Today, I want to get to give some kind of a more sketch less complete, more than a sketch less than a complete proof of the L2 extension theorem. Sometimes it's called the Osawa Takegoshi theorem. So I guess that it's more general than the original theorem they had, but less general than it could be. But this will be, you actually can't prove the full L2 extension theorem with this technique that I'm, or at least I don't know how to prove it with this technique. I'll give you some case which is maybe the easiest to explain. So we have a Stein-Keylor manifold, and then we have a holomorphic function that's bounded, so it maps into the unit disk, holomorphic. And then I'm going to let z be just the set of all zeros of this t. And I want to assume that it's smooth in some strong sense. So dt restricted to z is never 0. And then aside from this, we have a holomorphic line bundle. And then we have a metric, Hermitian metric, e to the minus phi with a familiar condition, db bar phi plus the Ricci curvature of omega is non-negative. Then the conclusion is that for all holomorphic sections of this line bundle L over z, such that the integral of f squared e to the minus phi a of omega finite, I need a little bit more. This holomorphic section over x, such that interpolates this initial data on z. And then it has a bound on its L2 norm. And I guess there's some constant here, which I'm going to write down in a second. The important part of this theorem was that the constant was universal. So it just sort of only depends on the universe, so it doesn't depend on anything else. But what the sharp constant is was not known until relatively recently. Anyway, with these kinds of normalizations, the sharp constant is pi, and that's going to be important in the last lecture. So the universality of this thing really allows you to do a lot of great things, like study sort of line bundles asymptotically in some sense, so a very, very large curvature. You can take twists of them, and you still always have this universal thing. For compact Kaler, if you have a smooth, well, okay. The answer is yes, but it isn't pi, so it depends a little bit. See, what's maybe hidden here a little bit is that this sub-manifold is cut out by a bounded holomorphic function, which of course you can't do on any compact manifold. But even if you're given any hypersurface in a Stein manifold, in principle, in general, you cannot find a holomorphic function that cuts it out. You'll need, right, and then the curvature of the line bundle, of which that is a section of, will enter into this. Well, it will depend on more than that, so it will depend on what kind of metrics you can put on that, and it's not completely clear in general. So you have to be given all that data, otherwise. But then once you know that, you can write down the sharp constant. It hasn't actually been done in all cases, only in a case where you can find a metric of non-negative curvature for this funny line bundle, correct. So this theorem wouldn't apply there, but there is an analogous theorem. So the analogous theorem is that you have, okay, so I'll just do it quickly, because I don't want to spend a lot of time on it, no, no, it's fine. So you have some z inside x, and then you take the line bundle associated to z. And then, of course, there's also a section t of this line bundle that exactly cuts out this z and generates the ideal blah, blah, blah. So what you need, and this is what I was telling Tomash, is you need this extra metric for this line bundle, and the curvature of this metric matters for this condition. So then the condition becomes something like d, d bar phi plus the Ricci of omega has to be greater than or equal to d, d bar lambda, and also greater than or equal to 1 plus delta d, d bar lambda for some positive number delta. So for example, if you have non-negative thing, then you can forget about this condition. It's just this one, but in general, we don't know. The other thing is that this metric has to restrict to z as something reasonable. Okay, and then, and then the L2 norm will change a little bit, and the denominator, you have to make sense of it, this will be the denominator instead. And then if this thing is positive, then the constant is I think it's 1 over delta plus 1 times pi. So if you really can find a flat thing and let this delta go to infinity, you'll recover the pi case, but anyway, that's what happens in the more general one. Okay, so well I made this claim that this is a sharp constant, so you at least have to see that it's true in one case, but it's easy to see. If you take x to be the disc, omega to be the Euclidean metric, and phi to be 0, so your line bundle is trivial. And then take t of z just equal to z, so that your capital Z is just the origin. So you're trying to extend something from the origin to the disc with a given value there, and the claim is that the constant will give you this. If you have a constant at the center, you just take that constant to be the function. And that extension will satisfy the sharp estimate. So, and somehow this looks like maybe a silly example, but it's the example we're gonna try to reduce to. So what we're gonna try to do is actually shrink x onto z in some nice way. So that the weight essentially becomes a constant. And then the thing you're trying to extend is already extended because you have some kind of infinitesimal neighborhood. And so it's gonna satisfy the sharp estimate. And then what we wanna prove is that as you grow this domain along this deformation, the constant only gets better. So that's the strategy, it's a kind of model case. Okay, so now let's start into the proof. So first, we have to do a little bit of reduction in order to apply the technique that we're gonna do. One of the reductions we're gonna use is to shrink to some relatively compact pseudo convex subdomain, which I'll keep calling x. And then, and therefore the section that we started with is actually gonna be defined on some neighborhood of this domain. So we can, in other words, we're gonna assume that f is defined up to the boundary as is all the data as r omega e to the minus phi t. I think that's all the data. So how do you reduce to this case? Well, the claim is that once you know how to do this on some relatively compact subset, shrinking the z into its intersection with this compact subset, it's only gonna be smaller norms than this one. So this will be a universal upper bound. And then you just use some weak star compactness to pass to the limit. So it's just basic real analysis to make this reduction. So that's what we're gonna assume from now on. And then the next step, so this is the reduction. The next step is that, so the claim, which I'm not gonna prove, is that there exists some capital F, maybe capital F tilde, homomorphic section on the closure of x such that the restriction of f tilde to z is this little f. So, oh, and another reduction that we need to, we need to also assume that this singular Hermitian metric is also smooth. And that was the spiel that I gave last, at the end of last lecture about how on Stein manifolds you can always smooth the sections and still keep their curvature and non-negative, or in this case, this Ricci twisted curvature and non-negative. Okay, so how do you do something like this? Well, this is really not part of the yoga I'm espousing here. This is a more standard thing. If you have this submanifold z, well, you can sort of make local extensions of f here and then you can take some other extension or some other any function in the rest. And then you try to patch them together. And then it's really a problem about some Schief-Kohmology. And if you use this Dolbo isomorphism thing then it's just about solving the D-bar equation. Hermander's theorem will show you on Stein manifolds there are no obstructions. If it's a domain in Cn, for example, then you can really just, because this thing is extending past the boundary, you can really just extend constant. I mean, you choose some holomorphic transverse section which you can do on Stein manifolds. In Cn, I guess. And then you're just going to extend holomorphically to some neighborhood, extend to f constant, then you cut it off, and then you have to somehow use the D-bar equation to correct the smooth extension to a holomorphic one. There's a little bit involved. You have to insert some singularity here because when you solve the D-bar theorem, you get some solution, but you don't know if it's the original thing you want. You want whatever you add to this to correct it to vanish on the initial data set. And so you need to introduce some singularity. And this is where you lose the estimate. So if you introduce some singularity, it'll be something like the metric 1 over t squared. Anything that's L2 with respect to this metric will have to vanish along the zero set of t. And then, but, well, it's not global in this, in general. I mean, in this case, I suppose it is. Anyway, you're going to lose some curvature when you introduce this singularity. But because you're on a Stein manifold, remember yesterday I said that the trivial bundle has a metric of positive curvature. And you can twist it, it's still a trivial bundle. So you can get back as much curvature as you want. And then it's another way of saying the vanishing theorem, I guess, more directly. So okay, so this you can do. And so if you do it on a slightly larger domain than the x you're interested in, then its restriction to this subdomain that we've reduced to is automatically L2 because everything is smooth. So it means that, so this guy, this f tilde is automatically in L2. So you've got some extension and therefore there is some constant so that that extension is less than or equal to this number. But this point, the constant depends on the data too much. You can't take limits or anything like that. So you need to make a much better L2 extension than this one because you don't know much about this one. So the thing to do is to take, so let f be the extension of minimal L2 norm. So the whole rest of the talk is about trying to get estimates for the extension of minimal norm of this extension. All right, so in order to estimate it, I need a manageable expression for it. So I'm going to formulate this, the norm in some dual way. So, okay, I'm going to introduce some notation. So let's let A for analytic be the set of all polymorphic sections with a finite L2 norm. X bar means the closure of X, sorry. Yeah, so up to the boundary. That's what makes it L2. Otherwise it couldn't be blowing up. So let me define this L2 ideal of Z, call it I phi of Z, is going to be the set of all G in this A phi such that the restriction of G to Z is identically zero. And so the annihilator of this guy, that's just going to be the set of all bounded linear functionals on this A which kill anything in this ideal. And so then this is some trivial linear algebra proposition. So for all f, polymorphic on Z, say smooth up to the boundary, maybe just write it like this, up to the boundary so that we have some L2 extension to begin with. Minimal extension f0 of f satisfies its squared L2 norm is equal to the supremum of Cf squared over norm C squared star for all C in this annihilator. Absolutely. I'm already assuming after this reduction that I'm working in a domain inside a Stein manifold where Z sticks out like this. And then I'm saying suppose I take a holomorphic section which is defined on this piece, say, which is therefore is L2. As I've argued, there's some L2 extension. And now I want to write down its norm for you by some dual formulation. And I'm claiming that this is the formulation. If you just take any extension for any f, which is in A2, A of phi, such that f restricted to Z is little f. Is it OK? I didn't let you finish your question, but did I answer it? No, I think so. This restriction to this? Yeah, yeah. It's nice. Sure. Yeah, I mean, or it could stick out a little bit. OK, so if you think about this, it doesn't matter what extension you put in here. If you have another extension, then the difference must vanish on Z. It's going to be killed by this expression. So you expect this somehow only to depend on little f. And then it's not hard to confirm that it is the norm of the minimal extension. OK. So essentially what you want to do is try to estimate this quantity. But the trouble is that these annihilators, they're not so manageable directly. I mean, how do you estimate something like this? Well, you'd like to try to estimate by some duality, and you could in principle do that with a re-representation theorem, but the trouble is here that you're in the annihilator, not in the whole space. So you have to be a little careful, but it's not difficult what to do. You choose a good dense subspace. So for example, if I take, say, H, which is, let me write it like this. So this is just going to mean sections of L that are smooth with compact support in Z. So this time it's sort of slightly relevant. When I mean compact support in Z, the support is a compact subset of this subdomain X. So it doesn't go up to the boundary. And then for each one of these guys, you can define this C sub H, which takes, say, some F in here to the integral over Z of F H bar, e to the minus phi dA over dt squared. So these guys, they generate a dense subspace of all the elements in the annihilator. And to check that, you just have to check that if all these guys kill some F, then F actually must vanish on Z. Then from Hanbanak or something, you see that it's a dense subspace. But if these are just these little bumps along Z, and so if this is zero for all little bumps along Z, then this F must vanish on Z. So this collection of all such things is dense. So therefore, in order to compute this L2 norm, we can just, in fact, we have to estimate this just for the C sub H. The have to is not the important part. The fact that we can is the important part. Okay, so let's take a look at... So therefore, enough to estimate... So you have your fixed guy, and then you're going to look at C H star in this annihilator. Yeah, right? Because this norm is the soup over these, and if you have a dense subset, you just have to estimate these guys. Okay, so let's take a look at the numerator of this expression. So let me write L2Z for the Hilbert space, which is L2 on the space Z with the weight e to the minus phi over dt squared omega. So just the L2 norm that I've been using all along there. But now I'm not asking for a holomorphic section, just L2. And then in here we'll have a subspace, which I'll call E because I'm running out of letters. This is just this L2 intersect with holomorphic sections. Those are kind of the ones I'm interested in. And this is very similar to the story we told when we talked about the Bergman kernel. This is a closed subspace by this Bergman's inequality again. And so you have, again, an orthogonal projection to this bounded projection, which is it also called Bergman kernel. I think maybe there's one person here that actually met Bergman. Did you meet him? Nope. He wasn't there? Oh, you did? Yeah, there is one person. Okay. I think he would have been really happy that I'm saying Bergman. Okay. Apparently you had to really not get cornered by him in the hallways because if he cornered you, he would try to tell you how important this Bergman kernel is. Anyway, it's a nice idea. Bergman's inequalities was his main contribution, I think. Okay. So anyway, in terms of this information, let me write down some proposition, which is not difficult. It's a lot like what we've already done before. So for each H, one of these compactly supported guys, C, H, F. Or maybe I'll say F. Yeah, it doesn't matter which extension I use here. And then remember that our F restricted to Z is little f. So if I want to estimate this denominator, this is less than or equal to the integral over Z of little f times the integral over Z of not H, but rather the Bergman projection of H. Okay. So this is almost the Cauchy-Schwarz inequality. The only thing is that if you look at this formula here, because this F is holomorphic and L2 on Z, if you split H into its orthogonal component in the direction of the holomorphic things and the orthogonal component, then the orthogonal component is killed. So you can replace H by pH, and then you apply Cauchy-Schwarz. So, all right, good. So let's see, all together then what we have now is that this C H F squared over norm C H squared is less than or equal to the integral over Z of pH squared e to the minus phi Da over dt squared divided by the norm C H squared times this L2 norm right here. So basically, we want to prove that this thing is less than or equal to pi. We prove that, then we're good. Okay. H is not holomorphic. H is compactly supported. Smooth. Yeah, I'm sorry. It's not the best. It should really be... That's really okay. It's infinity zero. Either way, I should write it. I'm a little bit allergic to sheaf theory, so... Okay. So this is what we're going to try to prove. And now is where this degeneration strategy comes in, and we're going to use this Berenson theorem I spent the last couple of days discussing to get some information about what happens along degenerations. So, okay, I'm going to be more degeneration. So this is going to be the first, and it'll be slightly off, but it's important to try it this way. First, see why it fails. Okay, so I'm going to use a notation L for the left-half plane. It's only convenient to use the left-half plane rather than the unit disk because of... I want to... Ultimately, I'm going to want to say that some function is increasing, and if I use the unit disk, I'd have to do something funnier. Convenient choice, but not a crucial one. And now let's let xt be our degeneration. So remember, what I said before is we're going to try to collapse x onto the initial data set. And if we do this correctly, then we will get some information about how... I mean, I can sort of repeat this process for every xt, and we'll get some information about how this constant grows when we do that. Okay, so xt is going to be the set of all x in capital X, such that log t of x squared is less than t. And then this t is just going to be some negative number. So eventually, this t will be the real part of tau. So I'm looking for something symmetric and you'll see why. So this is certainly a degeneration in the sense that x0 is x and then xt is approximately z for t approximately minus infinity. So now let's define some Hilbert spaces over this left half plane. So let me define h of phi sub tau to be the set of all f which are holomorphic on say x sub real part of tau, sections of l, such that and now I'm going to make a modification of the just normalized constants. I'm going to put e to the minus real part of tau. I want x real part of tau. And then the rest is the same as before. I want this to be finite. These are Hilbert spaces and then we get kind of a vibration of the left half plane by Hilbert spaces. And of course, there's a vertical symmetry, but so what? Okay, so now for each such Hilbert space I can repeat this procedure. And then now you see that the dependence on the real part of tau or on tau in general, doesn't appear in the numerator because that's integrating over the sub manifolds. It only appears in the denominator. And so if we could apply Berenson's theorem to this family of Hilbert spaces then we'd be in really good shape because we would know that the logarithm of this denominator is sub harmonic but it only depends on the real part of tau when you look at the definition. So the sub harmonic function of tau that only depends on the real part of tau is a convex function of the real part of tau. So then suppose you knew that this thing was also bounded. Okay, well if you have on the negative axis a bounded convex function it can never decrease. So it has to increase. That means that this constant will just get better as t goes to zero. If it goes down, then by convexity it has to go to plus infinity backwards. And so that's why I take the negative, the left half plane. Okay. Right, so if you could also show that this thing, that the logarithm was bounded or that this thing is bounded then you win because at time t equals zero you have the case you're interested in and you don't know the constant but at time t equals minus infinity you're in that infinitesimal neighborhood where you know the constant is pi just to take the thing you started with as the extension. So that's a little bit cheating but it's essentially easy to see. Well, if you have a really, really skinny, so here's your z and you have this sort of tiny neighborhood. So take any extension and try to estimate the L2 norm on this thing then it's essentially going to be the value at the center times the area of the transversal disk which is pi times the thickness. But we have the square of the thickness normalizing the measure here. So the constant will be pi for t very, very large negative. So that's the rigorous version. Okay, but the problem here is that we can't actually apply Berenson's theorem because we really don't know these are different spaces that we're looking at holomorphic functions of. So we can't compare different spaces for different t and so we might not get a vector bundle. Anyway, it's at least not clear. It's not a serious problem. I'm going to fix it in a second. So one way to do the integral over all of x is to just take the weight to be I guess identically plus infinity outside x t. It's kind of potential well. And then you'll get zero outside and then you can think about holomorphic things on all of x so by some density argument you see it's the same. But that's a problem too because we need smooth metrics. So what I'm going to do essentially is smooth that in a good way so I can apply. So I need to smooth it in a way that's still plurisubharmonic because the hypothesis in Berenson's theorem is that the metrics are plurisubharmonic. I mean after you add the Ricci curvature. So, okay. So, no I didn't say it yet because I haven't written the but you're right. Basically, once I write this thing down if you've been paying attention it's done. Yeah, I will. I wanted to say it before I write it. So that's my strategy for telling you things twice. Okay, so if you wanted just a quick repetition. You're asking about the deformation part? No. Okay, so let's let so the function that we want to add to our initial weight phi on x is the function psi t it's going to be a map from x cross L sub tau, but the tau is living in the left half plane. So it maps maybe I should write it like this. So it maps x tau to well so you want to sort of get a good plurisubharmonic approximation of this phi restricted to x sub real part of tau. So what you do is you take a little more space in the log of mod t of x squared minus the real part of tau and that's good as long as it's well that's good as long as it's positive but it can become negative when you get close to z. And so what you do is you take the max of this and zero. And so anyway for t of x less part of tau squared less than real part of tau this thing is zero and so you get this part but then when it gets bigger than when you get outside this region you get this contribution but it's not necessarily large. So what we do is define our metric e phi tau to be e to the minus phi plus multiplied by some number p times c tau and p is going to be just very very large but fixed. And so in the proof what we're ultimately going to do is just take it sufficiently large to prove certain estimates which I'm not going to do here but it's really just basic calculus to estimate those things but this is the right kind of approximation to get the kind of space that we're looking for for application of Bernstein's theorem. So let me just say it again so the limit as p goes to infinity of the integral over x of let me just try it. I might be off by adding some real part of tau here but I have blackboard amnesia so I can't really so this depends on p not putting the p dependence in the notation but as you go to infinity you get this integral so I think I must have to add something like plus real part of tau so you can take my word for it or read in the notes how you handle these technicalities but this is not we're going to work from here we're not actually going to take this limit I don't know what you said this in order to get this anyway that's not so important so I may have a typo but I can't tell here right so now you know all the data here extends up to the boundary so actually this is the same Hilbert space as if you leave out this psi sub t so now you do have an actual trivial vector bundle with a non-trivial metric given by this so now you really can't apply Bernstein's theorem and so we have to do what we said we have to do so I didn't name these things but these are going to live in the space h phi sub let's just use t now just assume t is real so we want to show that this is less than or equal to pi and I'm not going to as I said do all the details so I mean you have to you have to do some estimates that involve some basic complex analysis and it's not really worth doing here it's better to just do it the way I said before just think about if you know that you can go down to zero then you do get the sharp constant and so all you have to know I guess I'm done all you have to know is that this thing is a convex increasing function so you need to show that this norm is bounded and then Bernstein's theorem implies that it's convex strictly speaking the logarithm is convex but then the exponential of the logarithm right and the boundedness is essentially the same computation as this kind of thing so what is that ch acting on some section f it's not exactly that but it's the x analog well no it is so this is the integral of say f h bar e to the minus phi over dt squared omega over z yeah so there is a little bit to do here sorry I'm saying this a little sloppy but let me just explain how you get that this is bounded by the L2 norm of f so there is a step here you have to use this Bergman's inequality to say that the value of f at a point of z is controlled by the L2 norm on some neighborhood of z right and so once you know that everything else is a smooth compactly supported thing so that's really it there's some constant that depends on h times the norm of f okay so that's the end of the proof as far as I'm going to give it like I said there's some details to fill in but they're not the kind of interesting details of the Berenson theorem part of the story more some basic analysis but so let me give you a slight preview of what what I want to do next lecture and maybe end a couple minutes short nobody will hate me for that okay so what what have we what have we done today well we've proved this theorem right so this thing looks like a cylinder around z and the radius is t which is a real part of tau and so the integral of any extension if that thing is really skinny extensions more or less constant in the perpendicular direction so the integral is more or less the integral of little f over the disk and then integrated over z but if little f is constant it's the central value times the area so the area is pi times t squared but I have or maybe it's not t it's log t so the way I've defined it it's log t so this is one over the t squared as I'm defining it maybe that was not the right thing sorry it's defined by log t so mod t squared is less than e to the t so that's not right sorry e to the t very very small number because t is negative and you have the area as e to the t so the radius is e to the t over 2 sorry so that's is that the confusion many things many confusions okay right so just a couple words so we use this this Berenson theorem to prove this theorem here by sort of degenerating something and then we got this family of Hilbert spaces and if we had tried to use this approach


Hi, everyone. My name is Bosker. I'm a grad student at UC Berkeley, and I'll be talking about work that I did on quantum lightning. A couple years ago, Zandri defined a new cryptographic object called quantum lightning, which is similar to public key quantum money, except it provides a stronger form of unclonability. The paper made a number of contributions to this subject, but I'll just focus on one of them. They gave a concrete construction of quantum lightning and proposed a new hardness assumption that could be used to prove security. In my work, I'll show that the hardness assumption is actually false, so the proof of security does not hold. However, this doesn't mean that the construction is insecure because we haven't given a way to actually win the security game. Quantum lightning deals with unclonable quantum states called lightning bolts. A lightning bolt is a quantum state plus a classical serial number, and as with public key quantum money, the bolts can be verified using only public information, but it's hard to produce two bolts with the same serial number that will both pass verification. The difference is that the lightning bolts can also be generated using public information. This means that even an adversary could run the generation function and produce many valid lightning bolts, each with a unique serial number. Quantum lightning can be used to construct a strong form of public key quantum money, in which not even the bank that produces the banknotes can produce two banknotes with the same serial number. Quantum lightning has three functions, setup gen and bare. Setup just samples the parameters that are used throughout the scheme. Gen is the generation function which produces the bolts, and it's sometimes called the storm by analogy to a lightning storm. As with a lightning storm, there's some randomness involved in running gen that's hard for us to replicate. In our case, it will be the act of measuring a state. So when we measure a state, it collapses to some random value, and every time we run gen and make this measurement, we measure a different random value, and this is how we ensure that successive runs of gen never produce the same exact lightning bolt. Finally, there is the verification function. This verifies that a given bolt is valid, and the security guarantee is that it's hard to produce two states with the same serial number that will both pass verification. Now we'll describe Xandri's proposed construction of quantum lightning, as well as the hardness assumption that they used to prove security. We'll do this all at a high level. The construction of quantum lightning is based on a hash function that's assumed to be collision resistant. The hash function fA takes a matrix M as input and maps it to an n dimensional vector. M is constrained to be symmetric and low rank. Specifically, the rank is less than or equal to D. To compute one component of the output, we use the following formula. We're given a matrix Ai, and we dot its entries with M. What that means is we take Ai and M, we unfurl them into vectors, and then we take their dot product. There are n Ai matrices, so that's a1 through an, and they let us compute the n output components of fA. To generate a lightning bolt, we start with a superposition over all possible inputs to fA. Then we apply the hash function to it, store the result in a separate register, and measure that value. When we measure, the state collapses to a superposition over all pre-images of that hash value. This measurement is random, so every time we run Gen, we get a unique lightning bolt. I won't go into much detail about how VAIR works. The details are given in my paper, as well as the original quantum lightning paper. All we need to know is that VAIR uses a trapdoor matrix R, and R has the following property. R Ai times R transpose is the zero matrix for all components i. Finally, setup samples the parameters that we use in the construction, so it samples the trapdoor R, as well as the nA matrices. Zandri also proposed this hardness assumption and proved that if the assumption is true, then the construction of quantum lightning is secure. Essentially, the assumption says that fA is multi-collision resistant. Specifically, it's hard to find 2k plus 2 colliding inputs, and this should hold even when R is public. Our contribution is to show that the hardness assumption is actually false. We'll use the trapdoor R to construct many colliding inputs to the hash function. To understand our attack, it's useful to make an analogy to the cis-hash function. This analogy was originally used when designing the quantum lightning construction, and it's the starting point for our attack. The cis-hash function takes as input a short vector and applies a linear transformation to it. In our hash function, we take a low-rank matrix and apply a linear transformation. So in this analogy, the shortness of the vectors is related to the low-rank property of the matrices. One trapdoor that's commonly used with the cis-hash function is a short vector in the kernel of the function. And indeed, the analogy holds here. Our trapdoor R gives us a matrix that hashes to zero. So we can see, using the property of the AI matrices and R that was mentioned earlier, that R transpose R hashes to zero. Now with the cis-hash function, it's typically not collision resistant when we know the trapdoor because we can take any preimage, add the trapdoor vector to it, and we'll get a second preimage of the same hash value. However, this attack doesn't immediately work in this construction because the rank of R transpose R is larger than D. So R transpose R is technically not in the domain of FA. That means that if we took a preimage, added R transpose R to it, we won't necessarily get a second preimage in the domain. However, we can get around this problem. The key is to use the rows of R to construct rank one matrices in the kernel of FA. The set K lists the rank one matrices that we can construct in this way. And these matrices hash to zero for the same reason that R transpose R does. So now we've constructed E matrices in the kernel of FA. This is a good number of collisions, but it's not quite enough. So to construct 2K plus 2 collisions, we'll take linear combinations of the matrices in K. Just take D matrices from K, take a linear combination, and we've produced another matrix in the kernel of FA. By taking many linear combinations, we can produce more than 2K plus 2 colliding inputs, and we've broken the hardness assumption. For future work, I'm interested to know if we can break the security of the quantum lightning construction using techniques similar to the ones presented here. Intuitively, if we can construct many preimages of the same hash value, we can construct a state that is close to a valid lightning bolt. Second, even if we could patch the hardness assumption, it's still ad hoc and poorly understood. It would be better to construct quantum lightning from well-studied assumptions, such as those in lattice cryptography. I'm hopeful that we can construct quantum lightning from well-studied assumptions, and I'm eager to see where the field goes from here.


Hello people of the internet, my name is Johnny and welcome back to another reaction video. Now I will admit, I'm pretty late to this one. This video was released like two days ago, um, you know, the day that I took off so I can, you know, just chill for a bit. And of course it came out that day, so I'm here right now reacting to it. Sorry it took so long, but this is the food theory on the Chuck E. Cheese pizza. I said I was gonna do a reaction to this when my pet first announced that he was doing a food theory for Chuck E. Cheese, because you know, FNAF, Chuck E. Cheese, people like to connect the two especially recently. And I looked at the first like 10 seconds, I have not seen the full video, I swear. Um, and Foxy makes an appearance, so I'm guessing he'll probably throw in a lot of FNAF Easter eggs. So honestly, let's not waste any more time, let's just hop straight into food theory. Should you be eating the Chuck E. Cheese pizza? Because maybe it's recycled? The actual title is Food Theory, Chuck E. Cheese Pizza, Should You Be Scared? Now I'm guessing it's probably going to tackle the topic of Shane Dawson, because like in 2018, I wanna say, he made a documentary about the recycled pizza that Chuck E. Cheese uses. I don't know anything about that, so again, let's just hop straight into it. Alright, so again, this is food theory, Chuck E. Cheese Pizza, Should You Be Scared? Here we go. MatPat, enjoying some pizza? There's Foxy. Sponktrap. And Balloon Boy. Boy. A lot. Too many. I swear I haven't seen this. Interesting voices. New pizza for ya. I haven't done any reaction to Food Theory, so I'm hyped about this. Kool-Aid Man, of course. This is an interesting opening. I will say, I do kinda like it. Very nice. Ooh, the OG Helen Henning. I know a lot about Chuck E. Cheese and Showbiz, by the way. Let me just say. Chuck E. Cheese has it all, games, ball pits, slightly creepy animatronic bands. Sounds familiar. And of course, pizza. Sounds familiar. Because there's a bizarre rumor that's been floating around the internet about the pizza served at Chuck E. Cheese. And it's been out there for over a decade. Oh shoot! Wow, really? I didn't know it was that long. Hmm. Again, I don't know a whole lot about this. That's a yikes. Mucked up. Oh, it was 2019? Jesus. What an ominous YouTuber. Jesus Christ. Very nice. True. We're at the three! Good question, Matt. Stitch together? Like that's so in it. That's official? Oh boy. Something fishy. Let's go. Oh boy. Maybe. I haven't seen a recent pizza from them, so I can't tell. Or are they confident that they have nothing to hide? Also, do pizzas at every Chuck E. Cheese restaurant turn out this way? I swear, mine didn't. The one I used to go to. Satan Chuck E. I would not want that one. Chew's Entertainment Cheese. Hmm. No one was really doubting that the dough was prepared in restaurant. Like, the PR team, they saw people sharing these photos online, and they watched the video exposés, and that was the accusation that they felt like they needed to defend themselves. Our dough was fresh. Come on, boys. Our dough was fresh. I've had fresh dough from plenty of pizza place. I've made fresh dough myself, but those pizzas including my own janky pizzas never look as haphazard as these. Even in my worst-looking pizzas made at home, I've never had a fresh dough look that just randomly juts out like this at awkward, sharp angles. It just doesn't happen that way. The stuff about the shape not being uniform misses the point entirely. This isn't about the fact that Chuck E. Cheese pizzas aren't perfectly round. It's that the pizzas don't look cohesive like every other pizza in existence does. The pieces straight up look like they originated from different pies. You can't expect me to believe the reason that this pizza's perimeter looks the way it does is because Chuck E. Cheese makes their dough quote fresh in restaurant. Kind of an odd statement, Chuck E. And you didn't do that. What are you doing, Joe's? By the way, the recycled slices fiasco isn't the only scandal plaguing Chuck E. Cheese at the moment either. It may reports emerge that Chuck E. Cheese was selling its pizzas under a pseudo-nim on delivery apps. That is true. Pasquale. Let's go! Chuck E. Cheese's pizza with the exact same ingredients. So it's kind of the same pizza. Chuck E. Cheese has weathered more scandals in the past couple of years than any wholesome pizza place for kids should. But are the scandals of their own making? Does Chuck E. Cheese deserve to get dragged like this? I just can't bring myself to believe that any multinational restaurant chain could do something so dangerous. So brazenly illegal as intentionally recycling leftover pizza slices.  That is just a new level of low. Perhaps there's a benign explanation for why their pizzas look all Frankenstein together. Dreadbale pizza? New channel confirmed. I can't be sounding the alarm about it loud and clear. So what I want is evidence of wrongdoing. Security cameras. Come on. Put them in. Because photos of strange looking pizzas just aren't enough. It looks as though their crust edges don't line up. But what gives me pause is that the interior points of each slice are scattered about. As to say, the crust edges might line up if the pieces were arranged with the points touching at the middle. Same goes for the pepperoni halves that don't line up. Maybe. For another, I've cut enough pizzas to know that sometimes one of those pepperoni halves will just stick to the blade. So we here at Food Theory did what we always do when we need more info. We ran and experiment ourselves. Oh boy. Let's go get some pizza, shall we? Let's go! I'll make sure to check in the back. I'll check in the head. I'll check in the heads. Poople Guy! It's Poople Guy, dude, totally. Let's go. Chucky! Let's go, Chucky! Wow. Is that still on the app though? We're looking at your mouse. That's a yikes. Can I see? Oh! That's a yikes call. I mean Choles. I've never seen Hamilton. Cool. Oh! Interesting name. Hmm. Oh. Yeah. True. That don't look good. Thank you, but get out of my restaurant.  Looking good, Matthew. That is true! Good observation, Matthew.  Well, why does it look like that then? Yeah. Why? Just can't get it right, I guess? I'll see you in a minute. I'll see you in a minute. Makes sense. Hello? Oh. It's like what? Hmm. Hey, that does make sense. Hmm. Hey, that does make sense. Hmm. How ironic. Wow! Did you look better? Solved! Hmm. Yep. Oh, damn. Dude, I can't believe they got Chucky to say the outro. Well, I guess that was just a shockingly simple answer to the question on whether or not they do recycle their pizzas. Very nice, Matt, I will say. I enjoyed this one. Of course, I loved the subtle FNAF references every now and then, but to be fair, I think we were all expecting that this was going to be heavily based around FNAF references. Because not only do you got to get people interested in the video, it's like always talking about FNAF. But also, it's like FNAF and Chucky Cheese are being linked for some reason. Because Chucky Cheese are closing some locations and people once got to buy the locations and turn it into breadies, which of course is not going to happen. Yeah, overall, very nice theory. Again, I wasn't educated really in this conspiracy. I mean, I saw it happen, but it's like I didn't care for it. Because the location close to me was closed down years ago, so I've been lonely. I've been without a Chucky Cheese for quite a while now. Anyways, yeah, that was the video. Hope you all enjoyed. If there are any more interesting food theory videos, maybe I'll cover them. And I tend to keep my reaction to game theory, food theory, film theory videos when they're close to FNAF because that's what people like to see me react to. If you like this, maybe we can do some more sometime. But yeah, thanks for watching. I'll see you all on the flip side. Goodbye.


Hi, I'm Zor. Welcome to Unizord Education. This is the first of the mini-series of six lectures about inverse trigonometric functions, and today's subject is arc sign. I do suggest you to go back to Unizord.com and review the introduction to inverse functions. It's just general considerations what they are, et cetera. So let's talk about arc sign. So y is equal to arc sign of x. Now, when we're talking about any function, we have to talk about its domain, its codomain, its range, about whether it's monotonous or not, et cetera. But talking about inverse functions in general and trigonometric functions in particular, we really have to start from the regular trigonometric function. In this case, the regular one is sign, which this one is supposed to be inverse of. Now, is the regular sign an inversible function? Well, again, in the introduction to inverse trigonometric function I was talking about, that none of the trigonometric functions by itself is inversible because it does not establish at one-to-one correspondence between its domain and its range. Now, if this is a sign, for instance, function, then the graph of the sign is like this and domain is all the different real numbers and real number represents an angle in regions and the range is from minus one to minus one. But for any value, let's say one-half of the function, you have many different values of argument where the function takes this value. So there is no one-to-one correspondence between the codomain and the range. And to be able to inverse the function signed in this particular case, we have to reduce the domain to a proper interval where this function is inversible. And the best choice is to find the domain or actually subdomain where the function is monotonous because monotonous functions do establish one-to-one correspondence and completely fill out the range. So what is the interval which can be chosen where the sign function is monotonous and takes all the values within the range? Well, traditionally, it's from minus pi over 2 to pi over 2. So additionally, this piece of the sign function is used to inverse the function and convert it into arc sign. So number one job to inverse the function sign is to reduce it to the interval where it's monotonous and still fills up the range, whatever the range is. In this case, it's minus one-to-one. Once it's chosen, we basically do this. So we have this new function, which we still call sign, but it's the function which is exactly the same as the original sign on minus pi over 2 to pi over 2 interval. And it does not really exist at all. It's not defined outside of this function. I can call it a new sign function or just a sign function, but keep it in mind that whenever we are talking about arc signs, we don't mean exactly this classical sign function, which is the wave for the whole range of real numbers. We only mean the sign function reduced to an interval from minus pi over 2 to pi over 2. Now, why minus pi over 2 to pi over 2? Well, number one, monotonous. Number two, it fills out the range. Well, we can actually choose some other interval, quite frankly. I mean, if this is the continuation of my function, I can choose the interval from pi over 2 to 3 pi over 2. In this interval, the function is also monotonous. It's monotonous and decreasing. And on this interval, it fills out also completely the range. Can it be defined this way? Yes. Traditionally, it's not done this way, just because it seems to me a little bit analog. Easier, simpler, it's around zero. I mean, obviously, any piece of the real numbers axis, the x-axis, where the function is monotonous and fills out the range can be used as a domain of the new sign function, which is inversible in that particular range. But it's not done just traditionally. There's no other consideration except that it looks better. It's closer to zero. And it's still odd, by the way, which kind of easier to deal with. Fine. As soon as we have defined our new function sign, which is defined only in this interval from minus pi over 2 to pi over 2, now we can inverse it and now we can define the function arc sign. So its range is whatever the domain for the sign function is. Its domain is whatever the range of the sign was. So basically, x belongs to an interval for this function from minus 1 to 1. And y, therefore, belongs to an interval from minus pi over 2 to pi over 2. Graph is extremely important. It's really a great tool to see whether the function is monotonous, what's the range, what's the domain, et cetera. So now we'll use the same graph to basically draw the function arc sign x, the same technique. Now, the arc sign x is defined on this interval of minus 1 to 1. Now its range is minus pi over 2 to pi over 2. Now, function sign at 0 is equal to 0, which means sine of 0 is 0. So arc sine of 0 is 0. So our function must actually go through this particular point. Now, in this case, whenever my sine is equal to minus pi over 2, arc sine is equal to minus 1. Sorry, sine is equal to minus 1. So arc sine would be just the other way around. From the point minus 1, it has the value of minus pi over 2. What is the angle sine of which is equal to minus 1? Because that's what arc sine actually means. If you have defined something which is the value of the sine function, then this function returns the value of its argument. If you have defined that minus 1 is the value of the sine function, then minus pi over 2 is the angle its argument. So that's why arc sine actually points here. Similarly, here, so what's the angle if its sine is equal to 1? Well, pi over 2. Look at this graph. We are talking only about this interval, right? I'm not talking about all angles sine of them is equal to 1. I'm talking only the angle in this particular interval where the new sine function is defined. And here, the function actually goes very similar to this one, except if you remember the inverse function is, graph of the inverse function is symmetrical to the graph of the main function relative to the main angle bisector. So the function actually would be curved in this way. This function curves this way, and this function curves this way. So that's the graph. We are talking about the main. We're talking about the range of the function. That's the graph. That's the arc sine, arc sine of x. And one little detail, you see sine function is odd as we know. If you change the sine of the argument, the function changes the sine, right? If you have an angle, let's say pi over 4, then the sine is equal to square root of 2 over 2. If it's minus pi over 4, the sine is equal to minus square root of 2 over 2. So now, here is my question. If the main function is odd, does it mean that inverse function is odd as well? Well, the answer is yes. And here is the proof. It's interesting that we can actually prove something like this. And obviously, I prefer it. So how can we prove that this function is odd? Well, basically, I have to prove that arc sine of minus x is equal to minus arc sine of x. That's the definition of the odd function. You change the argument, then the function changes the sine as well. Now, how can I prove this? How can I prove that arc sine of minus x equals to a? How can I prove it? What does it mean that arc sine of minus x is equal to a? What arc sine means? It means what's the angle sine of which is equal to whatever the argument is, right? So that's the definition of arc sine. So I have to find an angle a sine of which is equal to minus x. So this is equivalent to sine of this should be equal to this, should be equal to minus x. So let's check it out, minus. So if I will show that the sine of this is equal to minus x, it actually means, by definition of this arc sine, that this equality holds. Now, let me just make it more visible, minus arc sine of x. Now, what is sine of minus arc sine of x? Well, we know that the sine is an odd function, right? So if I change the value of the argument to an opposite, then the value of the function itself is changing, right? So it's minus sine of arc sine of x, right? This is because sine is an odd function. If I change the sine of whatever argument of the sine is, then the function itself changes the sine. Now, what is this? Well, by definition of the arc sine, this is x. Because what is arc sine of x? Arc sine of x is an angle sine of which is equal to x. Well, let's change the sine of this angle. Then we will get x. So we got this. So what it means is if the sine of something is minus x, it means, by definition of the arc sine, that arc sine of this is equal to whatever the angle here is, which is this equality. So that's the proof. That's the end of the proof action. So function arc sine is odd. Well, that's basically it. There are certain problems about arc signs and as well as other trigonometric functions, which I will present in due time. But this is a small, very short lecture about just properties of the function arc sine. And I do recommend you to, again, go through unizor.com notes for this lecture. Read it. And well, if you understand everything, that's great. And then go to the next one. It's six lectures in this series for each arc function, each inverse function, which exists. So thank you very much and good luck.


So it puts things in perspective. Like when you attempt and you're really enthusiastic about a dream, you're like, where do I go from here? I was in my, my, um, I was probably 27 at this point, very young. I said, hmm, I'm missing something. So I recognize that awareness that I am missing something in terms of business. And I said, okay, it's, it's marketing. But I sat there and as, as I was really contemplating and going, I guess I'm having a introspection. I said, uh, what would it, what would move this needle?  And I really mean that when I say that, or I can find somebody that I admire, that maybe I can work for and I can learn.


So our next speaker is going to also present a short video clip and I will introduce him as well as the person who made the video clip with him. So Peter Kuznick and Oliver Stone together made the video clip that you were about to see. Peter Kuznick is professor of history and director of the Nuclear Studies Institute at American University. He and Oliver Stone co-authored the New York Times bestselling book and Showtime documentary series both titled The Untold History of the United States, the graphic novel of which will be out later this year. Oliver Stone has made many famous movies. Frank believes that his film JFK is the most important American mainstream movie ever made. His film Born on the Fourth of July, The True Story of Ron Kovic is one of the very best anti-war films ever made. He made the important documentary titled South of the Border and he made the 12-part series titled The Untold History of the United States. His film Platoon won the Academy Award for Best Picture in 1989. So here is Peter Kuznick to introduce the clip of the film and to discuss it. Hi Rachel, thank you. I was asked today to talk about Henry Wallace and the origins of the Cold War. Wallace, as some of you know, has been largely written out of history. He's an extraordinary man and one of the themes that Oliver and I were pursuing in Untold History was that the Cold War was not inevitable. It was insane but it was not inevitable. So let me talk for a few minutes about Henry Wallace. Wallace was born in Iowa in 1888 to a distinguished farm family. His father was Secretary of Agriculture in the Harding and Coolidge administrations and Roosevelt chose him to be Secretary of Agriculture for the New Deal. When Wallace took over the farm, total farm income in 1932 was one-third of what it had been in 1929. Arthur Schlesinger says that he was a great Secretary of Agriculture, the best we've ever had. So he was also the leading anti-fascist in those New Deal administrations. So when Roosevelt was going to run for a third term in 1940, he wanted Wallace on the ticket as Vice President. He said we need a real anti-fascist, a real progressive as Vice President because we're about to fight a war against fascism. But the problem was that the party bosses did not want Wallace on the ticket because his views were too radical. Roosevelt wrote an extraordinary letter to the Democratic Convention turning down the nomination for President. He said we already have one Wall Street-dominated party in the United States, the Republican Party. If the Democratic Party is not going to be a progressive party, fighting for social justice and it has no reason to exist, and I'm not going to run on that ticket. He was about to send the letter when Eleanor Roosevelt went to the floor of the convention, convinced them that he was serious, and they begrudgingly put Wallace on the ticket as Vice President. He was an extraordinary Vice President from 1941 to 1945. When Henry Luce wrote his editorial that the 20th century must be the American century, that the U.S. will dominate the world in every way, Wallace responded with a famous speech called The Century of the Common Man. He said the 20th century should not be the American century, it should be the Century of the Common Man. And he called for a worldwide people's revolution in the tradition of the American Revolution, the French Revolution, the Russian Revolution, the German Revolution, the Latin American Revolutions. He called for a cooperation between the U.S. and the Soviets, and to imperialism, and to colonialism, and to economic exploitation, and spreading the fruits of science and technology around the world. That was Wallace's vision as Vice President. By 1944, when it looked like Roosevelt was going to run for his fourth term, the party bosses who were much more conservative were very nervous about Wallace being on the ticket because they knew Roosevelt was not going to last another term and that Wallace would become the next president. So they staged with the party treasurer, Edwin Paulie, called Paulie's coup. Paulie was a California oil millionaire who said, I entered politics when I realized it was cheaper to elect a new Congress and to buy up the old Congress. And so he entered politics and they staged this coup to try to get Wallace off the ticket. It looked like it was all set because it was not very democratic at the convention to that point. However, there was one problem. Now Wallace was the second most popular man in America in 1944 behind Roosevelt. Gallup released a poll on July 20th, 1944, the day the Democratic Convention opened in Chicago. According to that poll, 65 percent of Americans said they wanted Wallace back as vice president. Two percent said they wanted Harry Truman as vice president. At the convention, it was all set for Truman. However, Wallace gave the second speech for Roosevelt. The place went wild. An hour-long demonstration led by, among others, Adelaide Stevenson and Hubert Humphrey. In the midst of that, Claude Pepper, senator from Florida, nicknamed Red Pepper at the time, knew if he could get to the microphone in the front of the room and get Wallace's name and nomination, he would sweep the convention to fight the bosses. So he starts to fight his way to the microphone. The party bosses led by Mayor Kelly in Chicago saw what was happening. They screamed, adjourned the convention. Immediately it's a fire hazard. Sam Jackson, who was chairing it, said, I have a motion to adjourn. All in favor, say aye. About five percent said aye. All opposed, no. Everybody screamed no. He said motion carried meeting adjourned. At that point, Claude Pepper was five feet from the microphone. What Oliver Stone and I argued untold history is that had Pepper gotten to the microphone five more feet, Wallace would have been back on the ticket as vice president. There would have been certainly no atomic bombing in World War II and likely no Cold War. History can be different. That's one of the things we try to show. Roosevelt asked Wallace to stay on in the cabinet while it shows to be secretary of commerce. Roosevelt dies on April 12, 1945. Truman becomes president. Almost overnight, Truman reverses Roosevelt's policies. Roosevelt's last telegram to Churchill said, I would minimize the general Soviet problem as much as possible because these problems in one form or another seem to rise every day and most of them straighten out. But that was not Truman's view. Truman admitted to everybody that he was in way over his head from the beginning, that he shouldn't be president, and he was right. The first day in office, April 13, he meets with acting secretary of state, Statenius, and with Jimmy Burns, who flies up from South Carolina. And they tell Truman that the Russians have broken all of their agreements and can't be trusted. He has a meeting 10 days later with foreign minister Molotov. In that meeting, he berates Molotov. He accused him of having broken all of their agreements made at Yalta. Molotov says, I've never been spoken to that way in my life.  Stalin telegramed in the next day to try to set him straight on what the agreements were. But from that point on, things are going to start to fall apart. Wallace was fighting against this still in the cabinet, trying to convince Truman what was happening and what needed to happen and what the agreements really were and why the U.S. and the Soviets needed to be friends moving forward in the world. The situation gets further complicated by the use of the atomic bomb. I mean, I spent 12 hours on this topic with my students, but I'll just make it very brief. The Soviets at Yalta agreed to come into the Pacific War three months after the end of the war in Europe. The joint intelligence committee of the Joint Chiefs of Staff gave several reports saying as soon as the Soviets come into the war, the Japanese will realize that continuing to fight is futile, that there is no hope for winning and they will end the war. We knew that. Truman knew that. Truman went to Potsdam and he had lunch with Stalin on July 17th. After that meeting, he writes in his journal, Stalin will be in the Jap War by August 15th, Finney Japs when that occurs. He writes home to his wife Bess the next day, say the Russians are coming in will end the war a year sooner now. Think of all the kids who won't be killed. Truman knew, they all knew that Soviet entry would end the war, but still the United States decided to use the bomb, even though it was militarily unnecessary and morally reprehensible. In fact, the United States had eight five-star officers in 1945, seven of the eight are on the record saying just that, that the use of the bomb was either militarily unnecessary, morally reprehensible, or both. As Admiral Leahy said, the Japanese were already defeated and ready to surrender. The use of this barbarous weapon at Hiroshima and Nagasaki was of no material assistance in our war against Japan. And being the first to use it, we adopted an ethical standard, common to the barbarians of the Dark Ages. How did the Soviets respond? The Soviets knew better than anybody, the Japanese were desperate to surrender and the bomb was not necessary, because the Japanese were trying to get the Soviets to intervene on their behalf to get better surrender terms. So when the when the US decided to use the bomb, even though it was not necessary, Soviet leaders from Stalin on down interpreted that the bomb was landed in Hiroshima and Nagasaki, but the real target was the Soviet Union. This was America's ruthless warning that there is nothing that's going to stop the US from achieving its goals in Europe and the Pacific. And if the Soviets interfere with this, this is what they're going to get and worse. And I wanted to let you know that we now have the clip. We were having some trouble getting it together, but we now have the clip. Can we move on to that? I mean, just finish one more, two more sentences. Wallace stayed in the cabinet and continued the struggle against the nuclear arms race and against the Cold War. And when he is fired by Truman for speaking out against US policy in September of 1946, that was the last chance for avoiding the Cold War. He was the last spokesperson anywhere near power who was had any influence in trying to stop it. And he warned that night that this is not just mean a problem with in terms of policy, this represents the possibility of the future annihilation of life on this planet. And that's what the Cold War was about. We're lucky to have survived as a species this insanity of the Cold War. And to start over again now with Russia and China is just as insane. So we're going to show the clip the last seven minutes of episode 10 of Untold History, which appeared first on Showtime in 2013, and has been out all over the world. The book is out in 20 languages, the documentaries are available globally. So we're going to show the last seven minutes. Bravo, Peter. Thank you. China may become the first new empire to emerge in this nuclear armed world, but an empire modeled on the US or British versions would be a disaster. Great Han shovinism would be no better than American exceptionalism. Former defense official Joseph Nye observed that the dominant powers failure to integrate the rising powers of Germany and Japan into the 20th century global system resulted into catastrophic world wars. History must not be allowed to repeat itself again. The Chinese must shun the American example and the US must reverse course. Henry Wallace worried that if the US treated the Soviets so badly when the US was riding high economically and militarily, how would the Soviets treat the US when and if the situation was reversed? It never happened. But this race to the bottom he understood would have no winner. As we close out this series, we must ask ourselves humbly in looking back at the American century, have we acted wisely and humanely in our relations to the rest of the world? A world in which the richest few hundred or a thousand or a couple thousand have more wealth than the poorest three billion? Have we been right to police the globe? Have we been a force for good, for understanding, for peace? We must look in the mirror. Have we perhaps in our self love become the angels of our own despair? The claims of victory in the Second World War and justification for the atomic bomb dropped on Japan, though aimed at the Soviet Union, were the founding myths of our domination and national security state. And the nation's elites have benefited from that. The bomb has allowed us to win by any means necessary, which makes us because we win right and because we are right, we are therefore good. Under these conditions there is no morality but our own. As Secretary of State Madeline Albright said, but if we have to use force, it is because we are America. We are the indispensable nation. Because we can threaten humanity with the bomb, our mistakes are forgiven, and our cruelties justified as benignly motivated aberrations. But domination doesn't last. Five major empires have collapsed in the lifetime of a person born before World War II, Britain, France, Germany, Japan, and the Soviet Union. Three more empires earlier in the 20th century, the Russian, Austro-Hungarian, and Ottoman. If history is a barometer, the United States domination will end as well. We wisely resisted becoming a colonial empire, and most Americans would deny all imperial pretensions, perhaps that is why we cling so doggedly to the myth of American exceptionalism, American uniqueness, benevolence, generosity, maybe in that fanciful notion lies the seeds of American redemption. I hope that the United States will live up to that vision which seemed within grasp in 1944 when Wallace almost became president of war, 1953 when Stalin died with a new U.S. president in office, or JFK and Khrushchev in 1963, or Khrushchev and Gorbachev in 1989, or Obama in 2008. History has shown us the curve of the ball could have broken differently. These moments will come again in a different form. Will we be ready? I think back to Franklin Roosevelt on the last day of his life, cabling in Churchill. I would minimize the Soviet problem as much as possible because these problems, one form or another, seem to arise every day and most of them straighten out. Calming down the situations that occur, letting things happen without overreacting, seeing the world through the eyes of our adversaries. This way lies in sharing in the needs of other countries with true empathy and compassion. Trusting a collective will of this planet to survive the coming period and the neat threats of nuclear annihilation and global warming. Can we not surrender our exceptionalism and our arrogance? Can we not cut out the talk of domination? Can we stop appealing to God to bless America over other nations? Heartliners and nationalists will object, but theirs has proven not to be the way. A young woman said to me in the 1970s, we need to feminize this planet. I thought it strange then, but now I realize there's power in love. Let us find a way back to respect the law, not of the jungle, but the law of civilization by which we first came together and put aside our differences to preserve the things that matter. Herodotus wrote in the fifth century before Christ, the first history was written in the hope of preserving from decay the remembrance of what men have been. And for that reason, the history of man is not only one of blood and death, but one also of honor, achievement, kindness, memory, and civilization. There is a way forward. I remember you start step by step like a baby reaching for the stars. Thank you for that. Thank you, Peter. Thank you, Albert.


It's time for the Lawn Jean Chronoscope, a television journal of the important issues of the hour brought to you every Monday, Wednesday, and Friday, a presentation of the Lawn Jean Wittner Watch Company, maker of Lawn Jean, the world's most honored watch, and Wittner, distinguished companion to the world-honored Lawn Jean. Good evening. This is Frank Knight. May I introduce our co-editors for this edition of the Lawn Jean Chronoscope? Larry Lissert from the CBS television news staff and August Heckscher, chief editorial writer for the New York Herald Tribune. Our distinguished guest for this evening is Professor W. Albert Noyes, 1954 priestly award-winner American Chemical Society. In science like all other walks of life, it's indeed uncommon when a son succeeds to his father's laurels. But our guest tonight is not only the distinguished son of an eminent scientist, but he has been honored with the highest award that chemistry in America can bestow, the priestly medal. Dr. Noyes, both sides of the world are now struggling for power with science in the forefront. Do you think that American science has a firm hold on the lead? I think we have a lead at the moment, but rather a precarious one, and the USSR is improving daily. We must keep track of it. Well, just how is that going on? Are they training more scientists, encouraging more young men? During the war, the USSR was, as far as I know, the only country which increased its output of scientists. We decreased ours quite noticeably for several years. What would you say, Dr. Noyes, are the major factors hindering the development of science in this country today? Well, it's very hard to tell. Right after the war, we had a certain amount of propaganda which indicated that scientists would be overproduced, that they would have trouble in getting jobs. And this, I think, is partly responsible for the large decrease in number of engineering students in our institutions of higher learning, for example. Well, Dr. Noyes, isn't it true that the government now is giving more money to research in American colleges than ever before in our history? Well, strictly speaking, the money before the war was mainly in the field of agriculture. Since the war, we've had instituted a large system of government contracts, whereby work in the universities is supported. Theoretically, it's not given as gifts, however. It is given for doing specific jobs. And I think Congress would object to the word gifts. Well, do you think that these gifts are actually furthering the development of American science? Oh, I'm sure they are. Very much so. There's no question about that. Dr. Noyes, in your own experience and in the experience of those who have worked with you, has the need for secrecy and the tendency to bend science toward the weapons of war, has that hindered the free inquiry that science rests on? It certainly has in some areas, but I think that gradually we are learning to know what should be classified and what should not. I am sure that for a time we hindered our own activities by a secrecy which was really unnecessary. Dr. Noyes, it seems to me that among the natural sciences, nuclear physics have made the greatest advances. Now, do you think there's any reason to believe that other transcendental discoveries can take place in the other sciences like biology or your own science chemistry? Well, the field of biological research is immense. And the impact of chemistry on that field is only beginning to be felt. Certainly we have a great deal to learn both about disease, about heredity, about the use of hormones and vitamins and numerous other things. And if I were a young scientist today, a young chemist, I'd rather think I might choose this field of biochemistry as one of the most important of all. What are the inventions out on the, and discoveries out on the frontiers of biochemistry that you would like to see in our lifetime achievements? Well, you've noticed within the last few years the discovery of cortisone, the importance of the vast field of what we sometimes refer to as the steroids. They seem to be related to growth, to heredity, to the control of disease, and possibly even to the cancer problem. We know too little about them and just what they do in the human body today. Well, what are the things that we're searching for, Dr. Noyes, that might rank with this splitting of the atom in these other fields? Certainly one of the important things is to learn how to use the sun's energy. Actually, we use it mainly through plants today, but we've not yet discovered in the laboratory a better way of using the sun's energy than by growing plants. Well, certainly there are areas in the world which are deficient in energy. If we don't want slaves, we must have cheap energy. If we don't want impoverished peoples and causes for war, we must have more food. And both of these requirements demand the use of the sun in some way or another. Is this a means, for example, of transforming the heat of the sun into power directly through mirrors or through pathways? That would be desirable and of course that's been attempted and successfully on a small scale. But to do it on a large enough scale to replace coal and oil is not feasible today. Well, Dr. Noyes, do you mean to say that the greatest discoveries in these fields that would rank with the splitting of the atom lie in the fields of new sources of energy? Well, in my own opinion, if one wishes to combat communism, one has to find a cheap source of energy today. People who have adequate standards of living are less apt to want to be communists than if they're down in the lower levels of economic life. Isn't that true? Well, in other words, you feel that the harnessing of the sun would be a discovery of the most transcendental import. I really feel so, yes. Well, how far would you say we are away from such a discovery, sir? I think we're disappointingly far. We skate it around the edge. We begin to understand some of the basic problems, but the actual progress has been very, very little. What about the whole field of creating foodstuffs and materials synthetically? Is that one of the great fields for work today? Well, I wouldn't say that's a great importance today. The important thing there is to learn how to use our present resources more effectively, how to farm the land better, how to get protein out of the ocean. The Indian nation, for example, cannot grow enough livestock to get the protein, but it does have enormous food resources in the Indian Ocean which ought to be used. Or would this actually be attractively addable to humankind? Oh, I'm sure it would be. I mean, fish isn't as bad as all that, is it? But beyond that, it's possible to create proteins synthetically and to flavor them synthetically, I suppose, and make foodstuffs in that way. Yes, it certainly can be done, and it can be done on a small scale, but to do it on a scale adequate to feed the human race isn't possible today. Well, surely you're not talking merely about raising more fish, but there are other things in the ocean that might be used for feeding humankind? That's right. There are great many things. Plankton, for example, might be used. Isn't that a fish, basically? Well, it's a lot of small microorganisms, I think. I'm not a biologist, so I'd better be careful at this point. Well, how far do you think we might be away from such a utilization of their food stuff outside of the normal things that we eat? Well, these problems are being studied, partly being studied through United Nations organizations, and in areas where the food stuff is at present deficient. I think I'd better be a little careful, however, to say we're making much progress. Dr. Noyes, these great inventions and discoveries that will come, will they be made, as they have been made in the past, by the lonely individual, or will they be made by team workers under a crash program? The great advance in ideas is very apt to come from the lone individual. Thereafter, the application is going to be a team job. With the man with the brains, the originality, the new idea seems to exist by chance to some extent. You can't create him. He just happens along at the right time and the right place. Well, Dr. Noyes, isn't it possible to accelerate these discoveries, perhaps by putting in crash programs, or going all out, and as we did in the weapons field? Only up to a point. I think in certain public health areas, for example, one can by team research do things which are not possible by any other means. But I still am a little skeptical about new ideas coming out of teams. One has to get them just when they happen along. Do you think we are giving the scope and the opportunity to what you call the lone individual that we should? Well, I'm a little worried about it. I don't think we've suffered too much so far by allowing team research to go too far. But we'd better watch the situation. We need to keep our universities as places in which men can sit at desks and do some honest thinking without being required to punch time clocks. Well, what are the limitations now on our people working in these lonely laboratories and universities, Dr. Noyes? The limitation is purely a financial one. The money to pay these individuals is, as you pointed out, coming to some extent from government, to some extent it comes from industry, and all too little it comes from university funds because the universities are somewhat broke today. So we need more unrestricted money because we can often recognize a good young man who hasn't the reputation yet to warrant a contract. And if we could put him aside and let him do his own thinking for a while, we might be a little further along sometime. What is the incentive, Dr. Noyes, that drives these younger men to these great discoveries? Is it financial? Is it prestige? What is it in your experience? Just innate curiosity, I think. Some people have it, some people are born with it, and some people are not. Well, Dr. Noyes, are we actually getting enough reinforcements from the secondary schools into the colleges to supply this advanced guard of scientists that we need? Well, we're doing fairly well, but we still lose a fair fraction of the upper 10% of our high school graduates. They do not go to college. Some of them don't want to, some of them can't go for economic reasons. But we ought to do something to try to get a larger fraction of those best students into the universities. Well, Dr. Noyes, we have time for me to ask you a question about some of the things you scientists have invented, and I'm thinking primarily of the weapons of mass destruction. Now, how do you think the next war is going to be fought or won? Well, the general opinion seems to be that the initial impact of the next war will be by large-scale air raids, probably with atomic weapons. Now, the question is whether we can survive that first impact. Then what do we have to do to win thereafter if we can protect ourselves from that initial impact? In my own opinion, it's going to be very hard to decide when the war is won or even when it's over. But we may have to do as nations have always done and occupy enemy territory to say that we have won. Thank you very much, Dr. Noyes. Very interesting to have you here tonight. The opinions expressed on the Launcine Chronoscope were those of the speakers. The editorial board for this edition of the Launcine Chronoscope was Larry Lisser and August Hector. Our distinguished guest was Professor W. Albert Noyes, 1954 Priestly Award winner American Chemical Society. In the air, on the ground and on the water, major sports events the world over are timed by Launcine, the most honored watch in the world of sports. Now, among the many Launcine timed events on the September calendar were the national air races at Dayton, where a new speed record for jet planes was established at better than 692 miles an hour. At Colorado Springs under AAA sanction, the Pikes Peak Hill climb. And on September 17th, the great motorboat classic outboards to unlimited and the President's cup regatta on the Potomac at Washington D.C. And of course, you know that among all of the world's fine watches, only Launcine has won 10 World's Fair Grand Prizes, 28 gold medals and so many honors for accuracy. For in truth, Launcine is not only one of the finest watches in all the world, but it's the watch of highest prestige. So when next you buy a watch, either for yourself or as an important gift, you'll find Launcine watches at your authorized Launcine Wittnor jeweler in large array priced as low as 7150. Launcine, the world's most honored watch, the world's most honored gift, premier product of the Launcine Wittnor watch company since 1866, maker of watches of the highest character. This is Frank Knight reminding you that Launcine and Wittnor watches are sold in service from coast to coast by more than 4,000 leading jewelers who proudly display this emblem agency for Launcine Wittnor watches. At Launcine Wittnor jeweler see Atmos a perpetual motion clock created by LaCoultre. Atmos runs without winding without electricity powered only by variations in the temperature of the atmosphere. Atmos product of LaCoultre division of Launcine Wittnor.


It's 10 o'clock 6 a.m. Sunday August 13th. We're headed out to get the car wash number one. It's filthy tree sap pine needles and actually a couple tree branches so yeah. Anyway we're also going to meet adopted kids Jenny and Brian and we're gonna go to see Oppenheimer today and I've got to go pick up some medicine before that some asthma medicine and I don't know what else we'll get up to but we'll see. Mr. wants to get some bark for the yard. I'm trying to talk him in just having a pallet of it delivered because we do need that much of it but you know we'll see what happens. Anyway that's it for the minute. I'll be back. Soapy storm. Look at that color of the water. I'm thinking it's a dirt on our car and not soapy. Yeah that was gross. Oppenheimer and it was a good movie I really enjoyed it. It has an A-list character sorry an A-list cast playing the characters and the one playing Strauss. I didn't even get that was him for like 40 minutes. Good makeup. Really good. I mean I didn't recognize Robert Downey Jr. at all and he did a great job. He was not the good guy FYI. He was not Iron Man. No. But it was a great movie. It did bring back some things from you know US history class and high school that I remember hearing about some things I didn't know about. I do know the movies based on I mean it is fictionalized you know but it is based on facts of what happened so anyway. It was good. It's 106. Well now the windshield says 103. Anyway it's hot. It's hot. We're having next three days 100 degree plus days. We're going home. I'm going to turn on the air conditioner and we'll maybe have a snack. I'm not super hungry. I did eat a whole bag of popcorn. So there's that. Yeah alright I'll be back. Good morning everybody. It's Monday morning August 14th just before 10 a.m. It's already 84 degrees outside. It's supposed to be triple digits for the next three or four days in a row. I am trying to get myself back into healthy routines because I've been on a couple of vacations recently and kind of got out of the habit. But anyway so we are starting off our Monday morning not at the computer or in the art room although that's where I want to be or on the couch. We're going for a walk and we're going to go get a few steps in. I've got some water. My asthma inhaler. I probably won't be walking too fast because it's already above 80 degrees so yeah let's see what we can see. I'll be back. I made another pair of big giant pants to go under my dress that I made this one. So I made this dress. A while ago I'll put a picture here. I made a pair of big giant pants. Are they maybe too big? Yeah maybe. We're in my closet by the way. But I gotta say they're super comfy though. But yeah you could probably fit two of me in them. But I mean they are sort of hair and pants and hair pants are big like that right? Okay so I have to hold the camera. So this is the dress I made which I could wear by itself. It's really cute. I really kind of wanted a pair of bluer pants. I don't know what else to call them. To go underneath it. Tina Gibbons always has women in her layered up and they're in big baggy pants under a dress with a vest. I thought it would be you know fun to just have some to play with. Now are they too big? Yes they're actually too big. I mean I have bike shorts on so don't get excited but yeah they're really big. Can I take them in at some point if I want? Yeah and I might do but I think before we do anything I'm gonna wash them because I want all the edges to fray and it is a hundred percent cotton. So I'm gonna wash them in hot water and we'll see what happens. Alright okay guys so besides a journal page and video which I'm gonna edit tomorrow.  The vlog needs to be edited for last week and I have two or key trio videos that's got to be edited so I'm gonna work on it. I also got a mock-up cut out of the mood fabrics and thea dress. It is a made style dress like this and I kind of mock up out of old bed sheets but you know what if it the mock-up turns out decently while fitting I might actually sew it properly it's a hundred percent cotton I could dye it and then make another one out of that intended fabric and if it doesn't work it's an old bed sheet so yeah and I had enough between two partial bed sheets that I'd used for other mock-ups I had enough fabric so pretty pleased about that. Alright so anyway I'm gonna sit down and just chill for a little bit it's I'm nearing the end of the day and Bob should be off of work soon and then we'll head downstairs. We won't be going walking cuz it is hotter than 80 downstairs 105. Oregon doesn't really get those temperatures often so it's everybody's like oh my god and where my dear friend and patron Kathy Whitney is in southern Oregon it's 107 so yeah and I got something on my shirt I don't know what that is yeah yeah I think anyway alright that's it for the minute I think maybe alright I'll be back it's 403 p.m. yes Tuesday August 15th and yes I turned her on and we are video editing. Joy? Not really it's a hundred degrees plus outside again we'll be again tomorrow I of course because you know because I'm getting older and stuff I woke up this morning my hip was bothering me you know I've got arthritis and stuff so anyway took me a little bit to get going this morning but I did and I got some updates to the computer system done that I think allows me to easier transfer a video from my phone to the computer because yes I do do a lot of filming with my phone. I don't know we'll see I still hate video editing I need an editor maybe somebody to help me with PR and merch I don't know I need people alright we're gonna get this done I've got a bunch of threads to hide on some crochet stuff so we're gonna do that and I'll be back five videos edited and uploaded and scheduled I can turn it off now yay we're gonna go out for dinner with our friends and neighbors the Pauly's from next door and they're two little ones who come over all the time I talked about them and yeah so we're gonna go upstairs and get ready for that I'll be fun we're in the car again it is 9 40 a.m. on Wednesday August August 16th anyway it's already 79 degrees outside it's gonna be another hot day so we have some errands to run and we're gonna go out and do it early and get it over with have a bunch of places to go I made a list places I want to go added those to the list I need a few groceries all that stuff so let's go get it done then we'll come back and I've got to turn the computer on again because I need to upload some of the video I edited yesterday to patreon along with the sewing pattern for one of the projects that's in an upcoming video I didn't think I was gonna do this today but I got most of the mock-up done I did have to make a few adjustments to the pattern from it's again from the mood fabrics website I'll put a link down below I had to lengthen the straps on the shoulders I had to widen the bust piece because I'm chesty I had to shorten the waist because I'm short and I'm gonna have to hem hem this just needs to be a lot shorter right now it's way too long but and I don't have the sleeves on yet but hey that's not bad I'm kind of liking it now this is the mock-up it this is the mock-up it's a hundred percent cotton it's bed sheets and I'm gonna put a zipper in the back of it I'm gonna put a blue zipper because I think I'm gonna just if I like the mock-up well enough yes I'm gonna make one more but I'm just gonna dye it I might even tight make it tight I I don't know yet but it's coming out really well I also spent some time winding up some yarn this is my collection of wool and silk and cashmere yes some of which is thrifted and yeah so that's all done and it's getting hot up here despite the air conditioning so plus it's after five yeah Bob's gonna head over to the gym to get some steps in because he didn't get any steps in yet today I did so yeah well he's doing that I'm gonna go sit downstairs and have some water do the I have to do the dishes oh all right I got chores to do I'll be back so it's almost four o'clock I haven't turned on the camera yet today till now I've just been sitting doing chores today I started assembling on my flower bag so I watched a few videos including Jenna's again Jenna Phipps and decided how exactly I wanted to assemble my flowers I'm not sure if I have enough to cover the bag the way I want to but I do have a lot so I figured it was time to at least get started and so I've just been sitting doing that all afternoon to be honest I did a little bit of cleaning and rearranging but other than that well in a few chores other than that I've done nothing else but you know all right anyway this is turning out really cute I'm really happy when I was cleaning I did find some leftover balls of yarn like this so I made a few flowers with it which turned out really cute I don't you don't really see that kind of yarn too much at the yarn shops anymore it was a thing in the 90s and 2000s I think but anyway I have a few leftover pieces so I'm gonna be using them here and there got project ideas in mind once the flowers are done so that's so I don't have anything else today but it's nice to just have a quiet day and it's also not a hundred today it's still in the mid 90s but it's not a hundred so the temperature is going down so yay I think my brain and creative energy is starting to just get heat stroke or locked-in syndrome or something for not being able to really go out of the house much for like a week so yeah anyway what are you gonna do oh I did start off the day by altering this little dress I have on just a little bit I got it when I we were in Hawaii it fits pretty good except for it I knew when I bought it that the armholes were really short and tight and when I went to go put it on I reminded myself oh crap you were gonna fix those armholes so I did that first thing this morning and I re-cut the armholes and fix them fits fits great now well it's a little tight over the chest but so is a lot of my clothes anyway I'm also slouching and yeah my hair really does look like Einstein today all right that's it for a minute I'm gonna keep putting flowers together I think it's gonna be my thing for the next few days I do have another project in mind I think I figured out what I want to do with some of that really nice wool that I bought when we were in Virginia but I need to finish this first so and I have a few other projects I think I've decided on to use the leftover scraps yarn with on so including some more granny squares and at some point we'll put all the granny squares together and make a blanket or something or a jacket or something anyway that's it for the minute I'll be back so it is Friday August something I don't even know 18th 17th August 18th and I set up a play space for junior when he comes and I'm babysitting which I'm doing tomorrow getting back to it and I set that up downstairs I'll put a picture here for you all I also sat and spent most of the day today once I had that done and some chores finishing the flower bag are you ready okay my dress form she's got a mock-up of a dress on that I'm working on but there is our flower bag yes it's a piece of art I think but it's also a usable bag with a zipper closure and I have added some matching yarn over the strap to coordinate with all the flowers she was a pain in the butt you guys but it is done she is pretty whoops let's come over here hold on yeah my table's a mess so she has finished though I love this giant daisy so making the flowers is not hard they're a lot of fun to make I think but then if you want to make something with them then you have to sit in some all together and that's yeah it's a lot of work but I'm glad I got it done now I have more projects to get back to hooding finishing said mock-up over there which is turning out actually pretty well and I think that I might actually make that an actual dress is white cotton cotton bedsheets so I think if it turns out and I like the fit of it not only will I make another one out of the actual fabric which is this but I think I might keep the cotton one and die her cuz why not anyway it's almost the end of the day and when Bob is done we're gonna go grocery shopping we are bypassing family dinner night this week because both kids houses are having construction done one is having something fixed and the other one's adding on so everybody's busy I'll babysit junior tomorrow while my daughter works and her house is being worked on and yeah so we'll just it'll just be us and that's fine all right I'm gonna clean up my mess and go downstairs and I'll be back morning everybody it is 847 a.m. Saturday August 19th morning I'm gonna be babysitting junior today which was always the plan and Bob was gonna go help the kids at their house but obviously I'm in the car and so last minute change of plans I'm babysitting at their house long story but anyway that's fine I've got my needlework bag and with me evidently there's babysitting help over there so you know I've got something to keep me occupied in case I have nothing else to do and I can make sure we're not there for 12 hours helping with construction and I'm not stepping outside so there's that I don't know how today is gonna play out but we'll see and yeah we've had a lot of police in the neighborhood lately I'm going to hope that they're looking for speeders and not there's not something else going on but I don't know anyway I'm not quite awake yet despite the two cups of coffee I'll be back okay guys if I have another opportunity and I had thought of it earlier well we would see if my five-month-old grandson can shoot any video and put it in the vlog because yeah junior liked playing with Alma's camera today that was a thing anyway we today didn't go as quite as planned so Bob did indeed go help with construction at my daughter and son-in-law's house his father is in construction he brought a friend with him and they were all over there working on the addition to the house and they junior was supposed to come over here and I was gonna babysit that's not how it happened I ended up going over there and babysitting with Pollyas's mother and spending the whole day over there so I didn't get any of my chores done but that's okay because I got to see the grandson so I'm good with that Bob is very sore and tired a lot of nails were hammered today something like over a thousand and yeah so it's been a long day but it's been a good day and a good week and a lot of fun I've I'm now working on a sweater and yeah I'll let you all know how it comes anyway I hope you've all had a great week and that you've been able to be creative and find time to do what you love and spend time with your family if you have questions comments or concerns please do leave them down below don't forget to like share and subscribe and above all go out and have a great day have a great week do something nice for yourself because you deserve it I'll see you later bye guys


This planet is alive. It has a physiology and its integrity can only be maintained if all of its organs and tissues are healthy and when you see the world as a living being then you start to think okay each of these beings rivers forests whales these are an organ these have a role to play in maintaining health when we understand earth is alive we have to respect and take care of all of its organs. The crisis and it's bigger than a climate crisis it's a full-scale ecological crisis it is calling on us toward a much deeper revolution than merely finding a cleverer way to power industrial civilization when's it going to stop it's not going to stop by itself it's going to stop when we see nature differently we relate differently and we understand our purpose here differently no longer the conquerors no longer separate anyone who is in denial of this is a denier whether you believe in climate change or not we are a relationship we are interconnected interdependent and inter-existent what we do to the world we do to ourselves what we do to the other we do to ourselves we're beginning to understand that that's what we're being initiated into so the important question then is not what do we need to do to survive the question we need to be asking what world do we want to live in a living world or a dead world i think that both futures are possible i can see the concrete world scarred and ruined and i can see a more beautiful world a flourishing world where the deserts are greening and the species are coming back the oceans are full of fish and flocks of birds cover the sky and humans living peacefully on it which one are we going to experience in our future which one are our great great great great great grandchildren i'm going to live in that depends on which one we summon