Hi everyone, Joe for Jaspy's Case Breaks.com. Sad times here because we're down to our final two boxes of that Disney 100. This is random pack break number five. Big thanks everybody for getting into all of this. Specifically this group for filling up the last break. Appreciate it. Here are the final two boxes right there. Let's pop these open. And let's label the packs. And then we'll randomize your names and the pack numbers. We did not see an autograph in the last two boxes. A few numbered cards though.  But I did not see an auto. Would love to see one here in the final two boxes. I think the shop, we had a sealed box here that some local person picked up. I think we only have a handful of packs left in store. I think Jason just finished his Disney 100 packs on the personal break stream at Jaspy's Breaks on Instagram Live. And we just finished our two boxes here. That is that. We may get some more. I don't know. But I cannot assure you that they will be at the same price though. Alright, great. Now let's flip back over here. Let's get you a pack number and then we'll do this alphabetically by your first names. Let's randomize it. Two and a one, three times for names and pack numbers. Good luck. One, two, and three. Joseph down to Tristan. Two and a one, three times for the pack numbers. One, two, and three. After three, we got pack ten down to fifteen. Alright, Joseph with ten. Rob with seventeen. Tristan with nineteen. Tim with eight. Joseph with twenty. Rob with fourteen. Tristan with twelve. Jeff with six. Michael with one. Aaron with seven. Jeff with eleven. Tim with two. Rob with thirteen. Michael with four. Rob with three. Tim with nine. Michael with five. Tristan with eighteen. Tim with sixteen. And Tristan with fifteen. So let's order these numerically. So you'll see Tim still has sixteen, right? Oh, by your first names. You can see Tim still has sixteen right there. Alright, we're going to pause the video, see if there's any trades in these packs. And then when we come back, we'll rip open the packs and see what we get. Stick around, we'll be right back. Alright, welcome back everybody. No deals are done. So let's get it started. Aaron, you're up first and then Jeffrey. Pack seven for Aaron. Good luck. Love these guys. And Candy and the Prince. Snow White and the Seven Dwarfs. This guy's Mr. Big is great too. Alright Aaron, thank you for getting in. Appreciate it. Jeff got a couple packs. Joseph, you're up after Jeffrey. Six and eleven. There's eleven right there and there's six right over here. Good luck. These packs are really using a powerful adhesive. We got Slinky Dog. Nice. And Mr. Potato Head. And there's Mater right there. Nice. Alright, Jeff, thank you. Appreciate you. Joseph, you're up. And then Michael, you're after Joe. Pack ten and twenty. Good luck. Credibles. We got a brave postcard. It's a pretty good one too. I like that. People turn into bears. There's some archery. There's Bruce. Die cut. Fish are friends. Another great one. Finding Nemo. Thank you, Joe. Appreciate you. Alright, let's see what we got for Michael. He's got a few packs.  One, four, five. One, four, five. Good luck, Michael. Jason, what's up? How many boxes is the lead break? I don't know. I know it's half a case. It should say in the title. Alright, thanks, Evan. See you, man. Nice. Finding Nemo postcard. The Cheshire Cat. Nice. And Mickey Mouse. Mickey Mouse Refractor. There you go, Michael. A few great ones here. A few great refractors here. I dig it. Oh, let's name the zones, the zones, the zones. Let's name the zones in the bottom of the sea. I hope that guy is in this set. Alright, thank you, Michael. Alright, Rob with four packs. Three and thirteen, fourteen, seventeen. Three, thirteen, fourteen, seventeen. Alright, Rob. Good luck. What's that over here? What is that? That looks different. It is blue. Twelve out of one twenty-five. I don't think I've seen this parallel. Is that maybe the Wonder Parallel? I don't know if the blue's in here. Look for the bare necessities, the simple bare necessities. Forget about your worries and your strife. He's also in tailspin. Hey, here's Aladdin. Aladdin Refractor for Rob. And we've got James P. Sullivan. Nice. And we've got a Toy Story classic group right here. Nice. Alright, nice. Nice numbered cards and good refractors here. Thanks for getting in, Rob. I appreciate it. These are a lot of fun. Cards and one pack. It's Tim and then Tristan. Alright, Timothy, two and eight, nine and sixteen. And then Tristan, you'll get, you should have the rest. Twelve, fifteen, eighteen, nineteen. Twelve, fifteen, eighteen, nineteen. Alright, Timothy, good luck. Thank you for getting in. Sometimes some crimes go slipping through the cracks but these two gum shoes are picking up the slack. There's no case too big, no case too small. Mike Wazowski. Alright, and there's Joe Gardner from Soul. Alright, what's that other card right there in the middle behind Mike Wazowski? It's 100 Years of Wonder. Now I know the character, but is it numbered or something like that? It is. 22 out of 225. Nice, Tiana from The Princess and the Frog. And Mowgli from the live action, Jungle Book. I feel like within a span of a number of years, there's Miguel. Thank you, Tim. There were a number, there was a couple live action ones. One, I think that this version is the better one, I won't say. Say I tried one a number of years prior that wasn't good and then you did another one that was good, I think. Alright, Timothy, thank you very much. Appreciate it. Tristan, you've got the rest. Twelve, fifteen, eighteen, nineteen. Good luck. Not seeing an auto, they're not guaranteed a box. I don't know how many are in a case. I think it's all just very random. Let's see if we can find one here. Good luck, Tristan. Thank you for getting in. Thanks for your patience. We got the genie, nice. And Tigger, too. We got Alfredo Linguini from Mata 2. That's one of my favorites there.  From the Lion King. Lion King. Alright, last one here. Behind Sadness is the cast, the crew of Onward. Classic reunion. Alright, no auto, unfortunately, but a lot of fun stuff here. Thanks for watching all of these fun little Disney brakes, ladies and gentlemen. I'm assuming we'll try to get some more and keep an eye on Jaspy's case of brakes.com for that. I'm Joe. I'll see you next time for the next one. Bye-bye.


Okay, so let's start off the day with this question. It says The value for Kc for the reaction to nitrogen dioxide goes to Dynitrogen tetroxide is 1.52 at 319 kelp What is the tent? What is the value of kp at this temperature for this reaction? So This is the reaction here. That's given to us It gives us the Kc and the temperature of the reaction and it wants us to find the kp Okay, so the first thing you want to do or the best thing is that you remember the kp to kc Equation if not, you're gonna have a hard time doing this problem So kp to kc, right? You have to multiply it by RT times delta in So What are these things? Well, we've got T And we've got Kc remember R is Just going to be the R of the gas constant 0.0821 liter ATM per mole Kelvin Okay, but delta in we get that from the reaction equation up here Okay, so delta in It's going to be so that's the change in the number of moles So just like any change it's going to be the final minus two pardon me the initial so The number of moles final well the total number of moles on this side of the reaction equation is just one Of gas So we're looking for moles of gas how many moles of gas we have on this side two right so two moles of gas so what we're going to say is one mole minus Two moles of gas and that's going to equal negative one moles We're not going to use that unit in this, but it's good to know what we're looking at Okay, so are we cool with this one? Okay, so I'm just going to put Delta in equals negative Okay, so now we've got everything so it's just really a plug-and-tie problem now so Kc 1.5 0.0 821 liter ATM per mole Kelvin 319 And that's all negative one Okay, so Go point zero eight two one multiply that by 319 Raise that to the negative one then multiply that by 1.5 two And you should get an answer Zero point zero five eight zero Okay, so no units that you're keeping any questions on that one


Well done, sunrise movement in PA. That was just, that was incredible. The look on his face, he kind of noticed that they were trolling before they made the switcheroo. He was kind of trying to look at the backs of their, their posters because they were bright yellow. So they were a little bit conspicuous. But the second that he realized that they were there to confront him, he said, well, I thought you didn't look like my supporters or something like that. That's because you don't have any supporters, Conor Lam. You're essentially a Republican running in a Democratic Party primary. Do you think you're going to make a lot of friends with this particular strategy?  Now notice how that coward didn't even engage with them at all. I mean, you're running to be a public servant.  So you're saying I'm running for office because I want to serve the people, but yet you're running away from them the second they try to push back against your corruption and your fossil fuel donations. Why not just spend a minute talking to them, explaining your position? It's because he has no explanation. He's just corrupt. Now, the sunrise movement in PA tweeted, the climate crisis is a life or death matter. Young people fundamentally understand that, but Conor Lam is okay with sacrificing our futures for fossil fuel money. Now, taking a closer look at the signs, they say Republican and Lam clothing and the other variation of sign says this guy voted with Trump 70% of the time. Now, whenever I post videos about politicians being confronted in public like this, there's always the pearl clutches that will chime in and say, well, that's so rude and improper, and it's not a good way to make your point.  And I hate this because when you have politicians with so much power who are refusing to act, knowing that their inaction could cost millions, potentially hundreds of millions of lives, I'm not worried about being impolite, right? This is a fight for survival. And if you think that that's hyperbole, take a look at this headline from Gizmodo, which puts things into perspective. It's now or never, we have three years to reverse course major climate report fines. Now the author of this article, Molly Taft goes on to explain, in order to avoid the worst impacts of climate change, the world needs to make a serious U turn over the next three years to curb our emissions, a stark new report finds. It's possible to do so concludes the report released Monday from the Intergovernmental Panel on Climate Change, but only with serious immediate and sustained action across all facets of society. And we have very little wiggle room when it comes to our addiction to oil, gas and coal. The amount of fossil fuel infrastructure that currently exists or is planned worldwide is enough to push us into levels of warming that are over the goal set out in the Paris agreement. The report finds it's now or never. If we want to limit global warming to 1.5 degrees Celsius, IPCC working group three co-chair Jim Schia said in a statement, without immediate and deep emissions reductions across all sectors, it will be impossible. So to see these headlines, to see scientists warn us repeatedly about how we have a limited window of time to act and our time is running out. If you think that activists being impolite to politicians is a bigger issue than climate change itself, then your priorities are asked backwards. I don't even know what to say. Now, whenever I talk about climate change, I understand that it leads to defeatism and a feeling of hopelessness. But I want to recommend to you a really good video by Chris Gazak on YouTube. And they talk about how the fossil fuel industry is still thriving specifically because they're weaponizing our demerism against us. They count on our demerism and because of that, they're still able to dominate. But the video is overall optimistic because it explains that even though the situation is bad, even though we're looking at a huge disruption to society because of climate change and mass migration, it's not as bad as it could be. So we are going to persist as a species. Climate change is going to get bad. Climate change is going to cost millions and millions of lives. But there's been enough changes. And renewable technology is a cheap enough option to develop in countries to where we're not looking at a temperature increase between four to eight degrees Celsius, which would actually facilitate the end of life on this planet. So what we're looking at is bad. And essentially, the situation is dire, but it's not hopeless. And that's the takeaway from that video that I would highly recommend. I'll link to it down below. And I think that that message is really important because when I talk about climate change, I don't know how to give people hope. The situation is truly horrifying. And politicians like Conor Lamb, they just refuse to act. And he's not the only one, but he's a microcosm of a broader issue. And the United States is one of many countries who are refusing to take meaningful action to mitigate climate change. But the situation is not hopeless. And even though we are going to see a really dark period throughout human history, the species itself will persist. Now, I don't know if that gives you hope, but it does give me a little bit of hope. But what we're fighting for, why action is so important is because we're talking about millions, potentially hundreds of millions of lives. If we act now, we can save these lives. But because of people like Conor Lamb, corrupt politicians, we're going to see a breakdown of society. We're going to see mass migration. We're going to see new political movements form as a result of the disruptions of climate change. Perhaps fascism grows as people have to leave their homes. I don't know what to expect, but I know it's going to be bad. And I know that not taking action is criminal. So if you're offended that these activists were impolite to Conor Lamb, spare me your outrage, because what's more important is saving lives. What's more important is taking care of the one planet that's habitable that we have access to. And I'll leave that there. Well done to these activists. They are absolutely brave. And I commend them for their bravery and just calling out these politicians relentlessly.


This investment in natural capital is very very important because human beings, the survival of humanity usually depends on the existence of natural capital, but despite this understanding, it's very turns out that the human beings have been at the forefront destruction of natural capital. So if you want to stimulate reel vary economy growthµ³³³³³³³³³³³³³³³³³³³³³ ¨¥£¨¯§¹¹¸¹¹¸º¹¸£¹° ¹¹... into accelerate investment in natural capital as they move to promotion of economic growth, reduce the level of poverty and of course, accelerate social and economic development of natural capital. The typical example of natural capital investment will be in the area of land degradation. To ensure that the land is not degraded. But again for example deforestation, We have to ensure that our forests are not destroyed because the forests, the source of rain, the source of livelihood and economic activities in general. So we have to ensure that while you exploit these forest resources for example, we have to ensure that we put in place some mechanism in order to maintain them so that we enjoy the benefit of forests for the current generation and of course the future generation, that is the concept of sustainability. There are many ways that can be used to finance our natural capital. The most common one for example in developing countries through the general budget, that you can set aside a certain amount of money that can be used to finance the natural capital. But of course you see given that the mega resource that these countries, for example developing countries they are facing, it becomes very very difficult for the national budget to finance this natural capital. And because of these we are proposing that we have to come up with new innovative ways of financing the natural capital. For example could be the payment for ecosystem services. This is a very very important way that we can finance the natural capital. But again there is another approach that is promoting the market for green products. These are the products that have been made up from the natural capital in a way that they do not destroy. The natural capital. So one way would be to promote the use of the market for green products. But of course again we have to move on the global agenda. Trying to initiate to strengthen further the already funds for financing. Financing for example the climate change and the general change in the environment that we are living.


Hello. So, in the last capsule we started the proof of the spectral theorem for a compact self adjoint operator on a Hilbert space. We could complete the proof I said that this proof will spill over into two capsules. We finished the difficult part of it namely we proved that there exists eigenvalues and there exists a eigenvector. So, existence of eigenvalues and eigenvectors were established and for that we used the Banachala-Glue theorem for Hilbert spaces which we took great care and we proved that. The Banachala-Glue theorem is a compactness result and the unit ball in the Hilbert space is not compact with respect to the norm, but it is compact in a very weak sense namely every norm bounded sequence has a weakly convergent subsequence and we use this critically to prove the existence of eigenvalues and eigenvectors. Now that the difficult part is done let us finish the proof and again so let us begin with a setup. H is a Hilbert space, T from H to H is a self adjoint bounded linear operator on H. Right now we do not need compactness we say that Y is a T invariant subspace this is a purely algebraic notion so this can be defined in the context of linear algebra. So, T invariant subspace means whenever V belongs to Y, T V also belongs to Y. So, T of capital Y is contained in capital Y if you like. Now let us prove that if T is bounded self adjoint and if Y is T invariant then Y perp is also T invariant so this is where self adjointness of T is going to come to play. So, let us take a Z in Y perp we have to show that TZ is also in Y perp namely TZ in a product with Y should be 0 for every Y in Y, but what is TZ in a product with Y it is Z in a product with TY because T is self adjoint I can simply put the T from the left factor to the right factor. But where is TY? TY is again in Y because Y is T invariant and where is Z? Z is in Y perp. So, Z is in Y perp and TY is in Y so Z in a product with TY is going to be 0 and that is all we want to show. So, we proved that Z belongs to Y perp implies that Z in a product with TY is 0 for all Y which means that TZ in a product with Y is 0 for all Y which means that TZ is in Y perp and the proof is complete. We are shown that if you have a self adjoint operator and if Y is T invariant Y perp is also T invariant. Now what we would do is that because Y perp is T invariant I can restrict T to Y perp and the restriction will be a linear transformation from Y perp to Y perp. Again it is obviously linear transformation and restriction of a continuous function is continuous. So, again the restriction is a bounded linear transformation and Y perp is a closed subspace. Remember that regardless of Y, Y perp will always be closed and the closed subspace of a Hilbert space is again a Hilbert space. So, T is a bounded linear operator from a Hilbert space to itself and the equation TX dot product with Y equal to X dot product with TY will hold for X and Y in Y perp. In other words this restriction T from Y perp to Y perp is again a bounded self adjoint operator and if T is a compact operator this restriction of a compact operator is also going to be a compact operator. So, this is an important reduction. Now you might have begin to guess that some kind of an inductive argument is going to be given and this is a kind of a preparation for that in inductive argument if that is the kind of thoughts that are creeping into your mind then certainly you are in the right track. So, now let us look at theorem 94 the completion of the proof of the spectral theorem. Suppose T from H to H is a compact self adjoint operator on a Hilbert space then there is an orthonormal basis of eigenvectors of H. Each nonzero eigenvalue has finite multiplicity. So, if you take lambda not equal to 0 and if lambda is a eigenvalue then there are only finitely many linearly independent eigenvectors associated with eigenvalue lambda that this is obviously the geometric multiplicity that we are talking about. There is no concept of algebraic multiplicity because we are in an infinite dimensional setup. We have already established the existence of an eigenvector and now we are going to apply the Zohn's lemma or the Hausdorff's maximality theorem to show that there is a maximal linearly independent orthonormal set consisting of eigenvectors. What is the Hausdorff's maximality theorem? Hausdorff's maximality theorem says that if you have a partially ordered set then maximal chains exist. So, what is this partially ordered set that we are talking about? We have a Hilbert space H it is an inner product space first and foremost. So, we can talk about orthonormal subsets of H. So, we are talking about subsets of H both finite and infinite subsets which are orthonormal and we want to further put the restriction that these are orthonormal sets of eigenvectors. We are talking about orthonormal sets of eigenvectors. That is family of orthonormal sets of eigenvectors is obviously a partially ordered set partially ordered by set theoretic inclusion. Now, the Hausdorff's maximality theorem maximal chains exist. How do I know that this is a non-empty family? To show that this family itself is non-empty remember we proved last time there exists a eigenvector and eigenvectors are by definition non-zero. So, normalize it. So, a singleton consisting of an eigenvector is obviously a orthonormal set. So, this partially ordered set is certainly non-empty and since it is non-empty I can apply the Hausdorff's maximality theorem and I can take a maximal linearly independent orthonormal set B in this Hilbert space H consisting of eigenvectors and this B is non-empty. Now, we want to claim that this B is a basis and that is exactly the first clause in the theorem. So, we have to show that B is a basis. What does it mean to say that B is a basis? It means the linear span of B must be dense in H or the closure of the linear span must be the whole of H. So, take the closure of the linear span of B. Take the closure of the linear span of B. It is a closed subspace of a Hilbert space. If it is not the whole of the Hilbert space H then it is a proper closed subspace. So, let us call this y and if y is a proper closed subspace then y perp is not the zero space and y perp is then a Hilbert space in its own right and the operator is self adjoint. So, I restrict t to y perp as an operator from y perp to y perp. Now, that is going to be a self adjoint compact operator on y perp and therefore, it must have an eigenvector v0 and by normalizing it I may assume that this v0 is a unit vector. And so, now I can look at B union this singleton v0. Obviously, this v0 is not in B right because B is sitting in y and v0 is sitting in y perp and v0 is a unit vector. So, this particular set is a strictly larger orthonormal system of eigenvectors and that contradicts the maximality of B and the claim is proved and the first part of the theorem is not established. Now, we turn to the second part namely the statement concerning the multiplicities of the eigenvalues, the geometric multiplicity if you like. Each nonzero eigenvalue has finite multiplicity. Take a nonzero eigenvalue lambda and let v lambda be the corresponding eigen space and we have to show that this has finite dimension. That is another way of saying that the eigenvalue has finite multiplicity namely the eigen subspace must have finite dimension. How do you show that a subspace has finite dimension? One way to do that would be to show the unit ball is compact. Remember that in a Banach space a unit ball is going to be compact if and only if the Banach space is finite dimensional. So, take u0 to be the closed unit ball in v lambda. If we show that u0 is compact we are finished. So, take a sequence of vectors in u0 and remember that these v lambda is an eigen space. Remember so, T vn will be equal to lambda vn, but T is compact and vn's are coming from a bounded set it is coming from the unit ball. So, T vn is pre-compact. So, T vn has a convergent subsequence converging in norm and lambda is nonzero. So, I can divide by lambda and it follows that vn's itself must have a convergent subsequence which shows that every sequence that I take in u0 has a convergent subsequence namely u0 is pre-compact. Since I take in the closed unit ball it is compact. Now the same argument also reveals another important result and if I fix a number c positive there are only finitely many eigen values lambda with mod lambda bigger than c. When I say finitely many eigen values I mean counting multiplicities and so taking into account the geometric multiplicities there are only finitely many eigen values which exceed c in absolute value. Suppose the result is false then we can select an infinite sequence of unit eigen vectors because the result has been assumed false and which are pairwise distinct eigen values because each eigen value has finite multiplicity. So, there are infinitely many eigen values with mod lambda bigger than c that means that there must be infinitely many distinct eigen values in the first place and so I can select these sequence of unit eigen vectors with pairwise distinct eigen values forming a monotone sequence. Remember that we have proved that t is self adjoint so the eigen values are real numbers and every real sequence has a monotone subsequence. So, passing to a subsequence if necessary I might as well assume that the eigen values that I got from a monotone sequence. So, you got a monotone sequence either it was converged or it must go to plus infinity or minus infinity there are only three choices in each of these three choices will get a contradiction. The eigen vectors are mutually perpendicular remember I am taking distinct eigen values and so the distance between any two of them is root 2. So, the eigen vectors definitely are not going to have a convergent subsequence. Image vectors t, v, n will be lambda n, v, n and the image vectors must have a convergent subsequence because t is compact and the v n's are unit vectors.  So, either it must converge or 1 upon lambda n, k must go to 0 in any case v, n, k's must converge in norm that is a contradiction because v, n, k's cannot converge because the distance between any two of them is square root of 2 that completes the proof of the theorem. So, far we are established that for a compact self-adjoint operator on a Hilbert space there is an orthonormal basis of eigen vectors. Each non-zero eigen value is finite multiplicity the eigen values from a countable set and they can only have one limit point if at all and that is 0 and the eigen values can also be generated successively by maximizing the Rayleigh quotients analogous to the case of the real symmetric matrix. So, all these things we have established and now we should apply it to the study of two-point boundary value problems because these eigen functions are going to give us the generalized Fourier series. A general solution is going to be written as a superposition of these eigen bases and that is generalized Fourier series. So, rho from closed interval 0, 1 to r is a continuous function whose 0's form a set of measures 0. It is not the case that rho is identically 0 on some small sub interval or something like that. So, we are excluding those cases by saying that the 0's of rho can at most be a set of measures 0. Of course, rho can have isolated 0's for example. Now, L2 subscript rho denotes a set of all real valued functions such that integral 0 to 1 mod f t squared rho t dt is less than infinity. In other words we are taking the measure to be rho t dt with respect to this measure I am taking the usual L2 space with respect to the weighted measure. Now, this is a vector space over the real numbers and the inner product of two of the functions f and g is simply integral 0 to 1 f t dt rho t dt. The usual inner product I am not putting the bar here because I am looking at real valued functions only. So, with this prescription L2 rho 0, 1 is a Hilbert space. The proof is exactly the same as the usual L2 space on 0, 1 with cosmetic changes that I leave it to you to figure out or if you have done a general measure theory course this is L2 of a measured space where the measure is the weighted Lebesgue measure either approach you can take. This is a space which is the correct setup for studying the Sturm-Lewel problem y double prime plus lambda rho y equal to 0, y of 0 equal to 0, y of 1 equal to 0. Let us see why that is so. We make the observation that the operator t from L2 0, 1 to L2 0, 1 given by t f x equal to integral 0 to 1 k x t f of t rho t dt is a compact operator when the kernel is continuous and is self adjoint precisely when the kernel is symmetric. We approve these things on the measure is the usual Lebesgue measure that is when rho t is identically 1 but the same proof simply goes through with cosmetic changes and so I leave the proofs to the audience because essential ideas are all being discussed. It is just a matter of writing down. Now, we transform the Sturm-Lewel problem into an Eigen value problem for a compact self adjoint operator of the form 7.39. So, that we can apply the spectral theorem for the Hilbert spaces and we can re-derive the results of chapter 6. So, let y of x be an Eigen function namely equation 7.40 y double prime plus lambda rho y equal to 0 with Dirichlet boundary conditions and I am taking the Eigen value lambda we know 0 is not an Eigen value. So, might as well assume that lambda is not equal to 0 we integrate 7.40 twice in succession and when you integrate it once we get y prime of x equal to y prime of 0 minus integral lambda y t rho t dt integrate again and use the fact that y of 0 is 0. The second time when you integrate you are going to get a y of 0 which is which drops out and we are left with this. We will get a repeated integral we switch the order of repeated integrals and that you know how to do integral 0 to x y of t rho of t dt integral d s and this can be integrated immediately and you get the solution in the form y of x equal to x y prime 0 minus lambda integral 0 to x x minus t y of t rho of t dt. So far so good. Now the other boundary condition has to be put in when you put in the other boundary condition we will get y of 1 equal to 0 of y prime of 0 equal to lambda integral 0 to 1 1 minus t y of t rho t dt. So, you substitute this expression for y prime of 0 above and we combine the integrals and we get y of x equal to lambda times integral 0 to 1 x into 1 minus t y of t rho of t dt minus lambda times integral 0 to x x minus t y of t rho of t dt and let me combine these two integrals as one integral lambda integral 0 to 1 g of x t y t rho t dt everywhere there is a rho t dt and so the other terms have been combined as g of x t. So, what is this prescription g x of course its prescription will differ from 0 to x and from x to 1 and you have to write them separately. When you look at this integral and write the g of x t from 0 to x I have to take both of these and from x to 1 I will have to take only this and this will have to be dropped out. But what do you get at the end g of x t equal to t into 1 minus x if t less than or equal to x g of x t equal to x into 1 minus t x is less than or equal to t. Lo and behold the Green's function is symmetric and lambda inverse is an eigen value the compact self-adjoint operator given by equation 7.4 to the Hilbert Schmidt operator given by g of x t and we know that the eigen values of 7.42 form a countable sequence with 0 as the only possible accumulation point. So, the eigen values of the original stem level problem forms an infinite sequence going off to infinity because of the presence of the inverse here. Conversely if y of x is an eigen function for this Hilbert Schmidt operator 7.42 with eigen value lambda inverse namely this equation holds y of x equal to lambda times integral 0 to 1 g of x t y t rho t dt then we have to show that y of x is an eigen function for the boundary value problem y double prime plus lambda rho y equal to 0 with this Dirichlet boundary conditions. Let us check that what is the starting equation ty equal to lambda inverse y differentiate this equation we get y prime equal to put the lambda on the other side lambda times integral 0 to 1 g prime x t y t rho t dt we have an expression for g prime remember here it is. So, you can calculate the derivative with respect to x from here and what do we get we get two integrals you just calculate the derivative and put them together and then you differentiate again y double prime equal to lambda times minus x y x rho x minus from here you will get this 1 minus x y of x rho of x which is exactly lambda rho x y of x the minus sign which exactly shows that it is a solution of the boundary value problem. So, we have transformed the solution of a boundary value problem for a ODE with Dirichlet boundary condition into a eigen value problem for a Hilbert-Schmidt operator and we re-derive the theorems of chapter 6. So, we have re-examined the contents of chapter 6 from a abstract perspective. Let us just summarize all these things in another theorem, theorem 95 the Sturm level problem y double prime plus lambda rho y equal to 0 y of 0 equal to 0 y of 1 equal to 0 has a countable set of eigen values tending to infinity each eigen value is simple and the eigen functions form a countable orthonormal basis for l 2 of 0 1 with respect to the weighted measure rho. In other words every function f in l 2 of 0 1 with measure rho t dt can be written as a Fourier series f equal to summation n from 1 to infinity c and yn where the y n's are eigen functions of the Sturm level problem. But this gives you the l 2 theory of course this will not give you the point wise convergence or anything like that that is of course is a very very different ball game. I think this will be a very good place to stop this capsule and also stop this lecture and in this lecture we have revisited many classical parts of Fourier series in the modern functional analysis setup. And moving forward in the next chapter we are going to look at an application to celestial mechanics. We are going back to the very first chapter and we will see how those results which we derived in the very first chapter answers a very specific question in celestial mechanics. It is a very nice short chapter consisting of two capsules we will take up next. Thank you very much.


And to discuss, we literally have, as we call, the titans from the gaming industry. We have Mr. Bharat Patel, the chairman and director of Yudhis, India's leading game development company. They are in the middle of an IPO as we speak.  We have Saloni, the founding managing partner from Lumika Adventures. The fund we always wanted as founders. That's a tagline. And they are doing some incredible support for the gaming industry in India. Ishaank, the co-founder and custodian for NDGG, India's number one play-to-one gaming platform. They are building communities across the globe to boost the space. And of course, Piyush, the founder and CEO of Rooter, India's biggest content platform, live streaming platform when it comes to mobile gaming. So can we have a huge round of applause first of all for the amazing panelists, please? Thank you. So I would like to really start from the top with you, Ishaank. You are literally so passionate about decentralizing the gaming business and putting the powers in the hands of the gamers. So much so that you recently removed the whole hierarchy of CXO from NDGG and introduced something as Eldest Council. So we'd love to know from you, how do you see this space? What's your mission and what is Eldest Council? OK, so three questions. I'll try to keep it brief, right? So what are we building? We are building a reputation system for gamers that goes on chain. Why on chain? So that it can remain transparent and it can be available for whoever the user or the gamer wants it to be available to, right? Why are we doing this? Because historically in the gaming value chain, games spend money on third-party platforms. Gamers come to those third-party platforms, spend their time, money, and skill. And in return, the people who benefit from this are those platforms. So Facebook, Google, all of these platforms have been monetizing the data of everyone sitting in this room for ages. And that's how they've become these bear moths, right? So what we wanted to do was we wanted to use the blockchain for giving people the ownership of their data. And in a way that when they are spending their time and their skill inside these games, they actually benefit in return. And those benefits can go back into the game themselves. So we actually have no problem in creating the circular economy, but we wanted people to benefit. And as a result, the front and center of our project becomes a community, right? Because we stand for the gaming community. And when we stand for the gaming community, it was imperative for us internally and externally to drive the mindset that all of us exist for the community. And therefore, we said that we are not here as permanent CXOs or permanent senior managers of a particular company. But instead, we are all building a community where we are dispensable, we are fungible. And over time, we will be replaced by members from the community. So even today, our entire community team has been sourced from the community. Our BD team is from the community. To the extent, our Vectree team is now started coming from the community. And that's why we went with something called elder members council, because elder members are the ones who are going to retire the fastest. And then new people will come and replace us. Interesting. Quite interesting. And if I can come to you, Mr. Bharat, on that note, for this ecosystem to become successful, we need a lot of games, right? And do we have, like you are literally leading and you have a 450 members team in the game development space, how do you see the talent space in this industry? Well, I think the talent, till now, of course, was a challenge for, I think, the past couple of years. But then with the advent of, I would say, the technology which people have been witnessing internationally, I think people have developed the skills. And re-skilling has become a common thing now. So be it in our company, whether we have a very large team of training the people who are which is needed. Apart from that, what I believe is there is an ecosystem which needs to be created right from the university level. Because me and my other colleague, we are on board of studies with many universities, where we tend to develop the course such that the talent which comes out are directly employable. So I think that's not a major challenge as of now. But I think with the technological changes, it needs to be upgraded and re-skilled to some extent, that's for sure. Interesting. And Saloni, from an investment perspective, how do you see this space evolving? Do you see enough adoption on one side? Because that is going to fuel, from an investor perspective, picking up the projects that you want to pump money in. Is there enough adoption that you see? And at the same time, are you seeing interesting innovations from a development cycle from the founder's perspective that really interests you and gives you the belief that, OK, this is going to be the next big thing. I think that's a really great point. I've been investing now in the games industry globally, as well as in India now for over a decade. So seen a lot of cycles of innovation which have come. And I think with Web 3, one has to realize that we have to go back a little bit and go back, let's say, about six, seven, eight years back. When gaming moved from a cottage industry to becoming a $300 billion gorilla, and that was largely propelled by mobile gaming. And the reason why that was the case was mobile gaming transcended barriers. It broke down barriers. You no longer needed very expensive hardware to play games. It expanded the demographic. There was a lot of demographic expansion. Women started playing games. Kids started playing a lot more games before. And it became very accessible, because now on the palm of your hand, you had these incredibly immersive experiences which became accessible. Now with Web 3, if you were to look at it, fundamentally, there are a few contours that make gaming experiences. And that leads to en masse game adoption. The first and foremost is, are they entertainment? Are they being used to propel fun and pleasure? The second most important thing is, is it easy to access? So currently, a lot of Web 3 experiences, which, especially the first cycle of innovation that has happened, were obviously there was a lot of friction there. It required six, seven steps to download a Web 3 game. You required a lot of upfront financial investment anywhere between $700 to $1,000. You then would require a, to get your, you need to understand how a token economy works as a user. You then require validators, and it would take time to get buying and selling and trading of virtual goods. So this created a lot of friction. Everything that was fixed in mobile gaming has now been upturned for Web 3, right? And there is a reason why a Supercell has 100 million daily active users, whereas a Decentraland has a few thousand, right? So until the technology layer becomes invisible, until we are able to fix these, you know, I'd say teething problems for the industry, I'd say Web 3 adoption is a little bit further off than everybody thought it was. Also, you have to understand the first generation of demographic which adopted crypto and Web 3, there was a very peculiar demographic, right? It was the early adopters. It was largely male, largely, you know, driven by philosophical and ideological beliefs, right?  And eventually there was the speculators who neither cared, but all they wanted was to make a quick buck. So once that demographic has now started to weed itself out, you've got the builders, you've got people who are looking at it, how to build it more sustainably, I think those become important. Now whether it's going to be as popular as mobile gaming, a lot will have to be fixed, but is there going to be a demographic of gamers who are going to want ownership, who want interoperability, who would like to make money while play games? I think that's a cohort of gamers that will emerge, but you have to think about it this way, right? A lot of people play mobile games, but not everybody becomes an esports athlete, right? So there is a subset of gamers within a larger Venn diagram, I'd say, who would be interested. And I guess these are businesses which are coming up, which are going to be building, and that next generation of what it looks like, we've backed a company which is building a tool and infrastructure strike. The founder was previously building Google Pay in India, so understands how it is to build tool stacks for masses. That's an interesting play for us, but of course, their ability to scale will depend on the ability of the industry to scale. So that's my view. Those are some really interesting points that you have touched upon, and Ishanga, I could notice you were smiling when Saloni was talking about the whole play-to-one concept, and I would love to pick your views on that, but before that, Piyush, if I can request you to come in, there are two things that Saloni are very rightly highlighted. Mobile gaming and fun, I would like to pick up those cues. You, as a router, is like literally India's number one live streaming platform when it comes to mobile gaming. You have, and please correct me if I'm wrong on the number, 70 million installs, 19 million monthly active users, and 1.8 million daily active users. That's huge. So you're already at the top when it comes to the live streaming when it comes to mobile gaming, and that industry works because people enjoy the live streaming. They participate. There is a lot of engagement. It's fun. Do you see the same trend happening in the Web3 side of things as well? What is, or if I can be a little more specific, what is exactly your interest? Already being at the top on the Web2 side of things, what are you looking for from Web3 games? So I think these are very early days for anybody to be at the top and to see things moving up, but to be honest, we have grown over the last 12, 18 months, and that is the result of a lot of active users on our platform, and now that most of the games are active, we are seeing good traction. See, for us, fundamentally, our DNA is to build the best content experience for mobile games in India. That's the way we define our company, our culture, which is that both in terms of the demand side, which is to get as many users as possible, we get about three, four million downloads a month, which is quite good. We are happy with the way retention is happening, so things are gonna move. Same is from the creator perspective. From the day we entered game streaming, we built the easiest streaming tool for people to become creators, and we have seen a lot of trends, we have learned a lot over the last three years, and then we moved to videos, and then we did reels, so there are different content formats and all that, so there's a lot to do in Web2 gaming, and there are few games in India which are popular, which are streamable, which are watchable, which is where there is a limitation of supply, right? In full admission, it's not easy to build a streaming platform right away when there are only two or three or four games which are streamable, and for us, we see that, so there is a lot of hope because there are at least three, four large Indian games which are getting launched later this year. I'm sure all four of them or at least two of them will do well, so that will bring in more content, so more creators and more brands engagement, et cetera. For us, the way we look at Web3 gaming is that, firstly, we come a little couple of steps down the line, the game has to first come, get a certain traction, as Sunni was saying, the ease of play has to be there, people have to understand it, and for us, we believe that in the next five years, it will start to play a very, very important role because of the volume of content that can be generated, and the interest because people have something to take away from the games rather than just giving their time, so people can earn money, people can create currencies or create different assets that can be taken into different games, so there's a lot of hope, and I mean, in the next point, I can talk about how it will affect us, but mostly, we are very hopeful. We, in fact, worked with IndiGG last year briefly to try out few games and build communities over there, and then, of course, there was a different trend that happened in Web 3, so we kind of took a pause, but we fundamentally believe that for Indian gaming market to become big, Web 3 gaming is very important. That's where the volume is gonna come in, and in whatever ways we can, we like to be a part of that particular growth. That's very interesting. Anishan, if I can request you to come in. We talked about the fun elements, the adoption, the platform that is required for the play-to-earn gaming and the blockchain gaming to become successful. There are two groups in the gaming world that kind of label play-to-earn gaming. One group says that it's not game, it's a job, because you are literally working on creating economic models, and you are not focusing a lot on building fun games. You're not giving importance to game logics, you are giving importance to how the player will eventually make money. So anybody who comes to play P2E games, they're eventually coming to make money, and not to have fun. That's one category. The second category is actually sees this as the next wave. This is, we are literally on the first step of the future of gaming, where the gamers get to own their assets, and this is a mean for them to have ownership of the time that they're investing. So how do you see this space? And accordingly, what's your vision towards driving mass adoption in play-to-earn games? So I think I actually agree fully with what Saloni and PO Chef said, right? Because the first category, which is where your objective is to come into a game, extract value from inside the game and move out, I don't think is fundamentally sustainable. Because for games to drive value to older players, they have to extract value from newer players, and at some point that churn stops, which is what we saw with the downfall of the early Axie infinity model, right? The reason the Axie economy crashed was because at one point the influx of money into the game stopped, and therefore the earlier guys were not able to withdraw money from inside the game, right? So in my head, I think bulk of the industry has moved on to the element that there are a few consumer insights, right? From the top, one, gamers don't care about web-to-vectory, gamers care about having fun inside the game, right? I think that's very clear to everyone who is building in the industry. Yes, there are still people who believe that they can come up with economic models which can sustainably drive value to the gamers. I'd be surprised to see something like that scale, at least what we in this room call mass adoption, right? Because anything less than 10 million dollars is not mass adoption for an industry, right? So that's part one. Part two is I think the economic models of gaming around blockchain can lead to interesting things being created. I'll give you certain examples, right? We are right now working with Riot for Valorant, right, in India. Now you would ask that we are a Web3 community why are we working with one of the largest Web2 games? And the angle there is very straightforward, right? Riot believes that their single biggest driver of engagement for Valorant in a large country like India is grassroot tournaments. Now if they work with the traditional agencies, they have to go through various layers. It's a long process when they go out and organize grassroot tournaments. Our community was able to self-organize grassroot tournaments at a scale of about 700 tournaments in less than three weeks across 66 cities in India without anyone being physically present in any of those colleges or any of those cafes, right? Now that's the power of bringing transparency on chain which is who is the tournament organizer? Why are they organizing it? Who is their community member? Are they real human beings or not? Do they have a Valorant ID? All of this information inside the game system on chain together can be clubbed but we are not using anything on chain with Riot because that's not their objective. But that's an example to say that these models where each person who's playing a particular part in the gaming ecosystem can generate value for not just the game but also for their community as a real one, right? And here, the question you would ask is whether that tournament organizer is having fun or is that a job? I think it's a mix of both, right? Because when I was organizing college festivals 15 years ago, I wouldn't call it a job, right? That's the same thing for that tournament organizer who's organizing that thing. But for a platform like Rooter Tomorrow, they might need 5,000 people to audit a particular game content and where they today might reach out to various agencies or tomorrow they can just go to the community platform and see on chain reputation to say whether Ishaank has audited tournaments in the past or not. And if he has, it might be a direct benefit for Rooter where they're eliminating all the middlemen, they're going straight to the community and the community guy is getting benefit by being associated with the tier one platform. So I think in the gaming industry as a whole, you might see the emergence of jobs but inside the game, I think it has to be fun. Interesting, and I think that's a very well placed point and as we can see the interest from the audience we're having a very engaged discussion but in the interest of time, we'll have to jump to one last question and Saloni, I would like you to come in here. There are a lot of young founders in this room today and the people who are gonna watch the stream online later, what is it from an investor perspective that you advise the young founders who are wanting to come and build in this space? What is an investor looking for? To place that bet, okay, I'll invest in you because this is a new space as much as we want so there's not enough pedigree of let's say web three games of course the gaming expertise comes into picture. So what is it that you look for before making a decision, okay, maybe we'll put money here. Yeah, I think because there has been, we've kind of gone through one hype cycle wave of web three funding and now we've seen several companies either not gain traction or implored. Whoever's looking to build in this space has to come with two things. One is a very unique insight of what they're wanting to build and the second is a very comprehensive understanding of the learnings of the first generation and the mistakes of the first generation entrepreneurs made and how not to repeat them, right? As Ishan said, if you are coming in with very complex economic models and assuming that is what's going to drive user adoption I believe those are some assumptions which have now clearly been challenged and also in web three it depends. Are you looking to build content? Are you looking to build tools, tech infrastructure? Are you looking to build platform plays and accordingly you need to tailor your pitch and you need to build a team as per what you're targeting but with respect to let's say even just web three builders, you know I would say they need to take a leaf out of the book of web two builders especially the game builders because they were real masters in understanding the craft of building games, understanding how to engage users, user and game psychology, right? Which I believe the first generation of web three builders didn't really pay much attention to. The second is the core competency of a web three game team needs to now include strong game designers, strong technologists with strong blockchain experience but also strong system thinkers. You know whether it's real world macroeconomists as part of your team which now several global web three companies have started to do because the complexity of a web three economy is far, far deeper than what, especially for rebalancing and level balancing is far more complex than what we've seen in web two. So if you are looking to build web three games I'd say come you know think about all the there's now enough material think about building it from all scopes and all nuances of what is it that you will do differently but also some market research in terms of you know the traction of existing web three games the good thing about web three is everything is transparent so you know how many wallets there are you know how many games are doing well how many even have more than let's say you know a few thousand users so perhaps use that to your advantage before you're pitching web three but also understand that you know this is a fundraising winter.


get started so can call this meeting to order so the first thing in our agenda second thing in our agenda is the approval of the agenda does anyone have any changes okay so I was going to get into that after calling order in that case we are not called order so we're lacking a quorum so this will be a working group of the Mobular Planning Commission tonight and our next meeting will be on July 29th in which hopefully we'll have a quorum and get business going so we had a number of things this evening that we'd plan to vote on there are going to have to be pushed off but first things first I will go ahead and go through the comments I'd plan to make with the quorum and that's that we don't have a new member so we have a vacancy on the Planning Commission right now and so we're hoping to have that seat filled by our next meeting that's all I have to say does anyone else have anything to okay there's no general business right because we correct just doing a working group no election of new officers tonight which then leads us to the Stork Preservation meeting from last week we plan to do a follow-up tonight and then we were going to do a walk-through in depth to the proposed regulations that came from the Stork Preservation Board next meeting and and offer our suggestions and Meredith is going to come and work with us I don't know if everyone's aware of that Mike were you thinking you were gonna come also or to the next meeting next yes okay you and Meredith both will be here yeah okay I just I mean I would have been there too okay I personally if you wanted to have a night off wasn't gonna have any issue with it but totally your call obviously okay well in that case what does everyone think about this current state of design review and the historic Preservation Commission's proposed regs I have some concerns just bigger picture about design review and I'm not sure that they're not sure where to sort of put them in the process but you know I think generally I'm concerned that design review you know maybe the boundaries could be adjusted because I'm especially concerned about you know homeowners who house that's technically historical like maybe there's a small feature over here because I used to own out like so I do have some I am bringing some of my personal experience and just the difficulty and the extra expense that it is to you know fix something or maintain something or change something so I have that sort of general concern and is there a way I mean I I do value the historic character of Montpelier I'm not a total anti historic preservationist but I think there are many instances where there's homes in the design review district that most people would walk by would not you know really have a deep appreciation of the aesthetics do you know what I'm saying versus you know obviously you walk through our downtown and you have a real sense of the aesthetics anyway so I have that concern about homeowners and also just want to raise the question of how this impacts you know if we want to develop more housing units and I'm not sure I've tried to read the regulations and I'm not really sure how that all and hopefully the next session will help me sort of visualize how that all is affected and fits in but so I just just have those two general concerns I guess about the design review but I'm not sure if that's appropriate for the review of this and another question I had which I didn't think to ask last time but was I'm just curious if they have any records of the public input they got or how much public input they got I'm a little bit curious about that too and I know they did they made efforts but I'm just curious about that. That's a good question I think Meredith next week will be able to or next meeting we'll be able to go into that because she's she staffs seven banks and so she would have first hand because yeah it seemed like there wasn't a lot and it was kind of vague. What do you think Stephanie? I think it was it was good to have them kind of I think there are some issues that I had in my original questions I had in my original review like the library example that someone from the community gave the addition of the library because some of the language was if you're adding a piece sort of like the new development question if you're adding a piece to a new building it should be they shouldn't try to match the historical nature but it should be compatible with it but it should be different and that some of that balance seems challenging to me but I think the library is a good example so that was but I still there's still a lot of arbitrary it's still a little arbitrary to me how exactly that happens and I think the development falls within that too as far as matching the nature but not copying the spark district I'm not sure that seems like a fine line to me so I wonder a little bit about that I think it was really helpful to have them come though and explain from their perspective what it is that they're trying to do I also think the found I think we're gonna need to talk about the boundary for sure sooner than later I think going through it next week first makes sense we have an understanding of what we're looking at but I think some of it some of where your question leads me to think about is specifically what the boundary is and if it's a house that's not actually historic should it be in the boundary between historic you can't like section out one house so yeah I know it's it's a complicated question but to me there are houses that are historic but are not and I guess it gets hard because it depends on the whole neighborhood and the whole look of the neighborhood but a lot of houses to me that are historic but I don't think most people walk to be you know just like appreciate it I mean I used to live in the old north end of Burlington and that's what I'm right there are a lot of just you know we're all under this like preservation thing but I don't think you would walk through a lot of sections of the old north end and really feel like you're in a historic neighborhood but maybe that you know I haven't I'm not sure exactly what's in this district and I don't maybe I should walk around I think one thing that will help next week is if we can have Meredith or Mike go into before we start diving in so we're gonna have a busy meeting but before that talk about how the document we're looking at will be applied in the real world because the the feeling of being heavily regulated either comes from or doesn't come from like the process that the doc that the regulations put into place with like for instance I mean some of it if it's just DRB review and jump in and crack me Mike a few you know but when when something's just up for DRB review a lot of it's really is just suggestions and they're working at the DRC sorry yeah yeah sorry yeah yeah I don't know why yeah so yeah DRC so and then the DRC were some of the folks that were here last week so we just I mean I can I can tell a personal anecdote where so my wife's expanding her child care business from our home and one of the regulations is you need a four foot tall fence so she applied to get a four foot tall fence put in around her house she had to go to design review committee for that and was kind of worried about it and I told her not to and then it was really painless and there and it was like things like suggestions like and like lots of questions about how it will fit into things and she kind of had answers and they accepted her answers and there was nothing like you shall do this nothing like walking out of it she was she wasn't really bound to anything or at least didn't feel that way but she's and then afterwards she tried to stick to what she told them as far as when we put the fence in and she told that for instance I mean we just painted it white she said it would match the house but she didn't really say which of the house's colors but they didn't really the trimmed whites we painted it white so that was her experience and so I think yeah and and I feel like they missed that opportunity last week to some degree to go into that and talk about how it's not always that intrusive although the new rules are gonna would change the dynamics of what they're regulating and how what standards they have to meet so there's gonna be a little bit of a shift how the DRC has been enforcing the existing rules is the existing rules are generally more vague today which we're concerned about from a legal standpoint I think they have to be more specific because of some of the recent court cases so we think it has to get more specific and then if it gets more specific how does that in the experience we had before from the Planning Commission was that we wanted to just start to narrow the scope of reviews if things aren't gonna matter so we tried in the original version to go through and say you can replace your windows so even on a historic house you can replace the windows but the windows have to be of the correct historic character so that's got divided light and it's a six over six then you're gonna have to put in a window can be new window but it's gonna have to be six over six whatever the thing is the DRC would review it but you could replace the windows and historic preservation division historic preservation wasn't happy with that so yeah so they wanted they pushed back and eventually we haven't just shelf the whole proposal but we were looking at those types of questions so when we get back into it we're gonna be kind of back into the same thing because we didn't want to have some people get required to keep the windows and fix them and some people get permission to replace them really should be consistent if it's either we're gonna make everybody keep the old windows unless they meet us clear set of standards unless you can demonstrate one two three you have to keep the old one doesn't fix them or is it we're gonna let everybody do it and the same came up with things like roofing and he was just replacing asphalt shingles take off asphalt shingles put on asphalt shingles and code officers came up and stopped him had seasoned assessed because he didn't have a permit for placing asphalt shingles on this roof did he have an old house yep he had a historic house but it never occurred to him that replacing the asphalt shingles on this roof well if you're gonna get a permit anyways so we wanted that's what we had talked about when we were doing this during the big zoning rewrite was roof treatments window treatments porches doors these things that we get a lot of we should have a nice clear rule this says you can replace your door with a modern door so it's a historic character place the roof as long as it's not the same character of the roof you're removing so we've got standing scene you have to keep the standing scene if you want to go from asphalt standing scene then you got to go to the DRC so we can have a bunch of these or vice versa if you had standing scene but you wanted to go to asphalt you'd have to go to the DRC to get approval and you may get denied because the character of a certain building may be federalist you tend to find federalists have more standing scene or slate you know they didn't want people going in and removing a slate and putting in an asphalt roof so what is the definition of historic preservation do they approve design regulations they only do they don't in our case but we are a certified local so that's a CLG we have signed up to as a community to hold ourselves to a higher standard and division of historic preservation gets to comment on whether we get to maintain our CLG status so they made some threats about whether whether we would be able to maintain our CLG status if we allowed to replace whatever we do we'll probably have to go back to division and get approved so those those are some of the balancing acts that we'll also have to get into is the requirement from the state in order to maintain our CLG status which gives the historic preservation opportunities to get grant funding to do various projects so I think they'll be a I think there will be a balancing act that goes in there between what we want to regulate and we just kept them as we transferred them over from the old regs the truth is it ends up being very strange because there isn't we don't get a lot of applications we don't run any applications because it's not the design there isn't anything in the gateway that's in the design review district and we haven't generally considered the entire district to be in design review and I don't know if that was the original intention I haven't seen it work out that way but when I've read it I'm wondering about that too it's whether whether all of these other districts are also added onto which is that all the other districts are treated the same and those two have like their own special needs for some reason yeah they end up in design review and some of this some of this has to kind of come down through the buckets you know you might have a rule here but if there's no way to get to the rule no we actually have to meet it it's we use that bucket analogy a lot because it's getting it starts the top and the applicability and you've kind of got to get your way down there and if the thing is it's regulated to the design review district and then it says everybody who's in the gateway has to meet these rules it's like well they're not in here so it actually applied to them even though there are rules that should be applied to them the only rules that would apply are people who are in the design for like Riverfront there are portions of you district and therefore they have to meet the extra I don't think there's anything west gateway west would be so those are in potentially a new district yeah the newest I made a set of comments as they were doing their initial review this is like their version 3.0 so I commented 1.0 and 2.0 and I didn't get an opportunity so for the boundary discussion because of the things this is where I want to start asking questions considering City Council removed a neighborhood and from stored preservation sign review are we currently do we feel like we're in compliance with state law with what this is what the boundary is now yes there's no there's no issues right now because the only requirement we have and it's not really under state law the only requirement we have is because we are a designated downtown everything that is in the designated downtown must be in design review that's what I mean by state law yeah like the even the things were voluntarily yeah that's the only requirement that we have is that that's that's where we'd have to start at the minimum okay has to be the minimum is the designated downtown which cliff streets not in whatsoever there are one or two hillside the one that comes up from court and are they it's not cliff till you turn right and they're and they're currently in that correct cliff street was in before yeah City Council removed close to us yes the first boundary was somewhat arbitrary this boundaries someone what a great place to start it was someone arbitrary national register district was also a little bit arbitrary through there as well someone they somewhat overlapped through cliff street so cliff street was is in the design national register district was in the national register district and then our design review district in that area tended to over so they were in so for a boundary discussion one thought is that we could just try to tackle this after we do the deep dive on the regulations as fresh in our minds but of course there's the public input component and there's a chance that we do something other than the bare minimum if we do the bare minimum I don't think there's any risk of like the public if we do as small as we are like legally can then I mean you know but our discussion is going to go beyond that right even if we end up doing the bare minimum like our discussion go past that which means that maybe there should be public input or definitely should be public input so with that in mind what do we think we should try to plan and like should we might do you think it would make sense to in a month or two from now maybe hopefully sooner than two months away have one of these meetings dedicated to the boundary question in which we make an extra effort to attract or invite the public yeah I think I think it should probably be in the fall a lot of people are busy during the summer and not here I don't think we'll be ready before the fall anyway so I think we waited till September to have a we could probably make three or four different map options that go through and say this is what we've got and this is kind of either the minimum or the minimum plus all of the commercial neighborhoods that are right design review district I think the designated downtown only covers half of Berry Street like both sides of the street as it goes down so I think there are times we could just add in the rest of certain neighborhoods that might make sense and then just go through it so we kind of have the smallest got the existing here it is out into the residential neighborhoods that includes anybody who's in the historic district which wasn't popular when we proposed it before but I think we could put in a range of options that says you know these are the options actually go all out to the entire city if you wanted it balanced and then you just kind of see what the public thinks is supportive of more of those protections because usually it's just a matter of talking to people to make sure they understand you don't want to regulate yourself be the first one to come in and we've talked about but I don't remember where we have ever landed on this but but we've talked about possibly having design review that's maybe a larger area and then within that having historic preservation limited to a smaller area if these rules can be easily broken into two pieces kind of the historic design review and then design review I'm not sure that can be that it's very historic focus and so this is going to be it for our design review yeah I mean I think it would be difficult for us to different without going back and doing more work I think this might my impression when I'm one shot the next meeting we go through it that makes sense I think we might come up but we can try to go through it first and see what we think and just it's just the historic piece but then I think it would be really helpful to see all the different maps so the historic register map the existing design yeah and then there's just zoning neighborhoods there's a lot of neighborhoods that kind of are historic and you can kind of add on or subtract off for hoods if it made sense because it might mixed use residential kind of goes out Elm Street past the bakery those right right along Elm Street started at some spring street out so should that be designed mixed use has some commercial in there I think it's more policy questions at that point but you probably put the whole neighborhood I think one thing Stephanie was kind of hinting at us I mean these things go hand-in-hand I mean I've said all along I'd be more inclined to have a larger area covered if these were flexible but the less flexible they are the more you want to focus them on the most oh yeah exactly and they seem to be oriented toward and I mean because I know what she was saying too like toward really trying to protect the resources are there in which case they may be more perfect for smaller area but since they go hand-in-hand it's like it'd be in a perfect world we do them simultaneously it's not looking like it's gonna come out that way I think we can still talk about it before having a better understanding of what the options are and why we might be leading this specific direction it'll help when talking to the public to know what are have a better idea of what exactly the regulations will be so I think going through them next meeting still makes sense yeah yeah I think that's a good idea for next time but then but then have the actual boundary discussion maybe the meeting after that where hopefully we'll we'll have we'll be close to what we want to suggest for the boundary and then have the public meeting a month or so after that so it's in the like September like you were saying the fall yeah it'd be easier once we're into the fall again okay so we can have the maps maybe projected or something at the next meeting because yeah I feel like that would help me I'm visual so I want to see yeah is that possible yeah let's see if we can get them digitally or some hard copies as I put this out from the internet but I'm like which boundary is that I think it's the design control district but it doesn't really make a lot of sense to me so I don't know did I put off okay yeah looks like I think I'm guessing yes that is the current design control and then they put in the ccb and they put in the vcfa parcels which is vacant land or am I no that's that's um we're not ccb but that other parcel this this one is vacant that they took all of the college owned part property this one's currently for sale oh okay that was all the college property yeah property but they are under state law exempt yeah based on the last decision these have been here for many years yeah the irony is that these are both exempt from design review under state law oh that's a little and they and we've had a lot of stuff from people but we can still I'm like no okay he can't it's a little bit frustrating but yes state house state property which is why under the new zoning they're some of the feedback we received in the new zoning was like why are you leaving the state out and it's like it doesn't matter if they're in or out like it doesn't apply to under state law so bcfa is selling this parcel which is vacant land which once they sell it it it won't be exempt right once they sell it it would still be oh it would still be yes oh i guess i was assuming it was exempt because of an educational institution it it would still be in design review it would no longer be exempt right that's what i meant to say if i said it should it be in design review it's an empty parcel right because it's only that piece is only in because it's owned by it was only in because it was formerly known by the college so then it shouldn't be in yeah so yeah whatever random boundaries we have would be helpful to me that's yeah and then with zoning if we want to make it match it's supposed to be districts so did we want those for the 20 so this would be good for next yeah so helping for the 29th just in case we get any questions based on right right i will i will do the best i can just just a couple of printouts maybe for that one yeah from the 22nd just in case it comes up something to look at that yeah current current current zoning map and current and current design review maps so i'll just try to get some 11 by 17 if you could see the national registered district too though it would be helpful for me but to see how different that is from our existing good call national registered district there would be helpful if you could make it actually a bad room that's for a reason yeah yeah the arbitrary one we just had but and that's the only thing that to me seems like a more solid line i'll buy none of that didn't understand you're saying that even the national map isn't wasn't the process that went into it wasn't exactly it's it's meant to be strictly just a study of the structures that were built within a certain period or theme so they just end up with a really big district and i'm not sure if that just was generated from the fact that there was a number of fires that burned most of the downtown 70s, 1880s, 1890s so everything ended up being built all at the same time and so therefore when they did the national registered district it all came out as this was all built in the same period oh it's really getting burned that's just a gas but we we have the largest district in the state by far yeah 50 years is the cut off got other places that could be the meadow is not in the is not in the district the college is not in the national registered district so their number neighborhood's college street isn't but their number place that could be their own district but probably would be a different time period that our current district so we probably have two or three we should have probably two or three historic districts so how different rules well they would these would be from the from the national register from the planning standpoint we would have different districts how what gets regulated how we regulate that it's just curious how many towns in Vermont have designed control districts I don't know off the top of my head a lot of them would there's quite a few of them that do I know there's at least 11 CLG certified local governments so I think you have to have design review just curious I'll try to get some okay so it's nothing else our working group is definitely narrowing down like what we're going to look at specifically the next couple meetings to push off the election the officers beginning a next meeting that's awesome okay yeah we have some we have some time to sort that out until September I'll email you someone might know it's about maybe the order of the discussion based on what we've been talking about now which is basically like what I'm thinking is we can start with an introduction based on process and then go into substance of the other proposed rags okay all right so the 32nd on the city plan so I've been continuing to do some implementation strategies with committees and I've been working with the historic committee so I'm actually meeting with them again so housing we did last year with the housing committee I'll probably go back and revisit with them historic for energy I'm going to try to set up a meeting with them so the plan is not much here but what this just did is the chapters there were about 12 chapters we were going to put for the plan certain things I was going to be working on you know prepping notes meet with the committee implementation plan meet with the committee again provides the implementation plan have the committee approved so I'll be meeting with each one of these committees three times then when it's done it could go to you guys so I've just started to fill this in and start to pull across but like historic resources I'll be meeting with them tomorrow it was was seven nine I mean I canceled so and then I'll get a revised one the same with housing energy I just I have one that's drafted and ready to go I met with Barb but natural resources and transportation were two of the next ones I had started last year I'd started utilities and facilities but there's no committee to review those you know no committee to look at sewer and water for natural resources is that conservation and parks yeah that's conservation and flood resilience well it's the report this is our requirement we have to have flood resilience and it has to go somewhere so that's where it would naturally fall talks about that no probably it's going to fall to the conservation commission and their discussion of rivers so I'm going to get those things so like I said I generally prep some notes for them I put a bunch of stuff out there of thoughts and ideas and I bring with me the the discussion of a city full of butterflies rainbows and unicorns thing and I go through that with them and explain to them where we're trying to get to and then you need to start just throw stuff out and then I galvanize it go back to them and say this is what I've heard and that's how kind of break into three pieces historic twice ready we'll hopefully get this finished up and as I said housing was the guinea pig that we started with implementation pretty much is done already that was the example that we did I'll just keep working these things through so my plan was just keep working on this on my end and then as we get these things up with the center planning commission then I can start handing them off to you guys and hopefully by then we've got historic preservation design review done it's not like nothing is happening but at some point you will be responsible for land use so we'll have to work on that as a group hopefully we'll start to be able to pull some pieces together and have some public input decide from that point once we have implementation plans the discussion we had last year was to work a little bit backwards most of the time we write the chapter and we write the patient plan afterwards but this one we decided to do a little bit backwards we'll work with the committees we'll do the implementation strategies and then because we want it to be more succinct with what we're saying let's write the plan of what we're going to do 2,000 1,500 to 2,000 words on transportation and really focus on telling the public what why we're doing this why it's important as opposed to starting out with a big blurb of all the statistics and data and everything and then you end up with a 500 page plan that nobody reads we wanted to kind of make it much more succinct that really focuses in on 1500 words on why our aspiration and our vision is what it is the appendices for all the other stuff that the data it's like on this link you get the data but turn those into short videos that would be because some of the plans that are nationally going on right now is their web-based plans and like 80% of the traffic are people viewing the videos so if you want to know the housing plan you would just you know got the housing plan in professional produced and it doesn't bore you with all the statistics it just kind of goes through the process of housing why it's important and what we're doing and why what we're doing is important and why it's going to help us achieve our goals same thing with transportation and natural resources and I think it would be good if we could get there but we first would need to improve the plan because you came in the video the city council has said that is our goal now we can go home approach that we agreed on before so even though it's we've been kind of sidetracked with a lot of stuff I've been trying to as this winter has wrapped up and gone through spring I've started to jump in and get more of these as I said energy took a bunch of time historic resources so hopefully we'll have four of them moving pretty well this summer natural resources and transportation next appreciate the implementation focus and the clarity of gravity focus also I think that's going to make for a much better useful product which sounds great to me feeling a little disconnected from the process so I would love to be able to just make sure the source is correct yeah just kind of see how the process feels a little more yeah because it's kind of not really clear on what to say yeah I think it makes a little bit more sense and and I can bring maybe for the rest of the group when we maybe after the next meeting because we'll be busy but I can bring in and kind of show you when when you guys get historic resources maybe I will show you this is the these are the notes that I gave when I did prep notes and they came back with me with this which I then turned into this and I then turned into this you don't really have to review it it's more just a matter of seeing what that process was and what you have at the end is the culmination of you know three months of this iterative process of developing something that we think is going to be effective here's our vision here's what we're going to do and if we did what we're going to do are we going to accomplish our vision hopefully the entrance yes set the vision we all agree on so are you working with these groups on something I'm just wondering how this is connected to like the three goals that some of these groups brought to us this is something different that you're working this is related to it we go back and look at what their three goals were and try and I try to integrate that into their notes that are being prepped of you know this is what's in the existing plan here's some notes here's some things I know from other communities I've worked with here are the things you mentioned when you when you gave your three things now let's start to build some things start putting some pieces together what are some tools that are out there that perhaps you're not even and we can start to get into you know what are some things in in some cases what are some things that we are doing and doesn't make any sense we have some energy things in our zoning that kind of just don't say is is regulating the shading of structures really a good idea it's only in there because they wanted to protect solar resources but it also forces buildings to be farther apart and make some shorter so they don't cast a shadow is that really is is that a magical thing not shading your neighbor's house really that important that we should be doing that as opposed to you know your energy plane is really talking about weatherizing and energy efficiency and we spend time regulating this other thing so sometimes it's the things we're doing and whether it makes sense for us to do them in other cases are there better tools that we could be utilizing stabilization be helping if we had points towards weatherizing buildings would that help people tax stabilization on those improvements points right now it's something to consider when you say people do you mean the members of the committee who have tax stabilization for any property only only because of the way our law is written it only applies to commercial properties yeah okay so well I appreciate that this background work is happening and is moving because we're going to need it and none of us are able to do it I mean so it's great so thank you Mike for me and moving all that along and it's looking like yeah we'll we'll get back to this in a couple of months and then hit it hard and try to work exclusively on that because I think once we have some implementation plans and especially I think once we have a number of the implementation plans I think this process will move a lot faster because once people have agreed on that then it's just a matter of writing a chat writing that 2000 to 3000 words that explains what we're talking about in the implementation plan and then just reviewing it against the state rags to make sure we've met have we checked all the boxes of things we need or do we need to add well I'm imagining these implementation plans so that the planning commission will give its input we'll get public input we'll try to take the public input and um make it work with you know with what with you know the other stakeholders and things so there will be that entire process though yeah we have to have the products because there's going to be a balance like I said I'm doing historic and we're doing energy and if historic comes out with you know very strong recommendations about maintaining historic historic windows and the energy committee is really big on saying we've got to get these things replaced I'm not trying to steer I want historic to write their their chapter to their thing understanding that this may change as it gets balanced with somebody else and the first people to balance it will be the planning commission and the second group or is there a section that's missing transportation rights its plan energy rights its plan then we get done we're like hey nobody talked about public transportation and it may come back up to here where we send it back to another go and say you know we think public transportation would be part of the transportation plan transportation committee we're going to ask you guys to work on a discussion of public transportation or the energy but in certain cases certain things are going to have to be addressed so is that the understanding of these communities is they go through this process that it will be sent to us we work conflict resolution we need to make decisions and send it back to update in some way or change at our level yeah if we make changes then it'll probably go back to them I don't even have that in there committee approval set to pc pc approval no it didn't really there might be a send back update process they might be a send back only if we feel like we need it if it yeah yeah if it needs to be necessary it may just be oh FYI we we remove we remove this because we don't believe it's you have this one strategy you had five strategies listed we don't think we're going to support strategy for we're going to take that one out so that was that was the only reason why I kind of printed this out yeah it was not really to talk about so much that what the dates are that are in there but really to kind of go across the top and say this is kind of the process I'm working on it although there aren't too many dates on there there's a lot more that has happened that isn't really reflected it sounds good can't consider so yes this is a working group there's no reason for determine anything but everyone feels good for the night we can come back in two weeks