Hey David! This is Megan with Oxmore Toyota. I just want to send this quick video greeting just to personally introduce myself. It has come to my attention through Truecar that you're in the market for a new 2016 Toyota Tacoma. When you can, go ahead and give me a call. You can reach me at<PHONE_NUMBER> and I look forward to hearing from you soon. Bye!


My name is Cassian Loshinge, original from Tanzania and I was one of the luck guys to come to Australia for a scholarship award. The environment in Australia is really great. Each day I am gaining different types of friends from different countries. That is one, learning better English. So far I really enjoy the vibrant, different environment that I see from my country. And just sort of see what makes Australia tech. In Australia, I have learnt a lot. Not only the knowledge for my future work in Vietnam but also I have the great opportunity to build a network. I feel every day I am learning something here. And the people, the people is much helpful. Well, I have enjoyed the hospitality of the Australian people. They are so friendly. Wherever you go, they will always greet you and make you feel comfortable and feel at home.


Okay, very good morning to you. It is Friday the 10th of December. I hope you're doing well and Going to talk about US CPI will do a short preview to kick things off first And then we're going to talk a little bit about Boris Johnson and a parent Tory rebellion on the table Then China ever grand moving into a restricted default. What does that mean? Is it important or not? Bloomberg economists survey update from the ECB in the timing going into their final rate decision about what they're going to do with hinting towards then the QE program their pandemic emergency purchase program and the APP and then a quick word on Tesla because Elon Musk has continued telling his shares for a fifth straight week fulfilling his pledge to Get rid of 10% of that holding that he has in the EV maker. So that's what's on the agenda very quick look at the charts and Not going to spend too much time here Overall, we've had a lower close on Wall Street losses of point seven in the S&P The most severe loss in the Nasdaq down one point seven But that again reflection of the outperformance that it's seen following a three-day consecutive winning streak So a bit of a pullback after those moves this morning You've got the dollar index just picking up a little bit as Europe has stepped into the market yields also Likewise, so the US 10 year down here in the bottom right's down nine and a half ticks this morning Equities also a little bit softer through the APAC session following that lower close on Wall Street If anything you could say perhaps a little bit of pre positioning then ahead of what is of course anticipated to be a super hot inflation reading coming out of the states at 130 this afternoon Why the big attention on this figure? Well, remember for the Fed it really comes down to two major forces to determine their Decision-making from an economic point of view and that is inflation and the labor market The other thing of course is going to be Omicron as we go forward But following the Fed Fed chair pals comments We saw just last week where he no longer viewed inflation as quote transitory eyes Then firmly on this it's the final piece of kind of intel that we get before next week's on the 15th Final FMC meeting of the year and a lot of the hints have been laid down around the acceleration of tapering of course in January And then that would mean the commencement of that Winding up by March at the end of Q1 of next year This is the look at where CPI stands at the moment on a year-on-year basis And you can see the previous reading came in at six point two percent year-on-year And in fact that was the highest reading we've had in 31 years If today's number comes in as expected So expected is six point eight percent the top end of the streets actually looking for a figure north of seven percent But even at consensus that would mean the highest figure since 1982 if the core comes in in line it'd be the highest reading since June of 1991 now one of the things then Well a couple of things to be aware of here One is the fact that inflation obviously has become more Acute of problem than what the Fed had previously foresaw in previous months and hence the reason why for this hawkish pivot That we've had from them and you can see here the actual CPI prints and then what's expected So today's one up right up here Expected to be generally the peak and then fading as we go further through into 2022 To cool off a little bit and move somewhere back towards the target value of around two percent or thereabouts The concern of course has been that just generally speaking that the movement has gone from being kind of in the idiosyncratic result of the pains of reopening after the bottlenecks we had experienced due to the pandemic to a more broadening out of inflationary pressures one of the biggest ones You can see here of a shift in components that we saw that that led to the height and figure last time as this yellow bar and The yellow bar being then energy and energy had been if you remember on an absolute tear for a number of weeks On that point then if then energy is becoming a more larger component of this remember the data we're going to see For this reading is November and actually the the actual kind of survey period of what that data Captures doesn't really then take hold of some of the pullback. We've seen quite aggressively in oil So one of the things that we had yesterday in attempt to kind of front-run what's expected to be an incredibly high figure Which obviously is going to be kind of sensationalized in the mainstream media is US President Joe Biden and his team have all been out looking to front-run today's figure and control kind of the Optics by suggesting then that the US inflation data due out today Does not reflect the recent decline in some prices Including energy and just to give you an idea energy prices obviously have come off as much as 15 20 percent And that won't be reflected in this report. We'll have to wait until obviously the next one that comes out So that's quite quite usual practice Obviously tries to try to get ahead of the game and to offset and mitigate any negativity of What then the public perception would be on the economic kind of handling of the administration being a failure if Then prices start to really impede people's lifestyle on the street. I if it severely outpaces wages now Couple of other things then to finish off I'd say this figure overall is not that surprising the inflation figure Is expected to go up? really, I guess what could really disturb then this idea of tapering being accelerated and so forth, which is the general market consensus at this point of time is going to be Omicron at the moment it does appear that Omicron is highly transmissible But of a more kind of mild nature to that comparative to say the previous strain of Delta Which is still much more prevalent on the global level if that were to change between now and next week's meeting on next Wednesday That being that it becomes proven more lethal perhaps than what we generally believe at this point in time That's really the only thing that could disrupt I think right now the overall process of just a faster tightening process going forward. So yeah today's figure It really depends.  Of course the intraday session How much does it really change things? Well? I don't think a great deal at this point because it's very much expected to come in on the high side So yeah, it's going to be interesting to watch nonetheless All right Before I move on to talk about some of the other stories Do not forget that we have a new podcast episode if you just jump on to Spotify or Apple podcasts and search Amplify me market maker. You better find this and we release episodes every Friday Myself and the head of trading have a bit of a conversation Informally about some of the major themes of the week And so we'll give you our take of the CPI number when we record that after the report comes out later today So don't forget to check that out. All right. The other news stories of note Not that I think this is particularly pound sensitive in the in the very immediate intraday environment But it certainly does have ramifications in the more medium term is Boris Johnson said to be braced for a big Tory rebellion over COVID measures and amid discontent over his handling Of course on the row of Christmas parties in Downing Street last year I've just actually seen a tweet come out from a UK journalist who was saying Along the lines of they were planning through WhatsApp messaging Three weeks sending out invitations to all the politicians from number 10 Whilst of course the UK was in full lockdown. So this really going down like a sack of coal at the moment for Boris Johnson and it comes ahead of Conservative unrest playing out ahead of a highly problematic Parliamentary by-election if you watch local news or BBC news and the news at 10 10 o'clock and so on you probably read about this a lot If you're not in the UK, you probably won't even be on your radar But an area in North Shropshire where the Liberal Democrats hope to overturn around a 23,000 Tory election the Lib Dems actually finished third the last time there was by-election there in 2019 Conservative MPs already Agreed by the way the Prime Minister dealt with the sleaze scandal that culminated with Owen Patterson Quitting as the Tory MP for North Shropshire. Hence this new by-election Now is that area particularly specific? Well, no it just generally acts as a bit of a litmus test of overall national sentiment at the moment as Boris has become Under-increasing pressure on multiple fronts and what this has led to is the UK Labour Party according to latest You gov times Westminster survey is now ahead of the Conservatives with a four-point lead Wouldn't read too much into that at the moment, but it just goes to kind of show the general sentiment At this present point in time All right, the other things to quickly comment on Evergrande is defaulted sounds pretty scary as a headline. It really doesn't matter a great deal Evergrande's stock price overnight. I think it was down about 2% but remember this company was seeing monster moves a few months ago And the main rationale there is basically that everyone's expecting this to happen. They're going to go into restructuring So a lot of the headlines you're seeing at the moment have a somewhat degree of inevitability about them Fitch ratings cut Evergrande to a restricted default over its failure to make two coupon payments by the end of a grace period on Monday And hence what's triggered this latest action Fitch applied the same default label to Kaiser group holdings which also failed to make some dollar denominated Payments earlier this week The main kind of reason there that not only because it's expected but also dual fold given the fact of course as well The Chinese authorities have been fairly active to look to cushion some of this expected Proceedings that are going to go forward in time The other thing then is Elon Musk. I mentioned briefly at the beginning that he's offloaded further shares So he actually sold another 934,000 shares for some just over 960 million US dollars to pay for taxes on the exercise of 2.2 million Options according to regulatory filings that came out last night So for context that brings the total amount offloaded so far since he did that Twitter poll a couple of weeks To go to 11 million leaving 6 million more to hit that target so likelihood is this isn't going to stop any time Soon also overnight you might have seen Musk did tweet that he's thinking about quitting his jobs and becoming an influencer full-time How much seriousness you should read into that? I think very little how What often have peers and I talked about? Elon Musk eventually stepping down from Tesla. I think that is going to happen at some point in time I don't think this tweet is necessarily a real telling sign that that's going to happen imminently It's just must being musk and causing more drama on Twitter Then the final thing just a quick word is the ECB And the latest economist poll conducted by Bloomberg these happens Typically on the week running into a major interest rate decision. We get them for the Fed the Bank of England This is the ECB and the findings are sometimes quite interesting This one suggests the ECB will seek to cushion the exit for an emergency bond buying Next year before a stronger inflation outlook allows for an end of all quantitative easing in 2023 It's a timeline. They're looking for In terms of what to expect Policy makers will decide on Thursday So next week to stop purchases under their 1.85 trillion euro pandemic plan in March Remember, this was the top up one of that pretty huge envelope commitment to buy bonds as a response to pandemic on top of their more standardized asset purchase APP program And what they're going to do to smooth the transition of ending the bigger one is increase the smaller Existing one and expectations are from economists that that's going to basically double from 20 to 40 billion purchases per month in under the APP for Three months and then tail that down incrementally to then come back to the The original level by the end of next year. So a smoothing out effect of the withdrawal stimulus Essentially, this isn't new information. This is very much what the markets are expecting more more broadly speaking terms of the data what we've had, sorry, this is Thursday, so I'm going to jump to Friday, which is here So we've already had UK GDP come out everything in line. No more great surprises there and no reaction to pounds I'm not going to waste my time Talking there US CPI really is the main event for the day for the week really from a data perspective Again, the headline expected at six point eight percent the core reading four point nine top end of expectations on the street seven point one percent The University of Michigan sentiment premium number for deck comes out thereafter at three o'clock Speaker wise Panetta speaking off topic on digital currencies at 10 a.m. And then that is it So with that, I wish you a good day ahead a fantastic weekend Stay safe wherever you are and don't forget to check out the podcast episode which will come out later today All right, take care guys. Have a good one


What we'll do tonight is The guts of section 27. We'll talk more about ideals. We'll talk more about factor rings And we'll get some sort of intuition going as to what these things look like Wednesday will do more game Wednesday will also be faculty course questionnaires and Wednesday will also be the day that I distribute exam 3 and final exam information So you'll definitely want to be here Wednesday to get all that stuff and to fill out the course questionnaires The following Monday We'll have a quiz. It'll be quiz five. I'll tell you about the quiz on Wednesday So Wednesday again is a really crucial day to be here then the Wednesday of the following week That's December 5th. There won't be any class. I'll just be in my office So it'll give you some time maybe to prepare review for the final in exam 3 and then exam 3 slash final Happens Wednesday the 12th from 430 to 7 so for those of you that maybe have to run out after class To go to work or something. Please make sure that you've made arrangements to be able to stick around till 7 All right questions on the overview here I mean I'll give you a whole lot of details and the stuff that I hand out on Wednesday But that's roughly where we'll be for the next Two and a half weeks till the end of the semester. Okay, so since it's been a week Let me remind you where we were where we wound up at the end of a week ago Monday and then Well, and then in effect Show you the basic construction that's going to allow us to get to this thing that I talked about last Monday this basic goal This place where we're headed So just to give you a brief recap of the goal recap is this I'm going to hand you field. We'll call the field e I'm going to hand you polynomial The coefficients of that polynomial are going to be in this field e And what we're interested in doing well, at least give me a polynomial that has some guts to it And the goal is this Try to find a field In which the polynomial has a zero in other words find a field in which there's an element So that when you drop the element in everywhere you see an x that zero comes out Find a field f So that two things occur The field that you start with lives inside the new field. Maybe it's the rational's inside the reels Maybe it's the reels inside the complexes. Maybe it's z2 sitting inside Something that we haven't sort of encountered yet, but we will over the next couple of lectures and secondly There is some element We'll call it alpha in the bigger field For which When you plug alpha into the polynomial zero comes out Feast of alpha of f of x is zero So the The sort of verbiage the The statement in English of the basic goal is take a polynomial find a zero for it somewhere That may already be that the field that you're working in contains a zero for it If I hand you the polynomial x square minus four and ask you to find some number In the rationals that you can plug in and have zero come out easy plug in two or plug in minus two makes no difference But if I hand you something like the field is the reels and I hand you the polynomial x square plus one Find a field for which That polynomial has zero where you got you got to look bigger You got to look maybe to the complexes Can you look at something smaller between the reels and the complexes? Turns out the answer will be no If I hand you the rationals and I hand you the polynomial x squared minus two and ask you to find a zero for it Find some number so that when you plug it in for x at zero comes out. You're thinking well square to two Square to two is not rational So you got to build a bigger field you got to find a larger field that contains the square to two Maybe it's the reels Yeah, maybe it's something smaller like this thing that we called capital s seeing it look like how do we build that new field? All right, so that's the goal goal basic goal All right, here's how method So the reminder is The following definition and then Again, this is something that we did a week ago Monday. I'm just trying to sort of Knock the Thanksgiving cobwebs out here start with the ring r We look at a subset of r Is called an ideal In case two things are true the first thing I can state easily if you look at the subset together with addition that you get a subgroup of r under addition Maybe I should have written this as a Proper inclusion like this so a subset is my deal and secondly this thing that we called the absorption property for every every element n in n And every element r in the ring When you multiply r n you get something back in n and when you multiply n r you get something back in n That's what it means for a subset of a ring to be an ideal So the first one requires that the subset is a subgroup And remember since addition in a ring is assumed to be commutative when we talk about a subgroup of a commutative or an Abelian group. It's automatically a normal subgroup So I could have put This it would have meant the same thing remember that was our notation for a normal subgroup when you Close the thing up here And what we looked at last monday was some examples of rings and corresponding ideals in those rings example Uh any n z inside z is an ideal example If you start with any polynomial you want What do you want to call it g of x or half of x or q of x? I don't really care. Let's call it g of x g of x in f bracket x where f is any field then look at this collection So what you're thinking is take any polynomial and multiply by this fixed one g Just like we're doing here take any integer and multiply That integer times all the other integers and tell me what comes out Take this polynomial multiply by all the other polynomials and tell me what comes out Intuitively folks what i'm asking you to do is look at all of the polynomials that you can factor this particular one out of And i don't care what polynomial you start with a good example to keep in mind is x squared minus two In the situation where f is the rational another good example to keep it minus x squared plus one Where the underlying field is the reals look at all the multiples of okay So it's the same idea is up here and as you'll remember over the last couple weeks i've been trying to You know keep this analogy going between what's going on inside the ring of integers and what's going inside in On inside these rings f bracket x We gave this subset of notation Is an ideal f bracket x just as a side remark because this verbiage came up in one of the homework problems Folks if i hang any ring No back up i hang any group Always inside any group There were two what we called trivial subgroups group consisting of Just the identity element and the subgroup consisting of the entire group Same thing happens inside rings if i hand you any ring commutative or not. I don't really care With unity or not. I don't really care. There are always inside any ring two ideals One ideal is the ideal consisting just of the subset zero And the other is the ideal of the subset consisting of the entire ring r so example in any ring For any r These two subsets the subset consisting of zero and the subset consisting of the entire ring are always ideals And i think he calls This author happens to call both of these trivial ideals In other parts of the literature you'll just call this one the trivial ideal Just okay, so they're always a Proof this one is a non issue. It just is it's a subgroup of itself under addition Of course because it's the entire group does the ring have the absorption property Well, yeah, if you take anything in the ring And you take anything in the ring and you multiply them together you get something in the ring So i mean the absorption property is a non issue for r the absorption property You have to work, you know a tiny bit for zero This certainly is a subgroup of that under addition. That's a non issue The question is whether or not this thing has the absorption property Well, is it the case that you take anything in this set?  It turns out that In z Every ideal ideal Is of the form nz for some integer n So if somebody says i'm thinking of an ideal of the integers Well, you may not know exactly what it is, but you know what its form is Its form is all the multiples of some fixed integer Maybe it's all the multiples of three. Maybe it's all the multiples of ten Maybe it's all the multiples of one Which gives you all the integers of course, maybe it's all the multiples of zero Which gives you this one So this statement, you know includes the sort of trivial cases the cases on both end similarly or analogously Or you could probably anticipate what i'm about to write down inside f bracket x where it was a field Every ideal is of the form something that looks like this Pick some polynomial and multiply that particular polynomial times all the other polynomials you get an ideal And that turns out to be all the ideals in f bracket x Every Ideal Is of the form g of x times capital f of x I prefer this notation folks because it's analogous to this notation this notation with the brackets Yeah, I might use it, but I just prefer this because it sort of more directly tells you what's going on You're starting with whatever polynomial you want. You're simply multiplying it times all the other polynomials in f bracket x Is of this form for some g of x In f bracket x so if somebody says i'm thinking of an ideal inside f bracket x Then necessarily there's some special polynomial floating around G of x for which that ideal is precisely all the multiples of that particular polynomial g of x G might change for instance It might be the case that you're looking at q bracket x and you decide to look at all the multiples of the particular polynomial x square minus 2 Or you're looking inside r bracket x where r is the reals and you decide to look at all polynomials of the form Multiples of x square plus one or you're looking in let me throw our third one in the pile here You're looking in z 2 x and you've decided to choose the polynomial x cube plus x plus 1 As g of x and you're looking at all multiples of that particular polynomial. That is an ideal And it turns out those will be special now it is not Coincidental that the three examples that I just sort of spotted out there Happen to be situations where you have an irreducible polynomial Inside the given f bracket x and you decide to look at all multiples of it So x squared minus 2 inside q bracket x look at all multiples of it x square plus 1 inside our bracket x look at all multiples of it x cube plus x plus 1 inside z 2 x look at all multiples of it Those will eventually play special roles Those will allow us to get to this thing that we're calling the basic goal All right questions comments remarks So the hope is by sort of continuing to To spout these many examples you're starting to get the the feel for what we're going to eventually do Well now we have these two pieces No, let me say a little bit more and then we'll go then we'll go from there. So turns out proposition No Okay construction the construction is this folks we're gonna start with A ring so start with r This is a brief recap, but this is going to be sort of the springboard for the guts of tonight's presentation Start with any ring r And let n be No, let me play it up this way Let let's call it Mm-hmm How about h b uh subgroup Of r with plus So what I want you to do is just focus on the added instruction now forget the multiplication for a minute Just look r with plus is an abuting group Take your favorite subgroup you want to take the multiples of two inside z. That's fine all right, so here's the point then Necessarily h is normal In r Reason because addition is assumed to be commutative inside a ring Plus is commutative. So as soon as you have a subgroup it's necessarily normal. So we can form The factor group All right, that was somewhat stomach turning for a while, but then you started got used to it and All right, I know what these factor groups look like these coset groups.   I don't know it depends if you start with the integers and you let the subgroup be 4 z Then there's four of them if you start with the integers and you let the subgroup be zero then there's infinitely many of them If there's many cosets it turns out if you start with q bracket x And you look at the subgroup consisting of all the multiples of x squared minus two under addition There's infinitely many different cosets. It's okay But here's the point big question question can We define a multiplication multiplication on these cosets on the collection Of cosets and notice folks the cosets are i'm going to refer to them as the additive cosets It's the cosets that we're forming By looking at the cosets under addition And that's legit because the addition is commutative and we know how to form cosets for any normal subgroup So that This set r slash h Actually becomes a ring becomes A ring that's the goal Hmm And the answer turns out to be this if all you've told me is that you've picked out a subgroup Of the ring under addition And you form the factor group under addition And then you simply try to multiply cosets together The result in general is going to be a disaster and it's going to be the same sort of disaster as we encountered when we were trying to decide when Uh the operation inside the factor groups was well defined remember what did we need we needed something extra Well when we tried to to make the Operation on cosets well defined we needed that the subgroup was normal All right, it turns out If you want to try to define a multiplication on these additive cosets in general, it's not going to be well defined So it turns out in general Well things crash Just like they did in groups unless you have an extra condition in general if we try To define a multiplication A multiplication on cosets well You know if there's any justice here's what you do r1 plus h there's a coset r2 plus h I mean what do you suspect a good Choice for a definition of multiplication would be just multiply r1 times r2 which makes sense inside the ring and look at that coset r1 r2 plus h Good idea. I mean this makes sense because we're living inside a ring Okay, the issue is that might not be well defined Uh this might Not be well defined. I'm not going to show you the examples, but they are easier to write down But and here's the theorem theorem if the subgroup that you start with Happens to have this extra property this absorption property So we put it together in one word if the subgroup that you're starting with inside the ring Is actually an ideal then the punchline is this multiplication on the additive cosets is actually well defined And in fact now that you've got an addition coset addition and a multiplication that's well defined It turns out that makes the additive cosets into a ring if n is an ideal of r In other words if we have this extra hypothesis on n that it has this absorption property then this Collection of cosets together with coset addition and the multiplication defined above Given above just multiply as you'd hope take the two cosets multiply them together. It's well defined is a ring We want to call it the factor ring instead of the factor group Now i'm going to leave out the proof the proof is i mean it's Omitted or left to the reader or whatever appropriate phrases the point though is We can now build new rings from existing rings and ideals just form the factor The thing well that looks mysterious it turns out folks. It's not mysterious at all Because you're totally familiar with these constructions at least in the case of the integers example Well take z There's my ring take an ideal I don't know how about 4z 4z All right now. What are we going to do? We're going to form the factor ring Well 4z is an ideal so that makes sense. So we're going to look at z slash 4z The point is folks. We've already investigated what this thing looks like as A group under addition and we wrote down the table of that thing many times That's just z sub four of the cyclic group having four elements So is well known It's just z four it's Just z four cyclic group of order four Remember the operation here's plus But now the point is because 4z is an ideal it turns out we can actually do multiplication here and Well, it shouldn't be any surprise and the multiplication that turns out to be multiplication Given by this definition just take the coset representatives and multiply them together Is nothing more than multiplication mod four. So here is the table For multiplication in the factor ring Looks like this Well, let's see. What are the elements in the factoring look like remember they could be written as These cosets. This is zero plus four z one plus four z two plus four z three plus four z and What's the multiplication the multiplication is just multiply the two representatives together And write down its coset So zero. Well, so that's easy. Look folks zero times anything is just zero So the first row is just zero That's easy And one time zero zero and two times zero zero and three times zero zero The fact that this is also seven bar. This is four bar. It doesn't make any difference You can use whatever representative you want multiply together and just tell me what that coset is All right one times one is one So look, this is a this is a perfect lecture to Run this video by because i'm about to do multiplication here. Why one Two times one times one is one two times one is two three times one is three. That's good One times two is two new to anybody yet Let's keep going until we mess things up one times three is three. All right now. I get to mess things up two times two is zero Because two times two is four four is the same coset as zero two times three is six, but six bars the same as two bar because Two is congruent to six mod four three times two is six So i'd write down six bar, but six bars the same as two bar And three times three is nine Which is the same as One How do i do there? Three times three is nine, but we're doing arithmetic mod four And nine is one mod four So there's the multiplication table questions Now all we're doing is multiplication mod four. So you may have seen this maybe computer science courses don't like that star mod four multiplication mod four But putting the bar on there is really just coset representatives questions there big example Is this r is q bracket x So polynomials with coefficients and the rationals the ideal i'm interested in is this one All multiples of the particular polynomial x squared minus two Well, it turns out folks that this ring well will turn out to be a Extremely important piece of this big puzzle that we're trying to solve this basic goal The slightly unfortunate thing about that ring is i can't just write out what its table is because it happens to contain infinitely many elements Okay, but here's a point i want to make about it note Arm on n at least has infinitely many elements And before the Thanksgiving break i wrote out some of those you know one plus n or one bar two bar three bar Now remember what it means to say that two expressions are equal in The coset group in the factor group What does it mean to say two cosets are the same it means if you compare the two coset representatives If you subtract the two that you get something that's in the subgroup That's what it means for two cosets to be equal so that for example when we said six bar was the same as two bar The reason that's the case is because six minus two This thing we called ab inverse right, but we're using additive notation here So a minus b is in the subgroup while six minus two is four which is in the subgroup Nine minus one is eight which is in the subgroup So here's the point note That if we take Any constant term constant means any rational or Any linear term that these The cosets for these terms such terms Must be different The statement is essentially this If I look at one plus n Should we call it one bar? Yeah, I'd prefer to do that. It's a whole lot easier to manage here That's a particular element of this coset group because I've taken something in the ring One it's a polynomial of degree zero. That's fine. And I've looked at the coset that it generates So I've added it to everything in here Is not equal to this which is not equal to Oops bad notation, sorry Apples and oranges Three plus n That's a lot silly. How could they be the same? Well, I mean think about over here when n was four z You know one bar was the same as five bar, which was the same as nine bar The point is that can't happen here. The reason it can't happen is How do you determine when two cosets are the same? You take the two representatives You subtract them and you ask whether or not you get something inside the subgroup You ask whether or not in this case you get some multiple of x squared minus two Folks if you've got something inside this subgroup There's only two choices. One is you're either looking at zero That's a perfectly good multiple of x squared minus two is x squared minus two times zero But if you look at something that's not zero inside here, it has to have degree at least two Because you're multiplying by some polynomial of degree at least two So here's the question. Can I hand you two constant terms and subtract them? And get a polynomial that has degree at least two, of course not. I get polynomials of degree zero Or hey, you know, I mean one bar is the same as one bar But that's only because you're looking at the same element twice if I take two minus one I get a polynomial of degree zero. It's not in there because nonzero elements of this thing are degree at least two if I take x plus n That's a perfectly good element inside r slash ny because well, I've taken some element of the ring I've looked at the coset that it generates technically what I've asked you to do is add x to everything in here And the claim is that this coset and for instance that coset can't be the same Why because when you subtract x minus one You can't get a multiple of x squared minus two because any multiple of x squared minus two has to degree at least two And x minus one is a polynomial of degree one So as long as you're mucking around inside either constant terms or linear terms There's no way that any two such cosets can be equal to each other That's going to be an important property that we will use later on In effect, what it means is this you know when we're working in z mod 4z the number one sort of behaves like the number one Inside the integers. It's just If you're working inside z mod 4z and you add one to itself four times you get zero Well, that certainly doesn't happen in the integers the point over here is going to be this if I hand you a rational number It's going to behave inside the rational numbers the same way that it behaves inside this factoring You know three plus three is six Plus three is nine plus three is 12 and none of those things are going to be the same as zero inside this factor Similarly x plus x is two x plus three x x is going to behave like x always behaves It's not going to somehow magically become zero Because constant terms and linear terms somehow can't ever trip over each other or somehow become the same as each other Because you can't ever take constant or linear terms and subtract them and get a multiple of x square minus two because x square minus two has to be two All right But and here is the key idea and I showed you this Before the break and I'll show it to you again because If you can sort of grasp what's going on here, then in effect you'll have seen the key To achieving this basic goal, which is this note if we look at this in Qx mod So inside this ring That's the same ring that we've been looking at here. I just wrote it out In in well in this notation just to start getting used to it look at I'm going to call this element alpha. It's the element that you get by looking at x bar I'll remind you what that means in other words take The specific element x Take the specific element x. Well, that's certainly an element in here And tell me what coset it generates inside this factor ring inside this coset ring in other words take x and add it to everything in there That's a perfectly good element in here. Now.  Well, I've asked you to take the same element twice In other words use the same coset representative twice. So this is by definition x times x plus Non-issue just multiply the coset representatives together. But here is the key This is the same coset as this coset. Why how do you decide when two cosets are the same you take This coset representative you subtract that one from it and you ask whether or not you get something inside the subgroup If I take x squared minus two do I get a multiple of x squared minus two? Yeah, I get x squared minus two times one So that's no big deal So the point is this folks what I've found inside this factor ring Is some element called alpha I wrote it down. There it is. It's not some mysterious thing. It's that thing With the property that when you multiply it times itself You get the same thing as two In other words you get an element whose square is two You might say well, and it's not really two. It's like, you know, it's two plus that it's the coset of two Yeah, but you know two walks and talks Inside the coset ring the same way it walks and talks inside a cube It doesn't become zero if you add it to itself or anything like that. That was these comments over here So somehow we've built a coset ring With the property that there is an element in there So that when you square it and you subtract two you get zero That's the same thing as saying that when you square it you get two So it would not be unreasonable to call this a square root of two Which I've built without this symbol at all I've just built by computing some sort of ring Inside which there's an element that behaves like the square root of two So here eventually is what our basic goal will lead us to I've just taken a specific polynomial x squared minus two That polynomial is irreducible inside cube bracket x y well, we proved that in class last monday You could use eisenstein's criterion if you want or hey, it's a polynomial of degree two It's got no zeros and q so we can use that other result however where you want to get that And what we've done is we've then built this ring And inside this ring there is something that walks and talks like a zero of this polynomial There is something with the property that when you square it and subtract two you get zero that thing happens to look like this So we've built a ring that has a zero for x squared minus two Does this ring contain the rationals? sort of I mean, you know, it's sort of The cosets of the rationals, but the cosets of the rationals behave like the rationals do Write down the details Wednesday But then the punchline is but i've produced a thing I've concretely written down a thing that behaves correctly whose square is two So the only piece that's missing is if we're going to try to use this as this System that contains the square to two We have to try to show that this thing is a field And this is what's going to act as our what we call field extension of the rational This is going to be the larger field inside which the rational sit and inside which we've found a zero for the polynomial x square minus two And that I think is the most daunting thing for For students to sort of grab their heads around the first time you see these factor rings. They seem like a mass And you're thinking well, how the heck am I viewing the rationals is sitting inside here? We'll play with that more But what's more important for you to see at this moment is that there is something Inside this ring that behaves like the square to whose square is two All right, so it will take I don't know and we'll take 15 or 20 minutes more tonight to start down that road and then we'll Basically be able to finish it up by wednesday this ring This factor ring turns out to be a field be a field Which and I'll use the words in quotes for now contains the rationals and Contains zero For the polynomial x squared minus two It contains some element so that when you plug it in for x Here's the element it's called alpha and you square it and you subtract two you get zero zero bar It's zero so goal Show that this thing that qx mod x squared minus two qx is actually A field we can do that We won't write down all the details, but we'll write down most of them What i'm going to be more interested in doing folks is playing up this Analogy between what's going on in the integers and what's going on in f bracket x and when we saw recall That let's see the ring z sub n Is a field if and only if n is what prime All right, so we've analyzed what these z sub p rings look like We proved this what two weeks ago. Yeah two weeks ago. Let's see it turns out Z sub n is the same as I could use the word isomorphic, but I'd prefer not to here is the same as the ring z Slash nz When I for example wrote down the multiplication inside z slash four z and I used The coset notation zero bar one bar two bar three bar, etc The multiplication folks was nothing more than multiplication mod well mod four there, but in general mod n So if you'd prefer to think of the ring z sub n as the numbers zero through n minus one With addition of multiplication mod n, that's fine Or if you'd like to view the ring z sub n as the cosets zero bar one bar two bar up through m minus one bar Just put bars on everything and have the addition and the multiplication being inside z mod n z You're getting the same sets with the same operations So I should be using the word isomorphic just because in one copy We're using cosets and the other copy. We're just using integers from zero to n minus one But you can view these as the same so the point is this When is the factor ring of the integers by some ideal a field answer Precisely when the number that you're using to generate the ideal is prime Now what did we do in our analogy between the integers and the polynomial rings the things that played the role of primes Are precisely the irreducible polynomials and so eventually what we're going to get to and we'll do it in the next I don't know 10 or 15 minutes and so turns out So restated restated We get z slash n z is a field Precisely when if and only if n is prime So the primes correspond to those integers that you use to generate ideals That when you look at the factor rings the corresponding factor ring is a field so I mean it's sort of interesting when you Hand me the integers It turns out there's three possibilities that can happen Hand me the integers then hand me an ideal Well situation one is that you've handed me an ideal That's generated by some prime number in other words that consist of all multiples of some prime two or three or five I don't care which one if you then form the factor ring what you've written down is the field z sub p If you give me a knot prime But don't give me zero yet. Give me a knot prime like six if you form z six Or in our new notation z slash six z If you form this factor ring Then what you get is something that isn't A field heck it's not even an integral domain. It's got zero divisors Inside z sub six Or if you want to think of it as z slash six z Take two bar times three bar You get six bar Which in z slash six z is zero So you've taken two non-zero things two bar and three bar and so you get zero divisors So things sort of crap out there the third possibility And it's one that we should take into account is The ideal that you've handed me is the zero ideal If you look at z slash zero z you look at z slash zero it turns out that's just z again Yeah, okay z bar, but it turns out you get something that's isomorphic to z Which is sort of in the middle. It's not a field, but it's also, you know, it doesn't have any zero divisors So that's sort of the third rail here You get either a field or you get not not an integral domain Or if you happen to mod out zero you get an integral to man It's not a field, but you just get the original ring back The punchline is the exact same thing happens in these rings f bracket x. So it turns out similarly The following is true in f bracket x Where f is a field Uh If you look at the factor ring ring f bracket x mod Let's call it g of x times f bracket x Is a field If and only if Well, if there's an analogous statement to what happens in the integers If and only if the thing that you're using For all the multiples of that fixed polynomial should be a type of thing that plays the role of prime integer And that was the notion of an irreducible polynomial g of x Is irreducible In f and we'll spend some time proving this We will prove this over the next 10 or 15 minutes of tonight and into wednesday prove this But this sort of again plays up this analogy between the integers and f bracket x We can go about producing or finding fields In the following way instead of finding a prime number like we did in the integers and go ahead and mod out We instead hunt around inside f bracket x find an irreducible polynomial Look at the ideal consisting of all the multiples of that irreducible polynomial and then forming the factor ring That will turn out to be a field So oh this factor ring Will turn out to be a field Precisely from This result why because in the particular case we looked at in q bracket x the polynomial that I handed you x squared minus two Is irreducible in q bracket x? And therefore when we form this factor ring in fact that field so how do we get here how to do this? How to do that And the answer is we need to talk about certain properties of fields. I mean we're right here To We need to yeah, we need to describe some ideals We describe certain properties that some I'll think of them as the nice or the special or the prime ideals special Ideals have And here they are definition Some ideals will have this property and some won't We're going to assume for the remainder of the semester that r is a commutative ring so r commutative It turns out you can talk about these ideas in the setting of non commutative rings as well, but We won't be interested in that and the technical details to start exponentially increasing So I don't want to go there with this then an ideal an ideal n of r An ideal n inside r is called prime Notice i'm not talking about prime numbers per se. I'm talking about An ideal being prime or not obviously in the setting of the integers it will be related to that idea In case the following is true for every pair a and b in r If a b is in n then either At least one of or b is in n So here's what it means for an ideal to be prime Remember by definition it's an ideal so it already has the absorption property So it means that if you take anything in the ring And anything in the ideal and you multiply them You're guaranteed to get something in the ideal that's already given piece of information by definition But what we're now requiring is something more than that the requirement is If you happen to multiply two things together and the result is in the ideal That the only way that that can happen is if one or the other of the things that you started with was in the ideal to begin with That's what it means to be a prime ideal And the second definition is this we call the ideal maximal in case The following is true First of all the ideal is not the entire ring And the ideal has the following property If j is any ideal of r With this containment being true n contained in j Which in turn is contained in r then the only way that can happen is if n is j Or n is r Here's what in english it means for an ideal to be a maximal ideal It means in effect that the ideal is as big as possible In the sense that well you have the ideal By definition, we're going to assume the ideal isn't the trivial ideal consisting of the whole ring So take an ideal that actually has some guts to it meaning that it's not all of r Maximal means that you can't slide any more ideals in between the given one in the entire ring I phrased it in the contra positive language Maximal means if you happen to have an ideal that sandwiched between it and the entire ring Then the ideal you're looking at is either it or the entire ring Okay, you can't sandwich anywhere in between question This should be Then oh j equals r. Yeah, thank you or j equals r Thank you. Yeah, so if you have an ideal We're calling it in then this ideal is maximal if it's as big as possible in the sense that there's no We'll call them proper ideals that you can sandwich between it and the entire ring Let me well, we'll get out here a little bit early today Let me at least Give you a couple of examples of ideals that aren't prime or maximal Just for contrast And then we'll go ahead and write down a couple of examples of ideals that are prime or maximal inside the integers And then we'll call it a night. So example. Let's look inside z in z Oh Tuesday, let's look at uh six z is not prime Now notice i'm using this adjective prime Corresponding to an ideal not to an integer Why What does it mean for an ideal to be prime prime means every time you have a product that lands in the ideal The only way that can happen is if one or the other of the two things that you've used was in the ideal to begin with It's not prime because I can find two things Both of which are outside the ideal folks neither of these are multiples of six That when i'm multiplying them together give something that's in the ideal So there's a not prime ideal in fact in general in general If n is composite meaning it's the product of two integers less than itself then And z is not prime Now if you're thinking well the next statement is if you look at all multiples of a fixed integer and the corresponding ideal is prime Then the integer is prime. That's good intuition, but it's not 100 true. It's like 99 true on the other hand example This one's sort of interesting zero is a prime ideal Of z Well, it's an ideal. That's not an issue question. Does it have this property? Does it have the property that if you take any two things inside the integers And you multiply them together And the product is in the ideal Is it the case that one or the other of the things that you started with had to be in the ideal? Well, yeah If you take inside the integers two integers and you multiply them together and you get something inside this ideal It means you've gotten zero That's the product of the two integers folks The only way you can get zero is the product two integers Is if one or the other of the two integers was zero to begin with in other words if one or the other of the two integers Was already inside this ideal So the proof is reason there are no zero divisors inside z Or the fancy word is z is an integral domain If you have the product two things that give zero then one or the other has to be zero All right now let's finish up what's going on inside the integers turns out And i'm going to haul out a number theory result here. It'll be a straightforward one In fact, it's one that we used like in week three or something like that turns out if p is prime A prime number prime integer Then The ideal pz Is a prime ideal What does it mean to be a prime ideal? So it means if you take two things in the ring and you multiply them together and the result lands inside the ideal The only way that could happen is if one or the other of the two things Was inside the ideal to begin with so suppose you take two integers a and b And suppose that when you compute their product That you get something inside this ideal Then what i want to be able to conclude is one or the other of the two things had to be in the ideal to begin with In other words, what we're supposing is that when you look at the product ab You get some multiple of p I don't know where z is some integer So what does this mean in other words what we're saying is that the product ab is a multiple of the prime p ab is a multiple Of the prime p, but then the point is but since p is prime p is prime If you have the product of two integers is a multiple for prime then Either a Or b Is a multiple of p And that results given a name. This is called euclids one Have a multiple of two integers that turns out to be a multiple of some prime number than one or the other had to Be a multiple of that prime number to begin with and that is the result i e Either a is in pz Or b is in pz. So in fact what we've just done folks if we've identified all of the prime ideals inside z They're almost exactly the ideals generated by prime numbers Where we understand prime numbers to include the negatives of the things that we're used to calling prime numbers But we also have to throw zero into the mix too zero is the prime ideal inside the integers If for no other reason than the integers it turns out to be an integral domain questions comments All right, what I want to do then is I'm going to give you the last homework assignment of the semester. It'll be due It'll be due a week from wednesday. So it'll be the standard homework Scheduled, but I'll have them graded and available For return by the following friday so that you can use it to study for the exam and here it is at home Again last assignment of the semester is this uh in section 27 Problems five through nine 14 18 and 19. I want you to turn in 18 and 19 And then in section 29 Problem 18 a and b I want you to turn that in and two more Give the isomorphism We'll give that word on wednesday from the complex numbers to this factor ring mod x squared plus one times r bracket x So it turns out we will eventually show that that's a field We're on our way to doing that in fact that field turns out to be a field isomorphic to the complex numbers. That's first and secondly mimic Example 29.19 To find a field Field having eight elements And let's see. What else do I want you to do here? Uh, give The multiplication table for the field table x bar b denoted by Alpha as we did here All right, we already at least tonight sort of opened up this idea that inside a factor ring Well, if you look at a factor ring that looks something like this There's the coset generated by x That's this thing and it might actually have certain properties that we can identify like its square might be two It turns out you'll be able to play the same sort of game by looking at an appropriate factor ring of z2x And they show you how to do that in Example 29.9. I want you to turn both of those in as well. Okay, and again, that'll be the last homework assignment Let's see right, so So this will be yeah, this will be due Wednesday December 5th, but since there's no class Just get it to me email Or fax or however you want to get this assignment to me will be fine And then I'll have them great


Let's just talk, try and get some exchange going between the two of you and then let's open this up for wider discussion. I was just, I'd be interested in both your reactions to this. I was very struck about your images of the gated community, the protection of private space, which inhibits people kind of living out. I was thinking about it personally in the context of the constituency that I represented for 23 years, where in the poorest parts of the constituency what people long for is precisely that. When the debate is about what you spend on a housing estate, what people want are entry funds, they want secure gates, they want a way of, if you like, sort of locking themselves in instead of living out. This sense of, which I think is incredibly attractive of living out that you describe, is something which in my experience, and I'd be very interested to hear other views, is something which is created by mixed communities, people from a range of social backgrounds, ethnic backgrounds, age and experience. That really is the absolute prerequisite, because it's that that creates a sense of safety. Safety is a sort of prerequisite to porosity and this sense of opening up that you describe. I was interested in your references to Daraf i, because I know, I've got to know, so you know, Daraf i quite well through the work I do with a charity which works in the communities there. And there are contradictions, you know, the contradictions are family shacks in which ten people live, which are spotless, beautifully ordered, but where the order within the shacks is constantly threatened by crime. But there is plenty of living out, because there isn't enough space for ten members of a family to live in. So, I mean, there are all sorts of contradictions here, and one of the contradictions or the facts I think it's important to build is the universality of the appeal of this, which builds on certain absolute prerequisites. One is safety, the second is actually a respect for property, what is mine and what is not shared. And then I think the third is the availability of space to live out. Now, you know, which takes me I think to the final point, which is, you know, where is the state in this? And you see the only state intervention in Daraf i is to spray the rubbish in the summer to keep the unofilus mosquito, which brings malaria at bay. But if you think of communities in our city, and I suspect in New York, what private places schools are when the kids aren't there, what private spaces, PFI hospitals have become where the community can't use them, except with the consent of those who own the school. So, I think that, you know, I think that sort of empathetically, there's such enormous appeal and a sense of warmth in this. Underneath, there needs to be a discipline of organisation which realigns the relationship between the informal community and, if you like, the property of the state. And it's the state that has to let go and trust the community. Yes, I think the way I... Do you want to think about that for a minute and maybe, Suket, Suket, I've had this bug and I know how wretched you could feel. No, it's all right. Absolutely, how rowy. Double whiskey, we'll see. No, I'll respond to you about this and something you and I have talked about. And I'll respond to you in a very personal way about this. I grew up in a housing estate in America, unbelievably grungy. I guess what you call in this country a sink estate. I mean, it was a place called Cabrini Green in Chicago in which people lived behind locked doors, two or three of them. There was nobody out in the lawns of the estate. People were afraid to go up and down the elevators and so on.  But there was nobody to see. The city had abandoned us. It was really... I'm not very romantic about poverty. We were something they wanted to disappear in time after 40 years. It was a huge project. At one point, people in the community, since cops wouldn't go in, ambulances wouldn't go in, hired security guards to be out in these open spaces from five to seven every night. And people, because they're these armed, it's America. The security guards are armed. They're willing to shoot to kill. It's not Britain. People felt safe to come out. Those two hours, which had formally been sort of adolescent criminal playtime, became the least dangerous hours. The least dangerous. Because there were people out and about. And what disturbs me about housing for the poor, I showed you something that the World Bank did in Delhi, which was appalling, which is create housing for the poor, which replicates what went on in Cabrini Green. It shuts people up inside. It puts the security as presented to them as a matter of a defeat of a boundary than porosity. To me, this is an issue about people think if they've got five locks on their door, they're safe. But they're not. If there's nobody about, they get in the elevator, they're going to get mugged. Or walking on the street, going to a convenience store. They're going to get mugged because they're the only person on the street. It's been sold to them, for the poor, that a gated community will actually make them safer. To me, this whole issue of security is a kind of, it's false, and it's a kind of very bourgeois notion of what makes people secure. That if they can only lock their doors and nobody can come in, that they'll be safe. I thought I have to say that. I spent a lot of time in Darwin researching my book and then going back since. I also spent a lot of time in the Brazilian favelas, particularly Rio. I looked at the whole programme of specification. The difference between the Latin American and African cities and Indian cities is that we don't have drugs and guns. This crime, and I've lavishly documented it in my book, but it tends to be more organised. You're not going to get mugged in a Bombay slum. You won't get carjacked. What happens in Darwin is that most people leave their doors unlocked during the day and often at night too. I remember going to a leather workshop in Darwin. He lived in a two-floor shack and his workshop was on the ground floor. He had four stations where he hired people to make little leather goods and purses and bags and so forth. He lived with his wife and two children above the workshop. He worked 16-hour days and he sees his kids for 10-15 minutes in between breaks. The government wants to demolish Darwin and there is this scheme that they've come up with called the Slum Rehabilitation Authority. 70% of the people in an area designated a slum and there's no heavier word in the English language than the word slum. Once you impose it on a group of people, they're finished. If the residents of what the government designated a slum 70% agree, then a builder can come in and demolish the entire neighbourhood community and create luxury housing along with replacement housing for the poor. Now I've looked at these replacement buildings and I know you have too Richard. They repeat the worst mistakes of council housing elsewhere in the world. As if we're beginning from first principles, we've learned nothing. He told me that the government offered him a 270 square foot flat which has its own indoor toilet which it doesn't have right now. It's brick and mortar. It's not bad, but they're not giving me a workshop in the same building. If I want to see my kids, I'll have to commute for an hour. As I walked around the area, I realised that they've actually built a community there. It's not easily transferable somewhere else into blocks of high rises. That community protects them against crime. They leave their doors open. They know who their neighbours are. In Bombay, this kind of anomied alcoholism drugs, you mostly see it in the transit or replacement housing for the slum dwellers who have been evicted from these places. The narrative of crime in cities all over the world, in Lisbon, there's a place called Calvado Moro, a group of people from Cape Verde. I went over there. It's a piece of the city that the developers want because it's very central. There's all these stories in the Lisbon papers about the crime in the barrio, in the tabloids of the police coming in and drug dealing in the barrio. In all of these places, I think the narrative of the crime is much more lurid than the crime is more lurid. It's exaggerated. If you compare the statistics to the perception of crime, we see that in the US as well. As soon as the Black Lives Matter women started going on, the police forces across the country started spreading a kind of propaganda about shootings increasing, the streets being given over to groups of rioting young black men. If you actually look at the statistics, New York has never been safer. So that perception of crime, I think, serves certain interests. When we read these stories, we've got to be very careful about if it's really the poor that want five extra locks on their door, or are they being convinced to put five extra locks to guard against some sort of unseen enemy. Let's just think about how this sort of transition from the, if you like, the kind of anxious community is achieved to, we achieve a transition to the kind of porous community. I think you're absolutely right, Suketu. I think that there are many geographic areas where the risk of crime is overstated. But it's also overstated by other people who live there because they feel unsafe. So there is this, if you like, this cognitive dissonance, but the cognitive dissonance is very destructive of what the kind of narrow place kind of experience Richard. The fact is that all over this city in New York and so forth, there are communities that show this kind of resilience and ability to, I love the idea of minimizing the importance of home because people live out more. And that is a very, I mean it's a rather wonderful ambition, but I think the point is it doesn't happen by chance that there's a contradiction between the impulse that creates it and the pretty clear dissonance. You know, I think one way to think about this, and I should have said this before, but one way to think about this is that we put, I think too much, if we think that a porous city is going to make everybody mutually tolerant and they're going to be nice, you know, it's rubbish. But because we need to learn from why it's rubbish, which is that there are dimensions of urban order which are purely physical and which are nonverbal. And the kind of porosity that I think ensures the kind of urban order is a bodily comfort being with people in the midst of people who are different. It's something visceral. It's, you know, the hand extended to the stranger who's trying to get to work. A lot of, in my experience, I mean one of the things that's terrible about academic urbanism is it translates the physical into the verbal all the time. And there are lots of translations that don't happen. People have a physical experience of the city. They have nonverbal knowledge, which they can't put into words. If you're comfortable being pressed up against somebody who is sweating profusely and you're in a carriage together, very familiar to any New Yorker in the subway, you're practicing a kind of civic order. But you couldn't put it into words. And I'd like to see urbanists concentrate more on what can't be represented or symbolized in the way of saying these, you know, talking about diversity, talking about community. I think these are things that are made with our body, you know. And the whole really comes from the agglomeration of fragments of behavior. I was observing exactly this this week getting on to from the northern line where you kind of bend over and you've got somebody's head in your armpit to the Victoria line where cues form.  And the way people fit themselves into each other, I mean, that's a pretty universal experience of living in London every day. But let's open this up a bit. And have we got microphones? Let's invite your questions or your challenges or controversy to Suketu or to Richard. Yes, gentlemen in the middle who's holding his. That's you. Hello. Thank you. Brilliant. Speak up nice and loud so everyone can hear you. Wonderful talk this evening. I feel very humble sitting here amongst the company. I have one question I'd like to put back to you, Suketu, with regarding to your three rules. Don't exclude anybody from the conversation. I say or ask that in relation to my own personal experience as chairman for a residence association that is currently under proposal for a regeneration. We just don't seem to be getting anywhere talking to our housing association and feeling that our views are being heard. What could you propose in light of that? So the question is that I understand that you're chairman of a residence association but you're being excluded from the conversation of the housing association. We're being condescended and patronised. Is the housing association wanting to do to you and your community things you don't want? Yes, yes. For example, it's a hot potato at the moment, isn't it? All over London everybody's talking about regeneration and I'm mindful of the fact that our estate needs it. I don't deny that, it's undeniable. But I feel we're not part of the conversation. Our thoughts and views just aren't being actioned upon. This is where you start reducing London's livability index by democratic protest. I think if they're not letting you into the conversation you have to live there and so you have to take control of the conversation. Really there is no other way other than democratic protest. This is that if you look at community boards, my son in New York just became a member of the community board of Park Slope. He has these meetings and there is a role for the gadfly. I'm all in favour of gadflys who go up to these meetings and declaim. At the very local level, like the housing associations, this is where it's really inspirational to see democracy in action. I'll give you an example. I've been following a group of a South Asian housing rights organisation in Queens. I once went with them to a building full of Bangladesh's in Woodside in Queens. It's a whole building full of recent immigrants. They're paying very high rents. The landlord is Greek himself an immigrant. I went to a meeting that the housing advocates had called. All the Bangladeshis got down in the lobby and there was the Greek man, the landlord in the back with his arms crossed, just watching the tenants as they were trying to organise themselves. This young woman gave this incredibly stirring speech about the nature of democracy in the US and how it really begins with this residence association. These people from Bangladesh should come from a place of great political volatility but they also understand that democracy, civic action can get them things. I went into the apartments and I saw the kind of accommodations that they had to make. For example, there was an air conditioner that had been left by the previous tenant but the landlord wouldn't remove it. It had been painted shut into the window. The residents put a big gift wrap around the air conditioner. It stuck out but it became part of the ornamentation. There were many of these compromises but ultimately what they wanted was to lower their rent and get services. When this housing advocate went there and explained to them, brought them into the conversation of civic engagement, they mobilised. They took the landlord to court, their rents got lowered and in this case there really is no substitute for legal action, civic engagement. That's what I think the whole Black Lives Matter movement is about.  We'll stand out your window and shout as loudly as we can until you listen to us. Good. Okay. There you are. So who'd like to follow that? Yes. Can I see all the hands because we'll get as many as we can. Okay. We'll take your question and then we're going to take all those contributions. Don't anybody else put up your hand and then we'll be able to get responses to all those before eight o'clock. Okay. So my question is to Richard. Richard's on it. It's not a Richard. Although I would like to read. Anyway, Michael, I really think this concept of porosity is a fantastically useful concept and I love seeing these illustrations of borders and boundaries. But what I was trying to understand is are these borders and boundaries physically constructed or are they also socially constructed? They may not have any physical manifestation. Well, I wouldn't put it as an either or. That in the case of the Van Eyck, that's an architect, a great great architect who has a social vision that children should learn the city and thinks what could I do in making these parks to make these kids learn the city? How can I make them street smart? And there are physical means he does it. I don't think he ever, he was a very dower Dutch. I don't think he could play with the child to save his life. In that case, it's, I mean, he enabled something physically to happen. And indeed he pushed it that way by not, you know, by leaving these edges unprotected. I don't think he was, what I'm saying about this is we often think that, you know, communities or environments that are design driven are somehow against the way people live.  And that design should follow dwelling. I think that's just too simple. With gated communities, for instance, you know, well, as a designer, I'd never do one of them. I think it's immoral to do that. It's something else, unethical to do it. But I think the object of design should be to take them down. Some ways you can do that are economic by making housing in covenants which exclude people racially or religiously illegal. That's a way to create a boundary condition. Sometimes you can do it as has been done in some communities in Latin America. By getting this great lesson of Bogota by taking away highways and just physically letting communities grow into each other. I mean that's a physically driven design but it has a social point. So I don't see it as an either or. What it takes as an urbanist who is not a servant of its developers. But works with the people. But once you get to that condition, it's not an either or. Right, thank you Richard. We're going to do, you've got about 20 seconds each to make your point, to change the world. So we'll move around quickly with the, let's start over here. Good evening, thank you very much for both of your talks. You'll need to speak up. Okay, hi, thank you. One of the things that I would like to ask you both, Suketu and Richard perhaps to play off against each other is Richard I really theoretically enjoyed your idea of living out as a way of developing a porous city. But the part of me that has been harassed and had friends harassed by the police for being out had a heart attack. But I did think Suketu of your first rule of being able to be inclusive, which is to be inclusive in the eyes of the law. And I wondered how you would both work together and to resolve those differences between living out and policing and the law. Okay, let's go up to the right-hand side. We need to worry about time. Okay, the gentleman who's got his hand up. Actually there are quite a few of them come to me. Tess, we can't do this because we have to leave here at eight. Thank you very much for your insights. I would just love to go back to the point about the narrative on crime and the narrative about porous. I'm a planning student from UCL. I'm just wondering how can we unwind this kind of forced narrative to convince people that mixity and porousity are actually good things for a city. Thank you. I've just been reminded that we actually have to be out by eight o'clock, so I'm afraid we're going to take two more. And then we'll ask for final responses from Suketu and Richard. The woman right in the back row, and then have we got anybody in the middle block?  You spoke about the vibrancy of poorer areas, but I was wondering whether you thought there was any way that the people who were putting out that cultural capital of vibrancy, so the poorer people could benefit from that, rather than just wealthy people who come in and have cheaper rents, but actually it costs the poorer people more and they don't really get a return. Thank you very much. Final contribution. Since this isn't talk about inclusion, I was just wondering what are you views on the refugee crisis and how can we make sure that these people are included in cities? What's the role of politics versus civil society? Right. Thank you all. Suketu, do you want to… It's a broad spectrum of questions, but I'll try to… Especially solving the refugee crisis. Yes, exactly. We'll do it tonight. You're actually right about the vibrancy of poorer areas. One of the ways in which slums are blighted is by saying that they are economically unproductive, but anyone who's walked into Dharavi knows that it's a tremendous production. It employs more people than the rich areas of the city. This is where… There's all kinds of little industries and it's not just in places like Dharavi. If you look at music in areas of New York where hip-hop has come from. Hip-hop is a cultural product which brings real economic value to the country. The same sort of thing in the Comunidadias of Brazil. That's a tremendously vibrant culture which translates into money. The thing about… You made this, I think, very valid point that being a woman in a Bombay train or a porous community on a street, this risk of getting harassed, you're actually very grateful for police protection against some of these people who are out to attack you. We need security, whether it's private or public, and we need laws. I grew up in a building in Jackson Heights in New York, which is the most diverse neighbourhood in the United States. I grew up in a building full of Indians in Pakistanis, Haitians and Dominicans, Jews and Muslims. The building was owned by a Turkish man and the super was Greek. All of these communities, these were people who were killing each other just before they got on the plane. So what happens when they come to New York? It's not that we start loving each other. We say horribly racist things about everyone else in our own homes. But there was a central court here where all the kids played together. So there were a couple of factors at work. One was that we understood we were all there to make a better life for our kids. But we were also sending money back to hate groups in our countries. But we couldn't act out on that hate in America because we realised here the law won't let us act on that hate. This is the benefit of things like hate crime laws. There is a role for a certain amount of state supervision. Refugees, I think it's going to be the defining issue of the 21st century, this kind of mass migration. Also because the other defining issue is the great surge of wealth upwards, the fact that the 80 richest people on the planet today own more than the bottom half of the world combined, and it's only getting worse, that there's going to be a channeling of the outrage onto the refugees as we see massive numbers of people on the move. So we're going to have to find some way of accommodation. And I think that Tessa has read another piece that I've been writing where I talk about interlocals, that is people who are not nationalistic but they have an allegiance to neighbourhoods, to the neighbourhood that they came from and the neighbourhood that they are living. And it's a beautiful way of belonging where you don't have to be necessarily British or even a Londoner. You could have an allegiance to Evelynton or Brixton and also to Anderi in Bombay. And you move between these and your allegiance is to the locals. So I think it's those local allegiances that might be the answer. Richard? Well about this refugee thing you bring up something that's very personally painful for me because I worked in the UN in the 90s. About resettlement of refugees in Lebanon, which had a 14-year civil war. The rates of displacement were like those in Syria today, which by the way I'd be amazed if it's less than a 14-year war. But what I learned about that, we made refugee camps because there were hundreds of thousands of people who were displaced. And we shouldn't have. We should have straight away gone into ways of filtering people into local shelters using found spaces. We should not have these, the standard way of making a refugee camp is to use a military model. They're all orthogonal, they're very efficient provision of services. And they usually make the experience of being a refugee worse because completely isolated. And the big challenge now, not in this country because you're very ungenerous about refugees, horribly. But in Germany, not something to clap about, deeply ashamed of, but in Germany which has been generous. The problem with dealing with those 680,000, that's our latest count of refugees is how to get them out of refugee camps. And the Germans are, I must say, it's really inspiring to me that they've understood that the whole problem is how to not incarcerate a refugee in the mentality of being other. But I don't think as a whole Europe is going to manage it that way. The idea of porosity I have, I guess is also built on that.  But to be absorbed into another culture where you can get on, you know, most refugees incredibly hardy. It's people who went across the sea and the grease, these aren't shrinking violets, you know, they're hardy. But for them, the politics of dealing with their situation is to get into an environment which is porous, rather than isolates them as suffering other people. So thank you very much for your question. OK, so we finish on perhaps the biggest challenge to porosity. And can I just say thank you so much, Richard and Tsuketu? I mean, I think you've given us the most stimulating, optimistic, but also challenging presentation. And I think everybody's going to take that away with them and keep on thinking about it. This session is going to have a long afterlife. So can I thank all of you for your questions for coming? And there we are. Thank you.


I mean, ultimately, you all have the North Star of winning a national championship. And you have the tools and you have the resources, you have the talent, you have the coaching staff, you have everything you need to be able to accomplish that goal. But in order to do that, it comes down to two things. There's two things that define whether or not you guys will be able to win at a consistent clip and whether or not you guys will be the ones that cut down those final nets. And those two things are preparation and performance. Everything comes down to preparation and you have the talent, you have the resources, you have the coaching staff to be the best of the best. And now it's completely up to you guys. And in order to do that, you have to hold yourselves accountable and you have to take full responsibility for every decision you make. You can't blame, you can't complain, you can't deflect, you can't make any excuses. You guys have the keys to the car and whether or not you do anything with it is completely up to you.


Welcome to a tutorial of Bookery, version 4.7 on iOS. This video was created with support from the Government of Canada's Social Development Partnerships Program Disability Component. The opinions and interpretations in this video are those of the creator, and do not necessarily reflect those of the Government of Canada. It was produced with site of assistance. Bookery offers an interface that is quite simple and easy to learn. While there is no read-to-end feature, VoiceOver advances automatically to the next page once the current one is read. However, advertisements are presented as you use the free version of this app, which can be problematic for VoiceOver users. The app supports books in EPUB 2 and PDF, along with a selection of popular classics ready to download as soon as it opens. Additional books can be copied to Bookery right from the Nells repository, downloaded from Project Gutenberg or side-loaded from Dropbox. Here, we're looking at the record for Treasure Island on the Nells website. When we press Download EPUB, we're asked where to store the book. You may need to press More first, but we're going to select Open in Bookery. Treasure Island is now open in Bookery, showing up in the reading pane. To ask VoiceOver to begin reading, just swipe down with two fingers. To access reading features, just double-tap the reading pane. This reveals seven buttons at the bottom of the screen in the center. We'll now go through each one from left to right. At the far left of the button bar is Navigation. To move to a different chapter, just press Navigation, swipe through the list until you find the desired section, and tap it to go there in your book. Annotate is used to add tags to your book. Theme and Display let you choose visual reading preferences. And sadly, the Listen feature is only available in the Premium Edition. To find text in your book, press Search. Type in the phrase you wish to find, then press Search on the right side of the keyboard. Bookery will then position you on the next page that contains your query. Three unlabeled buttons are also shown at the top right of the screen. From left to right, they are back, next, and close. The last button in the bar at the bottom of the reading pane is called Info. This displays the title, author, and publication details, along with file info of the book you're reading. To add a bookmark, press the unlabeled button at the top right of the screen. To review the bookmarks you've set, press Navigation, then tap the Bookmarks tab at the top right of the screen. Bookery makes it easy to find and read many different books, and has a clean and usable interface. Once you get the hang of it, it works well with VoiceOver.