Welcome, everyone. It's my great, great pleasure to have Ed Maziriad join us today to present the work of Architecture 2030, the nonprofit that he founded in 2002, in which has been instrumental in leading the transformation of the building industry and architectural practice in the US and around the world. On the eve of what we all hope will be a time of accelerated and intensified focus on addressing climate change across all of the dimensions of our lives, I cannot imagine a more inspiring figure to launch this sense of renewed commitment and engagement. Having been a great admirer of Maziriad's work and impact for many years now, I'm personally delighted to have him with us at such a moment of inflection. I'm also delighted to be joined by Alex Holliday, who as a highly accomplished scientist and engineer is currently the director of Columbia University's Earth Institute, which he joined two years ago after spending more than a decade at the University of Oxford. Alex is also building the climate school here at Columbia and we are so excited for what it is becoming and for opportunities for GSAP to partner in actively transforming our disciplines and practices towards a more sustainable, equitable and creative built environment. Maziriad has steadily and impactfully deployed an awareness of the necessity to protect the planet from climate change since his earliest days of teaching and practicing architecture. As early as 1979 when he was a newly appointed faculty at the University of Oregon, focusing on solar energy research, Maziriad published the Passive Solar Energy Book, a seminal publication which is still widely referenced to this day translated into five languages and with global sales topping 1 million copies. Soon after publishing the Passive Solar Energy Book, Maziriad put his research into practice in New Mexico, testing his theories in a series of now iconic Passive Solar and highly contextual buildings, such as the Stockerburn Residence, the Museum of Indian Arts and Culture and Georgia O'Keeffe's State, Solisombra. Every Friday, he taught seminars on passive building. These ongoing conversations led him to found architecture 2030, a non-profit think tank dedicated to developing implementable solutions to address 21st century problems across the built environment, supporting and giving concrete opportunities to Maziriad's seminal research into sustainability, resilience, energy consumption and greenhouse gas emission challenges faced by the built environment so that we may address and transform the role of architecture, planning, design and building as both cause and possible solution to the climate crisis. Maziriad tirelessly, Maziriad's timeless advocacy has resulted in massive changes across the building industry. He helped found the AIA's Committee on the Environment inspired changes to the AIA's Code of Ethics and Professional Conduct and participated in the Board of Directors radical 2019 realignment to priorities to address climate change. He has also presented climate related work to the UN, participated in the China Accord and most recently delivered a UN presentation called the two degree path for the building sector. Maziriad has too many awards to be listed, but of note is his winning of the AIA gold medal just this year, Cara Wedge FAA in a letter supporting Maziriad's nomination rights, the relevance of the work of architecture 2030, the impact on a strategic priority to focus on climate change. And now the advancement of embodied carbon are all areas where Ed has transformed not only the dialogue, but also the behavior of the AEC industry and the results we have achieved. As the new Biden administration joins the world in urgent climate action, Maziriad's pioneering work on centering the crisis around the built environment as both cause and with tangible and accessible design solution has never been more critical. And also hopeful in urging all of us to help ensure a positive future for all. Please join me in welcoming Ed Maziriad. Thank you. Thank you very much. Let's get right to it. I'll share my screen. First, just let me say we're in a full blown climate emergency. We all know this. But what's critical about this is that timing is everything now. What we do now is really very important if we're going to get a handle on climate change. We've all heard about carbon budgets. We've heard a lot of talk about carbon budgets, but very few people really understand what carbon budgets are and why they're so important in terms of timing. First, our remaining carbon budget for a 67% chance, so good probability of meeting the 1.5 degrees C rise in global average temperature above pre-industrial levels to meet that target that was set in Paris in 2015. Our remaining budget is 340 gigatons. The difference between 1.5 degrees and 2 is quite dramatic and the impacts are not very good for many, many, many people. So we want to stay within that 1.5. So how did we get that 1.5 degrees C budget? Well, the IPCC put out a report in 2018 and in that report, here you see the 1.5 and the 67% percentile, the remaining budget in 2018 was 420 gigatons. Today, in 2020, since we produced about 40 gigatons of CO2 every year, the remaining budget now beginning this past year was 340 gigatons. Well, what does that mean? And how does that impact us? Well, we know the issue is fossil fuel burning is the biggest issue. Our annual CO2 emissions globally is about 40 gigatons of CO2. So if we peak in 2020 and we've all heard the phase out day 2050, if we peak in 2020 and we phase out all CO2 emissions by 2050, that's 600 gigatons. That's less than a 50% chance of meeting that 1.5 of staying roughly at that 1.5 degrees C warming, planetary warming. So the phase out day 2050 doesn't really work anymore because we've used up so much of our budget since 2018. So the new carbon budget is 340. What does that translate to? It translates to a 65% reduction in CO2 emissions by 2030 and then phasing out all CO2 emissions by 2040. So the new date, the 2050 date is now the 2040 date, which is why timing is so critical and that we have to get a handle on this really quickly. Okay, we know that by 2060 world urban population. So this is urban population is expected to increase by 2.75 billion people. That translates into a global building floor area increase of 230 billion square meters. That's double the current worldwide building stock. Once we come out of the pandemic, building is going to explode. But what about the pandemic? We've heard a lot of negative talk about urbanism and density and the spread of the virus. So let's look at that. Is density a COVID-19 spread risk factor? Well, an analysis of 913 counties in the United States, a recent study this past year indicates that density is not a COVID-19 infection risk. In fact, suburban and rural areas have a much higher death rate than urban cores now because of less access to healthcare and the medical facilities. So what is the risk? It's overcrowding. So it's not necessarily density. It's putting more people, a lot of people in very, very small and tight spaces, very, very close to each other. So density is still on the table as a way to reduce emissions. So can we meet the 1.5 now? Can we meet that carbon budget and that 2030 and 2040 phase update? Well, let's look at that. Let's look at the built environment emissions. It actually consists of three parts. One is new buildings and that's building operations. As we design new buildings and we put them online, they operate, they use energy. And they produce emissions. That energy produces emissions. Second is existing building. We have billions and billions of square feet of existing buildings belching out emissions. And third is every year we construct and all that construction actually doubling the amount of square footage on the planet by 2060. That's a huge amount of materials construction and infrastructure, which is all in kind of our basket of design and planning. We have a huge impact on that as well. So those are the three areas we need to get a handle on. So let's talk first about building operations. This was 2005 we issued the 2030 targets. That's when we discovered the building sector that it was a big part of the issue. And we issued targets for reducing emissions in new buildings and designing new buildings and adding them to our building stock in the U.S. And in 2006, January 2006, the AIA adopted it and we started to talk about it within our sector. So what happened between 2005 when we first discovered this issue in the building sector and 2019? Well, GDP during that period, we had a lull in 2008, 2009 during the Great Recession, but then picked up right after that in 2010. GDP went up and usually when we have a good economy, floor area goes up, we added in that period 4.4 billion square meters of building, a huge amount of building in the United States. And you would expect energy consumption, adding all that square footage to go up. So what happened with energy consumption during that period? Well, the projections were that they were going to go up 24.2%. That was the projections in 2005. This is what actually happened. Energy use in the building sector actually went down even though we added 4.4 billion square meters to our building stock went down 1.7%. And emissions in our sector dropped all the way down 21%. This decoupling of emissions from growth has never happened before in the history of the United States. And since we started actually measuring any of this. So we've seen a decoupling and you've all heard, well, we can't reduce emissions going to cost too much and all that and it's going to hurt economic growth. That's out the window now. We've actually saved consumers a huge amount of money by tightening up the building sector and the energy consumption, even though we've added all that square footage. And where are we today? So what happened between 2019 and 2020? Well, building energy use obviously dropped because of the pandemic, but building sector emissions dropped even further down to 27% today. We'll talk about that a bit too. But this is the global building sector. You could see from 2010 on, world GDP increased, floor area increased, went along with it, and good economy, but look at energy use and emissions. You're beginning to see now a decoupling globally and that's good news because we need to peak and drop very, very, very quickly. This is the way we usually see the pie chart for building energy consumption and emissions. Building operations is 28%. Industry is 43%. That includes all building construction and infrastructure and everything else, along with everything else.  Transportation again, 23%. And then the rest, 6%. So essentially these three sectors. So how do we achieve a carbon positive built environment? Well, it's a two step process. Step one is what we call planning, design and construction. That's where we come in. Step two is renewables. We also come in there too. So in order to achieve a carbon positive built environment, two step process, we're at the center of this. And to get a 70 to 80% reduction in planning and design, we can do that really easily without, with all existing technologies. So we call that the no cost, low cost solution. We should be able to just through planning, design and how we construct buildings get 70 to 80% of the way toward carbon positive or zero carbon. The second is renewables. So what do we mean by planning, design and construction? Everything from growth boundaries, how we plan out cities, transportation, walkable communities, urban agriculture, how we design our buildings, how we orient our buildings, how we heat and cool our buildings, what kind of natural systems we use, and then how we build them and using carbon, using carbon sequestering materials, zero carbon materials and carbon sequestering materials. That gets us 70 to 80% of the way there. The rest, the renewables is everything from onsite renewables to utility scale, wind, solar, hydro. Some people, you know, we want to keep the renew, the nuclear that we have now because that supplies a fairly large amount. So this is how this is how we get the carbon positive. All of the strategies for what I just talked about is, has been put together in what we call the 2030 palette and the 2030 palette has everything from how you look at regions habitat corridors, mountain site settlements, transit corridors to cities and towns, parks and urban retrofit all the way down to districts, transit oriented development, how do we look at sites, solar access and sustainable sites, all the way down to the buildings that we design. And now we've added to that a materials palette to talk about all the different materials that we use. It has it has recommendations for all of how to design and plan all of that in the 2030 palette. And it's what we call a living document we keep up updating it as we get more as we get more information. So all of that now, we know how to do. There's no mystery anymore. So let's start with building operations. What do we have to do only buildings have to come in at zero carbon. And what that means is they have to be designed efficiently fairly efficiently. They have to be electrified. And we have to use renewables for that electrification no onsite fossil fuels. That gets us to zero carbon. And now we have a zero code. We put together a zero carbon code standard. It's now been adopted into the International Energy Conservation Code, and with the help of the AIA and other organizations, we're beginning to talk about it at local and state governments and actually internationally as well to start to get that in place so that all new buildings come in at zero carbon. This year, this year in Europe, they're all countries are expected to have a code in place a nearly zero energy building code with onsite and also renewables to get to zero carbon. All European countries beginning beginning this month are supposed to be putting in place zero zero carbon code standard. And we were over in China and we showed them the zero code. And within a few months they developed a nearly zero energy plus onsite and also renewable code standard. They're waiting to see how we implemented before they implemented, which is kind of the way that things happen things happen in China. We need to get them to the cities and provinces to adopt them right away. So we're all working on that. What about existing buildings? Well, here's New York City, right? See those little circles that's where all the huge buildings are downtown Brooklyn, Midtown, Manhattan, Lower Manhattan. 2%, less than 2% of the buildings in all of New York City and that's the boundary actually extends further than that than the than the drawing here. Less than 2% of the buildings in New York are over 50,000 square feet. So a very small number, 26,680 buildings are these huge buildings over 50,000 square feet less than 2%. That number of buildings is responsible for 48% of all New York City's emissions. So you see New York City now based on study that we worked on with them have adopted a big buildings policy to reduce emissions. However, this pattern of a few buildings responsible for half of all emissions in these urban areas and cities is worldwide. It is a worldwide phenomenon. You see it in Chicago, for example, you see all the big buildings along the waterfront and then miles and miles of small buildings. Same thing in Madrid, Spain. You see the same thing in Ho Chi Minh City in Vietnam, in South Korea, the downtown cores are huge, huge cities and then surrounded by miles and miles of small buildings. Same thing in Japan along the waterfront and Nagasaki and same thing in Sydney, Australia. The same pattern all across the world. So how do we get a handle on that? Well, we have a big buildings policy, which we have very few buildings. They're usually owned by fairly wealthy people because they're so big. And so we call for them, we give them 10 years to get to zero carbon to electrify and use renewable energy on site or on site and off site renewables. Why do we give them 10 years? Because within that period, they're going to hit a capital improvement cycle. And during that capital improvement cycle, it's really inexpensive to renovate the building to get to zero carbon. What about the millions and hundreds of millions and actually billions of small buildings out there? Well, you look for intervention points, point of sale. And when we look at building sales, they're almost all small buildings. So at building sale, the new owner coming in, the person who's buying the building, obviously has money, obviously has gotten financing. If you give them an incentive, they can go to zero carbon at very little cost or no cost. So and if you do that, point of sale every year or zoning or use change, you will get all the buildings to zero carbon by 2040. So we now have a big buildings and a small buildings policy options that cities are now beginning to adopt. New York was actually the first one to adopt the big buildings policy. Okay, now the third leg of the stool here. What about materials, construction and infrastructure? Well, there are literally hundreds of thousands or millions of products out there for every category you have. I don't know how many products and made all over all over the world. How do you get a handle on all of those? Well, we had a breakthrough two years ago. We actually took a slice out of industry that was building materials and construction, actually the core and shell of a building that's the steel and cement and brick and glass, essentially the shell and structure. And then all the rest of the hundreds of thousands of materials fell into the like H rack and lighting and equipment, interiors, infrastructure all fell within the rest of the industrial sector, 32%. However, that doesn't help us because it's still hundreds of thousands of materials.  Well, we reshaped the pie again. And lo and behold, we came up with two materials, concrete and steel are responsible for half of all industrial emissions. Again, everything from, you know, soda cans to books to, you know, the furniture, you name it. Two materials are responsible for half of all industrial emissions. And if we look at the rest of that that falls into the industry building finishes and equipment and plastics and glass and all and all the rest. We who design and plan the built environment and the building sector are responsible for over half of all global emissions. So we have a huge opportunity. So now what do we do? Well, with with embodied carbon, we need to and all these materials we need to change the conversation, especially those two materials, and the conversation is changing. We brought that to light about two years ago. And then all of a sudden, last year, we saw an explosion of media advertising and and articles exposing those two materials as incredibly destructive and that we had to get a handle on that. And the Guardian concrete, the most destructive material on the planet and Bloomberg steel makers are next in the crosshairs as climate pressure grows. So you see steel and concrete now being discussed and that we have to get a handle on their emissions. And the great thing is there's an alternative and that puts pressure once there's an alternative and competition, you get pressure and you get a race to zero emissions and so timber mass timber cross laminated timber is now giving steel and concrete a little bit of heartburn and that's really good because we're now seeing movement in all three sectors, even in the mass timber sector in order for it to get its its its timber sustainably forest. And we're now beginning to see some incredible policies put in place and where does it start in New York, New York State just proposed legislation. And they did something brilliant. Instead of looking at we have to set a benchmark and what is that and CO2 E and this and that it gets very, very complicated. They just said let's just do it during the bidding process. Hey, you do a life cycle assessment for your concrete will pay for that will pay for all the concrete manufacturers do a life cycle assessment. And when during bidding will give the lowest, the person with the lowest LCA concrete manufacturer will give him a leg up we'll give him a 5% reduction in his bid or 10% reduction in his bid in terms of what we look at in terms of price. So if he beats somebody out that has a higher LCA because he has a lower lower emissions. You better believe the guy who lost that bid, especially with a lot of New York State work and concrete and your concrete and in roadways and in overpass it you know it's just a lot buildings. It's a race to zero, because nobody wants to lose out. You know, on a project and on a commission. So this is this is incredible. It sets up also policy options for all sorts of other materials now during the bidding process and it sets the private sector up now to create bidding documents that actually do the same thing so they can now look at New York City and model their bidding practices over there. So, now what do we do, we still have a quite a bit to do so in in in products and in our what we can do our sector reuse, reduce and sequester so reuse it's planning design and specifications and policy, but planning design and specifications are huge. We control that. That's everything from repurposing urban areas and upgrading existing buildings and renovating and adaptive reuse and actually designing buildings that deconstruct them and reuse them after their lifespan is over. So all sorts of things that we can do, reduce, and it's also planning design specifications and policy. We influence policy by the way that's everything from growth boundaries so we're not sprawling all over the place infill and densification how do we do that optimizing structure. So we use less materials using low carbon and zero carbon materials and developing policies similar to the one I just talked about. That's a question that again is a design and specifications process so that falls an hour. An hour court. It's everything from designing using sustainable and cross laminated blue. I mean a wood, and also now we're starting to see a movement and just being talked about now to cross laminated bamboo, which grows really fast is real sustainable and is as structurally sound as an even better as than would and real inexpensive we're looking at concrete manufacturers now actually taking CO2 out of the atmosphere and creating aggregate out of CO2. And actually sequester it or injecting CO2 into the concrete makes the strength in it and shorten the curing time. Biomaterials made from, you know, from sheep's wool, for example, and in insulation, things like that. Landscape architectures is is actually now coming into its own it's it's it's an incredible new new area of exploration sequestering CO2 and in ours in our site designs and landscape design. So can we meet the 1.5 degrees budget. The flat arm building you see that with the spire right in the left hand side of the of this photograph that was in 1891 in Toronto now keep your eye on that building. This is what it looked like in the late 1800s. This we're going to fast forward to 2000s 2010, you can see the flat arm building still stays but look how that city has changed you see all the contemporary buildings modern architecture has really flourished that has happened in city after city. And we see the same building type now everywhere. How did that all happen and how long did that take. Well, in 1925. We had what we, what we normally call the first there are a number of modern buildings that that can it can achieve that or had achieved that during that period, but we consider this the first one, the bow house. There you see structure moved inside so it was not masonry walls and short spans, but structure moved inside it was concrete yet an open floor plan, and you hung the exterior wall from the structure and opened everything up and got light and air and everything into into the buildings. There was a huge, huge breakthrough that was in 1925 so what was going on at that time. We had 1925 we had the first model T pickup truck. That's where we didn't even have TV at that time 1925 we had radio vision, we projected something out of a box on a wall, an image and that was the first that the precursor to television. And the first transatlantic flight and I mean, a call didn't happen until 1927 so that was, that's what was going on around that time. In 1928, the global architecture and planning community got together and held the first international Congress of modern architecture. And they did that because conditions were really, really bad we had, you know, industry belching using coal belching out all the stuff people living in these areas. And they said enough is enough people, you know, the average lifespan was was was very low was in the 30s I think during that period. So they came up with a set of guiding planning principles function based on so that's where zoning came from was during that, during that period high rise housing blocks get the get the housing out put them in Parkland solar exposure, open up the floor plan open up the, you know, glass windows you get sunlight in the Corbusier developed the five points column wall separation. And again, modern architecture then we had the guiding principles for modern architecture, during that period and 29, 1928 29. Then in 32 Philip Johnson and Henry Russell Hitchcock came to in New York, they had an exhibit called the international style, we can now take that because we could fossil fuels were cheap dirt cheap we could overcome any exterior environment, we can have the same style all over the world. They had a an exhibit called the international style. What was going on in the 30s well we didn't even have a commercial airport we didn't have transatlantic flights yet. During that during that 3035 we had the first airport and commercial airport in Newark.  And in the 30s, then by the late 30s, we started to see modern architecture take off by 49 Johnson Johnson did his class house in New Canaan single glass. We can put the same thing anywhere in the world and climate control it and then by 52 we had the lever house and 56 we had the first city laid out on the principles of the modern movement. So, all that, think about this, all that took 27 years, the world changed in that span of time because of the architecture and planning community and the technologies that would develop at the time. But I want you to consider this. This is how we designed and planned all that with a T square or triangle and ink pen that we had to actually dip in a bottle. And it would always come in under the triangle and T square and ruin your drawing so you had to scrape it off with a with a razor blade. That's what we that's what we changed the world with in 27 years we couldn't even do a curve we had French curves but they couldn't dimension them. So you can only do maybe a half circle or full circle and everything structures was done with a slide we didn't even get the first pen till 1960 till after we had changed the world with those tools. And the first laptop came in at 1991. So in 27 years look what we did in that time span with the tools that we had and think about all the tools we have today we can we can structure anything we could look inside the building we can fly inside the building look at the daylight inside the building calculate the solar impact and content and what we can capture on every side of a building and we have the materials and the technology to do all of this. We did that 27 years and now solar is now the cheapest electricity in history in the world. Cheaper than anything battery power is coming down now it's threatening coal and now it's actually this year it's threatening gas. And in China it is and China has high energy prices electric electricity prices. It's cheaper to actually build solar than it is to pay for energy off off the grid now in most cities in China. And this just out on January 11 2021 just a week ago. This is what's projected for 2021 how much solar this is how much new electricity generation is going to happen right. Most of it is solar and winds batteries a little bit of natural gas which we have to get rid of actually. But think about this 75% roughly all the electricity generated goes to operate buildings. This is what's expected to come online because it's actually some of it's being built right now so we have a good handle on what's going to what's going to be coming online in 2021. If the building sectors energy consumption is still going down and we don't need any more electricity than where does all that solar and wind and the batteries and everything else goes. It goes to this place fossil fuels and mostly coal. That's why emissions are dropping it's because of the building sector. So where are we well this was 2005. You can see electricity emissions drop this is gigatons of CO2 on the left hand vertical column. We've dropped emissions in our sector in building sector by 27% from 2005 levels. We now have the Biden administration their their platform and what they're proposing is zero electricity emissions by 2035 if they implement that if we get that. And a few federal state and local government policies which we're seeing now toward electrification a little more efficiency. And we begin to adopt better building codes so that the new buildings coming in actually we can actually even get more reductions. This is what happens in the building sector we're down 72% from 2005 levels by 2030 and we completely phase out zero emissions in our sector by 2040 all really doable, but it depends on us. So can we meet the 1.5 degree seat carbon budget. Of course we can. And we'll be taking this success story into cop 26 and get the countries to agree to the 1.5 and begin to increase their ambition so that we can meet the 1.5 degree C. Emissions target and we'll be hosting a summit in the UK, along with the with Reba. Looks like a now architects declare our entire industry products come together just before the cop 26 and have a summit and illustrate that this can all be done. Thank you very much it's up to us. Thank you Ed for a wonderful and inspiring presentation and very hopeful. I wanted to jump in already. And I know Alex will join us to ask. Do you sense, you know, it's true I think I think as architects and designers and planners we've, we've, I mean we've known, I mean you've designed a passive house right in the 70s like the technology has been around for a long time and, and yet it's taken so long to to develop to change building code to develop, you know regulation etc. And for architects but frankly to to come together I think modernism and that epoch, you know of a small group that sort of, you know came together. It's, it's, it's, do you feel that we are at this similar moment where the mobilization is finally tangible and I know you work closely with the AI and, and for some time they seem to you know certainly they have members that are, you know, not on board so you know the AI maps out onto the, onto the geography and the politics of the country so I'm just curious if you are. You have a sense that this time there's a there's a significant mobilization the very tangible practical around. You know, what's amazing is that when we discovered the issue in 2002 and we published that article in Metropolis magazine actually and again another New York magazine called the architects pollute issue. I understand from from Susan's and asking the editor at that time that the first few months there was a lot of pushback from the architecture how could we pollute. I mean, to put up a cover that had three roles of construction documents with smoke coming out the top with the head with the with and this is on the cover which says architects pollute. It's like stabbing an architect in the heart we're taught, you know, you teach Columbia, you know, I went through architecture school, we're taught to make the world a better place we're not taught to pollute and we're responsible for the, you know, the biggest problem on the planet in terms of destroying the environment that us it was like it was met with with, you know, people were, were not very happy right. However, within three months, within three months of that, the AIA then came out and adopted the 2030 targets for the industry. And it started out in probably I would say it's it started with a lot of firms, but in terms of impact. The large firms began to pick it up, which had quite a bit of square footage and stuff during that period so that's why you see energy consumption, being flat, even though we kept adding all these buildings, because the new buildings coming in. Because of a lot of small practitioners, but quite a lot, many of the large practitioners began designing better. And we began renovating buildings, especially during the recession we had more renovations than new buildings. So it established this renovation pattern. So as we moved out in time and we got better designing buildings. And when we equaled out new buildings and renovations, we were designing down 50% in our new buildings and renovating down 50% in in in all our existing buildings and they canceled each other out that's why we will flat. And then as we transition to renewables, the emissions came down. So the United States has a our sector has a huge success story. But we need to step it up. We can't just keep doing that if you know, we won't make it so we need to step it up. I think there's an urgency now. There was actually the urgency started at the beginning of the last administration. It was starting to happen and then the administration, this administration came in and was pushing fossil fuels and trying to just suppress any advancement in renewables and everything else.  And I think we doubled our efforts in the last four years. And now with a new administration coming in and nearly every appointment in every, you know, department is someone concerned about climate change in the new administration. I think we're going to see an explosion of more good work. I think the universities now, who have all been doing, been doing things in every studio project, you need to have that as a basis as an overlay of whatever else you're trying to do whether it's low income housing or, you know, you know, commercial development or the design of a hospital, whatever that overlay now, I think will be there. And so I think, I think this is now the perfect time. The next storm. Everything now is really together. And I think you're going to see an explosion in our industry and emissions going to drop like dramatically and as I said, the architecture planning and landscape architecture now community at this community is the gatekeeper of all of everything pretty much. And everything else will, it will fall in place. So if we do it as the gatekeeper. Hey, I've heard from architects and I this I used to hear this remark, I don't know if I hear it anymore. But I used to I think I probably squelch but I used to hear my client doesn't want and if you know want me to do a zero carbon or an efficient building. I said what I said I've been practicing for 50 years. I've never had a client come to me and say look, I want you to design a building that uses more enter I want my bills to be like really through the roof. You know, he has no control over what you design, as long as you give him a building you build it within budget, you satisfy the program, you could design as efficient as you want. And you have a thousands of trade off. I can use three coats of paint with sanding between each coat which cost a fortune, or I could use two coats of paint with only one standing or no sanding. I could put that money into low low, you know, low e coatings and in solar clock I can do all sorts of things. As long as I bring the building within budget. That is finally getting through we are the gatekeepers. If we don't do it, it's not going to happen. I can tell you right now it's not going to happen. The good news is, we're all on board the recognizing me with the gold medal was not really recognizing me. It was recognizing our community that that's this is where we've come. This is a recognition that we are now on the front lines, we can do it, and we're going to do it. And I think that's what that gold medal represents. So anyway, I think that's where we are. And, and, and looking at the drop you can help but say, you know, wow, look what we've done, you know, all we have to do is we have to keep doing it step it up a little bit, and, and we get there. And we can show. We need to show all the other industry organizations all around the world that this is really doable. Because a lot of them are ahead of us. The UK just made a commitment of 68% production by 2030 EU the whole EU is 55% reduction by 2030 they were all within the 1.5 now. So you're beginning to see this happen all over I think I think we're at a, at a period that we could call a real Renaissance in getting this, this, this under control. And I think it's happening now. The universities are going to play a huge role, because if you, if you training the students with the know how, and the excitement that all this is happening and then you go out and they're going to do this. When they get into offices, they set the tone in all these young people set the tone in these offices and push the older guys who maybe well I don't know, you know, they push them like crazy. And change the whole culture within within within the professional community. So that the universities and the schools of architecture and planning and landscape architecture and interiors have a huge role to play and making this change. And they've been doing it actually so they need to step it up also just like the profession needs to step it up so we actually bend that curve down a bit more, and then influence influence everyone worldwide which is what we're trying to do a prior to the cop and we had a global teaching. We're going to web that out globally to our entire industry. Professional industry from the cop in in in October. Can I just dive in inside. I just wanted to say just amazing to hear you speak partly because it's a great honor and wonderful and to hear such a creative talk, but also that you provide such a positive view of the future. At a time when people have been wondering how on earth, we're going to decarbonize the planet and the way we do things.  And of course a major part of that is manufacturing and we haven't talked about transportation and things like that but manufacturing and buildings and heat and things like this are huge and so hearing is a huge issue of how not only we can do it but we're already doing it. I think it's brilliant here, but you ended up, I want to get back to Europe in a minute and talk about that but first of all wanted to ask you a little bit about this bit about the future and what role they should be playing because at Columbia we've been thinking very hard about an Amala and I have been talking about this a lot. What kind of a future university we need to be. Not just in terms of how do we decarbonize our campus but what kind of skill sets do people need in the future. I think there are some subjects that are going to be different in the future. And, you know, when we're now building a climate school, that's an amazing opportunity to rethink what a university needs to deliver in the area of climate. So I'd be really interested to hear your perspective on which subjects you think are just too small right now that we need to make much, much bigger, or maybe some subjects that don't even exist that you think are going to be increasingly important going forward. It's kind of like, let me remind me of this question because it's kind of like it's kind of like discovering the new pie chart with concrete and steel. We spent 10 years trying to figure out the industrial sector and materials and I did all the specifications in my office so I know how many, you know, sweets catalog back then you had a shelf of sweets catalog each one was this thick with products in it. We could choose from millions of products and the people in the office said, Ed, we've got to get a handle on products we've got to get a handle on products I could never figure out.  How do you do it. It was so complex. We couldn't get our handle around it until we finally we kept pushing and pushing and pushing and doing talks we finally got this, you know, looked at the International Energy Agency and looked at the energy consumption of steel and concrete and then at the emissions and finally got a handle on that that it was half of all industrial emissions and it was us. Now we only have to deal with two materials and then the others will fall in line right because now you're putting pressure on the whole industrial sector, and everybody wants to get into into the actual once we found that. And then it was doable before then it was not doable so there was nothing on and body carbon till 2018, when we first had the first meeting in 2018 and in San Francisco on body carbon. And look how far we've come now in just two years because of just those two materials. Okay, so what about education. So when you look at education, what's been happening. There's more research as well you know which is in research yes and research to. So when you look at when you look at the, the programs architecture programs and stuff some or more ahead of others and all that but when you look at it as a whole. And you start to see there's, you know, courses in environmental control systems in lighting and, you know, all the different pieces that in daylight and that go to the you know that go in together you have all these, but they're always adjunct courses there are either you know, and they, they're done by some of the fact that you know the studio instructors and they feed into their problems, but we're, but, but, you know, at least when I went to school, half of all the credits was the design studios, which was like I don't know how many eight credits or 12 or whatever and then all the other ones were one or two credit courses right. So where'd you put your emphasis you put it in design studio right. That's where everything happens that's where it all comes together. That's what you have to change designs. And so you have people who are tenured who could care less about energy. It's too complicated numbers. They want high design all this kind of stuff. So you've, you've got to bring all that into studio every studio project has to have an overlay of now. And I think we're going to see that has has to have an overlay of emissions materials day lighting all the things that we had in the palette every one of those things that comes into studio. If you get that in studio with every project, and you make that a core of every project as you go through from first year to let to the last year, those students coming out will know exactly what to do when they get into the firms, and firm culture. If you don't get it into studio. It doesn't have the credibility or the impact that it has to have in our profession. And I think we're starting to see the schools do that, you know, but we can't let professors who just want to focus on in a studio on and waste a half a year or a year on some other item, because this is too important and it's an overlay, you could still focus on that item but with this issue is an overlay. That's how you change the entire educational system and research. So now you start researching concrete and steel and wood and bamboo and where does that come from and how do you do it and cross laminate stuff you start building structures you go out and have design build and I mean, there are all sorts of, you know, crossings of that. So in terms of federal views of this I mean the, of course we've got to change the administration right now so a lot could change but I mean you could ask what should universities be doing in terms of playing a role going forward on the research front and what resources would be typically some of these federal funding sources are not that swift at changing and and moving in new directions. And I just wonder where you feel I mean it strikes me low carbon manufacturing is such an important area. It's a big one to do far more research on there should be zillions of dollars going into this, just like there should be zillions of dollars going into carbon removal techniques and things like that. So do you have any perspectives on on how the US government might change and do you think there and do you see this as a sort of an issue for research from the point of view of taking the lead in somewhere that could be very helpful. Absolutely. So you have architecture you're planning you have landscape architecture they all come together within usually under one umbrella. Landscape architecture is going to be used and we haven't even scratched the surface on landscape architecture and site design and everything else site designs everything from from sidewalks hard scape soft scapes planting everything else you can get to zero carbon.  That's one area for research that I think is absolutely right now how do you, how do you design how do you calculate all of that materials again is going to be huge. How, you know, I think wood construction is is another area now that is that has now been established, but is ripe now for, you know, fire. I mean, all the all the stuff that, you know, all the things that you hear about what you can't use it because of this or structurally it can't go this high or anything else. I'm starting to disprove all that so that's another area that's right. Boy, I can, I, you know, if I put my mind to it I can go through 20 of them. I will enjoy them down. The point of view of academia it's wonderfully rich and interesting so it's kind of like you're doing something useful. That's planning. Planning and transit now and coven. My God, all the renovation now that has to happen. You know, I'm not sure we're even going to keep our office. We're all working remotely and we seem to be doing fine. You know, and actually our staff is in Washington DC and in Washington State and Oregon and California here in New Mexico we have actually very small staff in New Mexico. I think now we may just, you know, go go remote. I don't think, you know, obviously we want to interact, you know, we need interaction as human beings and stuff so I don't think that's going away but there's going to be renovation that's going to happen. That's a whole nother area density. You know that study on density, for example, density was getting such a bad rap until someone did a study on it. That's research where they did a study and showed that it wasn't density. It wasn't actually density. It was overcrowding. It was stopping more people into a small space that was the issue. And so how do we get around that all these areas now with COVID, and, and, and the built environment and, and, and air changes and you name it this is all right for, you know, for, for study. You know, I, I was struck actually by, I think what Alex has said which is, at some point we get so bogged down by the complexity and, you know, as, you know, what material to choose how to calculate, you know, how do you get you know, I mean, we've been talking about the school and so it's so refreshing and powerful to almost over, not oversimplified but there's a sort of like let's, let's deal with the big buildings, let's deal with, you know, let's, let's just focus on these materials that's so I wanted to hear a little bit about your, your palette and how you're now kind of working through some of this and how do we broadcast how do we make that sort of foundational, you know, it doesn't get adopted in building codes is, you know, where there is a kind of very basic knowledge that doesn't get bogged down into the kind of nitty gritty about, you know, the palette of more design issues. So their recommendations for design so how much glass do I need in in New York, for example, to totally condition my space for heating, for example in the winter, then how do I shade it and all of that how do you design all that. So it's all design and planning strategies. That's really what the palette is. It's not really code issues. The zero code simple. It's you design an efficient building, and it lays out you can do it by checking off the boxes, you have two options or you can do a simulation. And then you add the renewables. It's as simple as that getting to zero apartment. So the design platform is really almost is, you know, is going beyond that. And that's what the palette does. And we're always looking for new information with school kind of uses the palette for a project and then it, it sends us some information and will incorporate some things into the palette that are new. So, I think, I think we can. So I think that's one of the things where a lot of schools, a lot of the design instructors use the palette as a basis for for designing. You know, it's out there. It's free. It doesn't cost anything. It's online. You can make your own, put your own information in for your own area. And so that's all there will.   So how realistic do you think it is that we're going to get all these other parts of the world that have got to play ball with with what we're trying to do, either here in New York or elsewhere, and do the same kind of thing. I know COP 26 is coming up. It's a great opportunity. But the many countries seem to be very much focused on their own economic growth and worrying about impacts on that and they're not looking for expensive solutions and looking for cheap solutions. And they're not looking necessarily particularly after the pandemic to actually come up with expenditure that will actually worsen their economic situation.  We can partner with Europe if you're we think Europe is being moving in the right direction and we can look at some of their brilliant ideas like the European Green Deal, etc. And we can build more of a sort of global block that way and apply pressure, but I don't know whether that's what you would think of doing or whether you think that actually this isn't going to be a problem because fundamentally the industry and and architects are going to drive this radical transformation. And, and people are going to want it anyway. So that's, that's actually a great question and something we've looked at. So let me. I didn't put this up, but what I could have. So when I showed the, the, that we're going to read, we're going to build the world out again between now and 2060 right well tear down part of it. 20% 25% but then we'll add back that back in with with with more more construction so that the built environment will essentially double. Okay. So we looked at where is all that construction going to take place from now until 2060, because that's important that sequence is important. Okay. So what we found, if you put bubbles on construction you have a map of the world and you say okay, where's more construction going to you look at North America has a big bubble. A lot of construction going to go on in Canada the US, Mexico in that that's a big bubble. Europe is actually a big bubble because of renovation and everything else that's going to happen. And the third big bubble is China. So the three bubbles, big bubbles are in the global north. Okay, then you have smaller bubbles in India and in South America and Southeast Asia you have smaller bubbles. That's the first 10 years. So the first 10 years is where we have commitments and a lot of know how the US and where we have these reduction targets, China is a little behind but I'll talk about China in a minute. So it's the global north where the next 10 years are critical. Then all the construction, essentially, the global north is totally built out moves to the global south, India, the bubble like explodes. South America, the bubble explodes. Southeast Asia, the bubble explodes. You know, some of the other countries above, you know, above the Middle East, the bubble explodes. So you have almost all in Africa is huge. Africa really explodes. That's where the biggest African India the two biggest. So, initially, we have 10 years to set the course and all of our firms in the global north are international in scope all of our large firms, and they set the agenda so if we begin to set the agenda in the global north. Then when the global south starts to build, it's already said it's kind of like the modern movement, what how that all happened and then before you know it everybody's doing right. So that's the opportunity now going into the cop that it's in the global north, and that we bring the global north in into this conversation in our sector, which is the biggest sector. And we begin to establish the norms for how all this construction is going to happen. Now, China is the big question mark in terms of all of this infrastructure and construction. They're kind of, you know, getting built out, but they still have another few years of really building out and then it shrinks. They don't do much building anymore. All the cities are built and everything else. The good news about China is that all our major firms, international firms have offices in China. So Perkins and Will has an office in China, Gensla has an office in China, the European, the English firms have offices in China. They all do work in China and set the tone in China. And in China, all non Chinese firms must partner with a local design institute, a Chinese firm. And these local design institutes in Shanghai and in Beijing, they are huge. They have their, their high rise buildings full of thousands of architects and and and engineers and everyone else. They partner with the so the international firm hooks up with a local design institute to do a project. The international firm does the design, the local design institute does the construction documents the bidding, and they oversee all the construction parts as well. Sometimes they have construction parts to them also so they're huge. The international firms and the local design institutes are like this. So once is so we issued the China court years back when we discovered this and we got the local design institutes together with all the with all the, the international firms together to sign on to an accord there is a actually an industry called CDA B which is kind of like the a but only for the local design institutes and there's one in every major cities local designs, every major city in every province in China, and they do all the work and design and construction. They have been learning really quickly from the international firms on how to do all this because you can't do any building unless you do it with a local design institute. And they are partnering on everything that's going on in China, they're getting to the point now where they're really sophisticated. They invited me when I was in, was in southern China to a meeting where that they showed me a whole city that they were developing it was a transit oriented development density, you know, all the, you know, renewables, everything you'd want from an international firm. So they showed me that so I said well which, which planning firm did you work with you know did you work with Skidmore did you do work with here. We've done all we did all this ourselves. It's the first time I saw that that the Chinese actually now have to know how to do all this stuff they picked it up really quickly. And so we will be bringing CDA B all the local design institutes to Glasgow, we invited them to Paris will bring them then. And they really need to step it up. They need to step it up. They wanted this, they want to do a design manual now kind of similar to the palette for China. They're working on that the local design institutes. They already developed a zero code a zero carbon code they haven't implemented yet, but they're trying to get it as a standard the government to actually do it and require it as a standard. So I think we're I think this cross pollination has been huge with with with China, and they're really smart and they're very talented also. And so I think we're going to start to see the global north, which with China, your US take a leadership role in the next, you know, five to 10 years. And then influence what happens in the global south similar to similar to how the modern movement happened in Europe, essentially, and then when global. Fantastic. I think that's I think that's I keep my fingers crossed that's how it's going to happen. But the CD AB and then the local design institutes have been unbelievable, real supportive, and always willing to learn and they just been incredible. We've, we've been working with them now for Let's see about seven, six, seven years, seven years, and we're very close to them now and they're always pushing the envelope so I'm hoping to see China move off of coal move more into. And actually the number one country producing renewables anyway they need to step it up though and basically begin to phase out coal, which is the big, the big issue there. I want to add, I know Alex is going to have to run in 10 minutes I want to make sure I got to go get my shot today. Pretty sharp. Just make sure to sort of ask some of the questions that the audience has shared to that are somewhat related the first one. Thank you so much for your presentation gives me hope but I do have one worry many parts of the country are also struggling with an affordable housing crisis on top of our climate crisis so many of the materials that will help us get to zero carbon are still cost prohibitive for low income families who are struggling just to find a home let alone an environmentally responsible home. How do you navigate this is the answer that 10 year delay for smaller buildings you spoke of and just I want to tie it to this other question as we expand on this conversation of CO2 emission reduction how does all this coincide with bringing worldwide poverty which is as important so questions of equity as we think of. Okay, so let me, let me do the poverty first and then the housing sector. Okay, so the poverty first I was at a meeting with Mary Robinson and a whole bunch of people in Europe way back, and they were talking about energy poverty. It didn't happen until you saw the energy poverty because if you didn't have energy access to energy, you know, you're not going to solve the poverty issue because that's what education revolves around it and everything else.  You know, I had my laptop pulled up a map of of solar. Solar energy falling on a square meter in the entire world. Okay, the whole world. So this was energy on an annual basis aggregate on an annual basis and on a monthly basis. Okay, so this how much energy falls on every square meter in the planet for square meter. The energy the end the most energy rich part of the world is in where all the energy poverty is.  It's distributed free. This is not, I have to build this after all I have to do is collect it and use it. There's two ways to do that. One way is, if I'm in the north energy poverty in the north just let it into a window just orient the window right and you solve the heating problem in no time with it with, you know, how you model your interior materials, at no cost by the way, we all build that a masonry in the in the in the energy poverty or in the poverty sector it's all major it's brick it's you know pouring some concrete columns and infill the brick and everything else. It's the way everything is built. So you have you have the materials, all you have to do is have the design know how and shade in the summer and you can do it without any energy.  The global north has to help the global south install on every single site, you know, affordable take and a little small, small battery, and that's all coming down in cost now. So, we could solve that problem energy poverty in a heartbeat. And I say this. So right now it's so it's insane. We dig up coal from somewhere else we transport it we build a railroads we have to transport it we have to build a big factory we burn it 60% of it goes out the window we use 30% we have to build transmission lines everything else to get it. And here we have free distributed to every site in the world, enough energy distributed free doesn't cost anything. All you got to do is collect it and stick it in a battery and use it. It's insane what we're you know what what we're doing we talk about energy probably now let's talk about housing. Okay. Don't tell me housing or cost more to do an efficient housing building or we can't do it orient the glazing right you'll solve the heating problem and housing. You use daylighting so you don't have lights on during the daytime at night we go to sleep we turn the lights off. So you have the lights on, you know, a certain period of time. You know, the design decisions you make will knock out 70 that like I showed 70 to 80% of the energy consumption of a building just through design, you don't have to do anything else. So you can't tell me oh we can't do it, or because it costs too much. That is a red herring issue, you can do it in affordable housing you can do it, you know you can do it in the smallest unit you can do it in larger you can do it, you know, and all you have to do is know how to design. And that comes out of where at a studio. And that ties very well with the. So one is the, you know, design and space and the tools that we have outside of technology that we need to really kind of re appropriate and reorient towards more sustainable building. And it ties to the two questions that I'm going to tie together on materials, do you think it's critical for architects to be more technically challenged in material research during the educational stages and university. In order to meet these standards and the second one also about the materials almost all materials we are using right now are carbon heavy and designing with low carbon materials is not yet embedded in design practice. We're going to crisis of timing how do we jump start changes in how we specify and design with materials right now. Okay, so again I told you the materials issue is very new. And we just really discovered the, you know, really got into it in two years ago. Since that time there's been an explosion now of tools and getting a handle on materials is really understanding the tools that you can use to actually design. So now we have EC three, which is a tool, a design tool that'll measure the carbon intensity of different materials within a region, and different product manufacturers and everything else. You have the code tool you have. I think edge now is doing embodied carbon. So you're going to see. There's now a site site analysis tool. All of a sudden escapes my mind it's a Pamela Conrad has a tool for carbon sequestering sites how you know, you know, landscape and all that how you can sequester carbon. So that. So it's only two years old and all these tools now are starting to come to fruition. We're starting to see them now we're starting to see money thrown into developing these tools. So that's, that's, that's what we have to use within academia in our design forces is start to begin to introduce these tools, make them better, get research projects, you know, like Alex is talking about on developing better tools for material selection. And just like that you're starting to see all that now begin to happen again. This is so new and it's so ripe for, you know, for, for research and and application and would, we have a big wood conference with all the wood developers and, and, and industry folks and the NGOs, and they want to see forest sustainably done more than what is actually very sustainable. Most of our forest and met our managed forest and their way on the capacity. So we could use wood and it's, and it's, and we're pretty sure we're going to get the, you know, the carbon content way way way way down. We're thinking at how you, you know, how do you detail what how do you I mean, it's just the whole thing is just ripe for for all sorts of innovation and studio projects and, and research and everything else bamboo is now we just have some friends of people just put out a big article on bamboo there's a come, there's a company that's making actually glue laminated bamboo out of, I think it's out of Indonesia or Southeast Asia, they're starting to market it all over the place. That is so ripe for, you know, for an explosion because it takes two or three years you can grow that you have to wait for a tree to grow for, you know, 20 years. It's a grass essentially bamboo, you can grow it and, and then harvest it and regrow it grows. You know, it's kind of like weeds. So, just so much stuff. Anyway, I think I know Alex is is running but so inspiring to hear you kind of share all of this and we feel really. We feel very energized and just kind of ready to, to, you know, launch into this intense moment. So I really appreciate you joining us today and hope hope you'll be back and hope we can make you proud. And G SAP in, you know, pushing further and faster in terms of integrating all of these ideas but also know how and kind of sense of knowledge in the design studio as you shared. It's been, it's been a pleasure. I'll let you know when we can travel and I'll let you know when I get to New York. Yeah, visit. That would be great. Well, thank you so much. I really appreciate it. Thanks, everyone.


Welcome back today's lecture 23 math 241. We are going to wrap up chapter 7 section 3 These types of problems. Obviously, they're separable differential equations. That's why they're in this section They take on a variety of different names. This textbook calls them mixing problems or Other textbooks might refer to them as a change in dilution of a liquid I think it's pretty appropriate to just call them tank problems. Okay because we're talking about some closed room actual physical tank some specific domain where we've got some Substance brine Fresh water something flowing into that tank Something flowing out of the tank the homogeneous mixture flowing out of the tank and we're going to determine when it's safe to Drink the stuff that's in the tank when it's safe to go back into the lake that had a pesticide spilled into it When the room is was that was formerly a real smoky room when it's Breathable air that's not going to pollute your lungs those kind of things now We don't start off with the real interesting problems We'll start off with kind of the real basic problems and hopefully we'll get to some Examples by the end of class today that are actually kind of solving some some real world type problems So they are separable differential equations Thus the location in the book This book calls them mixing problems change in dilution problems or I just like that name for some reason tank. It's just kind of got a concise Ring to it so we'll call them tank now not all problems that you discuss in a math class that refer to a tank are In fact what I would call tank problems, but where you've got Something going in something coming out at the same rate Then we're going to classify those as tank problems So We're going to have Something that we're talking about in the problem salt if it's a brine mixture coming in a Pesticide that we have spilled in a lake Carbon dioxide in a room we're going to have some substance that we're going to be talking about so we're going to Let some letter equal that substance actually Let's be a little more clear than that just We're going to let a equal the amount of substance salt carbon dioxide pesticide in the tank at some time t Well if a is the amount of this stuff Whatever it is that we're talking about In the tank at time t. What is d a over dt? What's that sound like to you? Okay, it's a derivative of this stuff, but let's put right. It's the rate of change of a with respect to t So it's an instantaneous rate of change So if you think about how this stuff in the tank might be changing it's going to be changed by And as far as memorization of a formula, this is about as easy as it gets for this class It's going to be the positive portion of this is going to be the rate at which a whatever this substance is is coming in Minus the rate at which a is going out pretty simple rate in Positive minus rate out because it's leaving So two components of each rate depending on the kind of how the problem is stated, but the rate at which this substance is coming in will be based on the concentration of that substance times its actual flow and we want the same Same things over here the concentration that is leaving the tank and the flow That it's leaving the tank now in this type of problem that we're going to deal with today and for this particular section The flow of liquid coming into the tank and the flow of liquid going out of the tank will be the same So we'll have the same amount in the tank now. There are other tank problems where this will Differ so you have possibly more coming into the tank Then you have going out of the tank and then you have to compensate for that in the equation, but for us The flow in and the flow out will be the same So there's our equation that will kind of get us started in these tank problems And we'll look at a variety of different Tank problems or mixing problems as they're referred to in the book Again, you've got a good example on page 518 in the book And Welcome you to look through that that I think this is a good textbook By the way, we are probably going to Look at other textbooks that are out there on the market We've got a committee looking at it, but you don't have to worry about it because once you've started the calculus sequence You will finish the sequence in the book that you started it, but if someone Next semester you're in calc 3 and a friend of yours your younger brother or sisters in calc 1 They potentially will have a different book, but then you'll everybody that started in this book will be allowed to finish in that Hopefully you appreciate the fact that that seems fair All right first example. These are problems that are in your book Let's look at this one first and then there's another version similar to this actually problem 38 sorry, you can see the kind of the Binding of the book I try to smash it on the on the Screen to get it clear, but it doesn't quite want to smash the way. I'm afraid I'm going to push too hard and break the glass First example a tank. I like that because it actually calls it a tank a tank contains a thousand liters of brine With 15 kilograms of dissolved salt. So that's what starts the problem We know how much salt is in the tank at time zero pure water Enters the tank at the rate of 10 liters per minute The solution is kept thoroughly mixed That's a little bit of a of a stretch for some of these problems. How do you keep the mixture in the tank? You know homogeneous, you know, why is it not less salty at the wherever the water is coming in the fresh water and more salty elsewhere That's where mathematical models although they attempt to model the situation may not actually model it completely So we'll assume. There's some mechanism that keeps this Saltiness in the tank pretty much homogeneous from top to bottom By the way pure water how much salt if we do let a equal the amount of salt in the tank And we talk about the amount of salt that's coming in If it's only pure water coming in how much salt is coming in the tank? Zero okay, so we do have to pay attention to what we let our Letter our variable represent if a is the amount of salt Then the rate at which salt is coming in and if it's pure water would be zero Pure water enters the tank at a rate of 10 liters per minute The solution is kept thoroughly mixed and drains from the tank at the same rate So that'll be true in all the problems we examine rate in or the flow in and the flow out will be the same How much salt is in the tank? after T minutes and then once we get that equation we can throw in 20 minutes to see after that 20 minute time frame how much salt is there so we start with 15 Kilograms of salt in the tank and then hopefully if we bring in fresh water, and we look at this 20 minutes later There'll be less salt in the tank So we're going to let a equal the amount of salt So we want to pay attention to the salt that's coming in and the salt that's going out So the rate at which salt is coming in Well, it's pure water entering the tank So pure water the concentration of salt would be zero And then we can put in the actual liquid flow coming in it doesn't matter because it's times zero But there's no salt coming in, but we've got 10 liters per minute of this fresh water The rate at which salt is going out Well, we know the stuff leaving the tank The flow is actually the same as what's coming in it's 10 liters per minute What we need is the amount of salt In the tank at any time t it is written on the sheet of paper What is the amount of salt at any time t? It's a a is the amount of salt. So we have a kilograms of salt out of What's the tank size thousand liters? So let's see if it sounds like I'll go ahead and put the units in there a kilograms is What we have at any point in time obviously that changes as the clock ticks in this problem If we reduce liters over liters we're left with kilograms per minute. Does that sound like the rate at which? Salt could be leaving the tank sounds like a rate. So this is also Kilograms per minute, but since it's zero that part kind of disappears Now the other thing we're not using thus far is that initially the tank had 15 kilograms of dissolved salt. Where do you think that will come into play? Initial value so at times it once we get our equation at time zero a will be 15 In fact, we're going to write that down. We'll use that later at time zero a the amount of salt is 15 we'll plug that in later So zero times this is just zero. So we have zero minus this Which is just minus a? Over what about a hundred reduce the 10 with the thousand and that units kilograms per minute That's the rate at which salt is leaving the tank. We don't have any salt entering the tank So we should have at this point in time And this is an easier first example because of the fact that the first piece is missing. It's zero We've got a separable differential equation. We have the first derivative of a and we have a itself So typically when we have a separable differential equation. What's the next step? Separate the a's and the da's from the T's and the DT's right So we multiply both sides by DT and divide both sides by a Or multiply by 1 over a So the a and the 1 over a knockout we're still left with a negative I Didn't give you a chance at the before class to see if anybody had a wet had a web assigned question Do we have any of those pending? I'll try to gear how many of these we do All right, so we've got negative one one hundredth DT does that look right? next step integrate both sides So what's the integral of 1 over a integrated with respect to a? natural log of a Normally we'd put absolute value in there A is an amount right? We're not going to have a negative here. So we don't have to worry about that We have a plus C or a K here. We'll roll that to the other side What's the integral of some number integrated with respect to T? T right we'll put a plus C there You can see why it's in this particular location in the book even though it's a different kind of problem Eventually we get back to the point where it's a separable differential equation. What's next? So for a so for a how do we get kind of out from under the natural log? Good you're catching on to that word. That's good. So if two things are equal e to those Quantities in the equation are also equal e to the natural log of a is a And if we have a sum in the exponent position that kind of goes backward Algebraically to the product of two things that have that same base base e in this case So e is a number C is a number. So there's nothing variable about that. That's just something Some number So now that we've kind of set it up rate which salts coming in rate at which salts going out Get rid of things that aren't really there like the zero and Separate integrate solve for a now we throw in at time zero The amount of salt in the tank is 15 so basically that says that B is what? B is 15 Because this is e to the zero which is one Sorry equation is a which varies B is now 15 So the questions that are asked at the end of this problem how much salt is in the tank after t minutes That's where we are now, right? We have an equation that gives us the amount of salt in terms of t and Then the specific problem after 20 minutes. I usually kind of check my equation to make sure that I Did the problem in terms of minutes and now I'm asked to give an answer in terms of minutes So I want my units to agree So we had leaders per minute, and we're asking for minutes so that agrees So at time 20 our units are in agreement and we have pure water coming into the tank So we would expect there to be less than 15 I mean you can tell from the equation that it's it's decreasing, right? Either the negative something times t is a decay type curve So we better get something less than 15. I don't remember what the answer is to this 14.9 point nine nine Nine nine three. I thought you said nine nine repeating. That's a different issue which we probably ought to take up with that 14.93 right nine nine three so we haven't had a whole lot of Watering down the brine yet, right with only 20 minutes or anybody else getting the same number Okay, I don't remember that number Okay, I'm remembering less. Okay, so let's we want a consensus here 12 now do we have a consensus? 12.281 So I knew that 20 minutes wasn't a long time, but it didn't seem like it could It would knock that down a little bit further than that. So anybody else run it through 12.281 Check that out Nicole and see what happened Questions on that problem with that setup find it okay parenthesis situation We're going to do some things other than just salt in a tank But let's take a look at the setup of problem 38 which is similar to this By the way, let's let's address that point nine nine repeating Which is what I thought Nicole said if we ever talked about in here that point nine nine repeating is Actually 100% equal to one Tell a couple of you didn't like that at all. Maybe we haven't talked about that Let's talk for a moment about that that those two things are equal Do you think most of you are thinking this is smaller, right? This is smaller than one. So if it's smaller than one, what would you add to it to get one? So something Can you tell me what you would add to point nine nine repeating decimal to make it equal to one? Which you can't by the way because they are equal Well, then why does my interpersonal teacher if you get like an eighty nine point nine repeat? She doesn't round it up to a nine. Well, she's mathematically challenged She doesn't do that because they are the same and it's not a trick. There's nothing there's not a mathematical trick about it Since we have calculators out because we just finished a problem. What is One ninth punch that into your calculator Point one repeating right? What's two divided by nine? Repeating okay, we know three ninths is one third, which is point three repeating well with this particular pattern When we get down here to eight ninths, we would expect that to be and you can check this with your calculator That's point eight repeating. Oh, well for goodness sakes What's nine ninths? That would be point nine repeating by this particular pattern, right? But nine ninths is really equal to one But that's not good enough like some of you aren't buying that So let's say we don't really know what it is. It's something it's in What if I multiplied both sides by ten? That's legal. I've got two things that are equal. I'm not saying what in is yet But what is this side? This side times ten is ten in what is this side? How do you multiply a decimal number by ten? Don't you just move the decimal place over so if ten in is that and In is that those are two equations now subtract Ten in minus in would be nine in What's nine point nine repeating decimals not a trick not a trick? nine point nine repeating minus the point nine repeating that Would be nine right divide both sides by nine and In is one. What did we start with in was that what did we end up with and is that so it is true Point nine repeating decimal is in fact 100% equal to one There's nothing you can add to it that would make it one it already is one So what is? Let's take that just a step further. What common fraction is that? That's point two five, which is really one-fourth So the point nine repeating kind of is a little bit Mysterious because it's repeating and we all have very finite mines mine is a whole lot more finite than yours Because of my age But because we have finite mines we are we have a hard time Wrapping our minds around the fact that point nine if you let it repeat. It's no different at all from one Sorry felt like it was time to address that All right, this example kind of comes off of problem 35 nicely It's also in your book. These are problems that are on page 520 from your book a Tank contains a thousand liters of pure water this time a little bit different brine that contains point oh five kilograms of salt per liter So that's its concentration Enters the tank at a rate of five liters per minute brine we have another Tube coming in here to the tank brine that contains point oh four kilograms of salt per liter of Water that's its concentration enters the tank at ten liters per minute. So we have actually two things Coming in to the tank The solution is kept thoroughly mixed and drains from the tank at a rate of 15 So again, you'll see we've got 10 liters per minute coming in another Port that gives five liters per minute. So that's a total of 15 liters per minute coming in We've also got 15 liters per minute going out How much salt is in the tank after two minutes and after one hour? Well, I do see a little bit of a problem with hours and minutes, but we'll just instead of using hours We'll just plug in 60 minutes So let a equal the amount of salt in the tank at time t rate of change of a Is the rate of change of in this case salt? Read at which salt is coming in we do have some brine emptying into the tank That couple different ports coming in Let's go ahead and write down the initial conditions at time zero, which we won't use right away But we'll come back and use later how much salt is in the tank at time zero Here's the statement that's going to tell us that a tank contains a thousand liters of pure water Zero right So at time zero we have zero salt in the tank it's pure water Now some of you might be thinking that you know pure water does have trace amounts of salt in it. We're not We're not visiting that particular proposal. Okay, it's pure pure means without salt So the rate at which salt is coming in we've got two Concentrations in two flow rates coming into the tank. Here's the first statement brine that contains point oh five kilograms of Salt per liter that's its concentration enters the tank at a rate of five liters Per minute I usually like to stop and see if that sounds like The rate at which salt could be coming in so if you again strike out liters over liters You're left with kilograms per minute sounds like a rate at which salt could be coming in the tank We're still dealing with rate in because we have some more coming in brine that contains point oh four Kilograms of salt per liter enters through the tank enters the tank at a rate of ten liters per minute So again Cross out liters over liters you've got kilograms per minute So now we've talked about everything that's coming into the tank We want to subtract the rate at which salt is going out Well, we do know it's going out at 15 liters per minute What is the concentration of salt in the tank at any point in time? How much salt is in the tank at any time is a So we have a kilograms of salt Uniformly distributed amongst the what 1,000 liters So there's concentration of salt in the tank at any time t and that's the flow at which it's going out So we've got point oh five times five Nothing variable in this at all and then point oh four times ten and then we're going to add those together What's the result is that point? two five and Point four point six five is that right and I was going to stop at this point But this is different enough from our first example that I think we need to see this one through to the end Can we reduce that at all? Three five goes in there three times In five goes in there 200 so we do have a separable differential equation Now you don't have to do this And we didn't have to do this in the first problem because this was zero right so we just had negative Some number and so we went right into the stage where we separated and integrated Did all that but we can't really do that yet because we have a sum on the right side What we would really like is to have some nice clean Function of a that we could then divide both sides by and Then have a natural log on the left and whatever on the right so what I would recommend is Factoring out you can do the problem without doing this, but I think it's helpful at this stage Whatever is the coefficient of a? factor it out so we have a By itself and it's going to be easier to move when a doesn't have any type of strange coefficient So if we factor it out of this term, that's clean that gives us a Now we've got to see what this other term would be if we factor out three over two hundred Well, if you factor something out, you're really dividing by it, right? So what's point six five divided by? three over two hundred yeah It's going to be negative I've already kind of accounted for that because I want this negative that's out in front times this negative to take us back To the positive where we were here 43 and a third repeating 130 Thirds okay, you see how that comes into play later in the problem. I think we'll revisit that particular number Before we're done with this problem All right now. I think we're in the position where we can separate Thanks, and then once we get them separated They're going to be easier to integrate than they would have been had we not factored out the code lead coefficient of a So we would want to multiply both sides by dt Divide both sides by the term that has a in it Sometimes I say things and it reminds me of something that somebody else has said Have I mentioned that Brian Regan is my favorite comedian in here to any of you know who Brian Regan is He's I mean he's really really funny, but he's also clean Very rarely will you hear anything? Dirty coming out of his mouth His science experiment in high school was he forgot it He woke up the morning of the science experiment He's had six months to work on it and he forgot it and he realized it's due today So he got a styrofoam cup and he went and put some dirt in it and so he took it in and his teacher said Brian, what's your project? He goes it's it's a cup of dirt and These he says it really funny and then she goes well explain it. He goes well. It's a cup with dirt in it You know I'm sorry anyway, so he goes just give me an F and move on to the next student But when I said something that Brian if you get a chance to Listen to Brian Regan. He's hilarious and he's clean And he's going to be in Durham September 25th next year and I've already bought my tickets It's a cup With dirt in it All right, so we've got things separated So we would then want to integrate both sides And I don't know if you can appreciate this at this point in the problem But if we did not factor out negative three over 200 This would be a let you equal such-and-such kind of problem So I mean it's doable, but I Just think it's easier to factor out that ugly coefficient Get it done kind of algebraically rather than have to deal with the calculus that results So what's the integral of 1 over a minus this number? Again, we're not going to have to contend with the situation where we're going to take the natural log of a negative number So we're kind of dropping that there is a possible C We're going to throw that to the other side the integral of a number times t is this Number integrated with respect to t is a number Times t and we'll put both constants together and on the right side So a little different than our first example because we had zero salt coming into the tank We want to solve for a what's next Exponentiate both sides e to the natural log of this thing is this thing And on the right side e to this power Write it as a product e to the c is a number So I'm going to call this something else just call it b and then we've got this negative 130 over 3 we'll add it to both sides So I'm just going to rewrite that same equation up here All right, we need to find out what b is What was our initial condition? Time zero the amount of salt in the tank was zero right because it was fresh water. So that means b is negative 130 over 3 Got to get zero. So this is b times 1 right, which is just b So b is negative 130 over 3 So we could write I just write in the positive term first the negative term second We could factor out and I think it's probably Worth while to factor this out Not that you have to do that, but I think that'll Be the last I want that to be the last thing we do on this problem is to examine kind of our final equation The questions asked at the end of the problem. How much salt is in the tank after t minutes? That's what we now have After one hour so that would be we want minutes since we put minutes into this equation So we'll put 60 minutes in for t Do the arithmetic? The calculators do the dirty work. See if we get a consensus on this one 25.7 Got a couple of those Did you get that Chandler? 20 still got it and what was our unit kilograms? Yes, you'll assume that you we got that okay Set it aside for a minute All right, let's go back to this equation Can you visualize from this equation? What happens as you let the clock? roll indefinitely is There a limiting value for the amount of salt in the tank What'd you say 130 over 130 over three Is that true? What happens as t approaches infinity? What happens to that term? That's negative the exponent is negative right and doesn't three over 200 times some huge number It eventually gets huge in magnitude, but it's negative right so what's e to some negatively very large number? Practically zero so this term disappears as T goes to infinity so it's one minus zero So this is just one so it's 130 over three so as t approaches infinity The amount of salt in the tank According to what was given to us in this problem It's closer and closer and closer to 130 over three which is what what we say that was 43 and a third Kilograms of salt so it kind of has a limiting value whether you go a hundred and eighty hours 3,216 hours eventually that's kind of it's limiting Concentration in terms of the amount of salt in the tank all right. Let's set up one other problem I was hoping we'd get all the way through at least three problems, but it doesn't look like what that's going to happen What I think is the next best I want to do one that even though it's called a tank problem It isn't really a tank So let's look at this one right here at least to set it up The air in a room so the room is our tank in this problem The volume excuse me of the room is a hundred and eighty cubic meters Initially the room contains point one five percent carbon dioxide fresher air With only point zero five percent carbon dioxide Flows into the room at a rate of two cubic meters per minute and The mixed air flows out at the same rate We don't want the room to get too much air and explode okay So we flow into the room at two cubic meters per minute and it flows out at the same rate That'll be true in all the problems we do at this point in time Find the percentage of carbon dioxide in the room as a function of time What happens in the long run so we kind of did that long run thing on the previous problem all right? So let's let's see Be the amount carbon dioxide In the room the room is our tank So DC over dt is the rate of change of carbon dioxide in the room So we want to pay attention to the rate at which carbon dioxide is coming in and Then subtract out the rate at which carbon dioxide is going out of the room fresher air With only point oh five percent carbon dioxide flows into the room. So that's the rate or the flow rate Or now the flow rate is two Cubic meters per minute and we have a concentration in terms of percent point oh five percent So how do I take care of that chamber? Well point zero five percent of the air that's coming in now We're gonna end up multiplying these eventually anyway, but let's make sure we write point zero five percent Properly one zero zero three zeros and then a five right so that's point zero five percent So if it were point oh five that'd just be five percent, but it's point zero five percent So you can tell how much and and that doesn't really have a unit So that means we're stuck with cubic meters per minute Does that sound like the rate at which carbon dioxide can be coming into the room so many cubic meters of carbon dioxide? Per minute a very very small amount, but it does sound like a rate Now the rate at which carbon dioxide is going out well What is the amount of carbon dioxide in the room at any time t? see And that amount of carbon dioxide at any time T is equally distributed in the whole room So it's we want to get a percentage a kind of a concentration So the room is what 180? Cubic meters. This is the amount of cubic meters of carbon dioxide The room itself the volume of the room which is our tank in this problem So those are going to be gone so there's a concentration of carbon dioxide And then it's leaving at the same rate So there's our equation Okay, I said we'd set it up and we'd stop and we'll pick up at this point in time tomorrow on this problem