I will be presenting a unified structural equation modeling approach for the decomposition of rank-dependent indicators of socioeconomic inequality of health. And this is joint work with Hido Eregers, who's a colleague of mine at the University of Antwerp. First of all, what is socioeconomic inequality of health? Well, it deals with two dimensions or two variables. On the one hand, we have a socioeconomic status variable, like, for instance, income, wealth, or consumption. And on the other hand, we have a health variable, which can also be an ill health variable. And then socioeconomic inequality of health tries to measure the degree of correlation between these two variables. And this is usually done by means of a rank-dependent indicator, which is a weighted average of individual health levels of individuals from a targeted population, where the weights are determined by the ranks of the individuals in the socioeconomic distribution. The most well-known rank-dependent indicator is the health concentration index, of which there are two versions. We have the relative or standard health concentration index, and then there is the absolute or generalized concentration index. And these indices, they express the relative or absolute differences in health between socioeconomic status groups. These concentration indices, they can be graphically represented by means of concentration curves. On the left-hand side here, you see an example of a relative concentration curve. Whereas on the right-hand side, you see an example of a generalized concentration curve. And the generalized concentration curve is linked with the relative concentration curve by multiplying the relative concentration curve with the mean level of the population health represented by mu. Now, further on, do we need to interpret these graphs here for this particular example? On the vertical axis, you see the cumulative proportion of our health variable, which in this example is an ill health variable. It represents the infant mortality. Whereas on the horizontal axis, the x-axis, we have the cumulative proportion of our targeted population, which in this example are babies that have been born alive, the live birds. OK, and so what do we see then here? Well, that infant mortality is concentrated among the poor people. Given that on the x-axis, we have ranked the individuals, the babies from poor to wealthy or from poor to rich. So we have ranked the babies in ascending order of the wealth of the households in which they have been born. So they are ranked from poor to rich here. And what do we see here? That most of the math is concentrated on the left-hand side, so that infant mortality is concentrated among the poor people. And the associated concentration index will then be negative, meaning that we have a pro-poor bias of the distribution of health. And concentration index is computed as twice the area between the concentration curve and the line of perfect equality, the 45-degree diagonal line. OK, so this is just in order to set the scene a little bit about the aim of this work. In this setting, in the setting of concentration indices and concentration curves, what we recommend is the use of a structural equation modeling framework for a regression-based decomposition analysis in order to explain the generalized concentration index denoted by the GC. So we look at the generalized concentration index, the GC, the generalized or absolute concentration index, which we wanna explain. So we wanna find out what the reasons are for a particular value of the GC by means of a regression-based decomposition analysis. And so the GC is our measure of the correlation between health and socioeconomic status. And we propose the use of a structural equation modeling framework since we are going to say that it will be a more proper way of doing regressions that correspond well with decomposition analysis. And there are several existing decompositions which we will run through. First of all, I will be discussing two one-dimensional decompositions, the most well-known of which is the health-oriented decomposition proposed by Wachstaff, Van Dorslar and Matanabe in their 2003 Journal of Econometrics paper in which health is subjected to a regression. In previous work of ours, we also proposed another one-dimensional decomposition in which we regressed the socioeconomic status variable instead of the health variable. And also we proposed a two-dimensional simultaneous decomposition in which we regressed both health and the socioeconomic status variable on a set of explanatory variables. Okay, and I will run through these decompositions. I will shortly introduce them to you. Okay, for that we need some notation, some machinery. First of all, we consider a population of N individuals ranked from one up to N. And then we have a health variable H with individual health levels. This health variable is a non-negative ratio scale variable or a cardinal variable. Then our data set also has SES variable with individual levels, Y1 up to Y1, which we are going to rank from least well-off to most well-off. So we have some households then and based on the SES variable, we will rank the individuals from least well-off to most well-off in order to get our rank variable in. Okay, based on this rank variable, we will be computing the fractional ranks for which the average equals a half. And then further on, we will be computing the fractional rank deviation, which is the deviation of the fractional rank from the average fractional rank for which the average equals a zero. And it will be this variable, the fractional rank deviation variable. That's also being used in the definition of the generalized concentration index, the generalized health concentration index, of which you find here two definitions, the product definition as well as the covariance definition. So it's basically the covariance between the health variable H and the fractional rank deviation variable D multiplied by two. And so measures the correlation between our two variables H and D. And this measure is bivariate. So it consists of two variables, two dependent variables. And so we say that it is bivariate. It's a bivariate measure. Okay, first of all, a quick overview of the decompositions that I'm talking about, the most well-known of which is the health-oriented decomposition, which starts from a regression of our health variable H that we try to explain by means of a set of K-expandatory variables, X1 up to XK. And then we use the product definition of the GC and do some math. So we plug in our regression for H into the product definition of the GC to finally end up with the health-oriented decomposition to which we refer to as decomposition one, which is a sum of K contributing factors or deterministic components determined by the explanatory variables X in relationship with the fractional rank deviation variable D and then we have a residual term. Okay, we can do the same thing for the fractional rank deviation variable D. We can propose a regression for D given by a set of explanatory variables Z, ranging from Z1 up to ZQ. And then using the covariance definition of the GC and we do some mathematics, we obtain the rank-oriented decomposition to which we refer to as decomposition two, which contains a set of Q contributions, one for each of the explanatory variables Z and then again a residual component. Okay, these are two one-dimensional decompositions. Now, since our measure, our socioeconomic inequality of health concept is bivariate, we can just as well regress both H and D simultaneously by means of a bivariate multiple regression model. And we have done so in previous work of ours. Now, typical for this bivariate multiple regression model is that we have used the same set of P explanatory variables as one up till SP. So the explanatory variables both for H and D are the same. And doing some mathematics using the covariance definition of the GC, we obtain the following decomposition. It's a simultaneous decomposition which we refer to as decomposition three. It consists of a sum of P direct effects given by the variance of the individual explanatory variables and then weighted by some coefficients plus a set of terms that reflect the correlation structure between the independent variables S and then again a residual term. Okay, so we have three components here that make up our decomposition to which we refer to as decomposition three. Okay, now, while having done this work, we got some criticisms related to it. And the first criticism that we got related to the use of the bivariate multiple regression model and the associated decomposition was that we used the same set of variables to explain both H and D, which may not be appropriate given that the determinants of H and D may not be the same. And then more importantly was that actually in all of our decompositions, we did not include the variable D as a predictor in the regression for H and also we did not include H as a predictor in the regression for D. We left those variables out of our regressions. Whereas actually in empirical work, it might be the case that health is potentially both a cause and a consequence of socioeconomic status, of our socioeconomic status variability. So it might be that there are some feedback mechanism that there's a reciprocal relationship between the two variables, but still we did not include in any of our regressions, we did not include any of the variables that are part of the GC. We did not include any of those as regressors in the regressions. And why did we not do that? Well, it's actually meaningless to do that because we are trying to explain the GC and which is bivariate, which consists of two dependent variables, but using one of those as an explanatory variable. So in order to try to explain it, it's just meaningless, it's just treating those variables both as a dependent and as an independent variable. So actually we are not explaining anything at all then. If we are just going to use either of these variables, both as an explanatory variable, as an independent variable, then what we get is an artificial result and that translates itself by means of a zero residual component. And so the residual will be zero because all of the variation will be absorbed by one of our dependent variables, which we use as an independent variable at the same time. So we will get an artificial result and this artificial result also happens when we use a proxy variable for one of the dependent variables, like for D, we use consumption, income, wealth, and so you see that often appearing in papers, but these variables are highly correlated with D because D has been composed from those variables. So it doesn't make any sense to include those variables in the regression, which is used as an auxiliary step in order to explain the GC. So first we have the regression in which we wanna explain health or D and then that regression, those results are used in order to explain the GC. Okay, here you see an example of a simple regression of H on just one explanatory variable, which is then D, and the definition of the estimate for the corresponding coefficient, the slope coefficient, is then the covariance between H and D divided by the variance of D and that gives us just the definition of the GC for which then the residual component is completely equal to zero. But actually we have not explained anything at all. It looks like we have explained a lot, but it's just an artificial result. Okay, still using decomposition one, our most well-known health-oriented decomposition, this procedure has oftentimes been done and it's indeed true that when using SES as an explanatory variable in the regression for H that SES comes out as an important determinant of health and then going one step further then in order to use that result for the decomposition analysis, it makes the contribution of SES to the GC artificially large because the GC is being defined by SES itself. So using SES in order to explain the GC is not a good thing to do in this way. Using SES in order to explain health, okay, but then using this result into this result, this leads to an artificial result. So how do we combine this empirical results with the regression-based decomposition methodology? So we have this empirical result but we don't have the right machinery actually to use it, to make use of it. Well, therefore we have proposed the structural equation modeling approach in which we have in a first equation adopted D as an explanatory variable in the regression for H and H as an explanatory variable in the regression for D. And both D and H are assumed and don't you then in that case, and we then estimate the parameters using a generalized method of moments estimation procedure in order to obtain consistent estimates. And this estimation procedure makes use of instrumental variables. It's an IV estimation procedure. Doing some rewriting by replacing the right hand side and dodging as variables by their respective equations. We obtain only exogenous variables, the X and disease, the X originally explaining H and disease originally explaining D. We only obtain exogenous variables on the right hand side and this way of rewriting is referred to as the reduced form of the salmon which we only have exogenous variables on the right hand side. And what do we obtain then by rewriting this? Well, we again obtain the bivariate multiple regression model. So which includes the same set of explanatory variables and which can be directly estimated using OLS. So we don't need GMM in that case. Okay, so the bivariate multiple regression model is just another way of rewriting the structural equation model. That's allowed to depend on different sets of regressors and that includes both D and A in the regressions for H and D respectively. Okay, so the same approach results in our simultaneous decomposition, decomposition three based on the bivariate multiple regression model. It integrates the feedback mechanism between the variables H and D which are allowed to depend on different sets of predictors. So this refutes the two criticisms of the bivariate multiple regression model and the resulting decomposition three. Okay, let's quickly illustrate the SEM approach using some data. Data that involves stunting or malnutrition of children below the age of five in Ethiopia and that come from the latest round of the demographic and health survey of Ethiopia. It contains 9262 observations and we define stunting or malnutrition as having a low height for HZ score where the Z score is smaller than minus two standard deviation from the median of the height for H a variable of well nourished population and reference population. And we transform to this stunting variable onto a unit scale, unit interval for which individuals have been assigned a value of zero if they are not stunted and a value between zero and one in which they are stunted and the value then indicates the degree of stunting. So actually our response variable is the degree of stunting which is an ill-health variable with one being assigned to the child that is most stunted. As explanatory variables, we selected a set of eight variables which we partitioned into exogenous and instrumental variables in the case of a GMM analysis and we performed weighted regressions. Okay, here are some descriptive statistics still. We used the weighted fractional ranked deviation variable based on the wealth indices provided by our data set. And then the question was, so what are the explanatory variables so explaining the GC? Okay, yeah, this is our set of explanatory variables. Okay, just let me quickly still talk through the results for two minutes if I'm allowed to do so. One minute. Oh, okay. Well, what came out of the regressions? Well, that's a fractional ranked deviation variable using the GMM analysis, has a significant impact on our age variable. But, so using GMM, but that the opposite relationship does not hold. So our health variable does not have a significant impact on our socioeconomic status variable represented by the fractional ranked deviation variable. Whereas using OLS, it does seem to have a significant impact. But the right analysis in this case would be a GMM analysis. And based on this GMM analysis, so one can do these decompositions, the most famous of which is the health oriented decomposition. So using GMM compared to OLS, we see that the contribution of our SES variable using OLS is close to 70% whereas using GMM, it drops to about 40%. Using OLS, we don't have a residual term, it's zero. If we include the D in our regressions, whereas using GMM, the residual component equals 28%. So we get a different picture, so whether we include D or not into our regressions here. With respect to decomposition two, we left out the health variable because it does not have any significant effect on D so that we can just use OLS and we don't have an equation with an endogenous right hand side variable. This is just decomposition three, but I leave it as such because I don't have much time. Okay, so yeah, this is some additional material, but I won't run through it anymore. So I hope that I convinced you of the fact that it might be better to assume a broader perspective on the regressions that are used for these decomposition analyses and that there might be a better estimation method in the context of a structural equation modeling approach. Okay, thank you very much for your attention.


Hello everyone, and good evening. My name is Taryn Urquhart, and I am the Arts and Special Events Programmer here at the West Vancouver Memorial Library. On behalf of the library and the West Vancouver Art Museum, I would like to welcome every run to tonight's art talk. While I recognize that we are all in different places this evening, I would like to acknowledge that the West Vancouver Memorial Library and Art Museum reside within the traditional ancestral and unceded territories of the Squamish Nation, Slava Tooth Nation, and Musqueam Nation. We recognize and respect them as nations in this territory, as well as their historic connection to the lands and waters around us since time immemorial. I am personally grateful to call the Pacific Northwest my home, and I'm thankful to the Coast Salish communities that continue to protect the natural beauty and animal diversity that surround me every day. It has been my great pleasure to work with Hilary Letwin and her guest tonight to bring tonight's event to your screens. A reminder that we will conclude tonight's conversation with a Q&A, so have your questions ready. And now I would like to pass things over to Hilary, who is waiting for us over the museum. Hilary. Karen, thank you so much for the introduction and thank you so much for all of your help in bringing this co-production between the Art Museum and the library to life at the library. We are so delighted to be working with the library on this project. And I'd like to thank Paul. Paul, go ahead and start your video now and join us so that we can talk about our project. Hi Paul. Thank you so much Paul also for helping us to bring this project to life. So Paul, you and I have been working on this exhibition for just over two years, which has gone by very quickly. And tonight is really an opportunity for us to reflect a little bit on the preparation of the exhibition. We just opened it on Friday. We've been open for a few days at the library and this is also a great chance for us to talk a little bit about the genesis of the project and your process in creating our Lego models in the exhibition and to consider the importance of West Coast Modernism in our community. So thank you Paul for joining us tonight and thank you to our viewers also for joining us. I'd like to really get the ball rolling with you just to talk a little bit about what inspired this project and as a little bit of an introduction to our viewers I should explain that Paul and I were introduced by Douglas Copeland, a resident in our community who has known Paul for a few years and of course saw your work Paul and said you have to get in touch with Hillary at the Art Museum and that's sort of how this whole project was born. So we owe our thanks really to Douglas for introducing us as well. So why don't you tell our viewers about the genesis of this project. Well hey everybody. So I grew up in West Vancouver. So I am officially a West Vancouverite and, you know, I've also a long time Lego builder. I've been building Lego for the last 30 years, just various models some pop culture stuff some, you know, trains and and I have done a fair amount of local buildings and over the last one years. So basically the project started during the pandemic. I had some some great downtime and I use my time wisely to create some new models. And I just got on the kind of mid century modern kick. And I made a piece called atomic ranch, which is, you know, a rancher style house, kind of loosely based on my favorite design magazine atomic ranch. And so I built this. And then just kind of when I built this little postcard version of the pink palace. Actually, which I have next to me just by plan to incidents. So I've talked about this a little bit, but here I can show it to you guys. So it's a little bit smaller. And it was just for fun, you know, I'm a fan of the pink palace and have been for a long time so during the end of the pandemic, I took these over to Doug's we hadn't seen him in a good year and a half or so and it was just nice to, you know, artists sharing our work and went over and he saw them and that was when I saw the light bulb go off in his head and he's like, this is the show. And I believe it was right around the time he was doing the rabbit lane project or was was planning it. So you were probably in his thoughts there Hillary and and he put two and two together and he connected us and, and that was really the genesis of how you and I met and and then after that we started planning the show together, but that's the not so brief history. Yeah, and for those of our audience members who don't know the pink palace is a building in the ambleside area of West Vancouver so it's it's adjacent to the water. And the official name of the building is the Villa Maurice. And it's a really iconic building on the West Vancouver skyline. It's highly visible from quite a distance away from Stanley Park you can see it. Sometimes on a clear day you can even see it. It's a lot of that's very distinct pink balls and, and to be fair that pink model that you held up for us call is pretty much the right color pink for the building. And it is the one example in our exhibition of work that is not technically West Coast modern but actually considered Miami modern. But it was, as you say the genesis of the project and we just couldn't resist not including it. Absolutely. And since building it I've learned that that sailors use the pink palace as a navigational tool, you know, maybe more so than lighthouse park I'm not sure.  But it seems like it's safe for the minute. And of course redevelopment and the knocking down of buildings is sort of one of the key reasons why the West Vancouver Museum, we are so focused on educating our community about the important role that West Vancouver played in the development of West Coast modernism. And, and that role is, is, is a very important one in that so many West Coast modern architects actually built their own family homes here in West Vancouver, starting in the 40s and 50s land here was relatively inexpensive, and our nice mountainous landscape, which of course runs down to meet the ocean is is a challenging environment for architects to build on so we had an incredible number of important residences that were built here in Vancouver and, and it's our hope here at the Art Museum that by educating people about the important role that our community had in this architectural development that, that we can essentially preserve these, these, these pieces of history that that are so vulnerable, especially as they get up to the point where they're 5060 70 years old and it's tempting to see them go. So, Paul I'd love to talk a little bit with you about how we selected the residences that we did. It was a little random at first, the pink palace model being one of the early ones the epic to I think house being another early one but it was much more intentional after that. Well, after my meeting with Doug, he emailed me in a couple days after and he's like, well if you're going to do West Coast modern homes. You need to do the epic, epic one and I think epic to it was probably the one he suggested but I was also familiar with epic one and I knew that both of them would be fantastic Lego models. So epic to was the first one I built. And that's the model that basically set the scale. The base measures about 20 inches by 20 inches and that it's not really micro scale but it's smaller than many figures scale for those of you familiar with Lego terms. So the doors ended up being three bricks high. And for the most part that is a scale I tried to stick with for most of the other homes that we ended up building. So that was the first one. Then shortly after that. I was introduced to the homeowner of epic one and I got to tour the house which was fantastic.  You know the indoors blend so seamlessly to the outdoors. It just has all all the trademarks of West Coast modern. So that I built that one. And then Smith House to was was on my radar too. So that was the third one. So we were, you know, definitely on Arthur Erickson themed theme show at that point. And I think that's where we, we put our heads together and tried to figure out, you know, what what other buildings we wanted to focus on. And as you say all three of those are designed were designed by Arthur Erickson, who is considered to be one of the sort of primary architectural fathers of West Coast modernism. And each of those three properties are extremely important in West Vancouver history they're all still standing still preserved. I think two house course was an interesting one to start with because it was primarily constructed the real house was constructed out of steel white steel, and I still find it absolutely staggering that you were able to replicate that in Lego because it's not. It's not really a standard post and beam house that that epic one and the Smith House to both could be considered. So can we talk a little bit about how how you sourced your, your Lego bricks I mean were these were these Lego bricks that you just had lying around in your studio or did you have to go to some effort to track this material down. Well, quite a few of the bricks were ones I have in my studio. You know, as I mentioned I've been building Lego for for about 30 years as an adult. So I have done a lot of garage selling a lot of buying and selling and buying collection so I have a fair amount of bricks on hand. The thing that appeals me about the epic to was that I, you know, with my my Lego vision that I've developed over these years, I could see the parts that I would need to make it and, you know, in certain cases, you can just look at a model or a house or prototype that you want to recreate and all you can just sort of go through all the different shapes and know that Lego makes them, you know in your internal catalog. And sometimes you look at a picture and you're like, Oh, no, Lego doesn't really make those parts it would just be more of a frustrating bill to try and replicate so the universe just happened to line up with epic to and they made all the parts the little curved white piece has been a very popular part since the 1996 I believe it first be its debut in a pirate ship of all things. So I repurposed, you know, into a an epic to model. It is really staggering and of course I think it's it's equally staggering that you did most of the residences interiors in addition to the exteriors. And, and that I think has been most exciting for me and for visitors to see that you can look inside the little windows and see the furniture and and and some of the art I mean it's just amazing. So let's talk. I know we, you and I have both had a lot of visitors ask about the technical making of the models and one of the first questions that we always seem to get is, do you modify the bricks at all. And of course, the extraordinary answer to that question is. Obviously, I don't modify any parts. That is part of the challenge. So within the Lego world, you know, if you're an a full which is an adult fan of Lego. There's the term purist and non purist purists tend to just use parts that Lego has released that have been available in sets. So purists may. Oh, I don't know use use non brand Lego parts or custom printing that kind of thing. I'm not strictly a purist but I tend to lean more that way. An example of a non purist would be a friend of mine in the Vancouver Lego club who wanted to make a roller coaster back in the day and took train track and put it in the oven and melted it to to form the, you know, the up and down curve. So definitely, I don't do anything like that. Pretty much all the parts were available in Lego sets. There is one of the, I call it the Star Wars kitchen in the Merrick house. There's a subtle clear canopy. And the mathematical name of the shape isn't coming to me right now but that part only came in one set in 2016 in a ninja, a ninja vehicle. And so I detract that part down and it cost me a fair amount of money between shipping from the US, none of them were available in Canada. So, you know, I've gone to quite a few extremes to to stay purist and use parts that are available. I mentioned the Merrick house and I'm happy you did because that is an absolutely extraordinary. I mean they're all extraordinary models but to me the Merrick house in a way is almost the most extraordinary. And I'd love to talk just a little bit about the making of that particular model because in my mind, it would be extremely challenging. Why don't you tell us a little bit about the Merrick house and how you made it as a model. Well, I've been aware of the Merrick house for quite a while.  And I remember when I was first looking back in the early days of the project, that was one of the ones in my mind it was no way, not going to do it. But, you know, you interest introduced me to the homeowners and we got to do a home tour which was fantastic. And let's just say there's a reason I saved that one for last, because of the complexity that one I didn't even contemplate doing an interior or a full interior. I did a partial interior, which is the living room which is kind of the most spectacular room in the house, and also the most visible from the outside. So that house has 17 levels. And really for my brain to comprehend it, I just had to start with the outside and just work at it sort of piece by piece and figure out, you know, took a few days to figure out how all the different sections related to each other. It's also famous for I think having one maybe one right angle in the entire house. So of course Lego is a very, you know, grid based system. So I had to change most of the angles to like either 45s or 90 degrees. But I found a way to make it work and to make all the three different sections of the house line up. But that was definitely the most challenging. But I'm also going to say it was one of the most fun to create. And yeah, it's everyone seems happy with the result. So I'm, you know, it's, you did it's an extraordinary replica of a very complex architectural structure. So let's just talk a little bit about about what I think makes your models, these models in particular very special. And in my mind, it's the fact that you've built the models within their landscape.  You've actually looked at the house on its site, or the building on its site and and figured out exactly where those very tall trees are on the Merrick plot or where that very important apple tree is on the binning plot, you've actually gone to each of the landscapes and really truly replicated them which I think is so remarkable. And the beauty of the inclusion of the landscape is that one can see how the house fits on its site on its on its actual natural site. It's not just, and one sees this with like, for example, the falling water model that the Lego model of falling water that has been created, where you see the house but you don't really see the landscape that it's on. In your models, you see the landscape. And I think that that works again as a sort of educational tool for people even like me who intimately know these buildings, and who may not look at them necessarily in the context of the landscape. And I think that that's really important because one of the very important tenants of West Coast water architecture is that, just like Richard Neutra, a style is to in his in his book on site, that a house needs to be situated nestled into its site, and you get that sense beautifully in in all of the models. Particularly in the case of the Merrick and the epic one and in in Smith to, for example, those are sort of the ones to stick out of my mind. So I'd love to hear your thoughts on and indeed the process in terms of including the landscape. Right. Yeah, well that was a conscious decision right off the bat, you know, starting with the epic to which was the first model. And I wanted to include just enough of the landscape so that you got, as you said, you get a sense of why the house was built the way it was, you know, the epic to kind of cascades down the hill in the three different levels. And yeah, you really need that, I think to tell the story of the house. The Smith house is quite famous for its floating living room, which is suspended between between two rocky outcrops. So of course, you can't build the Smith house without doing that. I definitely spend a lot of time cross referencing pictures and looking at Google Earth and trying to get as many, you know, different outlooks as possible on the site and. Each each rock is, is, you know, to the best of my ability place where it should be. But yeah, I mean the Merrick was the extreme case of that. The owners have told me that Pell Merrick only cut down one tree in order to make that home on a very slopey tree property. And in fact, when you look at the model, you can see the way that the shape of the house is it kind of works in between all the trees on the hill. And with the very spectacular tree that almost when you're inside the house, it almost looks as though the house is built around it but it's a very clever illusion that Paul Merrick came up with. So that's the one that's kind of off to the, the left side of the house, very close to a large picture window. Yeah, it's closed by the house I think or almost all sides. Yeah. It's a very clever illusion, you think it's enclosed by the house, but it actually isn't. So it's, it's really, it's one of my, my favorite parts of that particular house. Well and the pink palace of course has that beautiful inaccessible roof designed by the landscape architect Cornelia Oberlander. Can you speak a little bit about, about that particular roof design that you implemented? Oh sure. You know, as, as a fan of the pink palace but never having actually been in it up until recently, I was always curious I'd hear about this garden and I always assumed that the people that live in there had access to it. But it turns out it isn't, it's a garden that was made I believe 10 or 12 years ago and kind of added, apparently before that it was just a black flat roof, kind of over the apartments on the bottom and some of the parking garage. But they've, you know, Cornelia was asked to design the garden and it's got some logs on it and some grass and, you know, it looks, it looks like a path. But it's really mainly for birds and for the, the people in the apartments that really improves their, their view, you know, gives them a visual interest. Interestingly, I, I had to contact two different owners because you can't see it all from one particular balcony, because there's, it goes around the corner so you have to, I have people in two different units to take pictures, so that I can get it to get the information I needed to make it as close as possible. This is a good place to thank all of our homeowners for giving us access to the homes, because I think that was absolutely an essential part of the process. You know, some of these homes have plans that have been published in different places. Some of these homes have photographs that were taken maybe when the house was originally built. But there was, I think nothing like going into the homes for you and actually being able to see them up close and personally and being able to take photos of certain kind of very technical things that, that enabled you to make the models as accurately as you did, right? No, absolutely.  But, you know, there was some fairly really good real estate listings and there's a book published on it. So that one had the benefit of drawings and large amount of pictures. All the other houses, I took a lot of my own video footage and pictures and it really helped make the homes, you know, I was able to make them as detailed as possible. I think it would have been rather frustrating to try and build them without that. Because typically what I found is most homes get photographed from one, maybe two angles. And then of course, usually the backsides don't really get photographed. And that was one of the conscious decisions to do homes that still exist because there's a lot of really great homes that have been demolished, which look fantastic. But they only look fantastic from that one or two angles and they would be really hard to replicate because I just don't have the information or access to the information to build the rest of them, you know, accurately. And that kind of answers the question about how, you know, after we finished, after you finished the three Arthur Erickson properties, we became much more intentional, you and I about picking properties that we wanted to bring into the project. And yes, as you say, one of the stipulations was that they still be standing and that we could get in to see them so that you could gather that information you needed. But we were also looking to bring a little bit more variety to the project we wanted to sort of get away from all of the Arthur Erickson residences and so we, we also included the Merrick house as you've already mentioned the sky bungalow which of course was a house designed by Paulingsworth, the Benning house, as well as an example of a Lewis post and beam so we kind of, we got quite a few architects in there in the end. My regret is that we never did a Ron Tom house. The exhibition, for those of you who may not know the exhibition with the library now but it's actually going to the Harmony Arts Festival for the first two weeks in August and I'm wondering, Paula, between now and August we can get a Ron Tom model to add it to the canon of Lego West Coast residences, something to work on. Right. That would be cool, you know, I love making the homes. So yeah, hopefully we can make that happen. That's, it's not for lack of wanting to it just comes down to time and. But, you know, I agree, I mean, I would, I would love to love to keep going I mean, maybe there'll be a particular West Coast modern show part two. We'll circle back to that idea. So I we wanted something you mentioned just reminded me that we had a little bit of a decision to make with each of the homes because some of the homes have been renovated. And the most extreme example of course is the sky bungalow by Fred Hollingsworth. And we had to make a decision about whether or not to to show a home as it is today, or to show a home as it was when it was designed or at some point in its in its early life. So maybe you can talk a little bit about about sort of how you approached that problem with each of their residences. Sure. Yeah, it was pretty much on a residence by residence basis. I mean the first time that it really, you know, I put a lot of thought into it was with the Smith House to there have been several additions over the years and in fact a paint job. Originally it was it was wood. And now it's more of an olive green. And, you know, as a Lego builder, Lego makes both olive green and dark tan, which replicate the kind of the wood pattern. But in this case, the olive green elements, there wasn't enough of them to make the house sort of structurally sound in Lego. It was part of the decision. And then the second part was there had been extensive additions, including an extra studio building off to the back of the Smith House, which was Gordon Smith's new studio after the original studio in the house. So in that case, the footprint of the house would have just gotten too too big.  And, you know, I think that was kind of cool because it's, it's a, you know, a version of the home that no longer exists, except now in Lego form. Yeah, no, I would. And in the case of the sky bungalow, you took it back to the version that was down at the Hudson's Bay parking lot. When it was right by Fred Hollingsworth and put out by the developer for people to tour the original, the original tour. Yeah, yeah, that was really cool when I learned its history. Yeah, that one is built as the 1949 version. It's just remarkable to think that, you know, on Seymour Street on this ground level parking lot to this house on stills existed. Which of course now is a, I don't know, like a six or seven story parquet for the Bay. But yeah, that was a bit of a challenge because there was no color photos of that. Most of the better quality images are of the sky bungalow once it moved to its new location in North Van. And yeah, so I had a little bit of artistic license. And in fact, that's the only home that because it was slightly smaller in size actually scaled it up and made it what we call minifigure scale. So you get to use those little, little minifigures in that one. Whereas the pink palace was a different scale entirely that because it was a larger building I had to scale that one down and make the floors even smaller. So, yeah, there's definitely some decisions to make in regards to which periods build the homes, and then also some decisions as far as scaling. Well, I think that each of the models is is absolutely spectacular. They're extraordinary to see. So I think you made the right decisions. So let's talk a little bit about West Coast Modernism. As you say, at the beginning you grew up in West Vancouver. Did you grow up in a West Coast Modern home? And what, what was it about West Coast Modernism that appealed to you for this particular project? I grew up in mainly in 1930s style home. That home, you know, the rooms are all smaller. As far as I can tell, there really wasn't much consideration put into bringing the outdoors inside.  And, you know, it's a great house if you have a large antique collection. They fit in great. But as far as, you know, being West Coast Modern, it was kind of polar opposite. So I mean, in general, I'm just a fan of architecture. You know, in my essay, I basically traced it back to having a train set when I was young. That was the first time I looked at or kind of had to look at buildings and make some decisions about, well, which kind of buildings do I like? And of course, that led to a long lifelong passion for for studying architecture. In many of my creations, you know, I built some local buildings, but I kind of hadn't really done West Coast Modern or mid-century modern that much. I'd always gravitated towards Art Deco or Art Nouveau just because they offered, you know, fairly challenging build, you know, build situations. You know, I was like, I'm always up for a challenge. I found, so I thought initially West Coast Modern, you know, that's probably not going to be that tricky. But of course, you know, we've mentioned the Merrick House and a few of the other homes where there definitely were design challenges. But, you know, growing up, we did a lot of garage sailing, so it's, like, it's possible we went to some of the, you know, I'm sure we went to put a few West Coast Modern homes. And I don't think we went to any of the, you know, the sort of super famous ones. I can't say some of the owners having garage sales, but you never know. I mean, I've been doing that since the 70s and 80s. Of course, I don't really do it anymore, but that was kind of my history. So every weekend, I would go with my parents and check out people's houses and yeah, just sort of biosmosis living on the West Coast and seeing all these homes and being close to the properties. I think that definitely had an influence on me. Absolutely. And, and we touched on this a little bit, but I would love to hear about about why Lego, what is it about Lego that that you love working with and and how does it lend itself to projects like this. Right. Well, you know, I had it when I was a child. I have a picture of me at age three building with Lego. So it was just part, I think it's just been part of my history. You know, as Doug mentions in his essay in the program, it, once you've played with it, it seems to hardwire a certain way of thinking or a system inside your brain. I think Doug really nailed it, you know, on the head there in his essay when he said that as, as people as adults kind of, you know, age up a bit and get into their 20s or 30s, 40s, and they have some income. When you tie that to a sense of nostalgia, a lot of people are drawn back to, to the Lego system. Because it's kind of like a jigsaw or it's something meditative to do, you know, especially if you're just building the sets, Lego makes a huge variety of sets, and they've been very successful in recent, you know, why really in the last 20 years that, that, you know, bringing in licenses that are going to bring pretty much, I think eventually everybody on the planet, it can be have at least a Lego set or two. So, I mean, to answer the question, for me, directly, I think we're seeing Lego Land pictures of Lego Land and these giant models, I always had it in my mind that when I got back into Lego in my 20s, initially it was nostalgia, but I also saw the potential to create these larger models and, and to do them in a fairly realistic way. And then the, the bonus is you don't have to be good at drawing, and you don't have to, and you don't have to paint it, which, you know, for model making, what's always a, you know, kind of that extra step, there's instant satisfaction with Lego. Absolutely. And, and you've mentioned the publication a few times we did of course create a publication which is available both at the Art Museum and at the library for $20. And that includes an excellent essay by Paul as well as by Douglas Copeland, there we go. And also by Nathan Sawalia. And Paul, maybe you can speak a little bit about about about Nathan's essay and because he, he is a well known North American Lego builder as well. So you've heard about, about his work and, and his essay. Oh, sure. Yeah, I mean Nathan is, he's kind of the, I would say the first, you know, first Lego artist to really go mainstream, you know, he, he, he started out about 10, maybe 10 or 15 years ago. And I mean, he is most well known for kind of a yellow, yellow body, which the body is opening its chest cavity and yellow bricks are falling out. I believe it's just called yellow. I think you did a series of like, another one called red and another one called blue and they're, they're very iconic, you know. I just thought he would be great to have on the program because he has been so successful at bridging the gap between, you know, being a little Lego fan, an A-fold, a Lego, but he's bridged into the art world. So I thought that it would be neat to get his perspective on, on how he did that and, and his thoughts. So, yeah, he's a fantastic addition to the program and he's a very talented guy. He continues to have shows that travel around and I definitely aspire to, to hopefully follow in his footsteps and have a traveling show at some point. Well, I mean, I think that it's great to, to demonstrate in fact that Lego is more than just following directions and, and building a kit. There's the potential really to explore so much of our world through it. And I know from my perspective, one of the objectives of this project is, is to use Lego as a way to get people to think about West Coast Modernism differently or to introduce them to it. Maybe there are people out there who aren't familiar with it and, and who look at the models and, and become interested in that history and want to learn more. So, from my perspective, this has been such an excellent partnership for us to undertake and, and I've just, I've enjoyed every step of it, watching you kind of process the residences as you've seen them in real life and then turn that into something truly remarkable. So we get a lot of people, I want to finish with one final question, which I know a lot of people ask, and, and that is how long does it take you to build each model. Right. The magical question everybody would seems to want to know. Each, each home takes probably about two and a half to three weeks to build, you know, initially in my mind, I thought, I can do that in a week or so but there's so much information, especially when you include the interior of the building. There's so much cross referencing that you have to do to make sure all the walls line up and, you know, the rocks and the trees are in the right place. So, I basically about two and a half three weeks. And then the number of bricks does vary based on the house but it's kind of in the probably 3000 to 5000 or just over range.  And, and I tend to use the, some of the extra bricks that I have, you know, maybe some of the ones I used to get a garage sales that are chewed or faded, or, you know, was pick a brick wall where you can buy random elements and sometimes if they have, you know, say an orange two by two brick on the wall I'll just buy, buy a bunch of those and use those as to fill in the insides. So it's pretty much whatever is at hand that I don't really need is what goes into the interiors. Well, they're absolutely extraordinary Paul. I think this is a great time probably to answer answer questions from our audience. But before I turn it over to Karen I just wanted to mention that this exhibition, the particular West Coast modern show is the first of many parts that make up West Coast modern week. The West Vancouver Museum act as a hub for all things West Coast modern over the course of one week in July, July 4 to July 9. And I just would like to encourage anybody watching this to check out our website to look for more details about West Coast modern week, and, and indeed more details about this exhibition. So thank you very much, Paul and Karen, I'll turn it over to you to moderate some of those questions. Yes. Well, well, thank you so much. I'm so excited to have the great pleasure to work in the building where this exhibit is obviously housed at the library. And I look forward to going around now that I've heard some of the tidbits that Paul has been talking about tonight to look at them in more detail. We do have a few questions from audience members and please out there if you have a question type it into the chat. The first question is what happens to the models after the exhibit. That's a good question. Well, they are going to the Harmony Arts Festival after the library show closes on July 31. So they'll be at the that's an apple side basically, they'll be there until mid mid August. And then a few of the homes have sold already. And so they are all for sale, so people can can purchase them. And they are all they are all one of a kind. But yeah, it's, it's, it remains to be seen. Hopefully, some of them will end up with homeowners and if there's any, you know, architectural fans out there or Lego fans that would like to own them. Contact me and we can make that happen. Excellent. And Paul that actually is a great question around around your work, you actually work on a commission basis right. Yes. Yeah, for the last five years or so I've been doing commissions I've done some some huge brick cities for a restaurant in Wisconsin and I do private commissions for people. And basically I'm always building and so far it's been working out essentially I'm a freelance artist. I have a question of my own for you because I'm a little Dr who fan and I see a little dollop behind you or your shoulder there. Do you enjoy making these kind of structures, primarily, or are you just all freelance, anything goes. Oh good question. Yeah, I pretty much make anything you know I'm. I don't really have one particular style with, which, you know, maybe for better for worse. I like too many things. So, the doctor who once were were built really for my own enjoyment during the pandemic that was one of the pandemic ones I think I did a Scooby Doo one. A real variety you know some summer pop culture and then the ones that I really get the satisfaction out of is, you know, coming up with things for my own imagination. I have one that's called unshade my heart which is a steampunk robot, which you can see on my website it's also on my business cards. So, I like, I like too much, you know, I love recreating the architecture but I like the fantasy stuff and it's, it's really sometimes it's just which way the wind blows and other times it's a specific commission. And so that's why I focused on whatever I am kind of offered at the time. And I think we'll finish with this question, what was your favorite one on when people come to visit at the library we are, we do have your pieces throughout three levels of the library, all tucked in little will not corners but you'll have to try and find them all. And which was your favorite to build because I know we have some more fictional pieces from your imagination like you were saying but also the West Coast modern pieces. Right. I have a few favorites, you know, the pink palace, but so iconic and just fun to make it's such somehow that that pink is just so satisfying. I don't know it's a strange color to do in a building but it really seems to work. My personal favorite is probably the parking garage of the pink palace. You might quite see it in the model you can see parts of it but there's four levels and every each level of the actual garage is accessed from a different roadway or a different platform or different, you know, it's really cool. You know, I'm kind of partial to the, the Googie one downstairs and atomic trans I mean, those were, were fun. And, you know, the Merrick house was so intimidating, but the way it turned out. I'm really quite pleased. So, I like them all. They're all my children. Yeah, Hillary do you have a favorite because I think the Merrick house is mine. Oh, that's a good question. I think epic one. Yeah, because it has the water features and fall you've even gone to the trouble to include the works of art by the third epic brother which are sprinkled around the site. For me, epic one was really cool. And actually I remember. I think it was Doug and his essay was talking about the models and I believe it applies to epic one where the owner said nice model does the roof leak. So I, for me and a personal favorite is a big one but I just marvel at them they're they're really extraordinary. And I love, I love how Paul has taken the roofs off several of them so we can see inside to see the detail. So, yeah, it's there. They're fantastic. Thank you. I had really had so much fun making them and, you know, to getting the chance to do the show has been a real pleasure. You know, just so many thank yous to everybody. Like I said in my speech on Friday night and yeah, it's great and now it's so fantastic to just sit back and be able to see the public's reaction. It's a great time that I've been in the library in the last last couple days. I always see people at the cases like you said Taryn with with their noses up to the glass, looking in trying to see the details and so that really makes me feel great and gives me a really wonderful sense of satisfaction. To take both Hillary and Paul mentioned, we have this absolutely stunning publication available for $21 at both the museum and the library. I invite you to come by the library and take a really close look at the exhibit. It's located at 1950 Marine Drive in West Vancouver. We are open Monday to Thursday, 10 to eight and Friday to Sunday from 10 to six. Also come on by and get one of our souvenir postcards. They're available also at our help desk. And I get the privilege to work with Paul again on July 13, we will be presenting mostly Paul will be presenting something we've called behind the bricks. Paul Heatherington's journey to Lego artist. Please register on our website that's on July 13 it will be in person at the library, not virtual like this so come on down to the library happening at six to seven. Again, thank you so much for everyone for joining us tonight and have a great evening. Bye for now.


I want you to stop right now with taking everything in as a directive because it's shaping your personality and the people that love you are aware of it but the struggling to stay around you the struggling to continue to like you the struggling to keep including you and you wonder why maybe it's to do with this where have I taken every emotion and not seen it as data what do I do with this I'm gonna stand up and watch it a minute I don't think so no thank you if I was up here today and threw a ball out into the audience and it came to your direction and it was aiming for you you would instinctively catch it that's what we do with emotions you don't need to catch it even if people say even if people say this is for you says who


Welcome to the Anxious Morning. Every weekday morning, we'll take a few minutes to go over some important lessons that you can use in your anxiety recovery journey. Away from the endless noisy scroll of social media, the Anxious Morning brings you support, education, inspiration, encouragement, and empowerment. For more, visit us at theanxiousmorning.com For the last few days on the Anxious Morning, we've been examining the idea that much of our response to anxiety can be reduced to the fact that we're just hanging on as a response to fear. We've looked at how the path to lasting recovery is in learning that we can actually let go. When we loosen our death grip and allow reality to show us that we've always been okay, good things happen over time. I understand that letting go and loosening your grip is a very tall order. Allowing the chips to fall where they may probably sounds terrifying, especially if those chips have words like death or psychosis stamped on them. Like much of the recovery process, we can look at the act of letting go as a practice. This is a skill we first become aware of, then we embrace it, then we practice it so we may get better at it. Letting go is not an automatic thing for most people, especially most anxious people. This is a thing we must work at. Like all new things, we stumble, we get it wrong, and we learn and grow stronger as part of the process. Part of recovery is taking your letting go muscles to the gym to build them up. How can we do this? How can we practice letting go? The answer, as usual, is that we take small steps in the direction we wish to go, then we repeat those steps. Understand why you are learning to let go, accept that it will be a difficult thing to do, embrace the process of learning as itself valuable, then start taking your steps. This is how we learn to do the things that move us down the path to recovery. Letting go is no exception to this. This is how we learn to let go, little by little. The idea of allowing nature to take its course without intervention may seem completely ridiculous or even reckless to you. But that's because you are only considering the worst case scenarios where anxiety and panic are overwhelming and you feel an intense sense of danger. If I ask you to instantly let go in those situations, you would struggle. But if I ask you to start letting go of little things that you may not even be aware that you are holding on to, the process starts to seem a little less intimidating. Letting go is a big deal, but we can learn to do it by starting small. Tomorrow, we'll wrap up our discussion of holding on and letting go by looking at real-world ways to begin your practice. Hey, if you're enjoying the podcast and you'd like to get a copy of it delivered every morning into your email inbox, including a full-text transcription, head on over to theanxiousmorning.email and sign up for the newsletter. And if you're listening on iTunes or Spotify or someplace where you can leave us a rating or a review, take a moment and rate the podcast and maybe write a small review. It really helps us out. Or just tell a friend about us. Thanks a lot.


One lecture slide that was 180 slides. Damn!  It's Adana. I am back with another video for you guys. So you guys, you know, we talk about PA school tests as hard. You have no idea. And I talked about, you know, like how I'm like studying and how long I study and things of that nature. But I wanted to share with you guys like three just really quick, simple test taking tips for PA school. So with respect to taking tests in PA school, obviously you're gonna have to study. And you're gonna have to study a lot. So that is a no brainer, but the important thing is studying like actually effective, like effective study habits.  My like first tip for taking tests in PA school is knowing the type of study that you are, okay?  And obviously that is gonna take a little bit of time. Usually probably like that first two weeks that you have your first exam in PA school, you'll figure out if you're a group studier or if you're gonna continue to study by yourself or vice versa. Because how you studied in undergrad and in high school is not how you're gonna study in PA school for the most part. You may keep some aspects of it. You may write notes the same or highlight the same, but in terms of actually trying to retain that information, it might be better for you to switch up your style. So making sure that you understand the type of studier that you are is important to just kind of being an excellent test taker and just doing the best that you can do on your PA school exams. My number two tip for studying in PA school is having a study guide. So it's really, really, really, really important to have a study guide and have like your study material. So, you know, my study guide consists of literally that, a study guide, like a paper study guide that I have, and then also pants. The PA must take a general certification exam known as the Physician Assistant National Certifying Exam or Pants. Pants! Oh, man. Hey, y'all better get ready for your pants exam. If you need to answer these questions even further. Hey, ladies, where are your pants? I'm everywhere from emergency care, oncology, infectious disease. Pants prep pearls, and then some of the different study cue banks that I kind of pull questions from and I write them down and I study those question stems. But having a study guide is very important because it breaks things down. Like, it makes it really, really kind of condensed coming from all of the information that you're gonna get through those slides. But breaking it down into your study guide or looking at it via pants is very important to just making it a lot more attainable and retainable with respect to studying for the exam that's coming up. Because like my ortho exam, which was on all things ortho, but I had ortho slides, which was from one lecture that was like 180 slides. How are you gonna get all that information? And so you really have to do a good job of breaking that down. So make sure you have a good study guide and some great study materials, adjunct to that to help you condense down the information that you're getting and then it's gonna just be a better option for you when you have to regurgitate it and bring it back to memory on these exams. And my number three tip that you should actually, I think it's really important just in general, but that you should do to help with your studying for PA school is going over the slides at least twice. So I know that's difficult. It sounds hard. Like you're gonna have a lot of slides. Just like I just said, I had a one lecture slide that was 180 slides. Damn! But the more times that you see that information, the better. So if you're able to go through the slides twice, the first time you go through it, mark down the information for your study guide. The second time you go through it, look for any type of important, bolded, underline, italicized, starred information that the teachers may have put on those study sets, then you can add that as well as adjunct to your study guide that you just made. But going over that information more than once is essential. You cannot sit up here in school, have the teacher kind of just going through the slides and think that that's gonna be enough for you to get the information down. You definitely need to go over it at least two more times on your own so that you're familiar with the topics, but then you're familiar with the information and how it was laid out on the slide for those of you who are visual learners. Then you can also add that in your adjunctive therapy, I guess you could say, your study therapy to the study guides that you just made. So definitely do that. Don't procrastinate on that and just kind of keep ahead on it because you're gonna get a lot of information thrown at you and it's important for you to be ahead of the curve with respect to that. Those are my tips. You definitely need to know the type of study you are, have a study guide and go over that information more than once to keeping ahead of your studying and your exams and your tests because it's just gonna be beneficial. So I hope those are helpful for those of you who are going through this right now or preparing to go through it and for those of you who are in undergrad, maybe this might help you in how you're studying for your undergraduate degree as well and it might be just a more effective way for you to study. All right, so thank you guys so much for asking that and if you have any other questions, go ahead and leave that in the comment section below. I'll be sure to get to it as soon as I can of course and thank you guys again for joining me on this journey. If you haven't already done so go ahead, join me right now and subscribe to the channel and follow me on Instagram at AdanaThePA. Thank you guys so much for watching. I'll talk to you guys next time. Bye.


Welcome back, we have been discussing residual entropy, the entropy which is still present in the system or disorder which is still present in the system when the temperature is absolute 0. We have also discussed that the residual entropy can arise because of the disorder and the disorder arises because of the magnitude of the molecular dipole moment. Essentially, you want to understand how many minimum energy confirmations of a system can be present at absolute 0 and then by using S is equal to k log W, one can get the value of residual entropy. This formula is valid at all the temperatures, so therefore you can use it for S 0 also. So, we discussed that S is equal to k log W and in the example of carbon monoxide or an example of a molecule like AB in which the dipole moment of AB is very very small. Then there are two possible orientations AB or BA for one molecule and for n molecules it will be W will be equal to 2 raised to the power n. You can bring n in the along with k, so and then it becomes nr log S. I am replacing 2 by S where S is the number of orientations with about the same energy. As a general formula to evaluate the residual entropy, you can use S is equal to nr log S where S is the number of orientations with about the same energy. Take an example of FClO3 molecule. This FClO3 molecule can adopt four orientations with about the same energy with the fluorine atom at any of the four corners of a tetrahedron. So, four orientations that means the value of S that you are going to use here is 4. So, S is equal to nr log 4 and the molar if you put n equal to 1, the molar residual entropy turns out to be 11.5 joules per Kelvin per mole whereas the experimental value is 10.1 joules per Kelvin per mole. There is a fair degree very good degree of agreement between the calculated value and the experimental value. So, I hope it is clear how to theoretically calculate the residual entropy you are going to use the formula nr log S where S is the number of orientations with about the same energy. With this knowledge let us move ahead. Now we are interested in understanding the residual entropy of water that means entropy of water at at t equal to 0 or absolute 0. The question that we are going to address is that whether this residual entropy will be 0 or it will be non-zero. Non-zero means it has to be positive. For that you will have to go back to the structure of water and structure of water in different phases. Since we are interested in ice therefore we will talk about the structure of ice. What is the structure of ice? It is a regular tetrahedral network of hydrogen bonded structure. As a result of this hydrogen bonding the volume of the system increases and the density decreases. Therefore, ice is lighter than liquid water. Let us try to understand the arrangement of oxygen and hydrazones around each other in ice. Look at this figure shown over here. These pink spheres treat these as oxygens. One oxygen is surrounded by 1 2 3 4 other oxygen in a tetrahedral regular tetrahedral manner. In between these two oxygens you have hydrazones. We have shown two possibilities of hydrazones. What are those two possibilities? One of these is going to be hydrogen bond and one of these is going to be a covalent bond. Because when you talk about water molecule H O H you have lone pair. This is covalent bond and if some hydrogen bond is shown over here that will be hydrogen bond. So, that is what is shown over here. There are two possibilities. The covalent bond will be closer to this and if it is hydrogen bond this will be far away from this. Now let us read the comments. This figure shows the possible locations of hydrogen atoms around a central oxygen atom. This is the central oxygen atom. In an ice crystal are shown by white spheres. These are hydrogen atom which are shown in white spheres. Only one of the locations on each bond may be occupied by an atom and two hydrogen atoms must be close to the oxygen atom and two hydrogen atom must be distant from it. As I said this one oxygen is surrounded by four oxygens and in between oxygens there are hydrazones. There are two type of bondings you will encounter here. One is hydrogen bonding, other is covalent bonding. Covalent bond will be shorter. Hydrogen bond will be relatively lengthier. That is why it is written two hydrogen bonds must be close to the oxygen atom and two hydrogen bonds must be distant from it. Let us discuss further. Now we will consider n-water molecules. Let us talk about there are n-water molecules. We already discussed that each oxygen atom is surrounded tetrahedrally 1, 2, 3, 4 by four hydrogen atoms, two of which are attached by short sigma bonds and other two by long hydrogen bonds. n-water molecules means there are two n hydrogen atoms. These two n hydrogen atoms can be in one of the two positions either close or far. I repeat n-water molecule means two n hydrogen atoms and two n hydrogen atoms have two possibilities. One is the close means covalent bond other is away that is the hydrogen bond. So, there are how many possible arrangements two raise to the power two n depending upon the number of molecules. n is the number of water molecules. There are two raise to the power two n possible arrangements. This is a possibility, but there may be some constraints. In the past also we have talked about constraints. You remember when we derived the Boltzmann formula. We had to bring in the total number of molecules constraint. We had to bring the total energy constraint and what is the constraint here? The constraint here is that out of all the possible hydrogen atoms placed around some are forming shorter covalent bond with oxygen and some are forming longer hydrogen bonds with the oxygen. Two raise to the power two n possible arrangements, but all these arrangements are not acceptable because all the hydrogen bonds around oxygen cannot be of one type cannot be either covalent or hydrogen bonding. It has to be mixed two covalent two hydrogen bonding or two covalent whatever two raise to the power n possible arrangements are there. So, of the two raise to the power 4 that is sixteen ways of arranging four hydrogen atoms on one oxygen 1 2 3 4 and each hydrogen can be either covalently bound or it can be hydrogen bonded. So, therefore, two possibilities for four hydrazons there are sixteen ways of arranging four hydrogen atoms around one oxygen atom. Out of sixteen not all the meter arrangement only six have two short and two long OH distances and hence are acceptable. That means out of the sixteen ways of arranging four hydrogen atoms here discussed only six are acceptable all are not acceptable because there are some arrangements in which this restriction of two short and two long cannot be fulfilled. And what are those six orientations can be seen in this and here different color coding has been given these are the six 1 2 3 4 5 6 6 possible arrangements of hydrogen atoms in the locations have been identified in these six figures. The occupied locations are denoted by red spheres and unaccopied lotations are donated by white spheres. That occupied means either it will be hydrogen bonded or it will be covalently bonded. We know the formula s is equal to k log w that is the formula to be unimbiguously used s is equal to k log w and our focus has to be on w what will be the expression for w. What did we discuss that there are two n possible arrangements this is the total two n possible arrangements all are not acceptable only six out of sixteen ways of arranging four hydrogen atoms around one oxygen atom are acceptable. So, therefore, what should be the value of w two raise to the power two n possible arrangements. And then we have to worry about arranging four hydrogen atoms around one oxygen atom you can see four hydrogen bond hydrogen atoms around one oxygen atom. And out of the total number of arrangements sixteen ways of arranging only six are possible. And there are n water molecule this is for one water molecule for n water molecule this is n overall weight of a configuration is the product of two. What you have is w here is equal to two raise to the power two n I will write four raise to the power n into six by sixteen raise to the power n which is equal to four into six twenty four by sixteen raise to the power n which is equal to three by two raise to the power to the power n. So, therefore, w is equal to 3 by 2 raise to the power n. Once we have an expression for w, the next step is s is equal to k log w, s is equal to k log w, w we know is 3 by 2 n put 3 by 2 raise to the power n, n comes here and k times n is equal to k times small n into n a, k times n is k small n times n a which is equal to n r. I can consume this n and make it molar, I can write this molar you see per mole when you substitute n equal to 1. From this value of statistical weight you have s is equal to k log w and substitution here gives you a residual entropy of water as 3.4 joules per Kelvin per mole. Incidentally, the experimental value is also 3.4 joules per Kelvin per mole. So, here what we see that the entropy of ice at absolute 0 is not 0, there is some value and whatever is that value we call that as residual entropy which in case of water it turns out to 3.4 joules per Kelvin per mole. So, now our terminology, so now our terminology is that we have discussed one is entropy, we have also discussed residual entropy, this entropy can be determined spectroscopically, it can also be determined experimentally. We have now discussed a method where you can calculate the value of residual entropy. Experimental entropy measurements requires calorimeters, calculation of residual entropy requires a knowledge of various confirmations which can give rise to the same energy at absolute 0. So, in that the molecular dipole moment plays a big role. We also discussed the origin, origin of residual entropy. We discussed that the origin of residual entropy is prevalence of disorder at absolute 0. The concept of entropy is extremely important, we are interested in changes in entropy. In chemical thermodynamics you have come across various relations which connect delta S with other thermodynamic parameters for solid gas liquid. Delta S can also be calculated from the knowledge of absolute molar entropies and we should have a means of either calculating or experimentally determining the value of molar entropies. In the second law of thermodynamics what the second law says during the course of a spontaneous process the entropy of an isolated system increases. What the third law says that entropy of all the perfectly crystalline substances is 0 at absolute 0. We do have some residual entropy and we discussed that these residual entropy depends upon the molecular properties. Therefore, we should not blindly say that entropy at absolute 0 is equal to 0. That entropy at absolute 0 is equal to 0 only for perfectly crystalline substances. Therefore, when you use this expression S at t is equal to S 0 plus integration 0 to t C p by t d t and you might have seen that many textbooks towards the end provide a table which contains the third law entropies. What is the third law entropy? Let me write that also a term here third law entropy. What is the third law entropy? The entropies which are determined they based upon S 0 equal to 0 are called third law entropies. I repeat entropies which are based upon the values of S 0 equal to 0 are third law entropies. That means, you are assuming the system to be perfectly crystalline and we have discussed that for perfectly crystalline substances the entropy is 0 at absolute 0. At absolute 0 there is no thermal motion. So, things are frozen and in that frozen state if there is a configurational disorder that gives rise to the residual entropy. As first law is very important, second law is also very important, third law is very important. Understanding the of entropy requires a little more ah effort because the entropies can be connected with partition function. Entropies can be connected with heat capacity and there are many other relations which you can establish for the entropy. Sometimes to address the question can we experimentally determine absolute value of enthalpy or absolute value of Gibbs free energy and then generally we give an answer that we are not interested in knowing the absolute values. Taking our discussion a little further we have talked wherever we derive some expressions for for example, I talked about internal energy we talked about u minus u 0 Gibbs energy we talked about G minus G 0 Helmets energy we talked about A minus A 0 H minus H 0 each expression was with reference to some A 0 H 0 G 0 U 0 and similarly here we are saying with the reference to S 0. In a sense u minus u 0 is actually a difference because although we have derived some expressions by assuming u 0 is equal to 0, but the oscillators do have some 0 point vibrational energy which have to be accounted for. So, everything is relative to some reference here also the third line entropy is also relative to some reference S 0 and if S 0 is not equal to 0 there is residual entropy that the topic that we have discussed today in details. By now we have connected molecular partition function with all thermodynamic quantities except one which is remaining which connects the changes in Gibbs free energy with the equilibrium constant of a reaction very important discussion. How to connect equilibrium constant with the molecular partition function, but that discussion will require a knowledge of expression of Gibbs free energy in terms of molecular partition function and then for the changes in Gibbs free energy because it is delta G 0 which is connected to K that we will be discussing soon in the coming up lectures. Thank you very much.


Hey guys, Shabir 1000 here. I'm gonna do a little fishing for you, night fishing, so let's see if we'll catch anything. Okay guys, so I'm by. There's a lake over here and there's a lake over here. I'm just trying to find a good spot to put in or to get down into. As you can tell it's getting dark, but I gotta wait on monkey anyway. This is a bike trail while walking trail, they call it the Green Mile. This is where we put the drone up that one time and she had to run back the house, we're only a few minutes away.  I was like, well, not really. She said, well, you can fish. I was like, all right, I'll go with you hun. So I was getting stuff out of the truck and she said, you got your fishing pole? No. She said, I'll run back and get it for you. I said, well, I'm gonna start walking some here. It's only about not quite a quarter mile that way to the road and we're only about five minutes from the house. So she'll be back here in a minute, a couple minutes and I'm trying to find a good place. Oh, that's not safe. I mean, trip over that. So I need to find a place. I don't know if you guys, if the camera's picking that up, but there's like a trail like this through the water. That's like the current, where the current's going. I don't know if you guys can see that, but it's like an S trail right from here. Isn't that cool? A little bass just jumped over here. But anyway, there's a couple places down here on the left that I can get down into and get the water. I can get down in right here and I can fish. Whoa, a bat. I just got swooped. I maybe try to fish there. I might try that first. So anyway, I'll be back with you when I start fishing. So I ain't tight guys. Okay guys, I know it's windy. I got my light on my head on my hat here. So I'm going to go ahead and take that off because it is windy, but it's still a little warm out here. Some monkey made it back. She's walking up there. So I'm going to go ahead and bait up. All right. I'm going to go ahead and bait my hook and everything and I'm going to get casted out. And if I get anything on the line, I'll kick you on. So I ain't tight guys. There we go. I'm right in the current. So that should be pretty cool. Let me turn this off for you. So there's my pole. All right. Now we wait. Okay guys, change your plans. We're now down here at the river. Monkey came back and wanted to go fishing, so we came here at the river. No wind at all, which is good for fishing, but bad for bugs. Other place. I mean, it just got really windy, real bad. Of course, there was no bugs, but anyway, we're here at the river. So I'm going to get my, I'm already baited up, so I'm going to get casted out, get you guys set up and we'll see what happens. Well, we're not catching any fish, but there's a bunny rabbit over here. Cute one. Keep tension on it. Where do I bring them fish? Bring them up here, put them up here real quick. He's heavy. Okay. Well, reel him up to you. Put him down a little bit and reel, reel. And I'll bring them over. What do you want to do down here? That's a nice catfish. What you doing? A nice catfish there. Good eating size fish there. Yeah, flashlight? No, I can see. Give me some slack, please. All right, we're getting my tackle box there and get my pliers. And that's a nice one, right? Don't yell, please. Sorry. Want to hold him? No. Why? He's slimy. He's whisker.  Your hook's shot. Hook's no good. Pretty. Give me that bag, please. I got to catch one. I haven't caught any. This is the first one. Yeah. There he is. Give this footage. His mouth open. He's every bit as wide as my hand. I don't know. Got a measuring thing in there. Six watt inches. Joking there somewhere. I don't have my glasses on. I can hold it up. The fish here? No. Don't yell, please, hun. Sorry. He's approximately 16 and a half inches. That's a good size? Yeah. Want to hold him? He's pretty heavy. No, thank you. Okay, time. Bye. Bye. I catch you again. I don't like throwing them in like that, but the water's so low. Bye, catch. And he splashed all over my camera, of course. Okay, guys. So there you go. That was the last fish we caught. It was hers. The only fish. Reality, you know. This ain't a reality TV show. You know what I mean? No.  Sometimes you do good and sometimes you don't. We just had a bad night of fishing. So, I mean, she caught the one that was great, but we still got to get out. Yeah. That was a pretty good catfish. Yeah, he was big. Yeah. And we got to see a teen bunny rabbit over here hopping around. I got up to him. I was about this far from him. I'm trying to pet him, but yeah, it's pretty neat. Heard some interesting things out here. Yeah. Yeah. It's a couple of few things that were never heard before. This river is very mysterious, man, because this is the river we were on when we were going my solo. I'm telling them, only we were that way. But yeah, but I usually give fishing waters really low. Kind of chilled down a little bit too. Yeah. I mean, they had a couple bites. There's owls and monkeys over there. So there's a lot of monkeys around this area. Lots. I've seen a rattlesnake on the road on the way down here. Yeah, you did. Yeah. So that was pretty cool. It wasn't far from the house. Hope you don't come visit. So yeah, that was pretty, it wasn't real big, but probably two and a half feet long anyway. That's pretty neat. So yeah, pretty cool. What else? Anything else? That was it? Yeah, that's about it. It's quiet out here. So peaceful. So what'd you guys think of the yard cell finds? We did good, didn't we? Yeah, we did really good. Yeah, once we started looking and you were looking them up. Oh my god. If you guys didn't see that video, check out the last video right before this one. We did good. Yeah. That was all at one place. One place, yeah. So we had over a hundred, five hundred and thirty-some dollars worth of stuff on 11 bucks. Yeah, pretty good. Well, just the five dollars stuff that I bought was 493. All right, so we're gonna let you guys go. It's very late. We're gonna go home and we'll see you guys soon. Thank you so much for stopping out. Bye, y'all. Stay tuned for more videos of the boat and when we get on the boat, get the boat in water, I'll be doing my solo camp out on the island. That should be interesting. There's all these woods around here supposed to be haunted, you know, because there was, well, just a couple miles from here, there was a big battle at Fort Cooper. Yeah. And we found out they actually came through the area where our house is to get there and stuff. So very interesting. Yeah, so when I do that, I'll let you, you know, give you the info on that and links and stuff like that. But yeah, the Indians and the Seminoles, Seminole Indians, and you know, they were fighting the government. But the Seminole Wars, there are several of them around here. So, but yeah, that one battle happened just a couple miles from our house. So they were all over here.  There was, this was a working river at one time. So to me, I got some interesting stories to tell you. So that'd be cool on a solo, by myself on that island. So that should be fun.  She said, if I don't get eaten by a gator, she'll consider coming out and camping with me. On the island. Yeah, on the island. Pretty cool out here though. All right, guys. Shea Berry, Mr. Man-A-Legend, going for now. We'll see you guys soon. Bye. You gonna say goodbye? All right, did. Bye. Bunga-Sich-Sow. I know you said that part, but usually you go, bye. Bye. And I was sitting here. I was listening to all the sounds. It's noisy tonight. Yeah, but it's not a bad noisy like airboats. This is nature. Yeah, they're all talking. Mads and it's really cool. All right, we'll see you guys soon. Bye-bye. Bye. Now you say it.