John, why don't we turn now to you to John Palfrey. How did you get into privacy? Your class, Jonathan, Internet and Society, maybe 1999. Those were good times. Even back then, so you started with, this is yet another privacy conference. But I think even in the late 90s, you were saying this is yet another class on privacy with respect to cyberspace. Oddly, you've always seemed bored by the topic and yet always come up with more and more insights into it over time and seem to return to it. John is perfectly home to the art of, was that a compliment or an insult? I don't know. Total compliment and also fun. So it was value and actually the struggle in a way of what to say yet another privacy conference is made easy, I think, by the continued insights that you have, the idea of generativity itself, I think builds on that. And every time you learn something new about cyberspace, you create new problems in privacy, which I think is partly why we're back here. As we build more and more of this built space or design more of it, we come up with new and more intriguing problems. And I don't think we've solved yet the design problem of how to live a balanced life as between public and private in a cyber environment. And it seems to me that's sort of core to what's here. And huge credit to Judith and Jeff, along for pulling together this wonderful interdisciplinary group to talk about it. And you said earlier what was the punchline of the joke. Lawyers are usually the punchline of the joke, right? So you've left us for last, so I guess we're the punchline. But I think the reason that we're also engaged in this and interested in this is that lawyers on some level are also designers of spaces. I think that we like to hang out with Jeff Huang and Laurent and others because we perceive that we are designers of institutions and rule sets and so forth that make these spaces not just have low thresholds, but also have inviting environments where we can thrive over periods of time. And again, I think privacy is one place where we as lawyers haven't done a great job yet in determining what that rule set ought to be like. I wanted to hit three points that I think grabbed somewhat what Paul and Laurent have been saying, but maybe also throw some things forward to some later sessions. The first is the importance I think of the human experience in this space and Dana Boyd I think is the great expert on this and we'll be hitting it later. I think her basic insight that we are public by default and private through effort or private by design is a very important one in this environment. Also key to that the work that Dana's been doing, but lots of us also in focus groups and interviews and so forth learning from people, both young people and older people, that baby back there and up through the oldest person in the room that in fact, while I think many of us have the initial instinct that people don't care that much about privacy in this space, that simply isn't true. That I think we're learning much more as we live in this space that though we often trade convenience for control, we very often give information about ourselves out. You've always pointed out in that class way back then the CVS card or the Shah's card that you get 30 cents off the butter even though that might later make your insurance rates go up and so forth, we do it anyway, that we care about it in particular context and trying to understand that human behavior is I think crucial to the story and I think that's in part where Paul started us off with and that's a changing set of practices. Morse and I are now doing focus groups with kids again after three or four years of hiatus from it and hearing them talk about privacy in ways that they clearly at least in this tiny sample are more thoughtful about it. I think we are coming to greater and greater recognitions about the kinds of trade-offs that we're making and yet even in understanding these trade-offs not making great decisions, not necessarily yet having the handholds or the tools or the means to give expression to the things that people want as our sort of desires in terms of what to keep private and from whom and in what context. And again, I wanna throw this forward to Dana who I'm sure will talk more about that set of trade-offs later. The second one I think is sort of a classic lawyer's problem that we've dealt with for hundreds of years which is the intersection between the public and the private. We've debated this in many respects. The sort of obvious debates over this are the design of how the Fourth Amendment works for instance and it's analogs around the world. The basic question of when somebody, ideally in this case the state wants to get information about you, what are the rule sets that say you can under these circumstances by getting this kind of a warrant and this kind of a way and the extent to which in this environment things like the Fourth Amendment haven't been good tools for us because of the blurring of what is public and private and also the extent to which when things are in private hands, in other words they're held by a private player like a Facebook, the same rules don't apply. This is called the third party exception or third party doctrine. There are lots of ways in which our old designs of these spaces fit the rule system relatively well but in this new environment, this much more blurry environment those rules don't work as well and we haven't yet done the hard work to reimagine how those protections and those kinds of trade-offs ought to get played out particularly in a space where so much of the time it's private actors who control what are the public spaces and I'm sure we'll continue to talk about that theme. And then the third one I think is just to to reflect on the basic notion of the systems that we've built for the internet and social media and other things that go on top of it and sticking with the Goal and Foursquare and Scavenger example of the kind of check-in applications. I think the systems that tend to work best are ones that are highly interoperable with one another, right? So we don't want to have to type in to five different systems, my status update. I am in MD, Maxwell Dworkin, G115 at Pound Hyperpublic sitting next to at Ethan Z, right? You want to type that once and have that broadcast into a whole lot of different systems so that if Jenny Toomey is on Goala and Dana Boyd is on Scavenger they'll all see the same thing and the systems that are most highly interoperable have the most open APIs, have the most apps, those are the ones that succeed. Android passing, you know, the iPhone now with the number of installs and so forth. So we favor that most highly interoperable of systems as a design matter and we think of that as good for innovation, consumer choice, competition, all these things and yet that itself is one thing that gives rise to the problems of privacy in this environment, right? The extent to which we favor these things that do broadcast or, as you would say, promiscuous publication of this information across lots of platforms then leads to information seeping out of different contexts, the contexts that Dana and others say are so important. So as a design matter, getting back to these images, an image that came to my mind is the image of a breakwall. The idea that sometimes what we need to have in these systems between open systems is places where as between a harbor, a safe harbor and then a crashing sea, we need places that the data can either be slowed or stopped in instances in which you actually want safe harbors for the data that sometimes may be able to connect to the crashing sea but may not or places for the ships to pass and so forth. I don't think we've been as good about figuring out what do the breakwalls look like in these systems as we rush toward a highly interoperable system for reasons that are good, the innovation and generativity and so forth are good things, but I think we're now realizing the need to put up and maybe speed bumps to use a Charlie Nessan phrase is another way to think about it but ways that the data flow in ways that give the user much more control about when they go from one context to the other and I think that lots of the business models and lots of the kinds of public policy approaches have favored more data in more people's hands to throw more ads at it, to have more innovation, to spend more venture capital in it, to get more IPOs and so forth, right? That's been the cycle. So to me, it's as lawyers coming back in along with designers and others and saying, no, we haven't quite gotten this balance, right, and how do we do that? It's funny because it feels like you've you've basically given Lorenz's talk a second pass because you're talking all about thresholds and the ways in which I think implicit in Lorenz's talk was the way in which breaking down thresholds tends to be good, not entirely, not complete open space, but I don't, I think I maybe, this is me being a lawyer, perhaps I'm misrepresenting what Lorenz says. My argument was not about if it's good or not, it was first of all a kind of overview what is happening. Yeah, but I look at that Seattle Public Library and I say what makes it so interesting is that it has really played with thresholds and lowered them, right? But there are other examples actually, like the airport, which is just incredible. The Seattle airport? No, it's yet the conventional airport. And airport. Where thresholds and boundaries are extremely important. Extremely important. Yes, that's the total recall image you had. But I was trying to say something as a normative matter rather than a descriptive one, which is to say the descriptive matter is yes, we have lowered walls, and I think in some sense we favor lower walls. The Berkman Center itself favors low walls to have more people participate in our work or for us to learn more from others, right? As an example, or again you're building, you know, the next goala or force court, you want low walls, but I think that there are costs. Yes. Too permanently low walls, ones that are eliminated, and I think we have to think about how we work with that. To be able to just say one tweet and have it hit all platforms, arrested, as the person in Egypt did when he was arrested, then managed to have a lot of dominoes fall on his behalf. But then if you say something and want to take it back, it can be awfully hard to do. Or to selectively release it. It may be calls to mind back to Urs's opening example of Google Street View, which of course is also a great mix of the technological and the architectural, the landscape architectural, and our notions of private and public. And while it's only on the public street, you can imagine people would feel differently about Street View if it came up your front walk and dropped off a pamphlet and at the same time filmed its trip up your... Ah, it's going to... Trispass. That's my front walk. Right. No solicitors if you have a camera. But I then see it being taken to the next step in a hypothetical that I heard from Charlie Nessin prior to 1999. Charlie's been into life streaming since before there were streams. He's streaming you right now. Watch out. I... You know what? I think Charlie actually is relaxed because he's like, nah, someone else is streaming it at this point. It's someone else hasn't covered. But there was a time when Charlie, if not actually doing it, which he did. Oh, yep, there's his recorder. He aspired to a world in which basically he could wear a hat. Instead of it having twin cans of beer with straws coming into it, his hat has two recording devices. Yeah, no, I wasn't going there. Two recording devices and a camera and a microphone. And just as he walks around, you can, you know, you can ride along with Charlie's homunculus. Like that's the program. And see the world he sees. And he almost sees it as freedom of mind to be able to choose to do that as a person. But of course we connect that up with what you were just talking about in your interop zone. And you see a world in which that can be made interoperable and part of a market. So that I can say, gee, I was curious who was going in and out of Maxwell Dworkin today. And there's some query I can shape which immediately goes across the database of people like Charlie who've been life streaming and figures out for the past 30 days who was in front of Maxwell Dworkin with a decent view of the door more or less, and then give me an account of everything that was going on across all of their freedoms to have recorded it. And that seems profoundly weird to me. That makes the can Google film my front walk seem like a somewhat small problem next to the world we are building interoperably among ourselves. I don't know if you have reactions to that. I didn't end that with a question mark. I think you said it, as usual, the teacher better than I could the student.


Going on everyone, Sam here with late in sports cards, ripping six box NBA mixer, 22, 23, Prenu, Donaress, Hobby, Prism, Draft, Hobby, and Choice basketball number four, Random Team Style. There's a look again at your random results. As always, you can find these on the website, under the results tab, as well as the link that's in chat. So good luck here everybody. Let me really quickly just make sure that this is all the right. Yep, two of each, perfect. All right, so we'll start with Prism, Draft, Hobby. Again, so anybody not on the, so all right, here's how this is gonna go with the Prism. Anyone who is not on an NBA team, auto-wise will get random off to every spot at the end. And then after we do all the autos, the spot under it, so say there's five autos, the sixth spot will get all of the non-auto college cards. So whether that be numbered stuff, numbered stuff, and any like base and everything too, so. Like he's like the one I've been really trying to get auto-wise. Yeah, he's a beast. Hello, Paul. Karim Abdul-Jabbar. There's a blue Anthony Black, I think he's in the league. 26 of 149, let me look that up really quick. All right, he might be at Arkansas actually. Now he's still at Arkansas. Yeah, so that'll be a random. He's on Arkansas, he's actually pretty solid. Now I think about it. Nice one there, to 150 on the blue. So that'll be a random. Walker Kessler, Snake Skin, Walker Kessler. Benedict Matheran, Butler, and Jaden Hardy. Just keep him in order. So like the Black will be first, and then whatever's next go on top of that. For the random stuff, yeah. So that's a random. Ron Harper, Silver, Sensational Signatures. PJ Hall on the red, 190 out of 199. PJ Hall, that was real GM at. You're the man, Josh, I appreciate that. Real GM, PJ Hall. Still at Clemson, so that'll be a random. So that'll go to the second team in the random right there. PJ Hall. David Robinson, that is a blue wave to 249. Nice one there for Caleb Houston. Devin Booker, Osmane Jing. Silver D. Wade, RJ Cole, University of Connecticut. Yukon legend RJ Cole, I forget, he might still be in. Played for the Lakers, Summer League. He is currently overseas, but yeah. Played for the, so that'll go to Lakers right there. Most recently played for the Lakers in the Summer League. Lake Wesley, Red Palo. Nice one there for the magic, 2299. Ty Ty Washington. Payton Watson, Sheth Holmgren. Silver Christian Braun, there's a pink ice, Jordan Bohannon, or purple ice, Jordan Bohannon. He's on the Iowa Wolves. So I think he's Timberwolves, oops. Yeah, Iowa Wolves of the G League, so that'll go to the Timberwolves. Very nice, that is number two, 99. Kessil, get me a hat, thanks Joshua. Joellen B, Ripple Shack, 275. Silver, Marjon Bochamp, base. Oh, are you from Vegas? Yeah, yeah, Joshua lives out in Vegas. I was wondering where you were gonna see him. Our 10 box Tuesday spot, not two more 10 box Tuesday spots came in. We're down to 11 to go on 10 box Tuesday basketball, everybody, 11 to go. Let me drop you guys that link. Oh no, him and Joshua are gonna be getting into some serious trouble, serious trouble. Not wanna be on the receiving end of that trouble. He is Timberwolves, yeah. Silver, there's base auto, Isaiah Mobley, that'll be going to the Cavaliers. Nice one there, Cleveland. Cleveland Cavaliers, Isaiah Mobley. That is a red, Jabari Smith, 2299. Nice one here, it's gonna be a gold, Jimmy Butler. Going to the heat, three of 10, Jimmy Buckets. Marquette color match. Purple, AJ Griffin for the Hawks, 275. Then Nick Matheran, Rory Walker, Shady Sharp. He wants me to go to Vegas for his fitness this year too. Oh, this year, yeah. Remember him talking about that, Larry Bird. There's Justin Bean for Utah State, Justin Bean. Memphis Hustle, so he'll be going to the Grizzlies. Justin Bean will be going to the Grizzlies, part of the Memphis Hustle. There is Clay Thompson, it's a 49 on the Orange Pulsar. Julius Randall, Gary Eason, Patrick Baldwin. No, Justin Lewis, there's Armando Bacot, or Bacot, that's a random, right there. He's still at UNC. Let me just double check, I'm 99% sure he's still at UNC. Bacot, Junior. Yup, still at UNC.  There's a Jaylen Brown to 199. Red, Charles Barkley to 299. Jason Tatum, Mojo, Larry Bird, nice one there. On the 2013 throwback, 16 of 25 for the Cs. Very cool, Larry Legend. Dallin Terry and Jabari Smith. Yeah, that's a random, Bacot's a random, yeah. Yeah, that'll be a good time, Josh. Silverized at a time, it's Blue Ice, Jaylen Sims. Jaylen Sims, Blue Ice, Sensational Signatures. Greensboro Swarm, so that'll be going to the Hornets. On the Jaylen Sims, nice one there, that is at 25 of 75. Jaylen Sims, Zach Levine, Purple Ice to 149. Got Scotty Pippin Junior, Snake Skin. Instant Impact, Shaden Sharp, Chris Paul, and Orlando Robinson. Let's go on to Prism Choice now. I'll finish with Don Russ. That'll be a little behind going into the Optic Mixer. No worries though. Evan Mobley, E.J. Liddell, Kawhi Leonard, Silver, Jaden Hardy, and Paul George. Otto is gonna be a Trey McGowan's. He's, I don't remember where he is. Long Island Nets, that'll be going to the Nets, Trey McGowan's to 88 on the Red Scope. Nets, Trey McGowan's. We got Patrick Baldwin Junior, Green Scope, three of eight, nice one there. And a Rated Prospect, Derrick Whitehead, 48 of 88, so that'll be part of that college non-auto card spot during the random. Choice number two. They probably will, Joshua, they probably will blow it for being real with ourselves here. Probably will. That look is not even that bad, I don't know how. I know, it's a scary part. David Robinson, Blake Wesley, and Joellen Bede. Silver, Karim Abdul-Jabbar, and Jake Lerabia, got nice. Green Scope, Otto, seven of eight is Grant Golden for the Richmond Spiders. Golden. Grand Rapids Gold, so I think he's Denver. Yeah, so this'll be going to Denver, Grant Golden, seven of eight. Nice one here is going to be a Green Scope, Jaden Ivy, that is five of eight. Jaden Ivy and Keontae George to 88 will also be part of that Rated Prospect. We'll be part of that college non-auto spot. So we've got three cards to random in terms of autos, so the fourth spot will get all of the non-autoed college cards. All right, two Don Russ, Spencer Dinway to 99 for the Mavs. A.J. Griffin, Liddell, Jeng, Christie, and Shaden Sharp on your Rookies. Patrick Baldwin Jr. Pressproof Rookie, got Seth Curry to 199 for the Nets on the Purple. Paid, Benedict Matheran, Eggs Benedict Cumberbatch Matheran, Ty Ty Washington, there's a Palo right behind that. Marjan Bochamp, Vince Williams. Pressproof, Nikola Vucovic for the Bulls. Got Harrison Barnes to 149 for the Kings. Ravia, Jalen Williams, Ochi Gbahi, Jaden Ivy Rookie for the Pistons, and Patrick Baldwin. Herbert Jones, Pressproof. Tienzalo Russell to 199. Jovich, Walker Kessler Rookie. Ryan Rollins and Terry Eason. Tyler Hero for the Heat. Paul Pierce, excuse me, on the Throwback Foil for the Celtics. James Harden-Marvels, Yannis, Payton Watson, Chet Holmgren Rookie, Blake Wesley, Kendall Brown, Malachi Brannum. Jaden Ivy, Pressproof, nice one there for the Pistons. Larry Berg, Gold Pressproof. Donchich, Kiehl's, Jalen Williams Rookie. Jaden Hardy, Layson Daniels, and an Andrew Nemhard. Dub Gin, time is it here? It's 8.56 PM, 8.56 PM Eastern time. Pressproof, Moses Moody, second year. Anthony Davis, Gold Pressproof, production line. Gowens, Sochan, Christian Coloco, got nice. Terry Eason on the Rated Rookie Auto, 7 of 25, very nice. Congrats on that one there, Houston. Wow, 8.56 AM there, that's wild. It's crazy. Anthony Simons, it's so weird to think about that. Another Harrison Barnes foil to 149. Second one of those we fold now, kind of often junior. Manat, Dallin Terry, I'd say Mowbly. Tyrese Maxie, Pressproof, kind of often junior. Nice one there, two, 149 for the Grizzlies. Grossman, Jabari Smith, Wendell Moore. Travers, Braun, Tyrese Martin. Bowens Highland, Yacum Pertle. Basketball is the 75 for the Spurs. That's not super easy, I wouldn't say, Jen. Johnny Davis, Caleb Houston, Keegan Murray. I mean, it's a little easier on the years like this where it's a white border instead of like they had a couple of years ago, they had like brown borders for all the base rookies. So that makes it a little bit tougher for sure. Yeah, see how we're looking here. Still 11 to go on 10 box Tuesday, everybody. 11 at 2-0, break and zoom. Other than that, just one group break spot remaining tonight, it is in the either, I think it's in the impeccable PYT, I think there's one team left there. No, the Browns just got taken in the Phoenix Four Boxer. So I think we just have impeccable now. Still with spots, both 10 box Tuesday football sold out. The other basketball break is sold out, which is our mixer, that is gonna be Christian Braun. Nice one there, 275 on the rated rookie auto for the Nuggets. Just 10 box Tuesday, that's it. Oh, just 10 box Tuesday. Only group break with spots left tonight. Andrew Wiggins, McCall Bridges to 199. Roddy Minot, Terry, I'd say a Mowgli on your rookies. Commando Diallo, press proof. Craftsman at Donovan Mitchell. Nice, that's awesome. Thanks, Jen. Good luck. Ochaik Bahi, J. Nivey Rookie and Patrick Baldwin. Thanks for the support, do appreciate ya. See if we can get ya a big hit out of that big boot. Gordon Jabari Walker, press proof for the trailblazers. Marvin Bagley basketball, this is 75. I think I've pulled more Marvin Bagley parallels out of this this year than anything else, dude. Benedict, Eggs Benedict, Cumbermatch, Matherin. Ty Ty, there's Palo Bancaro, nice rookie there. Vince Williams on the back as well. On your press proof for the Heat. Lamello Ball, gold net marvels, press proof. Tim Duncan. Jalen Duren. Chandler, Davis, Houston, and a Keegan Murray. Cory Kisrop, press proof. Paris Martin on the rookie to 199 for the Hawks. Watson, there's a Chet Rookie. Blake Wesley, about to cut random. And guys, 11 to go on 10 box Tuesday basketball. That is the only group break with spots left and I thank you guys for getting everything filled up. Do appreciate it, press proof and call bridges. A crunch time press proof of Jason Tatum. Larry Berry. E.J. Griffin. Christie, Shaden Sharp Rookie as well. Danny Green. Jason Tatum, nice one there on the Holofoil to 149. So-Chan, Christian Coloco, three packs left. You got a random to do and then we'll do a quick recap as well, everybody. That is Danny of Dia, press proof rookie. Darius Starland for the Cavs to 149. Yovitch, Jabari Walker, Walker Kessler. Ryan Rollins, Terry Eason. Zach Levine, press proof. Vince Carter, nice one there on the foil for the Raptors. Jabari Smith Rookie. Wendelmore, Paris Martin. Nicola Yovitch for the Heat. There's a Victor Oladipo Red to 999 for the Heat as well. Trevor Keels. Jaylen Williams Rookie. Jaden Hardy, Dyson Daniels and Andrew Nemhard. All right, guys, let's do this random really quick. The way this is gonna work is we kept them in order so it'll be all the teams will have a spot in this. The first team in the random will get Anthony Black. The second team will get PJ Hall. The third team will get Armando Vacot Jr. And the fourth team will get all non-auto to college cards. So college, this. All right, guys, good luck again. We're gonna roll the dice. Got seven times, here we go. So one, two, three, four, five, six and seven. So all right, here you go, ready? Mavs get an Anthony Black. Mavrix get an Anthony Black. The Raptors getting PJ Hall. The Thunder get an Armando Vacot Jr. The Thunder. Now I'll just make a note on the sales sheet. The Pelicans will be getting the non-autoed college cards. All numbered stuff as well. All right, let's do a quick recap here. That'll go to the Pelicans. We've got Justin Bean, Isaiah Mobley, RJ Cole, Jordan Bohannon, Jaylen Sims, Trey McGowan's, Grant Golden, Christian Braun, Terry Eason, Anthony Black, PJ Hall, and Armando Vacot Jr. That'll do it for the break, guys. Thanks again for the fill. Next up we have our Optic Mixer.


So when you watch any strategy video and they tell you that in order for the strategy or the indicator to work, you have to change the chart to Haiken Ashi. That should be the first red flag. Let me explain. These here on the left are your normal candles and these here on the right side are your Haiken Ashi candles. The entries and exits numbers on Haiken Ashi charts compared to normal candlesticks are completely different. The reason why is because they have a different formula. The close on the Haiken Ashi candle is the open plus high plus low plus close divided by four. And then the open is going to be the open of the previous bar plus the close of the previous bar divided by two. So this is Bitcoin right now showing the exact same chart, but the left one is Haiken Ashi. The right one is candlesticks. You can see the difference here on how they look. Right now there's two red candles and in the Haiken Ashi chart, there's two green candles.


Just what was clicking for you guys so well? I miss this, man. 33. We moving the ball. I think we moved the ball all night. Got good looks all night.  Was you guys taking the foot off the gas a bit? Oh, I think they got a lot of three-point play. So they hit some threes, and they got a lot of end ones. And I think that just, you know, you foul somebody and make a shot.  So they got about four or five of those tonight. I felt like, especially in transition. So that slowed us down a bit. And you got to get us to the end credit. They play fast. They try to get up to court. They know that transition is going to be the way. They can hang their hats on on the offensive side of the ball. So they pushed it a lot. And they got end ones, and I think that was key. And the three-point line, they made some tough ones, and the end ones got them back into the game. So you would attribute that more to kind of the maker misnature of it, and them hitting some shots than, I don't know, natural human nature of you guys being up 20-something and maybe letting something slip after that. I mean, they pros. Like, I know we got high expectations for us, especially when we up, but we got guys that put numbers up on the board in the NBA before on that team. You know, so we got to respect them for that as well. I know we should have kept the lead, but you still got to respect them as NBA players. But I like our intensity. I like how we came out on offensive side of the ball, moved the ball, pretty much controlled the whole game. Kevin, Steve Clifford was saying before the game that as far as preparation and passion for the game, the guy who you reminded him most of was Kobe. I know you're used to getting praise at a lot of levels, but when you hear somebody that I know you respect, like Cliff, compare you to Kobe, what does that mean to you?  But Cole, somebody I've been around and still study to this day. And basically, I just try to copy everything he does. Same with Michael Jordan. Those two guys just set the tone for everything you want to be as a basketball player. So I just simply try to copy them as much as I can. And I guess that showed to Cliff. And I enjoyed being around him a lot. We talked a lot about the game of basketball. So I'm sure he can hear that in my voice how much I just enjoy that dialogue about the game. So that's pretty cool to hear, man. I love Cliff. In your time with Kobe, what do you think you learned most from him? Really, just don't be a crybaby, like. I was at that age at 23, where I thought the world revolved around me. So I know we talk a lot about Kobe. He was real humble in how he approached the game, how he approached his teammates. Just life in general. So I just learned just from watching his movements. He was an example. He didn't say much, but he was an example just by how he moved. I try to emulate, like I say, him and Mike are two dudes I emulate at, owning off the court what they do. And it only make me better.


definitely one question comes in J.E.Main from this chapter methodically, in the era of the geometry was evolving, I mean in the era of those mathematicians coming up, Aristotle and all was working on geometry, there were a group of travelling teachers which they called sophists, Now these guys, they had a reputation of arguing for any point and they used some kind of logic to confuse people.  They should give some weird arguments where they would confuse people. So there were some kind of travelling teachers which we call as the sophists. I mean I'm just giving you a bit of background, may not be very important for you. They were travelling teachers who used to give weird arguments to confuse people. And then Aristotle who was working on geometry at that time, he started writing a book called Reputation of the Sophists. That book was called Reputation of the Sophists. Where he started mentioning some kind of reasoning or logic in order to refute the argument given by the sophists. So what are we going to study today is basically logic which is a science of reasoning. So as you know in geometry we deal with points and lines and all those concepts that time. In logic we deal with statements. So first we need to understand what are statements or what are propositions. Have you done this chapter in school? Yes sir. Okay, so you tell me what is the meaning of a statement, mathematical statement or a proposition? It's not vague. It's not vague. What about you? It makes complete sense. Okay, now there are three things normally we tend to misuse. One is utterance. Utterance is something which is just a verbal expression which may include nonsense expressions. Like you know, aprakad aprakad, something like this. It doesn't make any sense. Or let's say like goodly goodly good. So something which you say which doesn't have any meaning to it. That's one utterance. Second is a sentence. A sentence is basically those utterance which have a meaning. So utterance with a meaning is a sentence.  It's a sentence. Where were you going in the afternoon yesterday? Okay, give me a glass of water. Wishing you best of luck for your practical exams. These are all sentences. Now those sentences which can be answered as a true or a false but not both. That means there should not be any ambiguity whether the given sentence answer is true or a false. Then that will become a statement. To give you some example, 2 plus 2 equals 4 is a statement because you can say true for it. Why is the rational number? That's also a statement because you can say false for it. Yes or no? Yes sir. So things where you can conclude or sentences which you can conclude with a true or a false but not both are called statements. Now if I say raise your hand, is this a statement? No. Why not? You can't say true for raise your hand, you can only do it. Yes, absolutely. May God bless you. Is it a sentence? Yes it is. Is it a statement? No it is not. No sir. All rules are white. Is it a statement? Yes sir. Okay. So I will not waste time on this. These are something which we have already done in the school. So we represent a statement by a symbol P. P stands for proposition. Okay. And whenever we have to write a statement, we write P colon and then we write that statement. Right. So if I have to say a statement that Venkat is happy. Okay. I will write it like this. Okay. Then there is something called denial of the statement or we call as the negation of the statement which we write as a symbol P preceded with a tilde sign. Okay. Hello. The negative of this statement. So if I say Venkat is happy is a statement P. What is the negation of P? Venkat is sad. Venkat is sad is not happy or it is not the case that Venkat is happy. So there are different versions of the same thing. You can write anything in the exam or it is all that Venkat is happy. All those things can be written for it. Okay. Now what type of questions can come on negation? There's something called quantifiers. I don't know whether you have done this in school. There are two types of quantifiers which we normally talk about. One is called a universal quantifier and the other is called an existential quantifier. Okay. What are the universal quantifiers? Have you done this? No sir. Sentences which contain all or every like that are sentences which are said to contain universal quantifier. For example, let's say I give a statement all cats bite. So basically this statement is having a universal quantifier. Okay. All prime numbers are odd. It may not be correct but I'm using all here to show a universal quantifier. Okay. Whereas statements which contains there exists or some. Okay. These are called existential quantifier. Right. So I'm sure you would have used this simple. For all. Or there exists. Okay. So these are basically representing universal and existential quantifiers. Now, why is this important is because whenever a sentence begins with universal quantifier, we have to be very careful while negating it. Let me give you a question. Let's say there is a statement which says all roses are white. Okay. What do you think is the negation of the statement? It's not the case that all roses are white. Wrong. There exists some rose that's not white. Right. Absolutely. So when you have a universal quantifier, remember its negation will start with or will contain an existential quantifier. You can say there exists a rose which is not white. Or you can say it in various ways. Some roses are not white. They are not every rose is white. They are not all roses are white. Are you getting my point? So please note that never say the negation of a statement containing a universal quantifier All roses are white. All roses are not white. Okay. Why, sir? If you say all roses are not white, it will be marked wrong. Okay. Why? All roses are not white. Basically, if you are able to show one of the rose which is not white, then you have negated the statement. You don't have to say all the roses are not white. For example, let's say everyone in France speaks French. Okay. So let's say I give you a statement. Everyone in France, let's say I give a statement to everyone in France. What is the negation of? There exists one guy in France who does not speak French. Will I say everyone in France doesn't speak French or all people in France do not speak French? That will be wrong, right? Because in order to negate this, even if I find one person who doesn't speak French, my job is done. Okay. Yes, sir. At least one person in France doesn't speak French. At least one person in France does not speak French. Or there exists a person in France who doesn't speak French. Or some people in France do not speak French. So there are various ways in which to negate it. Is that right? Sir, I have a doubt. Yeah. Sir, when language is being created. So utterance, statement and sentence was all the same, sir. They were all the same. Oh, when language was being created, there was, there was actually a meaning found out in the utterance. And then it was made a sentence. So at that time, like for us now, gouligouligou didn't make any sense. But that time when it was being. Right. For you now, very German will not make sense. Right. But now there's a pattern in which they are speaking it. So for them it makes sense. But don't worry about it. Okay. Okay, sir. Yeah. No way if a statement starts with an existential quantifier. Okay. Then what is the negation of that? It will start with a universal quantifier. For example, let's say there exists, there exists a cat which there is glasses. Okay. Okay. What would be the negation of that? All cats bite. All cats bite. So remember one thing. Negation of a universal quantifier should begin with an existential quantifier and negation of an existential quantifier must contain a universal quantifier. Okay. Let's see whether we have a question based on this. In our previous J exams. Yeah. Let's say I take this question. Question number five. I read this question. Let S be a non-empty subset of real numbers. This is the following statement. He says there is a rational number X belonging to the set S such that X is greater than zero. Which of the following statements is the negation of? C. Others, everybody has to participate. It's not like only one person. It appears no Venkat. They have given the speaking role to you. Other than you. One Dheeraj was there. That also has stopped coming. I don't know why. So Niyati says something else. Venkat you said C, right? Yes, sir. Okay. What about you, Amla? Dheeta? Dheeta? Say something. I talk a lot, sir. No, no, no. That's fine.  Screen frozen. But mine is working, right? Read the question. Question says there is a rational number which is greater than zero. It starts with an existential quantifier. Isn't it? Yes. I think C. That means you have an existential quantifier here. Okay. Then read carefully and tell me which of the options is correct. It says have a universal quantifier. Tautology. What's tautology? I'll come to that. Okay, sir. Tautology is a statement which is always true for whatever component values that whatever value the component statements are. Anyways, so in this case, can I say A is my answer? If I say x belongs to S, x is less than zero, implies x is not rational. Is this my answer? Yeah. Oh. No, I guess. No, sir. Okay. This is something else. This is actually complicated. There is a rational number x belonging to S says that x is less than equal to zero. Now existential quantifier negation cannot be another existential quantifier. So B is also wrong. Okay. Now there is no rational number such that x is less than equal to zero. Isn't it saying how is the negation of that? Yeah, this says here. Oh. There is no rational number such that x is less than equal to zero. That means they are saying all rational numbers are greater than zero, right? Hmm. Okay, so isn't it the same thing? Oh, yeah, yeah, yeah. Now every rational number present in S is less than equal to zero is a negation of zero. So D is the correct answer. Oh, yeah. Niyati gave the right answer. Good, Niyati. Okay. I have to deal with this kind of no problem. And let me tell you one problem and definitely


Module 16, budget constraint. Budget constraint in fact denotes the ability part of the consumer to how much quantities of commodities can be purchased by a particular consumer by using his limited income. If there is any change in income of the consumer, it has some impact on the budget line of the consumer. It has some impact on the budget constraint of the consumer. For example, in this diagram, if we take income of the consumer is equal to 200 rupees, then all different combinations of apples and oranges that a consumer can afford, we are denoting with budget line AB. And if we assume there is an increase in income of the consumer keeping prices of commodities remain constant. There is no change in the prices of the commodities. There is only change in income of the consumer. If income of consumer becomes double, then after doubling of income, consumer can purchase double of the quantities of both commodities. And we are denoting all those combinations with budget line EF. If income of the consumer is equal to 400, then he can purchase all those combination of commodities that we are denoting on the budget line EF. With reference to original budget constraint, if if we assume that the income of the consumer is half, and because of that decrease in income, the ability of the consumer to buy different quantities of apples and oranges, it will decrease. With reference to original budget constraint, if we assume income of the consumer becomes 100 rupees, then now he has to allocate this 100 rupees on the purchase of apples and oranges. And because of this decrease in income, budget constraint of the consumer will shift from AB to GH. So, if income of the household increases, budget line will shift outward. If income of the consumer decreases, then budget line of the consumer will shift downward. When there is no change in the prices, if income increases or decreases, it will result in parallel shift of the budget line. And similarly, it might be possible, if we assume the prices of income of the household, there is no change in income of the household. There is only, there is simultaneous decrease in the prices of both commodities. If we assume the prices of both apples and oranges reduced to half, initially if we assume price of apple is equal to 40, price of oranges is equal to 20. But if we make an assumption, if price of apples in the market becomes 20 and price of oranges in the market becomes 10, there is 50% reduction in the prices of both commodities. Because of that reduction in the prices of both commodities, budget constraint, budget line of the consumer will also shift outward. Similarly, if we assume there is proportionate increase in the prices of both commodities. So, because of that increase in the prices, when income of the consumer remains constant, our budget line will shift downward. Initially, our budget line is equal to AB, when price of apples is equal to 40 and price of oranges is equal to 20 and income of the consumer is equal to 200. But if income of the consumer remain constant, there is no change in income of the consumer, but price of apples become 80 and price of oranges become 40 because of that increase in prices of both commodities. Again, our budget line will shift downward. So, in nutshell, we can say if income of the consumer increases, keeping prices of commodities constant or prices of both commodities decreases simultaneously at a certain rate, while income of the consumer remain constant, our budget line will shift outward. Similarly, if we assume there is a decrease in income, but prices of commodities remain constant. Under that situation, our budget line will shift downward. This downward shift can be observed when we see prices of both commodities are increased simultaneously at a certain rate, while income of the consumer remain constant, then our budget line will shift downward. Similarly, it might be possible that there is no change in price of one commodity and no change in income of the consumer and there is change in price of one commodity only. For example, in this diagram, we are denoting one budget line as an original budget line and if we make assumption there is a decrease in price of apples, but no change in price of oranges and no change in income of the consumer. In that case, our horizontal intercept will shift outward. Our budget line will pivot outward along horizontal axis and similarly, if we make an assumption that there is increase in price of apples while price of oranges remain constant, income of the consumer remain constant. In that case, our original budget line will pivot inward. Our horizontal intercept will pivot inward and we are labeling that diagram by putting price of apples increases. Similarly, if we assume there is no change in price of apples and no change in price of income, again we are in fact, we are reporting a budget line that we labeled with original. This original budget line indicate that by using his limited income consumer can purchase at most 10 units of oranges and 5 units of apples. And if we assume there is a decrease in price of oranges, suppose price of oranges become half because of that decrease in price of oranges when there is no change in income of the household, no change in price of apples, our budget line will pivot outward along vertical axis. There is an outward shift of our vertical intercept. Similarly, if we assume with reference to original budget line, there is an increase in price of oranges while price of apples remain constant, income of the consumer remain constant. In that situation, the budget line vertical intercept of the budget line will shift downward while there is no change in horizontal intercept of the budget constant. From this discussion about the budget constant, we can see budget line has a constant slope. Budget line is a negatively sloped curve but slope of the budget line is constant. The budget line shifts upward or downward whenever there is a change in income. Similarly, the budget line will shift, there is a parallel shift in the budget line outward or inward when there is proportionate increase in prices of both commodities. Our proportion decrease in prices of both commodities keeping income of the consumer constant and budget line, slope of the budget line depends upon the price ratio of two commodities. If there is a change in the prices of any commodity, it results in results in change in slope of the budget line. Because of change in the prices of commodities, slope of the budget line will change. When price of the commodity that we are taking on horizontal axis decreases, then our budget line will become flatter. If price of commodity on vertical axis decreases, then our budget line will become steeper. So, slope of the budget line, slope of the budget constraint depends upon the prices of commodities that are under concentration. Hopefully, after studying this module you are very much clear about slope of the budget constraint, impact of increase in income and decrease in income on budget constraint and changes in price of commodities on the slope of the budget line. Thank you very much.