Hi everyone and welcome to this lesson on volumes of solids of revolution, the washer method. This is the counterpart to the disc method. Think of a disc but with a hole in it. So when we say washer, we mean like the hardware kind of washer. Or if you prefer food analogies, think of a lifesaver or a donut. That's the type of washer we're talking about. So let me take you to a couple of applets first to give you more of a visualization to set the stage for what it is we're talking about. So this first one is from mathdemos.org. If you take a look at the animation there, you can see that the washer is forming. It definitely looks like a disc but it has that big hole in the middle of it. So what we're going to have to do is come up with a formula to account for the hole being there because we don't want to include the area of the hole when we're finding our formula that we're going to use. Once again we're going to be using the idea that was built upon Riemann sums and the using the rectangles underneath a curve. And here once again we're going to have representative rectangles that we will think of rotating that representative rectangle about an axis of revolution and that's what's going to create our washer. If you go to this website I purposely left the URL there for you at the top in case you wanted to investigate it on your own. If you scroll down they have a lot more other pictures and demonstrations of the types of things we're talking about. There's our hardware washers right there. There's your good old lifesaver and the donut. I guess you could use a bagel too right? So they give a lot of different visualizations you can even think of like a DVD or a CD type of disc that has the hole in the middle there. So this is a great website if you care to explore it later on. Let me take you to another visualization. This is from calculusapplets.com and if you take a look at it you can see the rough outline of what looks to be a cylinder but there is a hole going down the cylinder there. So imagine taking this yellow region and rotating it around this black x-axis right here going through the middle. Alright so what you can see here is the representative rectangle that we'll be talking about in our lesson today that dark gray part and imagine flipping that around the x-axis and that's going to create the gray washer that you see here. Alright so that's what we're going to have to come up with a formula for as that's going to become our integrand for our definite integral. So let's go back to our lesson. So if we think once again of how in general we get volume of anything remember it's going to be the area of the base times the height the thickness. So just like we did before our volume calculations are going to be doing a definite integral of the area of in this case the washer face times the thickness dx if it's in terms of a different orientation of our representative rectangle that integrand is going to be in terms of y. So very similar to what we saw with disks. As a reminder again a solid of revolution is a solid generated by revolving a region about a line which we refer to as the axis of revolution. The solids we're typically going to be dealing with will involve a region bounded by a curve the x-axis and or the y-axis and perhaps some horizontal or vertical line. What we need to do is find the volume of the solid disk and take away from that the volume of the hole. So let's try to replicate that gray washer we saw on that last applet from calculusapplets.com. So here's the outer edge of our washer and here's the hole in the middle. Basically what we want is just this part. So we need to figure out how to do that and again we're going to build upon the fact that volume of anything is generally the area of the base so we need that area of that shaded region I just shaded in for you times the thickness all right well it's a circle so we know pi r squared. So if we thought of big r as being the radius to the outside circle so that's big r and little r as the radius of the hole we could come up with an expression for the area of the entire outside circle and then subtract from that the area of the inside circle so that would look like pi big r squared minus pi little r squared now that's just the area of the face of the surface remember to get volume we need to multiply this by the height the thickness which we're typically going to refer to as either dx or dy and we're going to turn it into a definite integral all right so typically what we're going to use notice you can factor out a pi here so the basic formula we're generally going to use is pi times the quantity big r squared minus little r squared minus little r squared and then either dx or dy depending upon the orientation of our representative rectangle so let's talk first about solids that are revolved about a horizontal axis when we revolve about a horizontal axis I have a picture for you on the next slide it looks like this we end up with a vertical representative rectangle so your representative rectangle would maybe go something like this all right so that would be a dx because the orientation of our representative rectangle is vertical that turns it into a dx problem so let me scoot back for a second the outer radius capital r is the distance from the axis of revolution to the far side of the curve of the rectangle which you'll see here capital r so it's going from the axis of revolution which in this case is the dotted line there to the far side of your rectangle the inner radius r is the distance from the axis of revolution to the close side of the curve or the close side of your representative rectangle all right so you'll notice little r here going from the dotted line again your axis of revolution to this closest side of the representative rectangle then you can see how you set up your volume integral again axis your limits of integration need to be x values because it's a dx problem now if we have a vertical axis of revolution that's going to turn it into a horizontal representative rectangle so it would be going something like this and that turns it into a dy problem so capital r is once again the outer radius the distance from the axis of revolution to the far side of the curve so once again from the dotted line which is your axis of revolution to the far side of your representative rectangle little r is the inner radius that is the distance from the axis of revolution to the close side of the curve or representative rectangle again little r is really the radius of the hole itself so you can see how the volume integral gets set up if it's a dy problem your limits of integration need to be y values but still you have that pi times big r squared minus little r squared you do just need to remember that your integrand here needs to be in terms of y now I want to point out to you two major characteristics of a washer method problem and think of this picture and this one notice in both cases your representative rectangle is perpendicular to the axis of revolution but it is not touching it that is contrast to the disc method which the representative rectangles were still perpendicular to your axis of revolution but with a disc method those rectangles were touching the axis of revolution in a washer method they are not so that is really those two characteristics being perpendicular to your axis of revolution and then whether it touches the axis or not that's really what differentiates a disc method problem from being a washer method problem as you go about finding your capital r and lower case r you're still going to adhere to that top minus bottom and right minus left ideas so as you work through practice problems keep that in mind that as you find your your expressions for capital r and little r you're always doing top minus bottom or right minus left


With each stroke of the key, Newton resident and Steinway artist Michael Lewin delighted an excited crowd at the Scandinavian Cultural Center in Newton, which broke in its brand new Steinway piano. The inaugural performance on the Steinway was a benefit that will help fund future programming at the center. We have a new concert hall now in Newton because we have a great piano that's here and there really isn't another room or hall or church or facility that has beautiful acoustics and a gorgeous new piano. Lewin is internationally known for his gifted piano skills and boisterous playing style. The Newton native has performed in over 30 countries. Having a man with that kind of resume be the first to play on the new Steinway at the Scandinavian Cultural Center was a source of pride for Christina Mealy, the director of the center. It is an extremely generous gesture that Michael made to offer this benefit concert for us, so we're just very excited to celebrate with him and have such an accomplished musician to kick off the series. Lewin was in charge of selecting the specific piano and there was just something about it that made him know that it was the right one for the center. This one had a huge range but what you don't know is how it's going to sound in the room where it's going to be and I was so happy that it sounded so great in this room. It's perfect. It's a perfect piano for the space. While Lewin was fond of the piano, the audience was entranced by Lewin's playing. Extraordinary if you didn't see it personally, you couldn't imagine. Two hands were making this much music. Obviously an enormously talented audience. Residents in Newton also believe that the piano will have a positive impact for arts and culture in Newton. It'll make a big difference to all their performances and will increase actually the number of people who will want to both perform at what's called the center. Now that the Scandinavian Cultural Center has a brand new Steinway right here in Newton, expecting an infusion of arts and culture that will captivate the Newton community.


Hello, my name is Mia Lamberana and today I'm going to talk about joining the work with Masayuki Abe and Miyako Kubo on black box extension of non-interactive seronautic argument systems and signatures directly from simulations on this. So let's start. So I will start by defining what non-interactive seronautic arguments are. And for this, let me first define the seronautic arguments. Well, seronautic arguments were first defined by Goldwasser, Mikhaili and Rakov in 1985. In the seminar work, the knowledge complexity of interactive pre-systems. I'm going to explain what they are with an example. So let's consider an MP language. So that is a set of words X for which there exists a witness such that certain relation is satisfied, relation R. And in these systems, there are two parties, the prover and the verifier. The prover has an instance X and a witness W of the fact that X is in the language L. And the verifier wants to check whether X is in the language or not. And because the verifier doesn't have the witness, it may be skeptical about this fact. So what can they do? Well, they can engage into a seronautic argument protocol. In this case, it's going to be a protocol where they send messages back and forth. And at some point, the verifier will either accept or reject the proof. Okay, so now let's consider non-interactive seronautic pre-systems or pre-systems. In non-interactive arguments, there is one single message sent from the prover to the verifier. There are several models for non-interactive seronautic arguments. And we are going to focus on the common difference string model, where there is a common difference string, there is certain piece of information trust generated actually generated by this algorithm called CRS or CRS generation. And this is given to both parties. Now, using this information, the prover can execute what is called the proofing algorithm that takes the CRS, the instance and the witness and produce the proof. And the verifier will run the verification algorithm. But in the seronautic pre-system, there are usually other two algorithms in a total of five, the CRS simulation and the proof simulation. I will talk about those later. Seronautic argument systems must satisfy three properties. The first one is completeness, which says that if the prover is honest and the verifier is honest, prover should always be able to convince the verifier about the fact that some X is in the language if the prover knows the witness for X. Soundness says that basically the prover cannot cheat, that a prover should not be able to convince the verifier about the fact that some X is in the language if X is not actually in the language. And seronautic basically says that the verifier cannot learn any more information apart from the fact that X is indeed in the language. So, in particular, for example, the verifier should not be able to learn any information about W. Seronautic proof systems are one of the most common building blocks in cryptography. I'm going to mention some of the applications. One of them is to go from passive security to active security. So, once you have proven you have built a cryptographic primitive that is secure against honest but curious adversaries, you can use seronautic proofs to enforce honest behavior and therefore achieve active security, security against adversaries that may behave arbitrarily. Also, in authentication systems, you can prove that you should be allowed to perform some actions without revealing any other information about your identity or what you should be able to do it. Or even in blockchain technology, for example, to prove that seroton transaction has been valid or in ferrets change, it's a hot topic now with contingent payment. Seronautic proof systems are also used there. But why do we need the non-interactive property? Well, in the first work about non-interactive proof systems, they gave this scenario where there are two mathematicians, one of them leaves for a long trip and whenever he discovers a theorem, he writes a postcard to his friend proving the validity of the theorem in serial knowledge so that the friend doesn't really know why the theorem is proof but is convinced about the fact that it's true. And they argue that the non-interactive property is required because this process of sending letters is non-interactive, is monodirectional. By the way, they say that they need to have played heads and tails for a while. You can think of this as the common reference string generation. They both need certain pieces of information that is trusted and shared by both. Well, this application may not seem very appealing but actually, serial knowledge proof systems are very interesting because they have one unique property which is that they are transferable. If you're given a non-interactive proof, you can give it to a friend and the friend will be convinced about the validity of the statement as long as this person trusts in the CRS. And now let's talk about one of the properties that we study in this work and which is simulation soundness. Well, simulation soundness basically says that it is hard to compute proofs on false statements even if you have overkill access to some oracle that performs simulated proofs. Okay, so more concretely, there is a challenger and an adversary. The challenger runs this CRS simulation algorithm producing a CRS and a trapdoor that is going to be used to simulate proofs. CRS is sent to the adversary and not the adversary can perform queries. The adversary can choose how with our instances XI and it will get as an answer a proof that has been simulated with this algorithm, not that this algorithm needs to use a trapdoor. Well, this step can be performed several times. Some models consider only constant simulation soundness where this step can only be performed a constant number of times, but we are going to consider the notion of unbounded simulation soundness where the number of interactions is not specified. It can be polynomial in the security parameter. And the adversary at the end of the game has to produce forgery. This is some instance X star and some proof by star such that X star has not been queried. And it's actually a false statement. It's not in language and the verification still holds. So the proof still convinces a very far of the fact that X is in the language. Well, we say some NISC is a satisfied simulation soundness property if the probability of the event accept is negligible considering all PPT adversaries. Well, simulation soundness has one nice property which is that the non-interactive argument system is non-malleable. This means that it's infeasible to change the statement on a proof. If you're given a proof or certain statement, it's hard to compute a proof on a related statement. And now let's see how simulation soundness can be achieved once you have a NISC. How can you upgrade the NISC in order to achieve simulation soundness? Well, there are many works trying to do this. I'm going to talk about a few of them. So for example, the work by Sahay in 1999, it is a construction that is based on the generation of multiple common reference strings of the original NISC and it results in a bounded simulation sound NISC. So this O stands for one-time simulation sound, but it can be lifted to a constant number of times. On the other hand, the work by DeSantis et al. is the first construction of unbound simulation sound NISC and this work combines a pseudo-random function with a commitment scheme and the essential idea of this work, well, they also use a pseudo-random generator, the essential idea of this work is to prove that certain statement is true or the PRF was computed correctly. And then they leverage this disjunction in order to achieve simulation soundness. Finally, I want to mention another idea which was initiated by James Groth and then followed by many other works. So for example, here we saw the work by Halthine St. Jagger, which is to combine the original NISC, the original statement, the indents action with a signature scheme. They use a signature scheme to achieve simulation soundness. So now something is common to all these upgrades, which is all attempts use signature-like primitives. This raises the question of whether they are needed or not. Can we achieve simulation soundness without using a signature-like primitive or not? Well, in order to answer this question, we may try to build a signature scheme from every USS NISC. So can we do it? Can we build signatures from USS NISCs? Of course, we can. Actually, we can do it from any NISC. Why? Well, because NISC implies one-way functions, for example, the CRS generation is a one-way function. And there is a big result in cryptography that says that one-way functions implies signatures. But this is not satisfying for us. It doesn't answer our question. We need a signature with similar computation space complexity. And there are some words that explore this idea. So I'm going to talk about a few of them here. For example, Pellaria and Goldwasser combine a pseudo-random function and a public encryption scheme in the form of a commitment scheme in order to achieve a signature from a NISC. And what they do is they use the NISC to prove this relation here. And they show that this implies a signature. Another attempt by Katz and Vaikon-Tenathan builds a signature scheme by using the unbounded simulation sound NISC to prove this relation here that involves a public encryption scheme and a target collision-resistant function. Finally, let me mention this work by James Groth and Mary Moller from Crypto 17 where they build a general framework for constructing signatures of knowledge based on succeed simulation extractable NISCs. And notice how the reconstruction requires the NISC to be such that it not only supports a direct relation, but it also supports this conjunction with a TCR. And now I want to point here that all these constructions of signatures from NISCs or from USS NISC, they require NISC support certain specific relation or they require this language extension. So in this work we focus on answering two questions. One of them is whether the language extension is general or not, whether for example having any NISC you can always modify it in such a way that you get the NISC support in this conjunction with a TCR. And if this was possible then for example the work by Groth and Moller would explain why achieving simulation soundness and bounding simulation soundness is always done with using signatures. Basically because once you have built a NISC, any NISC that is unbounded simulation sound gives you a signature with the same complexity. However the answer to this question is no, at least not in a black box way and that's one of the first results of our work, one of the main results, several impossibility or possibility results of language extensions of NISCs in a black box manner. I will explain in second what a black box language extension is. And the second question that we consider is whether we can do it without language extension. So now given that we cannot always extend NISCs, at least not in a black box way, can we build signatures without using the language extension? So from any NISC or have language, can we build, if the NISC is unbounded simulation sound, can we build a signature scheme and we give a construction for this that I will explain at the end of this talk. And now let's explain what a black box language extension is. First, what do we mean by language extension? Well I will explain it with an example, in this case disjunctive composition, given two languages, L and L hat. This is how we define the language extension for disjunction. So it's basically the set of pairs of words where the first word is in L or the second is in L hat. And when we say black box extension of NISC, what we mean is where we ask is whether there exists a compiler. In this case, I call it the disjunctive compiler such that for any two languages L and L hat and given any two NISCs, the first one for L and the second one for L hat, this compiler builds a NISC for the disjunctive language defined here. Of course, we can consider other extensions like conjunction for example, conjunction instead of disjunction. So both words should be in the corresponding languages and others. And actually, in this work, one of the main results is that we prove is that disjunction cannot be done in a black box way. However, it is well known that conjunction can be done. And actually, straight forward parallel composition works. What do I mean by this? Well, you can just generate a CRS for both NISCs and then prove both X and X hat under the corresponding NISC. And it can be proven. It's not hard to see that this defines a NISC for the conjunction. So only if both statements are true, the verifier will accept this proof. Now let me start building figure one from our paper. So what we have seen so far is that conjunctives extension is possible. Well, I mean, this was known. So I'm going to represent with black arrows, straight forward results or known results. And of course, you can also go from a NISC to just one NISC if not in one of the classes. Now let's consider the case of simulation soundness. It was first pointed out by Sahai 1999 that simulation soundness is not preserved by this straight forward parallel composition. Why? Well, because an adversary can ask the simulation oracle for proof on a pair and then a different pair. And then the adversary can combine these two proofs, for example, as follows. And this is going to be a valid proof on a statement that was not queried. So this actually constitutes an attack to simulation soundness. So what we have seen now is that the same does not happen here. And at least the parallel composition does not work. And one of our results is that this is actually impossible. You cannot compose in conjunction in a black box way and preserve the unbounded simulation soundness property. From this impossibility result, many other results follow. I'm going to try to give the intuition of how we can prove those. But this argument is a bit informal, I refer to our paper for more details. First of all, observe that from any U.S.S. NISC, you can go to U.S.S. NISC by ignoring one of the classes. And from those on the right, you can go to those on the left by just not using the unbounded simulation soundness property. Now, given this, this direction should be impossible. Why? Because otherwise, we would have a way of going from U.S.S. NISC to one of the U.S.S. NISC, which we have shown it's impossible by just following this path. This observation leads to a very interesting result, which is basically that achieving unbounded simulation soundness cannot be done in a black box way. So it cannot be done even if you restrict to NISCs or to languages that have certain structure, like in this case the conjunction. So of course, it cannot be done in general. And now we are also going to focus on other scenarios, for example, the lazy action extension or the label NISCs. So a label NISC is basically a NISC where the prover and the verifier take an additional input, which is a label, and forgeries in the unbounded simulation soundness game must be new as a pair instance label. So actually, you can you can use in your forgery an instance that was queried before if the label is different. In this work, we also proved the impossibility of the distinctive composition from a label U.S.S. NISC, even when dealing up the U.S.S. property and the label. This impossibility result has a side condition, which is that the languages must be hard. And here we use the standard definition of hardness of languages in cryptography, which is that it's hard to distinguish these instances from no instances. In other words, there are samplers that there are two samplers, one only sample these instances, the other only samples no instances, and they're output is indistinguishable for any PPT distinguisher. Let me give you an intuition of how this impossibility result has been proven. So the first thing we do is to define the notion of legitimate CRS. So a CRS is said to be legitimate if it has been generated by by the black box construction by just calling the CRS generation algorithms, either the one from the first NISC or the one from the second NISC. What we first show is that the verification, the compiler kind of uses legitimate CRSs on verification calls that are successful. The second step is just to observe that because all successful verification calls are not legitimate CRSs, then soundness must be compromised. In order to prove the first claim, we leverage the zero knowledge property that allows us to swap between legitimate CRSs and the simulated CRSs and the hardness of the languages that allows us to swap between yes instances and no instances. In the paper, the proof is done more formally, and what we actually do is to define an oracle O that is sufficient to build a hard language L and NISC for L, but such that any any possible compiler with access to O cannot be a NISC for the disjunctive extension. In our proof, the construction of the adversary against simulation soundness uses a new technique. Basically, we use a genuine prover to forge a proof on a no instance and we simulate the oracle so that the no instance looks like a yes instance. So this actually eliminates the use of the PSPACE power from the adversary and we believe this can be useful or it can be applied to other impossibility results. Now let's go back to our figure and let me mention a couple of possibility results. So in the case if we consider labeled and USS NISC, we show that this is indeed possible. So what was impossible without labels, it is actually possible if you have labels. And furthermore, we give also these possibility results that basically says you can achieve labels if you have this structure of an USS NISC. Furthermore, we consider these other extensions of the label or an OR unbounded simulation sound and we give these possibility results.  So basically you can use one of the two statements as a label and the other as the language. Considering all straightforward relations that we can derive from those that we have proven, the picture would work as follows and I just want to point out that in a black box way NISC and these two objects are essentially the same NISC and NISC and also these three seem to be the same object modular black box reduction. For future work, we leave to prove the missing relations here which we believe are impossibilities. Now let me conclude the talk by explaining how we can build a signature scheme from every SS NISC for hard language. Notice that NISCs for languages that are not hard are not so meaningful. Basically look at this Heinen algorithm. What we do is we simulate a proof on Y but Y is a false instance. So this is the we represent by D the sampler of no instances given by the hardness of the language. So the main idea is that you simulate a proof on a false instance using a trapdoor. So the trapdoor is a signing key and basically the unbounded simulation soundness game becomes the existential unforgeability game for the signature. So that's why this construction is secure. So I will conclude the talk now. This work started from the observation that all upgrades from NISC to achieve unbounded simulation soundness, they use a signature scheme or at least they leverage a signature like primitive and this seems to be a requirement given that as we have shown once you have an unbounded simulation sound NISC you have a signature scheme essentially and this signature is of the same computation and space complexity. In this work we have also studied composition of NISCs in particular Blackbird's composition and although several methods of composition exist for one example is CDS-94 that is a composition method for sigma protocols and as you know sigma protocols can be used to build non-interactive synology system so using the figure schemer heuristic. All existing methods for general composition of NISCs they assume certain specific structure on the NISC and what we have shown in this work is that if you don't assume any structure on the NISC there are many compositions that are impossible so for example this action cannot be performing a Blackbird's way or even conjunction if you want to preserve the simulation soundness property. So the conclusion is that in new settings and under new assumptions you will have to make extra effort to build the NISCs of general expressivity. So that's the end of my talk thank you very much for your attention.


Six Flags is the largest amusement park chain in the United States and has been the operator of a large number of amusement parks over the course of nearly six decades. Here, I will be going through the list of each and every one of Six Flags current 15 amusement parks and quickly giving my thoughts as to which coaster I think will be the next one to get the axe at each one of these parks. For Frontier City, there are a couple options I could have went with, but I ended up going with Diamondback, a very rare aerodynamics shuttle coaster model which originally operated as one half of Lightning Loops at Six Flags Great Adventure and opened at Frontier City in 1993 and just the fact that these are so rare nowadays and this one has stuck around for so long I could see this getting the axe next to this park. Next up, we have Great Escape and this was a pretty clear pick for me. I'm going with Alpine Bobsled which is a relocated Bobsled coaster and Intamin Bobsled coaster which opened at Great Escape in 1998. This is another model that's becoming very outdated, pretty rare now and I don't think this one will be around for many more years. Next up, we are going to Canada for La Ronde. For La Ronde, I had a little bit of a tough time deciding on which one I think would go, but ultimately I settled on Boomerang which is a 1984 Vekoma Boomerang model. This was actually the very first Vekoma Boomerang ever opened and it did open at this park. Just the fact that it is so outdated at this point, I could see this leaving in the near future. Next up, we have the first of the Six Flags branded parks in the chain. We have Six Flags America. There are a couple options I could have went with here, but ultimately I decided on Batwing which is a 2001 Vekoma Flying Dutchman model. As we know, Firehawk closed after the 2018 season at Kings Island and Vekoma does not support these coasters anymore. It's very hard to get parts for these and replace things on them and Batwing has not been operating a whole lot so I don't see a very bright future for Batwing. Next up is the recently reacquired Six Flags Darien Lake. I ultimately chose Predator here which was a pretty clear choice for me. This is a 1990 Den Corporation wooden coaster. Of course, it would be amazing if Six Flags gave this the good old RMC treatment and hopefully that does happen in the future instead of scrapping this entirely, but Predator is just known as being an overall really terrible rough ride. I think its days are numbered seeing as it's 30 years old at this point and most of these Den Corporation coasters are going by the wayside. Next up, we have Six Flags Discovery Kingdom. We have Boomerang Coast to Coaster another Vekoma Boomerang model. I chose this just because I don't really see any other coaster in the park going at any point soon and this is a Boomerang model so they could easily take this out and replace it with something small to medium size. It's a fairly small footprint but this coaster is a more outdated model probably isn't as popular anymore and for that reason I chose Boomerang Coast to Coaster. Moving over to Six Flags Fiesta Texas this was a very difficult decision. I honestly do not see any of their coasters getting removed at any point soon but I think Pandemonium would probably be the most likely. This is a spinning Gerstlauer coaster which opened in 2007 at the park. It's a very family oriented thrill ride, looks like a lot of fun and I think it'll be at the park for a very long time yet but since I had to pick one I went with Pandemonium. Next up we have the park which was the hardest one for me to make a selection at Six Flags Great Adventure. This is another one where I doubt anything will be leaving at any point in the very near future but since I had to pick a coaster I ultimately decided on the 1996 Intamin Indoor Coaster known as Skull Mountain. This actually looks like a really good indoor coaster. I've heard some pretty good things about it and I would hate to see it go. It's a very unique ride. I think it will probably be the next coaster to go from this park though even though it still probably has at least a few years left in it yet. On the contrary we have a park next that was a very very easy pick and I did not hesitate to make this selection and that is Six Flags Great America with 1981's Intamin Racing Wooden Coaster known as American Eagle. This has been rumored for some time to get the RMC treatment. I think that would be amazing. This is a huge ride. I don't know if they actually would RMC it just because of the sheer length of the ride and there's two tracks. There would definitely have to be a lot of work done to this. It would be a very expensive project and ultimately I would hate to see American Eagle go because I think it looks like an awesome ride. It's very historic but something does need to be done with this ride very very soon and Six Flags needs to make a decision as to whether they want to get new trains, put a lot of money into this ride or whether they would just scrap it or convert it into something else. Next up we have Six Flags Flagship Park and that is Six Flags Magic Mountain in Valencia California. For Six Flags Magic Mountain this was another pretty difficult park to make a selection at but I did pick Superman Escape from Krypton which is a 1997 Intamin Launching Shuttle Coaster. This just doesn't seem to be that popular anymore and I don't really see anything else at the park going at any point soon. We did just see the other one of this model get removed very recently in Australia which was known as Tower of Terror 2 and since this ride is just not very common and it's kind of outdated at this point I could see this getting the X next and it would open up quite a bit of space for a new attraction. Going to Mexico we have Six Flags Mexico and for this park I chose yet again another Vekoma Boomerang known as Boomerang which is a 1988 Boomerang. Once again I don't really see anything else leaving this park anytime soon. This is such a common copy pace coaster and not only that but this is one of the older Vekoma Boomerangs out there opening in 1988 so for that reason I think this will be the next to go. Going to Six Flags New England this was a very obvious pick and this is a relocated coaster from Six Flags Magic Mountain and it is known as Goliath. This is a Vekoma giant inverted Boomerang coaster and it was known to be a very very good ride in its original incarnation at Magic Mountain but unfortunately after it moved to New England they gave it new trains and now it's known to be a very unpleasant ride experience and it doesn't operate that much anymore. I think Goliath will be going in the very near future at Six Flags New England. Going to Six Flags over Georgia one of the oldest Six Flags parks out there I had to make a tough call here and I decided on Georgia Scorcher but this one has a little bit of an asterisk next to it. I think rather than removing the 1999 stand-up coaster Georgia Scorcher I think they would give it the floorless treatment and give it B&M floorless trains like they've done with Mantis at Cedar Point and Vortex at California's Great America. It just seems to make a lot of sense so I think Georgia Scorcher will either get converted or removed at some point in the near future though I definitely see a conversion coming before a removal due to recent trends in the industry. Next we're heading over to the original Six Flags park Six Flags over Texas and for this park this was a very clear choice once again and I'm going with La Vibora which is a 1986 Intamin bobsled coaster this did not originally open at over Texas it's a relocated coaster as it was part of the Six Flags ride rotation program back in the 80s. This is just something that isn't very popular anymore once again it's becoming outdated there's not a whole lot of them out there anymore and I think this would open up a pretty significant chunk of space for a brand new attraction and for those reasons I think La Vibora will only be around for a few more years. Finally coming to the end of the list here we have Six Flags St. Louis. Six Flags St. Louis has a couple coasters that I think we could see get the axe at some point but ultimately I think Ninja is definitely the most likely and hopefully that is the case as I've heard this is one of the worst coasters out there some people even call it the worst roller coaster in the world. Ninja is really interesting it opened in 1989 and it's actually a combination of a Vakoma and aerodynamics looper because aerodynamics was not able to finish it due to filing for bankruptcy so Vakoma had to step in and they finished the ride so both of them together just created one awful ride apparently. Do you agree with my picks? If you disagree be sure to let me know what you think will be on its way out at each park. This is always a fun topic to discuss as we try to figure out what is in store for the future. As always thanks for watching and feel free to subscribe if you would like to see more content like this on a weekly basis. I can also be found on Facebook as Coaster Daddy and Instagram as Coaster Daddy Official. I'll see you next time. This is Coaster Daddy. Bye.


What's going on everybody got Kyle and Jake here with late in sports cards. We are rip in 2023 bowman draft super jumbo six box case number four Random team style with the randomized before the break had Gary G with the d-backs down to Dale C with the Reds Good luck on this one guys. Let's do it Some super jumbo this time Some leftovers earlier turkey ham pigs and roast potatoes. Okay Okay, Mitchell. I see you Hello leftovers earlier as well. That was where I started my day with Paper base is donated in this Jumbo good luck everybody. Let's do it number four Random teams style. Hey, let's go strong Very nice That's awesome, dude No, very nice. Yeah, man. That's awesome. I'm a big fan of the cup really really cool products I like some bum and draft as well. So I like your choices there the girlfriend spoiled you That's awesome, man Not bad at all Starboard some paper at a 499 got drew Jones for the d-backs chase Davis first refractor Noble Meyer and our first auto is gonna be the 150 for the Tigers max Anderson blue wave and Colt Emerson Yeah, that's awesome, man Haven't opened it yet. Oh boy. Yeah, you gotta let us know man. I'll let us know really love the cup on Jealous there got one more case of the cup to man. I don't get to write to get to open It's me opening tomorrow. So I don't get to get in it one more case Jacob Wilson and it's who 50 gonna be Garrett bombing for the brakes Sean's boy with the Not the greatest picture.  Yeah. Good luck here guys packed to first refractor sliger Gordon Clemmy JB Shears and First auto nice one. There's a base auto match. Shaw. You go cubs This one there the first pick in the draft for the cubbies Lankford Lankford base Don't skunk young mosaic. Okay, Spencer I'll do my best me. You gotta remind me be sure remind me. There's a boom and glass noble Meyer and speckles same as a vala You should remind me not to skunk. Yeah true red color match auto. Oh boy. I'd be called worse. You hate that word There's our fractors Campbell Levinson got Jonah Cox Fisher Jaworsky and base auto Spencer Nivens gonna be for the Royals First base auto Jacob Wilson and Paul Skeens. I'm down for some Bowman's best. I always like Bowman's best It's a really good product lead better and a speckle first cold young.  Let's go boys. Yeah, I got Jase. I got Spencer Don grab the upper deck the cup spot and Patrick Grabbing spot in 10 bucks Tuesday 14 total group break spots 14 to go on the day to win mosaic and choice mixer or yeah No auto and choice mixer in the 12 in the 10 bucks. Appreciate that guys. This is a Max Clark base And is awesome take much convincing Paul Wilson con early fractors in these packs base packs Goes on the next one There is one hockey on L. It's one hockey. It's already full tonight though the artifacts hockey I have artifacts and a cup hockey tomorrow. That's not full though. If you want to grab spots in that The ones for tonight are full though. Just one one hockey break tonight to tomorrow There's a light blue to 499 Jack Hurley for the D-backs to Walters. There's Bryce Eldridge first Dylan head Kevin sim and Refractor out of 499 is gonna be Dylan head. I just won their Padres Felon Celestin drew Jones. We're sold out on the choice in the huddle mixer So just 12 spots left and it's all in that 10 bucks and a film mixer Just 10 bucks Tuesday football for the night. Let's go y'all. Let's go. That guy's almost full at 615 I'm in on that you guys are the best Appreciate that guys tonight Oh foster and blue to 150 is gonna be Christian Campbell Christian Campbell righty box to Like everybody and just one a break with spots left tonight 10 bucks Tuesday Boxed Tuesday football Thank you Derek closing us out on Mosaic Derek and Wally. Hey, there we go. You did get the last spot. I think I actually think Derek did Seconds the last though pretty good Still some mojo there Now, let's see it. Let's see it for everybody man. I'm excited for some mom. Oh, hey Rip too too much of it. You got a systems Spencer for getting Jason. I like it. I Like it for Stetmer bowmeister Teddy McGraw Abner we hear a white Trey Morgan and first base. I was gonna be Charlie Soto 20s Charlie so toe Jackson churril Pullman glass to me Matt Shaw and aqua wavy 125 Jacob Barry Blueberry Skeens is twice in bowman's best. I gotcha. Yeah, we've seen a good bit of skeens man I was gonna say he had a lot of autos We have pulled a good bit of skeens out of draft for sure. There's a gradient gonna be Jake Cunningham To 199 I've been seeing skeens pretty consistently since release day first Carrick capis Fisher Jaworsky and there we go Jacob Wilson to 199. There you go ace. Thanks the aqua lava Nice one there for the athletics get a mag on that Jacob Wilson Another Jacob Wilson on the base And speckle on the back is going to be gaping zollets for the Mariners Yeah, that'll work. Jackson churril true bowman's best That'll definitely work You do have some pretty good baseball luck. It seems it's a 499 guy AJ Ewing On the light blue first Fractors Arroyo Vraidenberg K. She'll Jacob Gonzalez First Langford and our auto is gonna be Travis honeymoon Cardinals on the first one base can call your max Clark back Wilson See another baseball player Use a former there's a first speckle of the jade hand play on the on the pirates, right? I think pirates That might be why I don't know practice first showmwetter ahuna first holland ham winniger Brock rodin and auto is gonna be Jack Mahoney the 250 on the purple True purple the 250 for the arachis awesome reverse local legend We're watching him my freshman year high or high school. It was a good for I think it was winter park and man Did he light us up paul skeens? I did 50 I think he had 50 against us bro Which is fair I didn't go the NBA There's a max Clark and true yellow is hunter owen to 75 first there for the royals Hunter owen jake knows his uh jake knows his baseball guys Jake certainly knows his baseball guys so Got any trivia that would be uh jake would be the baseball guy handle that rector first forester Carmelo Nolan the clean skeens And base out of there's gonna be hunter haas first base auto for the race Go race Second half. There's a colt keith transformer talented 250 Be back for the tigers Alrighty guys two boxes down Four more Four more Good luck guys box three colt keith thumbs up That is correct. That is correct Got to hey, thank you. Jabari taking a spot in 10 box Tuesday should be down to 11 Should be down to 11 here guys The 11 spots on the day as well. And thank you. Jabari like spencer's new name Yeah, that's been really green thumbs up Been the thing for a little bit They're haas to mcdaniel Yeah, sir chase davis noble mire and base out of jake conningham Base auto paul skeens jackson chariot the base relic that was pretty fire I don't remember that he got from us. Oh, yeah. Yeah, I do remember you saying that the other day you did get on fanatics That was fire There's a nice one jackson holiday on the sp You go or else a little sp holiday It may be safe to say There's a light blue paper that one's going to be mike both to 499 first for the brew crew Fractal vitrano balmin maraudis trawler wiggins Beshears and auto is going to be karson raka forte Or the orachis Or sorry, not the rockies the royals Sounds like it could be a rocky Rock the rock Why does the rock rigid on a rock? That's what i'm saying Rockerizio, do you know what i mean? There's a bum in glass paul skeens aren't they all the 250 we got key for lord first for the orals Keep it going here guys. I guess rock is a Yankee name Yeah So happy the raiders won. Let's go raiders. That was a good game and they uh They didn't let up they didn't let up for the chiefs There's a gold paper that one's going to be jacob cravey For the o's the 50 Yeah, it's the first uh first time in a while. I want a In arrowhead. I'm sure It's kind of wild There's a first travis honeyman christian cambell leavenson Jonah cocks and aqua lava autos luke schleiger to 199 Calling howt matt shaw Yeah, I think the uh giants had a 10 10 game road losing streak to the eagles they were trying to snap but Not this week not this time Nope They tried though. They they came back there There's a speckle first Jonah cocks They sure they certainly try No, you're not wrong malon. They do have a Good set of rookies good set of prospects, man 2023 was a good year for baseball very good year. There's a first key for lord dentin regio Joe redfield Forester and base. I was going to be zack leavenson go to the cardinals first bowman base matt shaw chase davis You know, I agree with you though the uh Some real good rookies real good prospects chase Was a good one True gold on the back a bowman glass jacob wilson And true gold is going to be saving sabiops there for the brapes Nice one there true gold chrome They won two years ago in arrowhead really I'm surprised by that We'll take it though. We'll take another one. All right. Keep it going max clark. I'll meet others calling halk refractor jack hurley sabios rhymer and refractor out of a 499 brock rodent or the mariners jacob wilson and holiday True blue on the back is going to be a reiner arias for the giants True blue to 150. Alrighty guys, that'll be halfway Good luck box number four Again only I think 11 total spots left on the night guys 10 box tuesday 10 box tuesday football everything else for the night is filled up. Appreciate y'all. We'll have uh lane back here in the morning Starting at 10 a.m. I'll be back tomorrow night We'll keep on ripping appreciate everybody We'll have some thursday fanatics with uh sam. He'll be back on thursday Some good stuff this week. Good luck here guys box four I wish I led the d-backs to the world series Would have been uh, it would have been sweet There's a light blue paper to 499 gonna be connor o'hallerin But yeah, I think uh, there's a couple I mean josh young another rookie who won the world series, so The rookies were rookies were showing out this year first camp alderman played uh braden taylor go race max clark person reed connor burns and auto is going to be brandy winnaker on the base auto One day 20s Yeah, right A lot of them did paper paper There's a speckle first. That one's gonna be philip abner For the d-backs I think 11 total spots on the day all in um 10 box tuesday football correct last break Last break last spots ethan o'donnell case dad tommy hawk Early smith nickels and green out of 299 is going to be a jake cunningham For the orioles on the green 299. I've seen that guy everywhere on saturday jake cunningham real oh, yeah Just flying out of the uh mixers and stuff. We're doing on fanatics Paul skeens and green 299 gonna be camcall. You're on the um green grass Hey, what's up puka? Evening puka. How are we doing? How you doing? You had a good uh christmas over the weekend Hope you got some fun plans for uh new year's also coming up this weekend It's a naked deathbird 299 nothing wrong with christmas and new year being on the weekend I'm in on it There's a first refractor gonna be coal foster mac whore veth charlie soto wall drip And base auto there's gonna be a hunter hollet for the reds first base Yeah, I can't complain It's pretty chill puka. That pretty good one. Corey seager Wish I was man Man Wish I was able to turn off that's what I like that.  I was dust in may. Let's go. Ooh There's a fire So heat boy jake goes heat First plate michael refractor emet olsen alberto rios got a michael caraco Delio opper and base. I was gonna be sean sullivan Sean's boy with the tan line Sean sullivan rockies Skeens and wood that kind of tan in colorado No I don't think so Maybe though there's a wild langford and speckle first gonna be patrick riley Or the pirates let's pack a box four Again, appreciate everybody hanging out with us today. We got um just 11 spots to go on the night For group breaks. I am way over full on personals. Um way way over full 499 white langford If you guys order today, it might not go tomorrow. It is it is pretty serious in there Uh, it's a white langford of 499 We have no personals tomorrow at least no, um No specifically personal streams So we'll do some more tonight after group breaks and then some more tomorrow after group breaks There is a lot in there barofin gravy newt woodward mohoney and auto is going to be cold foster for the giants base auto brain taylor max clark insert and there's a manual bonilla 199 on the fuchsia fuchsia crater All righty there guys so that will do it for box number four got two more Two more and we're on to mixer Good luck guys box five moment super jumbo with jake the interview and the cheater What are you interviewing him about Not how he cheated There's a light blue to 499 gonna be a how you leap I want you to want to open up about that Yeah, right We better keep quiet until after uh, you get the ring. Maybe there's a spencer jones first dylan campbell George It's chan silvin picard cooler and auto is gonna be luke asial first woman base auto 20s Spencer jones colt emerson Another speckle on the back. We got skeens and then we have a jonah cox speckle first I think we had jonah cox speckle first and last one True goal. All right Yeah, I don't think he does quite as much as kormin, but Josh certainly not a bad rookie Thank you. Eric taking a spot in 10 box tuesday should be down to 10 now 10 to go on 10 box football. They are last break with spots tonight And that's a chance to grab up some spots for tonight came to menachi tommy troy tanner hall colt emerson OV there's a nulla mclean and refractor auto is jack moroni or mohoney for the uh, rockets to 499 tommy troy jr jones quiet langford base first Colossae's the best for last braden taylor and a lunar glow first brady smith It's true mark. It's true We're getting there. We're getting there super coming I hope refractors lindsay ewing engle refractor picney Winnecker and base auto is gonna be set keener for the white socks A lot of brady's left. That's right A lot of brady's left. Uh They don't want us to find them for some reason At least the autos I'm trying to find one. Yeah, how about welcome back with a brady hiding from us. There's a, uh, bowman glass ty peat And a, um, aqua shimmer is going to be the brock ravenberg to 125 There's a gradient. It's gonna be a, uh, hostway to polo to 199 refractor davison. There's ty floyd I mean, uh, marique bradfield lauda coupé ty peat and base auto is going to be landing maraudis for the blue jace first bowman base jacob a kanzalas Spencer, I saw the lions or underdogs start for, uh next week against the cowboys I saw they started as underdogs So white langford and a speckle first of chase to warsky Let's go with the lions and that one one more peck and then one more box Nice number to 10. We got the uh green and red, uh gradient.  Thank you. I'm taking one in, uh, 10 box tuesday On the single digits on there Nice to the low numbered honeyman Yeah, there's toke Hacially waiting for a cardinal. There's a max clark refractor is kevin parada nivans homer bush Packenburg hit Watts brown and a first base auto of marcus brown nationals Yeah, I don't know. I don't really get it. I don't really get it spencer Why they would make the lions Dogs in that one notice that earlier they were saying because uh There's a bowman glass still in head into 250 sultabon. I think it's like the last like five or so, uh, monday night favorites have lost So they were showing the they were showing next week the lions or the uh underdogs So maybe that street continues. Alrighty guys last one here number six Bowman draft super jumbo Next we'll get a mixer going It's at 90k right now in golden. Oh, there we go. Happy to get the reds in a random number for the 10 box. All right, let's go See if we can get my man Lock here Last box number six of super It's a refractor first cj kafis Taylor huddapool wittman Keener and the 250 got calvin harris First bowman purple auto for the white socks the dj calvin harris selliston blake michael To the habies Nothing yet mill don't have any braid and taylor just yet We got too many short stops. I'm uh Haven't been stocking up on the most recent ones We've been uh only drafting short stops.  Yep Yeah one for nuns. Yeah. Yeah, so it should be on the right side. I believe it's been the whole time So it should be with the refractors Right at the end of the uh silvers on the right side There's a camilla ds the 199 gradient Astros so it should be right at the end of the uh Fractors here is a tj waltz refractor saltaban rockforte This is on a tello and based on it's gonna be tommy hawk first god guardians tommy hawk pro player tommy hawk pro player And so you get one per uh one per nun chuck old emerson chrome There's a bowman glass gonna be a white langford for the rangers and a speckle first andrew walters A few more nun chucks There you go rich Got another one tomorrow if you want to get another z-gross going I think it's our last uh last cup hockey tomorrow Kind of jealous i'm breaking out. I wouldn't like to get in it max anderson first matt shawl First wilson owen brown levi wells and refractor autos alberto rios the 499 Or the angels and first lunar glow is tj nichols Alrighty two more two more nun chucks Oh, did he rich? Yeah, I remember that uh, I hit that pretty nice most ciders to the uh Get which kind of was the explicit most cider that one was pretty sick too Yeah, red wings aren't a bad uh red wings certainly aren't a bad team to get in there The cup uh draft sapphire bkb. I'm not sure. I'm not sure if we've gotten any I'm not sure bkb There's a first refractor of k morris savakul cunningham tonsi Leadbetter and base first woman auto cold karak the Rockies Yeah, no problem bkb um Yeah, I guess keeping on the website if we do have it it would probably listed Soon enough, but um all I see right now is regular bowman draft stuff choice jumbo super jumbo I don't see any sapphire listed at this time, but not necessarily meaning we won't get any So max clark first Bowman glass could be brice eldridge and the 125 haunts muntero All right guys last nun chuck here. Good luck. Good luck It's at that 25 or 2100 auction. Oh man So the cider exclusives are pretty nice then I like it It's a 49 got a aqua of jake de leo recta first far mellow. There's a skint cold miller santana Cold karak and last i was going to be michael karakoff base auto for the cubbies Paul skeens insert and solace Is it really more than the base? I guess we'll just like the exquisite set so much maybe Maybe that's why ready guys. There's a max clark first Zonatello and on the back is enrique bradfield on the speckle ebj On the speckle All righty guys that will do it for 2023 bowman draft super jumbo six box case number four Do a quick hit recap then we are on to the mixa onto the mixa Yeah, jr. My that was not the best. That was not the best. Uh, super jumbo case there. Sorry about that guys Not the best collar or anything there Quick hit recap We had the sp jackson holiday to 99 debtmer and cam collier the 75 hunter oan gold cravey and savaios We had the uh green and red honey men to 10 base auto honey men Cunningham haas foster sullivan keener maraudis. There's tommy hawk winnaker charlie soto leavenson colkerrick We had base uh michael carrico brown keyshaw holland rocka ford's a nevins base auto matt shaw Uh to 409 mahoney alberto rios dillon head rock rodin to 250 calvin harris mahoney 199 schleiger 150 anderson just 99 was gate cunningham And on the back we had to 199 was jacob wilson On the aqua wave or aqua lava 199 there six picking the draft for the ace All righty there ready that'll do it for 2023 super jumbo case number four get that right out to you


next item is consideration of four parliamentary bureau motions motions 10210 to 10212 an approval of SSIs and motion 10213 on the budget bill these questions will be put at decision time sorry sorry sorry class jophus patrick to move the motions first of all move together thank you very much these motions will be put at decision time to which we now come and the first question is that amendment 10183.1 in the name of murder Fraser which seeks to amend motion 10183 in the name of Derek Mackay on stage one of the budget scotland number two bill be agreed are we all agreed we're not agreed we'll move to a vote members may cast their votes now the result of the vote on amendment number 10183.1 in the name of murder Fraser is yes 30 no 95 there were no abstentions the amendment is therefore not agreed the next question is that amendment 10183.2 in the name of James Kelly who seeks to amend the motion in the name of Derek Mackay be agreed are we all agreed we're not agreed we'll move to a vote members may cast their votes now the result of the vote on the amendment in the name of James Kelly is yes 23 no 102 there were no abstentions the amendment is therefore not agreed the next question is that motion 10183 in the name of Derek Mackay on stage one of the budget scotland bill be agreed are we all agreed we're not agreed we'll move to a vote members may cast their votes now the result of the vote on motion 10183 in the name of Derek Mackay is yes 69 no 56 there were no abstentions the motion on stage one of the budget bill is therefore agreed I propose to ask I propose to ask a single question on the four parliamentary bureau motions does anyone object please see so now no the question is that motions 10210 to 10213 be agreed are we all agreed we are agreed and that concludes decision time we'll move now to members business in the name of Ross Greer on bus services and we'll just take a few moments for members to change their seats


We're very pleased with the ministerial conference that's been held in Dhaka. We had an extremely strong participation, around about 50 ministers, and the president of Mauritius. What I think we see is that there's a widespread recognition amongst all of the participants of the importance and the key role of innovation in the creation of sustainable economies. And that is a very important recognition to have at this stage in Africa, where growth rates are stabilizing and are rather favourable. Now of course we have only several hundreds of participants here, so it's a question of spreading this recognition throughout the continent, it already is happening. But we think it's a very important result. There's also widespread recognition of the importance of intellectual property as the key element, I would say, or one of the key elements in a successful innovation ecosystem. And that again is an achievement. Now I think what we need to do is to focus on concrete programmes, practical programmes, that will add to this very large agenda, because of course as a single organisation, we are not the only ones involved. There's the African Union, who are our partners in this conference. There are a number of the sub-regional organisation, African organisations, who are also present at the conference. And there is any number of private entrepreneurs who will be interested in establishing businesses and investing in Africa as it grows. So this now is I think the key question. What are the practical initiatives that we can take? We have a number of platforms as it is for access to scientific data, for example the establishment of technology and innovation support centres, in the field of copyright and the creative industries, the wiring of collective management organisations to connect them into the global digital marketplace. So there are lots of concrete programmes we see, as well as of course our capacity building programmes. But taking these forward so that we are able to provide a supporting role for this journey, which I think is a very optimistic journey for Africa in the future, is now the task. The common theme is, as I've said, recognition, and then also how to create a priority of this area. So for Africa of course there are many priorities, and urgent and pressing priorities, health, education, infrastructure, natural disasters, many, many priorities, then taking something that's rather abstract like innovation and putting it into that list of priorities is rather a difficult task, of course. And that's why I think it's important to get this recognition that innovation is a major component in economic growth. And it is a contributor to the improvement of our quality of life, and it's the way in which some of these major social challenges that we face can be tackled by doing things in a different way, in a new way, and overcome. Once that recognition comes, then of course you can make a priority of innovation, and by making it a priority, and by creating sustainable economies, then of course you insulate yourself to a greater extent, let's say, against some of the disaster and other challenges that exist.