I'm Scott Darby, Creative Coder at IOHK. I'm the lead developer and creative on the Symphony of Blockchain's project. We are now heading into the WebGL build of Symphony version 2 and I'm going to give you a quick progress update and show you where the project is heading. So just to give you a quick overview of the project. Symphony of Blockchain's is an interactive tool which allows users from a wide range of backgrounds to explore and learn about blockchain technology. It is an audiovisual experience which represents the underlying mechanisms and mathematical concepts underpinning Bitcoin, Ethereum, Cadano and other blockchains. Users will be able to hear the sound of a blockchain at a point in time and be able to ascertain properties simply by listening to it. The audio will expose transaction density, network health, user adoption and practical efficiency. All of the structures and visual elements in the visualization are there for a reason. Form follows function. The experience will be varied and dynamic encouraging users to keep returning to the experience to explore and learn more. The experience will be information rich and aims to be the most comprehensive tool available for exploring a blockchain while being visually stunning. It will be extensible and modular which will allow several blockchains to be compared and allow other developers to contribute to the project easily. But just to recap and show where you've come from, here's a selection of the static concept work which I created for the project. You can hopefully now see some of this coming to life in the real-time version. As there are many parts of the blockchain world we're creating, we've decided on some locked off camera views to guide people through the experience. This will also help from a performance perspective as we can control what is being loaded and rendered on the screen. The user will be able to seamlessly switch between these camera views and go from viewing the entire macro blockchain structure to viewing individual transactional detail. The views we're focusing on are first person or cockpit view, this will be the main view that we use in VR. Underside Merkel tree view, the top-down view, a macro blockchain view and an isolated block view. So the top-down view, once the user has zoomed in from the macro view they will enter the top-down view where the transaction detail blocks is displayed. The controls on this view are like that on something like Google Maps and you can use the mouse wheel to zoom in and out and click to pan around. This view could be a good opportunity for augmented reality as the top-down view of each block is unique and will work well as an AR marker. The user could hold their phone onto the screen and see the transaction crystals extrude out. Here's a shot of what this currently looks like in the build. You can see the UI at the bottom with the details of the block currently being viewed. So just to recap on what you're looking at here, this is a block with each of the transactions represented as hexagonal crystals. The crystal height is controlled by the transaction value and the color is controlled by the ratio of outputs which are spent.  The crystals are ordered by transaction age from the top left to the bottom right of the screen. The pattern of distribution on the plane is controlled by a simplex noise function. The noise amplitude is greater the less healthy the block is, resulting in healthy blocks looking much more ordered than unhealthy blocks. In the cockpit view the user can fly around freely using the standard first person controls at WASD key and mouse. The user will be able to focus on transactions and see information about them in an overlay. The sound will change dynamically as they move between blocks. The sound in the first person view. The user can explore an ambisonic soundscape generated by the transaction data. Each block has a unique piece of music or sound design which is created using additive synthesis to combine sine waves generated by the data in each transaction. The closer the user is to a block the louder the block sound will be. So as they move along the chain sounds will morph into one another creating a blockchain symphony. The audio is created using the following rules. Each transaction is assigned a fundamental pitch from a musical mode based on the transaction value. Higher values result in lower frequencies. Each transaction has 16 harmonics. The number of transaction outputs which have been spent control the volume of these harmonics. Transactions with all outputs unspent play all harmonics at full volume and transactions with all the outputs spent play only the fundamental pitch. The health of the network when the block was mined controls the range of randomness assigned to the pitch of the harmonics. This means that healthy blocks sound much more harmonious and unhealthy blocks. Here's some screenshots of the first person mode. You can see this UI overlay here that's been designed by Julie. You'll be able to click on individual transactions and see them on the right there with all the detail about them. Here's just a few more shots from the WebGL build. This is showing the Merkle tree from underneath each block. That's showing a series of blocks all connected together with the Merkle trees on the bottom. So as you can see the WebGL build is starting to look quite a bit like some of the offline render concepts we put together in the beginning. The user interface is a really key part of this. We're including lots and lots of data in there for people that want to use it. So here's a design concept of how that interface can look. We're imagining this will be on the left hand side of the screen and the user will be able to pull this out so they can search by date, search by block hash, pull up lots of information about what's going on. This is the underside Merkle tree view and this will let the user explore the Merkle tree and see how the Merkle tree connects to the crystals on the plane above. The isolated block view will allow the user to isolate a block from the chain, rotate it around, really explore its entirety. Okay I've got some examples of the sound design here. So this is an unhealthy block so the means of fees were very high when this block was mined. You can see the crystals coming in there based on the transaction time. When they're glowing white that's when they're emanating a sound. Here how the healthy block sounds much more musical than the other block. Here's a block from a very early on in the blockchain. You can hear it's got a much simpler sound to it and that's just due to the the amount of transactions which are in the block really. And as you fly around the blockchain you can hear each block kind of blending into each other and there's the a few of the macro view. So this is the overall view of the blockchain. It's kind of a map with which the user can use to explore the entire structure. This has changed slightly in the build actually which you'll see from the demo shortly. So this is another screenshot from the WebGL build so you can see how it's really coming along. You can see this large sphere in the distance like a planet. We're planning for this to be the mem pool which is where all the unconfirmed transaction activity is. Okay so I'm just going to show you a live demo of this just to prove that it is coded and working. So this is the entire blockchain structure here which you can see in these rings around this planet. And if I zoom in with the mouse wheel you can see all the individual blocks. The closer we get you see the UI pop up and you're kind of within the certain boundary of the block and you can hear it's starting to play the sound there. So basically when each of these crystals are glowing white there's a sound emanating from and I can enter the cockpit mode here. This obviously needs a bit of UI design so I'm just using the keyboard and mouse just to fly around this. So this is all using real data being pulled in from Blockchain Info API. And if we go underneath you can see the different merkle trees there connecting up. And if I go in somewhere closer like this is where this is where all the latest blocks are being mined. Hi I'm Andy Buchan with Creative Studio KUVA. We've been working alongside Richard Wilde and Scott Darby in developing Symphony as a Turing installation. In order to best frame what follows I thought it worthwhile just to give you a brief idea of the intended ambition we're aiming towards. We're looking at the intersection of technology and innovation to create a unique augmented physical installation that can appear everywhere from a gallery space to a piece of more traditional marketing. A physical installation in a gallery space that allows users to interact interrogate and understand a series of aspects within the blockchain through the use of augmented reality. The installation will launch with a focus on interrogating the mem pole. Echoing the work initiated in Symphony 2.0 we will create a physical globe. A sphere will be sunk into the wall of the gallery space creating a visually intriguing and inviting moment. Participants will be able to see the rest of the globe with geolocated memes and interact with the content through their handset and an augmented reality view. As with the web experience for Symphony 2.0 this augmented installation will be information rich with an aim to draw visitors in. It will be widely accessible in its approach and engaging for experts and academics along with the general public. The augmented reality experience will also be accessible outside and beyond the gallery space giving us an interactive tool to support education and engagement opportunities further afield. Project outcome. There are four key main areas here ownership education attention and engagement. Again as with Symphony 2.0 the physical installation and its augmented view enables us to continue to carve out ownership around how the industry articulates the underpinning concepts. It allows us to own how the world visually understands the blockchain and cryptocurrencies. The installation will provide a one-of-a-kind experience and the first moment the general public will be able to physically interact and interrogate with specific aspects of the blockchain. It will drive understanding. Lastly it will generate meaningful PR attention and ultimately interest in both IOHK and the wider symphony project. So just to touch on live data and its importance the project itself will be built from live data and we feel it's vital for its integrity and success. The work in the visuals that follow are built from real data gathered last Thursday with around 6,400 unconfirmed transactions in the bowl. Just going into a bit more detail in terms of our approach to data and our current thinking on it there are four key aspects to the visualization. Fee and value, size and movement. So shape all transactions are represented in the same way and fundamentally they are identical apart from size, value and fee. Size, the value of each transaction is represented by the object size larger objects are more valuable. Fee level, using a predetermined clamped and fixed color gradient a transactions fee level is represented by its color. Motion and animation, the memes will move and animate the project should feel alive. Transactions appear as they are sent and are removed as they are mined into the block. So just having a look at the physicality of the installation itself and what you see here is a very initial scamp effectively for it and our current thinking is that we would show a thin sliver of the globe itself as opposed to the entire object with it peppered in these crystal like structures again referencing Scott's work in Symphony 2.0 but really creating a physical moment that is intriguing and engaging really drawing viewers and participants over to the installation itself and encouraging them to engage with it. And on the right hand side what you see is potentially how it might look through an AR screen and AR portal so revealing the remainder of the globe and allowing people to see behind the wall effectively again giving them a really strong visual reward for that digital engagement. And here are a couple of quick materiality studies and animation tests as to how this live data would come in and as you can see in the left hand side there is this video plays really creating this kind of interesting dynamic physics based animation that really gets a sense of the frequency at which these mems appear and are pushed into the pool itself effectively and then on the right hand side just a quick materiality study giving a kind of glassy structure to the individual mems which is almost crystal like which again flows through into the work that Scott is doing within the wider context of Symphony 2.0. We thought it was important just briefly though to break out and talk about the opportunity that augmented reality really gives us within the wider context of IOHK and you know within the installation and certainly what we detailed above we think it's tremendously valid but we absolutely see the potential for AR being used as a tool within the wider team so whether that's something like Agilos or Charles and beyond really using it to interrogate specific aspects of their research or outputs and really giving them a unique tool for presenting. As you see here we've quickly done a couple of mock-ups of exactly how we could see augmented reality being used within the context of say Agilos and him presenting a particular aspect of his work but really feel like it could be something that drives audience engagement and ultimately we feel a deeper understanding of the concepts or really whatever Agilos and the team within IOHK want to present and talk through. So getting back to the installation and really we thought it was important in this next segment really to explain the work ultimately and so the goal within this sprint as we'll go through it shows off the potential of the augmented reality installation really to explain and outline the potential to the key stakeholder team. So in order to do this we created a quick again internal facing script ultimately that goes through the user journey alongside the experience inside the gallery space. So what we have here is a user flow effectively and we have three components down the left user action the behavioral goal and ultimately the emotional result of that and then we have five key stages within that process of discover approach engage interact and learn. As the user is outside of the gallery space or as they're consuming information about it through media really the the kind of behavioral goal is curiosity and driving them to the gallery space and obviously this allows us to build awareness as the approach the physical installation it's core that whatever physical aspect there is to it that it really draws attention and intrigue the behavioral goal is visual surprise and that kind of physical attraction and then ultimately when they get close to it it's important that it has that level of detail that drives that aspect of surprise when they get up close to it. So moving on to the engage segment obviously it's important that there's an informational aspect that in brief explains the exhibit and the installation in front of them and whether that's a URL that pushes them to an augmented view or an app for download ultimately that's the behavioral goal that we want people to understand what they're looking at and understand the interaction and really in terms of that last piece that emotional result really again driving curiosity and pushing them in terms of an action towards download and towards that potential if we need it registration and then with the augmented view accessed obviously they're in the interact state and fundamentally this is all about the emotional goal and we really want to make sure that the visual layer is something that's in its first instance delightful to look at and really rewards the user and the participant in the installation for that action of downloading and engaging with it and really drives that kind of linger within the context of the exhibit and they're allowed to explore it and are really rewarded for that. So then moving on to the final stage really and this is fueled by the engaging aspect of the content so the better it is the longer they will dwell and really kind of driving that understanding so the more they'll learn and that's the ultimate goal here really is to kind of fuel that learning and fuel that engagement so that people linger in the space and are really captivated by it and really it serves as a potentially a jump off point into symphony 2.0 and certainly into IOHK in general which we think is certainly the ambition. So just moving forward into being more explicit with how we feel this experience will flow we've done a quick storyboard effectively and blocked out some of the key moments and some of those key scenes as we see them in terms of how people will enter into the gallery space and interact with the installation. So as you can see outside the gallery space it's a traditional passing by engagement however it's obviously key that we have something in the window that grabs attention from the passing public and really draws them in but when they're inside the flow and the intrigue driven by the sphere buried in the wall and then the engagement and the interaction surrounding that physical moment the use of the mobile device to either scan the QR code or go directly to URL for a potential download of an application and then looking at the augmented view and exposing or revealing the rest of the sphere and allowing participants to scroll around or spin the globe and either zoom in or physically move closer to explore the data that's woven into it and really that ultimately completes the experience ending on that final lingering moment of interrogation and exploration. So just to wrap up we thought it worthwhile visualising how augmented reality could be used in the wider context of IOHK as an additional installation or as a tool to support presentations we think there's a great opportunity a great utility in the technology to facilitate audience engagement and deeper ultimately deeper understanding and just again kind of to kind of summarise yeah we certainly feel that this work around the mempo the kind of initial work is only scratching the surface of the opportunity certainly for positive attention and really kind of meaningful engagement and that really concludes our presentation on the augmented installation thank you very much for your attention


I dream of a world where every woman and man girl and boy and every wonderful in between where people of every size shape and Contour every shade and hue the queer gay by the cis the trans and all of the magnificent middle that those who call on the name of Allah Yahweh God Jesus as well as those who do not call on the divine at all would be able to look in the mirror seeing only the beautiful reflection of self gazing back at them and not the destructive fear and hatred projected at them by those who won't understand this is the world of which I dream this is the world I dream can be


Welcome back to our lecture series, Math 4230. I've checked out for two for students at Southern Utah University. As usual, I'll be your professor today, Dr. Andrew Missildine. So in our conversation for lecture 20, we're naturally gonna continue what we were talking about in lecture 19, which just as a reminder at the very end of lecture 19, the very last video, we proved that a polynomial ring whose coefficients come from a field always forms a Euclidean domain. Therefore, there is a Euclidean norm, and we claimed that this is the division algorithm, but it's somewhat suspicious to call the Euclidean norm, the division algorithm, if we don't have an algorithm, right? There should be a process, there should be steps that we should take. But in the proof, in the proof where we prove that a polynomial ring over a field is in fact the Euclidean domain, we actually were able to construct the quotient and remainder recursively. And this is in fact the division algorithm that we know from previous college classes, like college algebra is a setting where I would teach students about polynomial division math 1050. It also comes up in maybe intermediate algebra, math 1010, or high school algebra, whatever. But the algorithm that we use in these classes, such as math 1050, is exactly the algorithm that was embedded inside of the proof that a polynomial ring over a field is in fact a Euclidean domain. So let's talk about, let's be explicit about the algorithm now instead of more of the proofy approach to it, right? Let's take two polynomials, f and g, which belong to our polynomial ring, f adjoined x there, where again, f is a field. And let's suppose that g is not the zero polynomial, otherwise we really couldn't divide by it.  And r is either the zero polynomial or it has a polynomial degree, strictly less than g. And so I should perhaps amend what I said earlier. When we prove that f of x here is in fact, a Euclidean domain, we didn't construct the Euclidean norm, we argued that the degree function was the Euclidean norm in that setting. And the process of doing so, we recursively were able to construct these polynomials, q and r. So let's be explicit in this example here. So what I want us to do is we're just gonna use the setting, we're gonna use the setting of, well, basically the rational number. So q would join x, like so. This would be a Euclidean domain by what we've seen before. We have the Euclidean algorithm, but the division algorithms course what we're focused on right here. And just to make life easier, I'm actually just gonna assume that my coefficients are actually just integers in this situation. Cause we will see by the end of this video, the factorizations of polynomials over the integers are actually the same thing as factorization of polynomials over the rational numbers. But for the moment be in this video, we'll assume these are rational polynomials cause they are. And so take the polynomial 6x squared minus 26x plus 12 and we're gonna divide it by the polynomial x minus four. And so the process that we developed in the proof was the following. I'm just gonna look at the leading terms for a moment, right? And I'm gonna ask myself, how many times does the leading term of the divisor divide into the leading term of the dividend in this situation? And in this situation, well, I mean, x is gonna go into x squared x many times and then the coefficient here is once that makes it a lot easier. So six divided by one is gonna be six. And so we can do that calculation, six squared, oh excuse me, six x squared over x is equal to six x like so. We then record that number on the top of our bar right here. That was the quantity we computed generally in our theorem there. And so what we did is we then took this number and we times the divisor by this partial quotient we have right here. Six x times x minus four is going to give you six x squared minus the 24x. So we can write it like this. So we have the six x squared minus 24x. That's just six x times x minus four. But then we took that quantity and we subtracted it from the polynomial. So we took, so again, this right here is just the six x times x minus four. We subtracted it from the polynomial above. So if I distribute that negative sign we end up with six, negative six x squared plus 24x. In this situation, because we chose this number perfectly, these leading terms are gonna cancel out. Six x squared minus six x squared gives you zero x squared, it's gone. Then we also have to consider negative 26x plus 24x that's gonna give us a negative two x and then we'll just bring down any other terms that are left. And so now the dividend has been reduced to a degree of, to a polynomial of strictly smaller degree. And this is then where the algorithm recurses itself. We then consider dividing this dividend by x minus four. The process repeats itself. How many times does x divide into negative two x for which we get negative two x over x? That's just gonna be negative two. We record that number up here. We then are gonna take that number negative two and times it by x minus four. That's gonna give us negative two x plus four but we're subtracting this, excuse me, plus eight, two times four. But we're just gonna subtract this from above. So if you subtract this, it becomes a positive two x minus eight like so. And then combining like terms, the leading terms cancel out again. You have a 12 minus eight, which leaves you a four. And this is now gonna give you the remainder here because notice four as a constant polynomial has a degree strictly smaller than x, which in this case it's a leading polynomial, its degree is one. So that means the division algorithm doesn't fact terminate in this situation. And so therefore we end up with the following. We have actually the formula we were looking for, f of x, which was six x squared minus 26x plus 12, it factors as the quotient q of x, which is six x minus two, times the original divisor x minus four plus the remainder four.  And like I said before, I was doing this over the ring q adjoined x, but as we went through this entire process, we never actually used any fractions. It really was done inside of z. So is z adjoined x? Is it a Euclidean domain? And the answer of course is no, it's not. Because as we also know about Euclidean domains, Euclidean domains are principal ideal domains and z adjoined x is not a principal ideal domain. One example to see of course is if you take two and x, this is an ideal. So the ideal generate two and x, this is an ideal in the ring z adjoined x, but there is no single element that generates that entire thing. So it's not a principal ideal domain, so it can't be a Euclidean domain. But nonetheless, we can do division in this setting. Why is that? Well, because honestly when you do polynomial division, you might have to exit perhaps to the rational numbers, maybe you have to divide. But maybe you can fix that, maybe not. It turns out that division of course is related to factorization. And factorization over the integers is very similar to factorization over the rationales. Of course I'm talking about the polynomial ring and not the rings z and q themselves. And this is what we're gonna explore later on in this lecture. But what I wanna do first before I switch the slide here is I also wanna remind the viewer about this notion of synthetic division. Synthetic division is a trick that is commonly used in a setting like math 1050, college algebra, to help us factor larger degree polynomials. And synthetic division works in the following manner. What you do is you take your dividend and you write down all of its coefficients in descending order. So we'd say six minus 26 plus 12. And we don't need to put the plus, we'll just put 12. Like so. And if there was any terms that were missing, you put in a zero for placeholder. So it is important that you have this x squared spot, this x spot and this constant spot over here. All of those are necessary. You're gonna separate that with the bar.  So you're dividing by x minus four and so you just record the four right here. The synthetic division only is applicable when your divisor has the form x minus something. You record that number here. Now the algorithm that we take in the place here is you're going to, whenever you see two numbers in a column, you add them together, which in this case is there's nothing down here. You're actually just adding a zero. That's how you initialize this. Six plus zero is just six. Then you're gonna take numbers on the bottom row and times it by this number right here. So four times six is 24, negative 20s. So then you add these together. Negative 26 plus 24 is negative two. You're gonna take negative two times four to give us a negative eight. And then you're gonna take 12 minus eight and that's gonna give you four. And this last number I'm gonna delineate it because it's the remainder. And then this right here gives us the quotient that we put back in the variables x. So we get six x minus two. And then we get that this is the quotient and then we have a remainder of four. So synthetic division can actually go through this process very, very quickly, a lot faster when your denominator is x minus a number C. Why does it even work though? I want you to, before I erase too much, right? I want you to see these numbers look strikingly similar, right? Notice what we had here. We ended up with, of course, the six right here, the 24, the negative two. Really I should write it more like this. We had this, whoops. Sorry about that, my four got deleted. We have a six right here, 24, a negative two, a negative eight and then a four, right? We're able to predict all these numbers. I forgot to mention the 12 as well. We could predict all these numbers and why does that work? So I'm gonna empty my tableau this time and think of the following. Okay, since the leading term here is just x, remember, this has to have the form x minus a constant. Since your first term is an x, how many times is it gonna go into the leading term? Well, it's gonna go on that, you're gonna reduce the power of x by one and then you're gonna have the exact same coefficient. So we just drop down the coefficient we started with. Then you're gonna take this six x right here, six times some power of x. You're gonna times this by that.  That'll cancel out with the leading terms here. But then you're going to end up with this number, which in our case is four.  This is where the 24 comes from. Notice you have a 24, but shouldn't it be negative, right? Negative four times positive six x here. Oh, remember, you're subtracting it, right? So yes, six x times x minus four does in fact give you six x squared minus 24 x. But since you're subtracting it from above, when you distribute that negative sign, you end up with these terms canceling out, but then this becomes a positive 24, which is what we saw right here. You're then gonna add these numbers together because you're combining like terms. Negative 26x plus 24x ends up with the negative 2x, which is when we add these together, you end up with the negative two. We just aren't writing the powers of x because it's okay, but we get that negative two. So then we repeat this process. How many times does x divide into negative 2x? And this x could be any power of x potentially. Well, because again, this is a monic divisor, the leading coefficients one, all that's gonna happen is that the power of x will reduce by one, but the coefficient is gonna carry up here. Again, you might have some power of x, but it'll just be smaller. The coefficient's gonna be the same. And so when you take negative two times x minus four, this will give you the positive two because we're subtracting it, it cancels out the leading terms. But what happens to the other term?  So we end up with this negative eight right here. Notice a negative eight is just four times negative two. You end up with negative eight like so. And then we have to add these together. You end up with a four. And this process will continue to repeat itself until you've exhausted everything. And so synthetic division really is just capturing all of the information from long division. And this can be very, very useful, of course, when you're trying to divide by a linear factor of the form x minus four. We were doing this over the rational numbers, the rational field, but I want you to be aware that this makes sense for any, any polynomial ring with field coefficients. Because we can divide the scalars, we can divide the coefficients, we can divide these polynomials using this division algorithm. And we can always get our polynomial is equal to the divisor times a quotient plus a remainder. And then synthetic division also applies in the setting where you have x minus c of some kind. The algorithm is not gonna change. Now the arithmetic could change. Don't get me wrong, right? What does it mean to add two numbers together? What does it mean to multiply two numbers together? That's a very curious thing, of course. And so that's what one has to investigate in this situation. I also want to mention that synthetic division, of course, makes sense in any ring because, well, I should say any polynomial ring where the coefficients are somewhat irrelevant because when it comes to synthetic division, you add and you multiply, which every ring can do that. So whenever you're dividing by x minus four, excuse me, x minus c, you can use synthetic division with when it comes to, of course, to long division, you might need to actually have fractions but again, in a field that's a non-issue. So why am I talking so much about division and particularly synthetic division? What's the dealio? Well, I want to remind us about a very important result that a student often sees in a class like College Algebra Math 1050. And I want to convince us that this result is actually a general theorem of polynomial rings where again, f is a field. And so this is known as the remainder theorem. If f is a field and little f is a polynomial in the polynomial ring f of joint x, then if f of x is divided by x minus c, then the remainder f of c is actually the evaluation of the polynomial f of x at the number c itself. And so let's look at this to see how that happens. So this polynomial f of x with regard to the divisor x minus c, the division algorithm applies because we do have this Euclidean domain here. And so therefore there exists polynomials, unique polynomials q of x and r of x such that f of x equals x minus c times q of x plus r of x here. Now as the divisor is x minus c, the remainder here has to either be zero or it has to have degrees smaller than the divisor x minus c but the divisor is a linear polynomial. So the only thing smaller in degree would be degree zero. That is it has to be a constant polynomial. The zero polynomial of course is also a constant polynomial. So because r of x is a constant polynomial, we really can just call it a number. It will just call it r and not think of it as a polynomial anymore. And then I want us to consider what happens when we evaluate this function at x equals c. So at f of c here, we end up with c minus c times q of c plus r. Since r is constant, it doesn't depend on the c there. Now of course c minus c is zero and regardless of what q of c turns out to be, zero times q of c is equal to zero.  And so this remainder theorem is a very critical important thing. f of c is just gonna equal r. And we did this over a polynomial ring with field coefficients but it does have to be field coefficients. Well, we just need to have a setting where this can happen, where there exists polynomials q of x and r of x such that this happens. Which that does happen over z of x as well. And this mostly has to do with the fact that it can be extended to its field of fractions like so. And so this remainder theorem has broad reaching scope. And so if you want to evaluate a polynomial, let's take the polynomial we saw a moment ago, right? Let's take f of x is equal to where did it go? It was 20, excuse me, 6x squared minus 26x plus 12. And so when we evaluate it at the number four, you're gonna end up with six times four squared minus 26 times four plus 12. Work through this thing here. We're gonna end up with four squared and of course it's 16. So we get six times 16. Over here we have 26 times four. If you don't know that up the top of your head, the nice thing about multiplication by four is you just double it twice, right? So if you double 26, you end up with 52 times two plus 12 right there. Here, what's gonna happen here is three times, three times 16 is 48. So you get two times 48. So then if we double that, we end up with 96. And then we're gonna subtract from that. We then have to take 52 times two, which is 104 plus 12, continuing on with this thing here. 96 take away 104. That is going to give us negative eight plus 12. That ends up with a positive four, like so, all right? Now that calculation wasn't too brutal, but I didn't even use a calculator, amazing, right? But you can see that with the exponents and such. This thing potentially get quite nasty if you have a much larger degree polynomial. But remember the synthetic division, okay? Six, negative 26, 12, you divide by four here. Well, by synthetic division, you bring down the six. Four times six is 24, minus 26 is negative two times eight, is negative eight plus 12 is four. And this is evidence of the remainder theorem, right? The evaluation is equal to the remainder of the polynomial divide by x minus four. For which when you look at synthetic division, I think most of us would agree that actually the synthetic division, you never have to deal with exponents whatsoever. It's just add, multiply, add, multiply, add, multiply, over and over and over and over again, right? And even the products never really got that big in comparison, right? You know, we had like a 96 over here and a 104 over here. But over here, the biggest number we ever had was negative 26, which was one of the coefficients. The remainder theorem does allow for us to much more efficiently compute evaluations of polynomials using division. And this is just the first of many applications we're gonna see of the remainder theorem. The factor theorem being a big one, which we'll talk about in the next video.


What is up everybody this is Chris from the Rewired Soul where we talk about the problem but focus on the solution and if you're new to my channel, my channel is all about mental health and what I like to do is pull different topics from the YouTube community to try to teach you how to improve your mental and emotional well-being. So at the end of that stuff make sure you subscribe and ring that notification bell. So yeah I want to send a huge thank you to everybody who joined me for the Shane Dawson conspiracy theory part one viewing party that we had over on my channel. For most of the live stream we had between like 160 to 200 people very cool very very cool I love all of you and like Tristan was in it too so make sure you watch the replay because my beautiful girlfriend Tristan was in there alright but yeah anyways I asked you guys on Twitter what topics what mental health topics you want to be to talk about for you know recaps of this first conspiracy video and a lot of you mentioned the one about the cartoons and you know like depression medications all that stuff and yeah I'm going to do that tomorrow and there's a lot of psychology and also some philosophy that goes along with that but tonight I wanted to focus on the marketing techniques alright so those of you who don't know me a lot of you know me but you don't know me know me you know what I'm saying but anyways my background is in sales and marketing and one of the things is that I've always been fascinated by marketing and sales and everything just because I've been fascinated by psychology right so if any of you watched my video I did about like this guy is crazier than David Dobrik and it was about the psychologist who did like the original like clickbait right he was the first guy to like blend products with celebrities and he was a psychologist who left psychology to go work at an ad agency alright but anyways what Shane Dawson talks about in this it's not really it's not really a conspiracy it's just psychology it's psychological techniques that advertisers use marketers use retailers use okay so he talks about like children you know in the grocery store they put you know sugary things on the lower shelves because they're there for kids but something I mentioned on the live stream is this if you notice in grocery stores as well they put milk and eggs in the back they're always in the back of the store don't believe me check next time and the reason behind this is because those are the most commonly bought items and they want you to have to walk past everything else in order to get there right so that way you're more likely to buy other things alright so a lot of these things that marketers are doing is to get you to buy now this goes way deeper than that way way way deeper than that and I'm glad that Shane brought this up in a video to kind of get your wheels turning alright like here's the thing there are so many psychological techniques that are using you to buy things and it's important to be mindful of those so you spend your money in the right place and you're not doing the wrong things and you know like because a lot of us are chasing that idea or if I can buy this and buy that then I'll be happy right and this goes back to the psychology or not in psychology but the philosophy from Buddhism called the hungry ghost right we as people we as people are like these hungry ghosts we keep trying to get more more more more more more more and we're never fulfilled alright so there's other things that happen and it's actually with the foods that you eat so there's a book that was written by an investigative journalist called sugar salts and fats alright and this dude did research and of the food industry the different food producers the people who make foods they have scientists there that scientists there who designed food to make you crave more of it through sugar salts and fats okay so you know how I talk about your brain and how we're wired to repeat certain actions okay this is something called the habit loop so they will find ways to make food trigger different parts of your neurotransmitters in your brain to make you crave that food even more alright so this is something that happens but when we look at advertising as a whole something that's in that book lost connections congratulations to all the winners who won over on Instagram like one of my favorite parts is when they talk about the advertising industry and one of my favorite quotes from that book is something along the lines of the worst advertisement ever would be one that told you that you're perfect just the way that you are right because why would they do that how are they supposed to buy get you to buy something if you feel great about yourself if there was an advertisement that said you are perfect the way you are everybody loves you you don't need anything right how they're supposed to sell any product so they're always trying to push something make you look better feel better right oh if you buy this you're gonna get that guy you're gonna get that girl or if you get this and your friends are gonna appreciate you and all that right but these are techniques used all over the place and the answer to all these things is mindfulness that's right ladies and gentlemen mindfulness once again checking in with yourself and saying why do I want to buy this thing why do I want that car why do I want this furniture right like I know so many people like right now I know a lot of people are struggling with money but like take a look around your house like pause this video real quick and take a look around your house and see how many things that you bought to impress other people right maybe you got this couch right maybe you got this dining room table or maybe you got you know these fancy you know little statues around your house and they're not for you but you want to impress people when they came over okay so there's something that I actually learned from the philosophy channel wisecrack which is called conspicuous consumption okay and this is a philosophy about how we buy things to impress other people okay I think about that think about why you bought the type of car you have is that a way for you to flex on other people to show people your status because we have creatures that are trying to show social status they actually did some really interesting experiments not even experiments just observing gorillas out in the wild they do the same thing it's pretty crazy how they do the gorillas don't buy cars or anything but whatever but like this stuff's happening all the time and this is why like us youtubers a lot of us kind of laugh when you get upset about like clickbait and things like that because all youtubers are doing it and I was actually cracking up and tweeted out attacking Liam Lush because I respect his game when he said this so also if you've been a fan of the channel for a while you probably notice I did title the video these youtubers are pretending they're dying version 2 or whatever and yet for two reasons a because they are pretending they're dying in a different capacity than our boys over at Extreme Games aren't too because that title performed so well the last time I uploaded it I'd be an idiot not try it again that's all that's right like Leon explain why he titled the video the way he did like that's one of the reasons I title my videos the way I do I know they're gonna get clicks I know that you're gonna check them out and why do I want them to want you to check them out because I want to teach you how to improve your mental and emotional well-being right so be mindful of these things somebody called me out in the Facebook group the other day and said Chris which are next mindfulness thing that's based on youtubers and I'm thinking about showing you a practice that you can use mindfulness when you're browsing through YouTube thumbnails and titles things like that so make sure that you stay tuned now the last thing I want to talk about when it comes to marketing advertising buying things trying to fulfill ourselves with external things is extrinsic values first intrinsic values all right so extrinsic values are people who value themselves based on items right based on things based on things they have and it might not even be items that you purchase but it might be a person right you value yourself based on you know the person that you're with or some people value themselves based on the position they have a job all right and these are more likely to make you depressed as well as anxious why because those are things that are really outside of your control people who have intrinsic values are far happier less symptoms of depression less symptoms of anxiety okay so when you work on finding happiness within without all the other things then you'll start to be happy now there's something called minimalism you might know some people who do it I don't personally do it maybe eventually someday but this actually comes from more like kind of Buddhist philosophy there's actually a channel that my friend Kay from the channel by polar pug introduced me to I forgot the name of it but anyways I had a really cool short documentary about minimalism but it's kind of living in this way of learning how to not need all these fancy things and it actually comes from like you when you see like Buddhist monks who don't have anything it's because the part of their practice is learning how to be satisfied without all the fancy stuff right but anyways I do want to give a shout out to my buddy Carly steel she just made a video that I'm gonna link down below but she just opened up and got really vulnerable and she actually touched on this and part of being a youtuber she has over a million subscribers and like I always tell you like I'm trying to learn from other people who are you know bigger youtubers like what what's making them happy what's making them sad what's you know what's going on right so Carly opened up and she said this and we're sad too we all especially with YouTube I know so many youtubers that feel alone and it's just crazy because we have so many people that love us and we still feel alone and that's because this world is just so superficial and so flooded with with social media what you want to see it like I literally go on Instagram and within five minutes I want to shut it off because I'm like this girl has the perfect body she has the perfect hair she has the perfect face she has the perfect life she's the perfect boyfriend she lives in a nice place she has the perfect car but I don't know what she's going through and nobody does and nobody knows her struggles and it's just really messed up it's so messed up if you really think about it so messed up so yeah I'm super proud of Carly for this like kind of self-awareness that she's getting and Tristan and I were watching and I'm like man I wish I wish some other youtubers made videos like this like getting that self-awareness and realizing this is such a young age because Carly's like a little sister to me she's like 20 years old but she's realizing it but now Carly needs to check in with herself and be accountable for this but anyways like she's working on being a better influencer to her audience and all that and I'm actually going to LA next week to film some collabs with people and Carly is gonna be in LA too so her and I are gonna be doing some collabs as well but anyways go check that out because this is what we need to see we need to look at other people like something I always try to teach you guys is like if things or fame or money or whatever could make you happy we would never we would never have any depressed celebrities you know what I mean I was focusing my camera whatever it keeps like walking in on Shane but we'll let it slide all right but anyways if you liked this video please give it a thumbs up if you're new make sure you subscribe and ring that notification bell because I make a ton of videos and I got some more Shane Dawson videos coming up very soon but anyways thank you so much to all of the people supporting the channel around patreon you're all amazing and if you like some exclusive content become a patron to my clicker topper right there alright thanks again for watching I'll see you next time


Hello, and welcome back to the craft box. My name is Brenton today. We're in episode a hundred and seventy-five of the wizard 101 death walk through the last time if you haven't checked it out already We made our way into mooncliffs. We finished off the silent market So if you haven't checked that out already go do that today, we are entering a tunnel So that's fun This is the Basically the first area first actual area that is like filled with mobs of the um World so yes, someone found my tunnel and collapsed it The rat returns to the mouse trap Mouse hall you mean What never mind that kill him kill them both Okay, um don't need you It should be fine hopefully let's go So yeah, not too hard this is not too hard life and myth worried about earthquake, but I Mean We're gonna go anyway. I don't really care. Say it's quick. Oh well, and if they don't well, that's better for us Starting off with elephant of life Well Doesn't do anything at all. Oh a blade. Hello some of these news don't actually know how to Earthquake from memory, so yeah, it's always good. That's always nice But I don't know whether it's these ones or not. Okay crow.  That is fun We will spur blade And then I think we might hurt If we don't get another blade that is Still has an earthquake like what the hell But what's the pips though if the earthquakes just before I had I'm gonna be kind of salty. Oh Pup can serve. Thanks Didn't need it, but thanks 4,000 we boost on both. So yeah, let's go for this since we haven't been hit We don't need help. So we'll just go for this.  Okay, stun. That's fine. That's fine. We can live with the stun. Just don't throw Thanks This is gonna do a bit of damage The overtime's gonna do even more, but you know whatever Stunned we won't hit we'll hit next which is unfortunate but understandable Okay, and there we go Let's go for a dear night because I wanted a night. We haven't done it enough I Mean I spent so long trying to get the spell and then we just don't use it So, you know, you just got to use it somehow life love using goat monk and Chrysalis I've learned Yeah, there's a lot It's a cool spell, but you know Doesn't do much But maybe they just have no damage and no p.s. Which surprised me vengeance. Hello Let's go no fuzzer, which is good and Dear night dear connect No crit that's unfortunate, but triple blade plus boost Should be good. Yep that did well. That's good.  I'm really keen to see how much this overtime's gonna do 1000 okay, that was good. That was good. Mm-hmm Dear night, I pee what can I say? Fantastic Why mouse plers? Let us Hit on out and talk to divum Or dive in I don't even know how to pronounce that and I'm not gonna try anymore. I'll just call him to them Yes, definitely. Good idea brain Where is it down very well before your peace sure is let's collect some of that health thank you and Hello, let us use the tunnel which brought me here in order to avoid the yellow jacket centuries With the tunnel closed to us the apidae village and the fortified apiary stand between us and the last wood Once this region was well traveled with burrowers and bees We do not always see eye-to-eye, but we traded goods and knowledge Then the shadow queen drew all the arachna into her web turning them into living weapons and filling their hearts with hate We have to sneak through the bee territories Luckily the bees can be tricked if we can get some black light powder the banded hornets often have black light powders stuck to their bristles Defeat some and collect several portions of powder Well, I love the defeating collect quests Okay, I'll be back in just a bit once I've defeated a whole bunch of these guys Okay, I am back. I'll coat us with the black light powder be eyes work differently than ours So they will see us as their own kind Follow me up the road when we get to the yellow jacket sentry just act naturally, okay Finished off that wasn't too bad met up with a couple people who are on the same quest and We did a battle all together and that took forever, but like they're bad So I mean I understand that you there. What do you think you're doing speak to him? But remember to act naturally Just act natural boys. Yes drone. I'm speaking to you You are clearly undertasked if you have time to frolic with the hornets The hornets are all so delinquent on their nectar deliveries.  Hurry up Savage okay, um this I think is boss Yeah, probably Or maybe it's mob. Who knows This place is very Like you would think it would be a boss, but then it's actually a mob fight and it's like what okay So yeah, you never really know what you're getting yourself into But you just kind of hope you know what you're getting yourself into But I mean you could say that there's just life in general Nice dialogue there boys doesn't sound friendly. I thought that buzz sounded really friendly But okay if you say so, let's do this storm. So yeah, again just a mob fight Okay, just put it behind a sigil that makes sense doesn't it nope, but anyway, we're gonna do it So yeah the The battle that we just finished the defeating collect wasn't that bad. I think I got one Every single time so it was really really really good. The drop rates were fantastic, and I'm like whoa That's right. We're not in there sticker anymore Whoa, that's right. We're not in Safari anymore. Yeah, so it was good Pretty much a hundred percent. I think well, yeah But yeah Not too bad not too hard. They have like not much else. They're also a myth. So We boost death boost on them So even better get that damage and do good and all that stuff. So yeah thumbs up from me Or else do we have we will enchant this blade? We will enchant day and night and We will blade We will probably don't because I'll thank you Um We'll probably blade once more and then hit I'm thinking with a deonite just because I'm really loving deonite at the moment Unless they do lots of damage, but I don't think they will In this with like three pins. Nope. Not gonna do much Didn't even crit Good must have been like no pips 85 congrats. Do you want a medal? Nope because you don't deserve one That's right In fact, we will do this player actually doesn't matter. We're gonna do this one just to save pips because we can why not Maybe a bad choice. No, that's fine. They don't have enough pips to Destroy blades unless they do in people which is a possibility And I would be very salty if they were people But I'm yeah, exactly highly doubting that they would do that Deonite yes Haven't used denied enough haven't it given haven't it given it haven't given it enough love So we're gonna do Does more in the end anyway, so if we don't kill we've also got the overtime so it's fine That's a lot that's nice 302 oh fantastic Bye It's got like what to health probably Okay, bye What's us, okay, that's fine I thought that would be fortified, but it's fine. How much after they have like 180 Okay, well they did anyway. Bye Yeah, we did it. Good job. Good job. Fantastic Yay Definitely wasn't friendly Okay, there is the nectar cask not too difficult at all What's next probably have sir I Think we go into the place Next do we break the wall down? I think he does. I think he lets us in basically the whole idea is to try and Progress all the way through to the last wood There's like a wall there. We're at this one here. I think there's like one in between there as well So, yeah, lots of things that we have to like go through in order to get through the gate Well, that was fast Good job drone now get back to work Why are you still here you want to get into bubbler town not likely the gate is stuck I've reported it many times, but no one repairs it You get along well with the bandit hornets. They often have leftover saplower oil from the seeds they eat If you ask the bandit hornets for it I'm sure they'll give some saplower oil up that might fix the hinges We're going to have to fight the bandit hornets again. Won't we yes, we will Anyway, I'll be back in just a bit once I've defeated another lot of these guys. Okay. I am back 100% click drope fantastic You got the saplower oil done drone and stick the gate hinges with the saplower oil You go into the night watch tower and throw the lever to open the gate Okay, that is good nearly a new level 92 Not too far away about a hundred thousand, which is nice It should be getting there very soon probably in about two quests Or two important quests No, I'm not a bee that's unfortunate for you good good eyesight though, I'll give you props for that one Oh, yeah, we also got Avenging fossil if you haven't checked that video out go and do that Yeah, I posted that yesterday or the day before Yesterday I think I don't know I don't actually know when this is going up I'm trying to like record a whole bunch of videos in advance. So sorry about if I don't exactly know when things are coming up but yeah I'm going away soon and I need to get some videos pre-recorded so I can have lots of videos for When I'm away, so you guys can enjoy my videos. Well, I am absent from making them Yes But yeah, he should not be too bad most bosses and chrysalis are I'm not gonna say easy, but like they're As far as I've gotten on my life. They're fairly just Normal bosses until you get later on and you get a whole bunch of cheating bosses, but Um, yeah, basically, I really love the story and chrysalis is the one thing that I really love. Um The story is fantastic Uh How are we going to get off that I have cleanse Um, let's just play I've got cleanse. It's fine I'm really worried that this fall over here my earthquake, but As I say, if you're worried that he's gone earthquake, he probably would Ooh, that shield's nasty. Dear knight, where you at fam? Um, I'm gonna have to deonite. I think Oh, uh We will discard you and we will use This we'll just see if we get oh we got cleanse that is tempting That's a very tempting Not what I wanted, but I might use it maybe I mean why not We'll see if I get a We might that would be good So, yeah, be careful. He um death shields. He probably also does the fire ice and storm one as well. So Be careful. Just a normal balance bosses though. So, you know, just Deal with that. I think we've got infall anyway, so we might put up an infall before we hit Uh, just to make sure we will faint again double faint. Hopefully a triple faint Just to get as much damage. Um through that Cheeky wee death shield that he's got up. Um, fizzle unlucky unlucky Yes, you do this. Good job. Waste all your pips. Don't get six pips because we all know what happens when you've got six pips Um, the big old ecu whoo The spell takes forever It truly does Okay, good job. You're done. Finally. Thank goodness. Um, luckily we're going first, which is always handy dandy Um draw. There we go. There is another faint. We will triple faint. Sounds good Um, still looking for a d and i. We also need some other blades We've got two we probably want We've got at least one. We've got one more in our hand right now and hopefully we get a couple more I want to enchant it. Um, get a blade. Definitely. Plus 50 is fantastic um, yeah Speaking of there is a Plus 50. I'm pretty sure we didn't have one of those. No, we didn't. Sweet. Do spirit then plus 50 Then we will either cleanse or infall Maybe both Cleanse and infall infall then cleanse probably cleanse and infall then deonite And then fill up with a dr. Von if we have to Um, but deonite should do quite a lot Oh, let's just put up all the blades. Why not? Let's have fun. Let's go ham I mean we can have a bit of fun. It's a game. We can have fun once in a while Don't always have to be super serious Being efficient and hitting when you're just when you can, you know Get up a lot of blades and then hit just for fun Um, okay. There's that that's nice. Um I want to save that for deonite. So we'll do this then we'll want it and then we'll hopefully have a infall and then a deonite And hopefully then He should be dead or close to then we can fill up with the dr. Von if we must Thank you for coming deonite We will do you So we've got two infalls and probably a Um Definitely an enchant to come so hopefully we can get one of the two infalls. I think I still got two I don't think I took them out Hopefully I didn't because that would be bad 900 that did a bit that did a bit of damage You better not earthquake on a few earthquake. Whoo Someone about to be slapped Okay, maybe I did take the um things out Well, we'll um We'll deonite Okay, we're not gonna deonite um We're just gonna chill for another round if we get infall I'll do infall Um, because he may not earthquake. You might do something generously. Nope.  Oh my gosh, that did so much. Whoa, we're op Do we sort of I don't think we have dillium I don't think we do Oh, we did I was so worried, but we had we had him anyway. So we had like 126 damage I can't wait until we get that much damage or something along those lines That would be so good. We'd do like so much damage Like I can't wait until we've done dark more. I don't actually know how much um How much extra damage I'd get but I'm also looking at getting a bit of pit because zena is bad Um, I think I said that in the last episode anyway, but zena's bad and we need a new pit What took you so long drone at any rate? You got the gate open. Yeah, I did Drone go into appaday village and find first wing zam. He'll find work for you We may as well find this zam if only to keep up the disguise and get a lay of the land Okay, let us go and find zam and then I think we'll end off the episode there just because we'll start this but tomorrow or next time and you see you're in the middle of a crisis File borrower agents attack the village and set the house as a blaze the fire and smoke are too intense for us to put out Hey, you aren't cat with anything. Do I have a job for you? Go to the casary cave and convince one of the whirlwind elementals to help us Extinguish the burning houses. This may be a good way to earn their trust so we can learn more about the burrowers in the region Um, okay, uh, we're really close to leveling up so we will 100 definitely level up next time to level 92 Um, what is the we got a deck the other day that's like good 93 so we need a couple more um One more level after tomorrow, but um next time we will head on into this cave um Probably do a lot of this area will definitely Um put out all of the fires around here. I think we have to collect the pollen and the What are the props for? What are they from? I don't know. I think we have to click those as well with the pollen. Um, you'll probably have to defeat a whole bunch of these and eventually Oh gosh, hello We will get over to here and we'll defeat some of those life things and then we'll get through this gate Probably in two episodes time and that is through to The next area where the royal guard are so yeah, thank you for watching Remember to leave it. I can subscribe and if you're very subscribed press the bell So you know exactly when I post another video and remember craft outside the box


What's up everybody, it's Jason here for JaspysCaseBrace.com. 2022, Bowman Chrome Baseball Hobby Edition, 12 box case pick picket teams number 11 just sold out. Remember, all cards shipped and let's rip. So, last brick of the night too, guys. Gotta sell out a team round to get this done, which we did. This is everybody's name there. So I will post up case number 12, later tonight when I'm done with this. I'm gonna rip the first six all together and then we'll go to the next six. Appreciate the fill folks. Good rally here towards the end. Got the HTA done a little earlier today and then the hobby right here at the end. I love Pizzle to have the biggest brick of his life because he has the raise and I feel like that could be one of those teams. I said I am not seeing any like better rookies, autos for myself since like better than like Jurellis, honestly. It's like I hit so much Jurellis. Now, remember, they all have the same amount of numbered cards. It's just, where are they, you know? Base, I can see that happening more, but numbered? Yeah, see they're out there, right? I just haven't seen any one of those. So, I mean, at least here with us so far with me. I don't know, did Joe Henney any bigger rookie autographs when he was breaking on Wednesday night? I wasn't really watching, so. I know he had a Super Fracture and stuff like that, but the only thing I've been able to hit is a red base of O'Neill Cruz and then obviously a couple of those Jackson Jurellis, Gold and all that stuff. So, no Baccaro and stuff, but I have not hit any big rookies at all. So, I'm trying to just kind of speak it into existence honestly. I want it to happen. Yeah, you didn't get back teams. It's just obviously I personally haven't pulled any and haven't seen much of those guys. And I pull Wander colors. I think I'll pull Torboson colors, just not autographs. Mayer, I don't know if I've pulled any of him, but obviously I feel like we see more first than anything, so. But I guess Tampa Bay also has firsts. Guys, here we go. I've got Dylan Carlson to start us off. Walla Won Bin Cho. It's the first auto. We got Yeri. Now we got a Willie Finass. And for the Orioles, Greg Cullen to 75. For the Dodgers, Trey Turner. First autos, Daniel McLevaney. First for the Red Sox, going to Joe Pizzle. And Francisco Lindore for the Mets. Going to Sean Matic. Christian Hernandez. And for the Nationals, Evan Lee. And another show to 50. Averson Artega for the Giants. Share with that one. And Cade Marlowe to 499. Yerlin, Refractor. And Samuel Zavala to 250 purple. For the Padres, that is going to David. And we got a Roderick Arias for the Yankees. Now it's just a one per box shimmer, but it's still a very nice one though. Third box, or fourth box, I should say. Curtis Mead for TV. And Daelyn decided not to sign his base autos. That's a redemption there. For the Nationals, going to Sean Matic. Juan Soto, Edward Carrera for the Marlins. That's a blue. All right, Westcalf, Michael Burroughs. All right, we got Lonnie White to 150. And we got a Willie Vazquez for TV, Green Shimmer. Our next one here. Jose Ramos, Willie Finas to 499 for the Metz. Peaker Armstrong, Refractor. And a Tyler Collins to 25. For the Braves, Bill Norton with that one. Roberto Campos. We got Willie Borgala, or Willem Borgala for the Phillies. Canvao with that one. And nice Jackson Mero for the Padres. David with that. Dylan Carlson to 499. Willie Vazquez, that looks like a little orange, gold. Number to 75. And Antonio Pinero. Man, a little bit of a teaser. That is for the Brewers, David to 250. Carson Williams. Oh, what's up, John? No problem, man. Um, yeah, just remember though, for those Hipporates, we never actually pull all the full spots up. We always pretty much do like 12 full spots plus two fillers. So what happens is that if you notice that there's nine back in stock, that's just because I canceled the second filler. So now if you'll look on the website, the filler says last one. And then the nine spots need to sell, basically. Kind of like a little bit of a mind trick. I feel like people will buy in more often when they see it at little spots left. And then we cancel a filler, and then it just goes by a lot faster. Because we can't really predict what's gonna go faster. Sometimes the straight up spots sell faster, sometimes the fillers sell faster, so kind of like to have it half and half. So that's what happened, basically. So just remember to always look at the filler next to it. So if it says last one, then those are officially the last one plus whatever's left on the website. If it showed like two left and it didn't say last one on the filler, then most likely we'd have to do multiple. I don't have worries, man. That'll most likely go tomorrow. So basically all of our hip parades, baseball and football are kind of in the same boat where we just need to sell one filler in the straight up spots. The basketball one, we still need to sell six plus two fillers. So Chris was covering Joe tomorrow. What he would have to do is if those six spots sell overnight before he gets on air, if Nick had it already, he'll have to just cancel that second filler and then put the nine spots back in. If we didn't have to do fillers, we would just put all the spots out there. But sometimes fillers are needed. You guys are river bowl gamblers sometimes. People would rather spend a third of the price in the 30s rather than a hundred plus and win a spot there. A fraction. Ribbon the last, I would love to, man. I've hit like seven different reds already. Definitely do for one of those. It's too early for that, man. We won't talk about depth, how about the 76ers? They have all their main players out and they're still winning, or at least winning some games. Well, it depends, Rex.  But when you have like Embi, Harden, Maxi, like all of your main starters out, like we're not just talking one starter, two starters, we're talking like multi. Like it's a lot. Yeah, that's right, go thunder, aft them. Aft them, Pizzles. No, I actually didn't even watch the game. They lost to the Rockets today. That's one thing I do hate about being in LA is that they, I mean, just in general, there's really not that much thunder coverage right now. They're at that time where they're obviously just get the minimum national coverage. But I think SGA probably had a baller night tonight. Let's take a look. They lost by 13, but SGA again, 32 points. Giddy 18, Wiggins off the bench, 15. Oh man, we have a lot of injuries. Mo Scala didn't play. Oh well. I mean, he's their best player by far.  He's still averaging 31 points a game, five rebounds, six assists, and shooting almost 36% from the three. I mean, besides the Memphis game, he was on a tear at 37, 37, 42, 30, 30, 32 and 32. That's all right though. The game, the season is still pretty early. It's still young in the season anyways. Plus, I don't expect the Thunder to be a very big playoff team anyways, even if they might not even make it again. But we'll see. Sal Firlick. I know the fact that the Lakers won first of all, and then they won like 140-something or 130-something was amazing. Emmanuel Valdes, for the Astros, Josuar Garcia, and we have a John Rose to 250 for the Orioles, Aaron Billingsley. All right, we got Byron Buxton, Eli Delacruz, we got Jason Moribel, Drew Baker for TV, Refractor to 4.99, and Simon Musialti, Wander Franco-Rookie. We have a Eloi Jimenez-Gold, and Alexander Ovales. That is a Speckle-Gold to 50 for Tampa Bay. It's going to Joe Pizzo. It's a nice-looking card. First, Michael Hernandez. And again, I only hit Drew Ellis. I swear to God. He's like the only rookie I hit in every case. Man, this guy must have signed way more Golds and way more colors than everybody else. Or we just got the shipment of all the Diamondback Autos. That's Paul Kovac, sir. I swear, dude, I always hit him. Like, that's the only dude I hit rookie-wise. Ooh, ooh, wow, no way. Roderick Arias, that is a red shimmer to five. That's probably a pretty big card. Three out of 10, though. Actually, probably not to five, actually, to 10. Well, I thought that would be out of five. Maybe the shimmers are actually out of 10 now? Oh, who cares, though? Very nice. Joe Speckle. We got Andy Thomas. We got Jordan Walker. I'm Paul Reynolds. Thanks for buying in, buddy. Marcello Mayor. That's a nice purple there. 250 to Pizzle and the Red Sox. And for the Dodgers, Gavin Stone. It's a 2.99 Speckle. Brandon Marsh, the Fractor. Alrighty, guys. Two more boxes left. Here we go. Jose Ramos to 150. And we got Ian Lewis. Whoa, this was signed right over the hook. We signed right next to this crotch. Come on, man. Jordan Walker. And a Bowman Ascension, Khalil Watson. We got a Ricardo Carrera and Borosa for the D-backs. Cal Raleigh, Blaze Jordan. Andre Mendez. We got George Kirby for the Mariners. Wow, another one of this dude. Jesus. Getting sick and tired of Jorellus already. Nice though for you, Paul. Sorry, he's the only rookie auto I hit. I mean, is Jorellus like good, Pizzle, or no? Like, should I just? Am I, do I have a valid reason to be like that? I mean, he is in the league, I'm not, but. Alrighty, folks. Well, there you go, guys. That was the break. Ended up still being pretty solid, but looking for a little bit more. But here you go. Quick little recap here. Some base, Speco Auto, base, base, Refractor, Green, Blue, Purple, Redemption, Finas. Orange to 25 of Tyler Collins was pretty nice. And then here towards the end, regular shimmer, Ascension, red shimmer. I thought this was out of five, but I can start at 10. Jorellus gold, and then a gold Alexander Duvalis. So, there you go, folks. That was the break. Appreciate it, guys. This was Pikachu number 11. Number 12 should be in the store soon. Jaspy'scasebreak.com.