you? I don't know, Niku. There's no telling what Buckland's been saying to them. I'm going to find out. Where are we going? Back away. We'll build an igloo. All right, on, King! The sergeant put half a mile between the sled and the village before he called out a command to stop. Okay! Then, cutting great blocks of snow with his snow knife, he quickly built an igloo. He carried his primus stove inside, lit it, and soon the interior was snug and warm. He fed the dogs, cooked some food for Niku and himself, and after they had eaten... I'm going to leave you here awhile, Niku. Where do you go? To the village. King and I.  I'm not going to let them see me this time. The dogs will catch your scent. They will bark and tell villagers you are coming. They won't get our scent this time. They'll make our approach in the south, which will be downwind. Our scent won't be carried to the dogs. They will crawl through the snow, so none will see us. Let's go, King! Outside the cabin, it was impossible to see more than 20 or 30 feet ahead. But using his compass, the sergeant made a wide circle to the south, counting his steps. At last, he stopped and dropped to the snow. Well, it should be due north of the snow, King. Crawl until we get there. It was 10 minutes later that the igloos loomed ahead through the snow. The sergeant headed for the one at the edge of the village. He reached its tunnel without being seen. He pushed aside the block of snow that filled the entrance. There was one dog inside the tunnel. Keep him quiet, King. A woman's voice called out. Sergeant threw back the curtain at the end of the tunnel. It was warm inside the igloo, and as he stepped inside, he opened his parka. The Eskimo woman inside saw his uniform. You red devil! The woman picked up a knife and started for the sergeant. But he caught her wrist and twisted it from her grasp. I won't hurt you. Tell me why you called me the red devil. Let the seal come back. We are starving. We have no meat to eat. The flame in our lamps is low. So you haven't been catching any seal? You know we have not. And it's my fault, I suppose. Yes. Who told you that? The man with the black beard? Yes. What else did he tell you? That if you are killed, we will find seal again. Anything more? That if you enter the village, we will starve to death. And now we are lost. No, you're not. Where is the man with the black beard? In the singing hut. Who's with him? All the men of the village. My husband, I get to cast a spell on you. Oh, so your husband is the shaman. Yes, but he has failed. Now listen to me for a minute. He has failed. He has failed. Just be quiet and listen. I'm not a devil. I'm a man. I'm the servant of the great white mother across the waters. And Sergeant Preston of the Northwest Mounted Police. I've come here to arrest the man with the black beard who has killed two men. I'm going to take him before the judges who will punish him for his crime. No. No, the men will not let you touch him.  I'm going to change their mind about that. I'm going to prove to your husband and the other men that I'm a friend. A friend? I mean no harm to anyone in this village. That's why I'm not going to make an arrest now. But tell your husband this and don't let him tell anyone else, especially the man with the beard. I'm going away and I'll return with seal so that you will have food and fuel, which will prove I'm a friend, won't it? Yes. Give me one of your husband's harpoons. Yes. This side of the lamp. Good. You'll tell your husband and only your husband. If you bring back seal when there are no seals, then you are good spirits, not bad ones. I'm only a man, a policeman. I will tell my husband. The sergeant left the village under cover of the storm and returned to the igloo he had built. Niku was pathetically glad to see him. I was afraid, sergeant. I was afraid they killed you. Don't worry, Niku. I found a way to help the villagers and make them our friends. Do you remember back about 20 miles and the dogs tried to head out to sea when King had a hard time keeping them straight? Yes. They had caught the scent of seal. Right. That's where we're going. Here, King, at the center of this harpoon. Find seal, King. Seal it. Sergeant, he understands. Yes. He'll lead us to the right spot, won't you, boy? And so once again, Sergeant Preston and the Eskimo boy braved the arctic storm for long hour after hour. It was King who let them know when their destination was reached. But there was no sign that a man could recognize them at white wilderness. All right, boy. All right. King was unharnessed and the sergeant followed him, harpoon in hand, across the trackless snow. At last, the dog stopped and looked up at his master. An airhole here, King? Sergeant probed to the snow with his harpoon and found the seal's airhole. Then he built a windbreaker on the north side of it as a protection against the bitter northern gale. Now we wait, King. The sergeant crouched with his harpoon ready, watching a slender piece of whalebone which he had thrust down through the snow to the open water beneath it. He waited without moving a muscle for one hour, for two hours, for three hours. And during all that time, King crouched in the snow as motionless as his master. Then the piece of whalebone rose and fell and the sergeant struck. Got him, King! It was Angotuck and his wife who first heard the sergeant's dog team. What? A traveler? It is the man with the red coat. I know. We will see. Come. Together they hurried from the igloo. The wind was dying down and only an occasional flurry of snow blurred their sight. They could see the team, the sled, the man and the boy clearly. It is he! The villagers joined the shaman and his wife. The devil again. We must wake the man with a beard for the red devil's first stick will kill us. No! No, this man is our friend. Yes, it is true. Look on this sled. A seal. Hear my words. This man is servant of the great white mother across the waters. He comes as a friend. Bringing us food, we must welcome him as friend. What at that moment? Buckland elbowed his way through the crowd. He carried a rifle and he leveled it in the sergeant's direction. The shaman's wife screamed. At that moment a terrific gust of wind hit the village and a solid wall of white obscured the sled. But only for a second. The wind died, the snow cleared and Buckland raised his rifle once more. His target was no longer straight ahead. The sergeant had swerved to the left and was heading for the rear of the shaman's igloo. Buckland shifted his aim. But now the sergeant was in pistol range and his gun spoke before Buckland. Buckland misjudged King's speed and his shot passed behind the sergeant. But the sergeant's bullet struck the killer in his right shoulder. Still he took aim again. He never pulled the trigger. The sergeant's second shot caught him in the right arm and the rifle dropped to the ground. King's, King's! King swerved to the right at the sergeant's command and drove straight toward Buckland and the villagers. A second later, the sergeant halted the team. Well, Buckland, it's been a long chase. You're under arrest in the name of the queen. You have kept your promise. You have brought us food. Yes, shaman. Before I leave with my prisoner, I'll take you to the place where the seal are. My good, Spinnock. We will move our village to this new place. Hey! Sergeant! Sergeant! Here's Tony. May I have him back? Of course you may, Niko. I'll go with us to Herschel Island. The school is there? Yes, Niko, and both you and Tornack will be welcome there. And you? I'll be taking my prisoner on to Dawson. There's no doubt of your guilt, Buckland.  When you face the judge in Dawson, this case will be closed. In just a moment, President Preston will give you a preview of Friday's adventure. Oh! When you get up tomorrow morning, there's nothing that'll taste so good as delicious Quaker Puffed Wheat or Quaker Puffed Rice with milk or cream and fruit. Every crisp, luscious bite has that swell, nut-like flavor that hits the spot. Try it tomorrow morning. When the alarm rings, think of those big red and blue packages of delicious Quaker Puffed Wheat and Quaker Puffed Rice waiting for you. Yep, the packages with the smiling Quaker Man on the front. That's the sure and only way to get the original crisp, fresh Quaker Puffed Wheat and Quaker Puffed Rice. They're never sold in bags or bulk. Listen Friday when Sergeant Preston and Yukon King meet the challenge of the Yukon in the case of... the miners' meeting. When King and I reached Gaunaway Creek, Young Johnny Johnson found guilty of murder by a miner's meeting. Already had the news around his neck. We didn't know then that the real criminals were part of the mob who were about to hang him. But the moment came when we were facing death and the killer's guns. Be sure to hear this exciting adventure Friday. These radio dramas, a feature of the challenge of the Yukon Incorporated, are created by George W. Trenble, produced by Trenble Campbell Enterprises, directed by Fred Flower Day and supervised by Charles D. Livingston. The part of Sergeant Preston is played by Paul Sutton. They are brought to you every Monday, Wednesday and Friday at the same time by Quaker Puffed Wheat and Quaker Puffed Rice. The breakfast cereal shot from guns. Remember for delicious hot breakfast, enjoy Quaker Oats. The giant of the cereals is Quaker Oats. Delicious, nutritious, makes you feel ambitious. The giant of the cereals is Quaker Oats. And here's why Quaker Oats is called the giant of the cereals. There's more growth, more endurance in oatmeal than any other whole grain cereal. So make your hot breakfast, nourishing Quaker Oats. Quaker and Mother's Oats are the same. This is Jay Michael wishing you good bye, good luck and good health from Quaker Puffed Wheat and Quaker Puffed Rice.


In previous videos of this lecture series, we've talked a lot about proving conditional statements, things like P implies Q. We have the method of direct proof where you assume the hypothesis and then you derive the conclusion through logical inference. You can also prove this using indirect proof methods like contra positives or proof by contradiction. What I wanna do now is then develop a technique to prove a biconditional statement. So if you wanna prove P is equivalent to Q, how do you do that? Well, the thing to remember about biconditional statements is that they're logically equivalent to the conjunction of two conditional statements. So the biconditional statement P is equivalent to Q is the same thing as the conditional statement P implies Q and its converse Q implies P, right? Which I intentionally drew this one backwards so that P and Q are in the same order here. Now we've talked about before, how do you prove a conjunction? A conjunction is just two statements. We have to both be true for the conjunction be true. So you first prove this one to be true, then you prove that one to be true. Now the first one is a conditional statement P implies Q. So you can prove that by any of the methods we just talked about, direct proof, contra positive, contradiction, et cetera. Then you have to also prove that the converse is true. Now in general, given a conditional statement, its converse might not be true, but if the biconditional statement is true, then the conditional P implies Q and its converse must both be true. But this converse is itself a conditional statement. So you can prove that with direct proof or indirect proof. You can mix it up. This one you can prove with direct proof. This one maybe you prove using contra positives or contradiction, that's a possibility. So these biconditional statements, the way we often read them is we often read it as P if and only if Q. So this is what we mean by biconditional. And this if and only if statement is often abbreviated in mathematics as IFF. So if you ever see an IFF that's not me misspelling if, that's actually an abbreviation for if and only if. So if and only if, you have the last F there, squeezed it together. So if and only if is a biconditional statement. You have to prove that P and Q are logically equivalent to each other. Now because of this observation here, proving if and only if statements is actually two statements that you have to prove. There's the if part. The if part means you will then prove that P implies Q. This is often referred to as the sufficiency of the problem or that P is a sufficient condition for Q. And the reason for that is, if you know that P is true, that's sufficient to tell us that Q is true. Now there could be other reasons why Q is true, but if P is true, that's sufficient to show that Q is true. So that's the if part. The only if part is then the converse. It goes the other way around. Q implies P. This is often referred to as the necessity of the equivalence there, the necessity of the proof or the necessary condition. Which means that if P is true, that means Q is true as well. So for P to be true, it's necessary that P has to be true as well. So be aware that the sufficiency goes in the direction, the first direction, necessity goes in the backwards direction there. And a pneumonic device that logicians sometimes like to use to help you remember which one's sufficiency, which one's necessity. The idea is that, let me see if I can remember it correctly. It's about Socrates. Let's see, it is, oh yes. One can say that knowing that someone is called Socrates is sufficient to know that someone has a name, all right? So knowing that there is Socrates knowing means that people know there's a name. Sufficiency comes before necessity S and N. Knowing Socrates exist implies that names exist because Socrates has a name. So sufficiency comes first, the necessity. But I confess, I forget which one's which all the time. You can survive without the vocabulary, but it's important. It's important I introduce it in this video, right? So what's the general if and only if proof template?  Then you prove the converse, which is not written correctly here. You prove the converse that Q implies P. So you prove conditional and it's converse and that's what it is. So an if and only if proof comes in two parts always. The necessity comes typically second, but you could do it first if you want to. The sufficiency P implies Q, typically do that first. But again, it doesn't really matter because if P is, if you prove P implies or P is equivalent to Q, that's actually equal to Q is equivalent to P. So this is what I meant earlier. If you mix up the sufficiency and the necessity, it doesn't make much of a difference. You just need to prove that P implies Q and Q implies P. Let's see some examples of that. So let N be an integer. We're gonna prove that six divides N if and only if two divides N and three divides N. So I'm gonna first prove sufficiency. So if six divides N, I didn't wanna prove that two divides N and three divides N. That's the easier direction. So in the first direction, you might say that four sufficiency or something like that. But so the first direction, suppose that six divides N. Well, what does it mean to divide six divides N? Divisibility tells us there exists some integer K such that N is equal to six times K. Now, working with this equation, if N equals six K, that means that N equals two times three K. And since three K is an integer, this shows that two divides N. Now, if I take the equation N equals six and factor it slightly differently, this shows us that N is equal to three times two K. And since two K is also an integer, this shows that three divides N. So we've now shown that if six divides N, two divides N and three divides N, this shows sufficiency, the first direction. Now, for the other direction, for which that's actually how I phrase it here, you should usually give the reader some clue that you're doing the other one. Since it's an if and only of proof, there's two directions. It's good to put some type of Q to show that, oh, we did the first direction. That's now done, which is what this told us right here. We're done with that direction. Now, for the other direction, we're starting the other direction. So suppose that two divides N and three divides N. We have two assumptions here. We need to show that six divides N. Now, because two divides N, that means there's an integer R, such that N equals two R. And likewise, because three divides N, there's some integer S, such that N is equal to three S. Now, I want you to focus on this part just for a moment. Two R equals three S. Since two clearly divides two R, that means that two must also divide three S. Now, by Euclid's lemma, if two divides three S and two was a prime, that means that two divides three or two divides S. But wait a second, two does not divide three because three is also a prime number and it's only divisors are one and three, not two. Euclid's lemma then gives us that two divides S. Now, if two divides S, there likewise has to be an integer T, such that S is equal to two T. And if I take this equation and substitute it into the equation above, we then discover what we're looking for. N, which equals three S, is also three times two T, three times two is six. And so therefore we now see that six divides N. This then proves the necessity of the problem. And so since we've now proven both directions, we get the equivalence we're looking for. Six dividing N is equivalent to two and three dividing N. So we've now proven this if and only if statement. I wanna sort of make a parallel here that when you wanna prove that two sets are equal to each other, A equals B, we do this by showing that A is less than or equal to B and B is less than or equal to A. There's two directions to that proof that's very similar to this statement of logical equivalence. To show that two statements are logically equivalent, that is if and only if, we show implications in both direction, both the sufficiency and necessity.  We did both of those using direct proof. We assume the hypothesis and then derive the conclusion. But you can also prove implications using some type of indirect proof like contra positives. Now, if you apply that to an if and only if statement, you can actually vary it in the following way. If you wanna prove that P is equivalent to Q, you can first do the first direction, the P implies Q direction. You can do that directly. So assume P, then prove Q. To prove the other direction, Q implies P, this is logically equivalent to the inverse. So Q implies P, the converse is logically equivalent to the inverse, not P implies not Q for which as this is also a conditional statement, you can prove that by assuming not P and then proving not Q. And so basically, if you're gonna prove the converse using contra positives, you're actually proving the inverse and you can clean up the language by using this template here. Assume P, then prove not Q. So assume P, then prove Q. And as a second step, assume not P and prove not Q. So this can be a lot simpler than having to introduce contra positives or contradictions when you come to equivalence. So I'm gonna use that technique on the following proof here. The integer N is odd if and only if N squared is odd. So I'm gonna prove sufficiency first. So N being odd implies N squared is odd. So first suppose that N is odd. Well, if N is odd, that means there exists some integer K such that N is equal to 2K plus one. And then I'm gonna plug that into N squared and see that N squared is equal to 2K plus one squared. Which if you foil it out, you get 4K squared plus 4K is equal to plus one. For instance, if you factor that, you can write that as two times 2K squared plus 2K squared plus 2K plus one. And as this is an integer, you get two times an integer plus one that's odd. So this shows that N squared is odd. This gives us the sufficiency. Now to go the other direction, if we try to prove that directly, we would have to assume that N squared is odd, which we've looked at this before, it gets a little bit awkward. We'd rather plug the simpler term in the more complicated term. So when we try to prove that N squared being odd implies N is odd, we usually did that like contrapositor or contradiction. Since we have an equivalence here, I'm just gonna use the inverse. I'm gonna assume that N is not odd. Suppose that N is not odd, that is N is even. That's gonna be a lot easier in this situation. Now be aware, since we're going to the other direction, it's good to offer some type of guidepost to the reader, so conversely, helps me know I'm considering the other case, which admittedly I'm doing the inverse right now. So if you wanna say inversely, you can, but conversely is a more natural thing to say in English there. So suppose that N is not odd, that is it's even. So there exists some integer K, such that N equals 2K. Now if you're wondering, I already used the symbol K, but that wasn't the first half of the proof. Kind of like in a computer programming setting, I have a local variable. K only mattered for that proof. Now that I'm in a different proof in a different locality, that I can reuse that symbol. It's fine, no big deal. If there's not all any confusion here, you can introduce a new symbol, but honestly I think K works just fine. So N equals 2K. Well, if N equals 2K, then N squared equals 2K quantity squared, which is four times K squared, which is the same thing as two times 2K squared. This shows that N squared is even. So this proof template here was really, really nice. To show if and only if, you prove the implication in both directions, or in this case, what you can do is you can assume one, prove the other, then you can negate that same one and then prove the negation of the other, which we ended with of course a not, we ended with an even, which is the same thing as not odd. And this shows us how we can improve if and only if statements, which occur all the time in mathematics.


Well, as you know by now, Donald Trump was acquitted. Now, um, I wasn't necessarily in a rush to talk about this I think that it's not a surprise to anyone who is paying attention since the beginning of this entire process This was pretty much a foregone conclusion Having said that though, I do still think that the process itself was important Even if we kind of know what the outcome will be it is still important to go through the motions I think that there needs to be at least some level of accountability Even if it doesn't necessarily amount to much but part of the reason I think why Elites in this country politicians in this country have become so terrible isn't just because of capitalism and money in politics It's because they know that regardless of what they do how egregious and criminal quite frankly their actions are they will never be held Accountable George W. Bush should be in prison right now for war crimes but Obama's administration chose To move forward and we now know it's because Obama was also going to be committing war crimes Rich people in this country Wall Street Executives they get to rig the economy crash the economy in their favor bright politicians and nothing happens It's just the entire system itself is rigged at every single level basically How many times have we seen police officers? Murder unarmed black Americans and get away scot-free zero consequences The system itself is deeply unjust So even if I could have predicted that Donald Trump would have been acquitted because like all elites He's not going to face any consequences for his actions literally inciting an insurrection. It's still important to try Right once you've given up and you stop trying to hold elites accountable then you know It just the situation gets even worse. There has to be at least some minimal level of Fear that if they do something that is illegal or violent There will be consequences and for Donald Trump in this instance It's just that you know He gets to live with the fact that he's the only president who was impeached twice and even though he wasn't convicted both times I still think that it's important. Now in terms of Democrats presenting their case. I think that they absolutely Were competent. They did a good job. I do disagree with their refusal to call witnesses I think that's still that that would have not necessarily made a difference but been important for the American people to see But like when you juxtapose their performance in their case with the case presented by Donald Trump's lawyers Especially Bruce Caster, Jr. It's comical like to be that incompetent to be that moronic and still technically win it It just Our system we're making a mockery of it, right? So this entire process essentially was a sham because Republicans Regardless of what evidence they saw were not willing to change their mind The only one who arguably did change his mind genuinely was Bill Gassidy But that doesn't make him a hero the Republicans who voted to convict Donald Trump Mitt Romney Susan Collins Lisa Murkowski and others That doesn't make them heroes You're just doing the bare minimum and now we get to see the insufferable elites in media prop up these Republicans as if they're good People because they did the very very bare minimum and sure they're better than ghouls like Lindsey Graham Who's a Trump bootlicker? They're better than ghouls like Mitch McConnell who did not vote to convict Donald Trump But then went on to argue that Basically what he did was illegal. He just doesn't think that you can impeach a president who's no longer in office. I mean look Our system is corrupt. It's rigged elites get away with everything They shouldn't surprise everyone but that doesn't necessarily mean that we as individuals stop trying to hold them Accountable right until we can get a better system in place reform the system that we have then that's that's all that we can do Right once we stop trying. That's a victory for elites having said all of that though It is now time for Democrats to Sharply shift gears. I think that this was necessary. I don't necessarily know that they should have occupied like a hundred percent of their time Impeachment was necessary. I'm glad that they're finally trying to hold others Accountable who break the law but now we have to get back to work There was a pandemic going on Americans are losing their livelihoods. They are still dying Cases are decreasing for the first time in a while We are at less than a hundred thousand new cases having said that though There's a lot of work to be done And I think we are owed the $2,000 checks that was promised to us now look we already know that that was a lie Joe Biden lied and now it's supposedly gonna be $1,400 checks Whatever amount you're going to give us at this point get it out the door people are suffering and Now there's no excuse. It is time for you to deliver to the American people, right? Impeachment was necessary. Impeachment was important But now you have to shift gears There still may be the potential for Donald Trump to be held accountable the New York district attorney Is investigating him. There's no ongoing investigations throughout the country still taking place But now at the congressional level nationally speaking Now we need Democrats to all collectively shift their focus to delivering for the American people And I'm not saying that because I want Trump to get away with the crimes that he did I want, you know, the focus to shift so that would be kind of sweep what he did under the rug That's not what I'm saying But what you have to demonstrate now to the American people is that you are going to fight for them That they didn't elect you For nothing that there's value in having Democrats in office over Republicans Because if you do not demonstrate that value then in two years during the midterms You're going to get wiped out and we're gonna have a divided government Again, where the prospect of doing anything is diminished unless we're talking about like Terrible reforms of cutting social security and doing some type of compromise with Republicans even further It's time to deliver So it should be $2,000 checks, but if you're gonna send out $1,400 checks Do it. Don't wait till March Send out the checks raise the minimum wage actually put up a fight That's what Democrats have to do now. That's what we need from Democrats right now And that's all I'll say about this. I think that this again, not surprising the outcome was kind of predetermined from the beginning Um, but now it's time for Democrats to get to work Trump is out of the way There's no long-granting excuses, right? You have a couple of members in your party Kirsten Sinema, Joe Manchin Who are obstacles to progress having said that though, they're not gigantic obstacles They can be, uh, I think Pressured and it really There's gonna need to be leadership here. I'm gonna need to see members of the squad Actually speak out and hold Democrats accountable even more so than they have been Actually fight for real change and not incremental change because with how bad of a situation we are in Economically socially like to get ourselves out of this ditch We can't just dig incrementally. We need substantial reforms We need a forklift to get us out of this ditch to pick us up carry us out So what we need now is a fighting chance and Democrats have to absolutely direct all of their energy towards saving the country Now, I know that Joe Biden Isn't up to the challenge, but that's where other progressive members of congress have to continuously apply pressure. Otherwise He isn't going to do anything. He's just going to do the bare minimum to get by So I need Democrats to actually fight now and I don't want to make this video about Democrats because this is a video about Donald Trump Getting away with you know inciting in its direction, which is egregious and disgusting But there's so much going on right now Accountability is one of many things that is necessary in this country And there will be no accountability at least for now with regard to Donald Trump. He got away with that so all we can do now Going forward is try to help the American people and Democrats need to do that Activists at the grassroots level organizations need to apply pressure Because if they don't feel continuous pressure, then they're not going to act If they're not just going to on their own goodwill on their own volition shoes to do the right thing unless we pressure them Constantly, so that's all I'll say. I think that we all expected this outcome. Um, not surprising at all nonetheless I think that we need to see a renewed focus On relief and thankfully all of the headlines that they are showing that Democrats want to do that. That's a great sign Let's actually deliver and not make the American people wait until march to get crucial survival checks that they need right now The humanist report is fake news Mike only cares about crazy bernie and his wacky socialist ideas Sad very sad. I'm unsubscribing