Hello guys, it's Crypto Grounds here welcome back to another idle game tutorial video today We're gonna be doing OCD buy so last video we did the buy mode Button where we can switch between one five or not one five ten and a hundred and max So today we're gonna do it so around up so for 83 around up to 85 Okay, this shouldn't be too difficult So we need to hop into our upgrades manager, which is located in our earth game object Open that right up Also, if you're new here, make sure you leave a like subscribe to my channel and turn on those notifications So you can know when I publish videos almost every day and Comment your suggestions below if I have a I have a little plan here. Let me pull that up right here So what I'm doing here. I have tons of videos. I'm going to make so I'm not gonna This is just kind of what I have so far. It's like I have tons of see-tart crash course videos to do obviously because there's a lot to learn Um clicker heroes. Yeah, I'm gonna do some more clicker heroes I'm gonna do some other series like I'm gonna continue the adventure capitalist series Since I was my 500 subscriber special I feel like I should just continue that on and just keep building up and Yeah, that should be fun. Let's hop right into it. So make sure you subscribe to my channel so I can do more of those videos and It means a lot to me. You can help me grow. All right. So here we have our Our by mode right here, right? So what we're gonna do is that we're just gonna round this up, okay? And now if we can buy less then we need to just Like if we can only buy one then we're just gonna make it so only buys one or we can just make it so it just Round automatically rounds up and people love this. Okay? so we're gonna have a button here and That method is gonna be public toggle Togo OCD Okay, and this is a pretty self-explanatory. We need to open up our player data script And we need to add a so this can be considered a setting I guess so this will be public Bull and this will be OCD by OCD by Okay, we're gonna set this to false. So automatically you will not do that Okay, this is an our player data class inside the full reset method. We're setting it to false So in here, we're just gonna We're just gonna toggle that so we're gonna do game data dot OCD by is equal to itself But the opposite which is with an explanation mark just like that. So now I'll toggle between true and false and We can also manage our text here too. So let's add that real quick Okay, so we have our by mode text so we're just gonna copy and paste this and we're gonna replace it with OCD text or something like that OCD text Okay, and then in here we're just gonna Set the text equal to whatever by mode is and Let's just say what if it's true. We want OCD on And if it's not then we want OCD off and to simplify this what we can actually do is since this is the same thing We can just grab this right here and let's put the dollar sign so we can put variables in here And then in here we need print or parentheses So we'll copy this Bring this in here and replace it with just on and off Looks like that Okay, so now if it's true it'll display as on if it's false display as false Okay Now we want to load this at the beginning of the script too because it is a variable that we are saving So we need to load that text in So we should put that in our start method Cool. All right. So now what we're gonna do Is get this rounding going, okay So this is by max obviously, so we're not gonna worry about anything here but n equals five is We're just gonna change things up. Okay, so we're gonna grab an if statements if if game.data.ocd by is true Then we're gonna set n equal to Okay, so we need to let's write this down in a note document real quick. Okay So let's say our level is 83. We want to round it to 85 So we need to set n equal to two right if it's 80 And we want to get to 85 then we need to set n equal to five. Okay, so how do we do this? So we set whatever our Our level is right now Okay, so how we're gonna calculate this is we're using mod right here. Okay, so if we do 83 mod five, we get three. Okay We have three. Okay Now if we subtract that with 83 we get 80 So then all I gotta do is plus five. Okay. Okay. So now we know our steps. It looks like this It looks like this 83 or whatever our current level is minus Our current level Mod whatever the number we want to do. So for example five We add that whatever our level is again. And there we go OCD in a nutshell. So we put this in here. We need to replace some of our things, right? And obviously let's have an else And this will be n equals five. We can clean this up in a second. Okay, so Also, let's see Okay, so let's say we need to get our current level which is k Yep, so that's k k. Okay, so we do k minus k mod five plus five. All right Cool pretty simple equation. Let's see. Can we yep, we convert this to a question mark operator So now if it's true, it will be k minus k mod five plus five Well, if it's false, it'll be five. Okay, we're gonna do the exact same thing for the rest So this will be 10 plus 10 And this one also be 10 And let's just copy this here. I don't know zero and this will be 100 instead Cool. So now it'll just round up Okay, only if it can afford it So let's try this out. Oh, this is the wrong game I just was in the wrong game. How did I get that open? Um, okay Uh sink sink. I think it did Yep, it did. Okay so now We need to talk we need a button for by max because we don't have that yet So let's go to our Main screen wherever that is Oh, this is the upgrade screen. Yeah in our upgrade screen. We're gonna add our ocd button So next to the upgrade by mode, we're gonna call this the ocd button or ocd mode Whatever you'd like And we can just clean this up a bit Okay, and then we're gonna do ocd on Okay, and in our upgrade upgrades manager, we need to drag our ocd text Into the inspector and save it And we need to assign a method to this which is upgrade manager dot toggle ocd make sure you have the upgrades manager dragged in here Alrighty if you enjoyed this video so far make sure you leave a like subscribe by channel new and turn on those notifications Okay, yeah, we've been gone for five days Uh, that's a long time Okay, I want to turn off this letter notation because I don't like it Ah, I still need to fix that Let's do that real quick. Um So where is this happening? I think this is happening in our main script. Where is that right here? Okay And let's just do coins Right here. Okay. I see why is it f2? I don't remember or why is it f0? I don't remember changing it to that Weird I usually don't do that Um, oh, yeah, we got a lot of f0s. So let's just do Let's just replace all and in writer you do shift control shift f and you can see this where you can find everything Okay, so let's do f0 Um, I think this is supposed to be f2. No, it looks reasonable Okay. Well, that should fix automatically every time you load it. So now let's go to our upgrades and turn on ocd Okay, so on five our upgrade is 249. So when we can afford it, which we can't This should be able to round up, right? So let's do it to this one. So this one is uh, it costs 69 or 68. Okay um, looks like the other level texts are off. So I need to fix that too, but Oh, our level texts aren't incorrect. Yeah, aren't correct either. What's going on? Something is going on with our user interface And I guess this is something I did a long time ago and I just never noticed So that's kind of a bad thing because I'm letting people down Um, okay, let's see. Oh Click upgrade cost. Oh, this is an array Okay, so our these are That's production. Okay. So production i is equal to this text. Why is that? Okay, so it's level I see here. Okay So this is the wrong one. This should be production upgrade levels. Okay. I don't know how I didn't notice that I think that's all that was incorrect, right? Yeah, that's it. Okay. So if you ever see something like that and you see a text using the wrong thing First things first, you need to just trial and error make sure you replace variables. Check to see if it's the right one And that's my only advice because I get a lot of questions saying oh the coins text shows the cost or something like that So just make sure you're signing the wrong text or the correct text or string or whatever And the right variables because it will mix up Okay, so everything seems to be working now. Let's go to upgrades. Cool. Everything looks good Okay, so now I can buy max 173 so we can do a lot. So let's see now five. So this is all 17. So this should round up to 20 Uh, it's 22 Why is that? Okay, well, that's not good. This isn't working. What about 10? It's still buying 10. Okay. Well, that's an issue It looks like our Is our uh, I guess the only way to see this is to know if if it's even toggling Yeah, it is so it's on. Okay. So now upgrade manager. What's the issue here? So if it's true Oh, I see this is only for our click upgrade by max. So if we do this to click upgrade to Oh, okay. I see the issue here. So if we only do this to click upgrade to right here Um, let's yeah, so let's do 10 right here. It should round up to 20 Oh, it's buying more than that. It's buying out. It's actually buying 20 Okay, so that's another issue is that Okay, I see what we're doing wrong here. We're kind of getting this calculation or incorrect. So let's go back to this So let's copy and paste this calculator So let's say the level is 83 again, and we're buying five So the problem is that we are rounding it up correctly But we want this to be two because we're only buying two, right? So How do we do this? So now removing this again, we get three again, but that's not what we want Okay, so we want our actual level So then we get 80 Plus five. I feel like this is really like redundant, but It should work Minus 83 again. Okay. Now there there might be a way to simplify this big time Let's go to wolfram So wolfram alpha is good for okay. So that doesn't seem to really care. He just wants to get out Okay, it just wants to output what we get here But wolfram is very cool. I think you can do so many really cool calculations in here with really big numbers and Yeah, I give you so many answers to and it's really fast. Which is really cool Okay, so this is our equation here. So we need to just subtract it all by 83 again Because before was 85 which is correct, but we need to minus it all again by level Okay, so in here Let's put in parentheses. We need to subtract by k. Let's see. Do we need this? No, we don't Okay, so subtract by k This seems like a really weird equation, but trust me it'll work and this can probably simplified if I thought about it Because I'm just developing but I'm just making this on the top of my head right now Because that's kind of how making games works if you want to make an equation you kind of just kind of experiment with it Okay, so now it should work. So if we do 10 it should round up 20 Yay, I did it. So now if we buy say it one around up to 40 Now this is only if you can afford it, right? So we can't just do it with this one because we can't afford it Right. So now let's do 100. So now this will just round up to 100 And perfect. So let's hold by max 90. Yeah So if we can just keep doing five, so if we buy one it'll round up to five Okay, so our final test here Before we add it to production Is this five work? Yes, it does it does perfectly does 10 work Yes, it does perfectly now. I've already tested 100 Now, what about OCD? What does this do? Uh, I kind of here let me get rid of my upgrades Uh, what just one is this click upgrade to nine. Okay. So now does it work with um OCD off? Nope, it just keeps Going right it doesn't round up. But if you turn on OCD then it works Perfect work beautifully people love this and it's such an easy thing to implement It is a very very very easy thing to implement Just a simple equation right here. How many you're buying Or it's um your current level Minus the current level mod what how many how many you're buying or how much you want to round up to Plus how much you're wanting to round up to again minus the level again And that is a total of how many levels you should buy Perfect if you don't understand that make sure you kind of go back and just look at the equation So you can see how things go if you don't know what mod is here. I can explain real quick So let's do mod 30 mod 10 It's gonna be zero right because 10 divide evenly into 30 so 30 divided by three is 10 Okay, so we have no remainder. So this technically this is like the remainder. I guess we can say So if we do 31 mod 10 then we get one because mod is one is the remainder if we do clean division Right 30 divide by 31 divide by 10 we get 30 with a remainder of one. Okay So if we do 39 we get nine, right? This is really really good with um doing true or false stuff Okay, so if you want to have Something occur every 25 Okay, so let's say you have 100 you want something occur every 25 And it's true when it's zero right So if for example, this is a level. Let's say if it's 99 This is false right now because it's not zero But if we make this 100 100 mod 25 then it's zero So hopefully that makes sense if you don't make sure you do some research on that because it's very helpful Okay Now we need to copy and paste this for our production and obviously I should have just made this into a method for both But I wasn't thinking here. You know what? Let's do this. Okay And this right here we can also copy and paste this And use it for all because this is our count. So obviously the tech wasn't displaying the way we want it to be Okay So what we can do here is set n We're going to copy this method right here or this switch case right here. Okay, so now we're going to make a method um It's going to be a big double A big double obviously this should really be an int But for casting purposes for larger equations, this really gets ugly in the future So that's why it's good to cast if you have an int You want to cast n as a big double here or else it really messes things up. I don't know why happens, but it does You get infinities once your equation gets really big Past the e308 of course, even though if it's a big double it's kind of strange how it works that way But I didn't make this brick infinity. Anyways, I need to keep I need to keep going so In here, we're going to do calculate Uh by count right here Okay, we're just going to paste this in here And now what we're going to do in here is instead of n equals. We're just going to return Okay We're going to do that for all And the only thing we need in here is okay, we're going to need quite a bit. So we're going to need a big double c a big double r big double b for base costs And remember r is our cost molt. Of course, I should have done m That's probably a better one to do and c is our currency So we need k which is our levels and I should have done l for that Big double l Okay Uh, oh no big double k. Sorry Okay Okay, so this is an issue now um Okay, so this is where k needs to be an int Okay, so I'm going to cast this big double as an int to prevent issues in the future And we can get rid of this break as well because we don't need it Okay, so now for our calculate by count we do n equals by max count And we put in our stuff. So c r k b no, it's just b in k Oh, yeah, it doesn't always return something. So if it's for some reason nothing, we're just going to return zero, okay And this should be by max count or calculate by count and we can make this big double bar cool So we just now we can use this wherever we want to we can use it here So var this we can get rid of This here I think we can also get rid of this we can just return the count Okay Same thing for Where else do we have this right here? We can just return that And get rid of all this excess code And Where else do we have this? Okay, we have this right here. We can do var n equal to Calculate by count and then we have our method right here And everything should work perfectly fine. I'm going to move this above all of this Just to prevent future confusion. This is lower bicep right here Okay, so let's save that Hopefully I didn't go too fast But basically what I did is that I instead of copying pasting that same switch statement for every single by method and by count I just made it into one and we can use it wherever we want to even outside those two methods and future upgrades Okay, I'll make your code a lot cleaner So now if we do by five with ocd on it should say, okay, it's only gonna buy one Then it's gonna buy five And it's not one. So now this should work for production upgrade too. Yep See now it subtracts Now this is really cool. Look at that ocd buys king Okay Really cool how this all works together. I'm glad it does Okay, so Well, I earlier like I copy and paste all these uh calculated by counts But the b and r are actually flipped. Okay So make sure you flip all of them for every single one of them or also kind of just screw things up All right Otherwise, I think I that's that's it. Yeah, it looks like it's working now. Just fine Alrighty if you enjoyed this video and it was really helpful Make sure you smash that like button subscribe my channel if you're new and turn on those notifications because those really help me And they will help you too. The videos will help you Anyways, thank you guys for watching. Have a good day. Check out my other videos in the top of the corner See ya


Okay, let's continue with the last lecture of Sasha. Thank you, works. Today I will be talking about something quite unrelated to the subject of the first three lectures, namely in the, let me remind you first we discuss this universal infrared aspects which do not depend on the UV details of the theory and that's why they're so universal. And of course, whatever the theory is we know that at long distances it reduces to Einstein theory but of course for string theory as well it's very interesting what happens at intermediate energies or high energies. Namely, what is the UV completion of gravity? What is the theory of high energies? Of course, this is a very hard question and especially we don't have an experiment. So a version of the question which seems to be promising and very popular is to understand what are the consistent low energy effective field theories which admit a UV completion. So sometimes this consistent, this question is called I guess landscape versus swamp land which is a landscape being a low energy effective field theory which do admit UV completion and the swamp land being the theories which looks a priori they look fine but if you try to make them gravitational and make them UV complete you run into some problems. Of course, figuring out what are the borders between swamp land and landscape it's a very hard problem but today I would like to talk about the version of the problem which is a classical which is that we will not don't want to talk about quantum swamp land but sort of consider a classical theory. Say we start with the Einstein theory and we add to it some high derivative correction. Let me write an example, some famous example but you can imagine all kinds of terms. This term is called the Gauss-Bonne term. It has two prominent features first in four dimensions when D equal to four, it is topological and also if you consider equations of motion and some background for perturbations are second order still. So it's a well it's one correction but the question which I would be having in mind is completely general which is that imagine that you have some theory with many high derivative corrections maybe extra particles, et cetera, et cetera and the question is how can we constrain these theories? What is the landscape of consistent classical theories of gravity? So important point here when I want to emphasize that this question is classical. By this I mean that we have a say Planck scale which controls quantum corrections which would be very high and there is an extra scale which is more like a string scale which controls this extra high derivative corrections. So I will be always working to leading order in the Planck scale but to say to order in string scale that's an important point. And of course an example of such theory which has this kind of corrections is a string theory. That's one example. And from the studies of these questions there are two sort of two messages maybe that one can see is first that this type of high derivative corrections for theory to be consistent. You need the higher spin particles. You need an infinite number of higher spin particles. The higher spin I mean here spin larger than two. And let me remind you that graviton is a spin two. That's a graviton. It's the first thing which I would be talking today and it's related to again some as the previous lectures was some modern twist on the old topics. This will be also some modern twist on the old subjects, old general relativity experiments. And the second message which I don't have time so much to explain is that if you think about this classical theories of high spin particles in certain things they have strings, these theories of strings. It would be nice to turn it into a theorem and to prove that if you wish that the string theory or strings is this universal mechanism of having consistent interacting theories of high spin particles. It's not that you, well there are probably many ways to end up in string theory but from this point of view you start with this problem, you correct clavities and you want it to be consistent and you see that the only way you can do it is to have strings classically. Of course I'm not proving here that string theory is a theory of the universe because it's a classical problem. But if you can do something like that for the full quantum theory of course that would be something very great for string theorists. So that's the two messages and I will talk today about this because it involves many sort of simple and classical experiments structures. If you have any questions? This was a motivation, very good. So by this I mean that it has at the moment that it has infinitely, infinitely many, say asymptotically linear retro trajectories and all the other predictions of effective theories of strings but I don't know how to prove that. So far I know only that you can show that the four point amplitude in some universal region looks like when it's a anode. Okay, that's... That's what I mean, yeah. That's what probably, well, ideally one would like to show more. That's what I mean at the moment. The object which I would like to discuss today, it's scattering amplitudes, it's a nice object because if you're dealing with actions there are field definitions. But if you want to talk about invariant data it's packaged in the scattering amplitudes. The object which we would like to discuss is a two to two scattering and the S matrix is usually written like this. It's one plus I.T. It's unitary, well, I will not use it too much. Placed in this sense and the ZT has a sum of a momenta times an amplitude. Amplitude is a function of Mandelstam invariance. Okay, what is the source of the problem? Why is it that suddenly we started with a theory and we would like to constrain it? So what would be where would the juice is coming from? How do we get these constraints? How do we get these claims? To do that it's useful to recall some basic facts about scattering amplitudes and then and then we will find that what is special about gravity in high spin particles is it's high energy behavior. And we will see that the high energy behavior is very constraining. Recall that if you have a, let me start with something simple that you have two particles and you exchange particle with a spin J and show you can compute the amplitude. Then this diagram behaves as T as to the J. This is a known fact. Well, if you simplest example is consider a scalar field then you have take this diagram it will be equal to one over T which is at large has the case like as to C zero. Now you can consider instead of a useful formulas to or useful experiment would be to consider instead of scattering in momentum space. Imagine two wave packets. So we have particle one and two which are separated by some distance B. That's now you imagine two wave packets which in the transfer space separated by distance B. And yep, you can, if we add the diagram it will be one over S, yeah. But at large energy this dominates, yeah. Now in the impact parameter space, sorry this guy's called impact parameter in the impact parameter space the S matrix takes this form one plus say I delta. Delta is called a phase shift and this one is the same one but this one is secretly a bunch of delta functions and this one is literally one and the phase shift is related as follows so the scattering amplitude that's one over two S integral over transverse transfer momentum and you take an amplitude S and S and T minus Q squared. So S you think about it as just the energy of scattering and Q is the exchange momentum. So if you do it for your transform, oh, something is missing. You do it for your transform as respect to exchange momentum you get a phase shift. Now where is the problem, where the problem comes from? So the problem would like to impose is causality. For example, that's we want our theory to be causal and we'll motivate it in two steps. Let me first think, you can think of scattering as a, especially if it's a high energy scattering whereas there is no much deflection going on particles just acquire some phases which then you can think of scattering as a propagation through the medium. So imagine I send the many particles and then you send the probe. You can think from the point of view of these particles this other particles is just the medium and then we would like this medium to be such that the propagation is causal. So it's not faster than speed of light. A simple model to think about when we think about propagation through medium through the medium is to think about some signals.  In this case, this black box can be made of gravitons. So this black box made of gravitons transforms in going signal to out going signal. Then, well, let me consider the following model and you can then show that it's a good model for this. We can imagine that the black, this black box does transform the signal through some S-metrics. It is diagonal in the Fourier space. So F out omega is equal to S of omega. F in. And let me imagine that, and this is related to the unitarity of the original S-metrics, that this medium cannot increase, if you wish, the amplitude of the signal, namely that in this language, the unitarity is a statement that the norm of the L2 norm of the outgoing signal will be less or equal. Now, if you, you can ask, okay, what are the constraints, what are the constraints from causality and this unitarity on this S-metrics? Well, that's a simple problem. Some of, probably you've all seen that, that it's a, for example, if you take an in-going signal that would be zero on negative times, then you want the outgoing signal to be also zero on negative times. So if you send some signal from time zero, you cannot get outcome before. That's a statement of causality here. This implies that this S-metrics, it is analytic in upper half plane in omega. And together, if you, if you, but you can imagine that S of omega is something which is analytic in upper half plane, but it can be some growing function. But you can show also that this unitarity, it's a simple exercise that it's, if you go to the upper half plane, that it's less than one. It can only decay. Otherwise, you will get that the norm will be growing. So this is a kind of medium we would like to have. And now we can think of the scattering amplitudes if we imagine this set of scattering events. I, let me repeat again. Everything what I'm saying here, I consider the signal model where the incoming signal is transformed to the incoming signal through the S-metrics, which is a function of omega. I assume that it's unitary. And by unitary here, I mean that the norm of outgoing function is less or equal than the ongoing function. And now I impose that this S of omega is causal. Namely that for incoming signal is zero, the outgoing is zero, and then that it's unitary. And I'm saying that the condition that S of omega should satisfy, it's analytic in upper half plane. First condition. And moreover, it decreases in the upper half plane, so it's less than one. When you go to the upper half plane. For example, you cannot have something like, it was i omega cube. This is analytic in upper half plane, but it blows up in some directions in upper half plane. On the other hand, you can have something like this. This is analytic in upper half plane, but it decays in upper half plane. This is related to the difference between particles spin two and higher, as we will see now. Now it's a little bit of work, but morally you can see it even from here that you can think of the scattering events as this medium and that providing this S of omega with S of omega being controlled by delta. And then we see that the condition of this type that S of omega is less than one becomes in our model, something like one plus i delta S of B, the less or equal than one in upper half plane. And say S is S naught plus some i gamma. Recall again that we said that if we exchange a particle of J and this model is a good at high energies, so particle just rush through each other without deflection. So what happens if we imagine that this is we exchanged a particle with spin J? Well, this thing becomes one plus i C S J minus one plus equal than one. Now you can see the following things. Well, first you can consider, and here I'm working to first order in C because I assume that this is a small phase, otherwise I have to say, I assume that the coupling is weak, so I'm working to first order in C. Now you see that something special happens for say, let's take, let me take say J equal to and this S, this is Mandelstam S. It's a roughly times some number, a product of energy of a particle of a probe times the energy of a particle of a medium. That's a scattering event here, delta, delta, delta, which we repeat many times say. And this energy of a probe plays a role of this omega here and you get that the causality constraint become the analyticity of this thing in upper half plane in this way. You can think, you can connect this scattering through with a signal model and you get that the phase shift should be analytic in upper half plane in the S variable. And you see that if you take J equal to two, that this is imply, this implies that C is positive. And as we will see, this is related to the fact that gravity is attractive. Then if J larger than two, this is always violated. You will always find the direction in a complex plane where it grows, no matter what C is, is bad. And this is related to the fact that higher spin particles are problematic by itself. So it's very constraining. As soon as you add one higher spin particle, you should add infinite number of them. Because imagine you just added one higher spin particle, then it grows like S to the J, then you will violate this, we are in trouble. That's why when we add one higher spin particle, they always come infinite number of them. Yeah, so the, well, it fixes roughly that you have to resum, and when you resum, it becomes softer, like in string theory. So this is not a correct formula anymore. We have to resum infinite number of particles and the resum in phase is in such a special way, such that the high energy amplitude becomes small. Well, maybe it's not the correct model, but you can imagine something. Oh, it's resum X to the N, and there is a finite radius of convergence, but the large X asymptotic is controlled by information. Now you can ask what happens, yeah. Yeah, here, here, this is in the upper half plane, so it's not physical region. It's, well, it should not because it's a two to two scattering and you can create other particles. So if scattering is purely elastic, it will be one, but generically it will be less than one. You can ask what happens to J equals zero and J equals one. Well, for J equals one, this is a pure phase, and to first order in C, the absolute value will be one. So if we exchange a photon to first order in C, this is not a problem, and if J equals zero, if we exchange a scalar, you can, if you carefully go through this model, so I kind of use the connection of the scattering with the signal model, and you can show that for the scalars, this connection is not, doesn't quite work. But the message from here is that we see that when we have a graviton, we have fine potentially, and when we have hard spin particles, we have to worry. This is the source of these constraints on the classical landscape of classical theories of gravity and high derivative corrections, and the idea will be roughly that as soon as you start adding the hard spin, as soon as you start correcting the gravity, you can find a regime where the C becomes negative, or you will violate causality in this medium, and then when you will try to fix a problem, we would have to add all of these guys, but each of them is by itself problematic, so we'll have to infinite number of them, and then the problem is fixed. That's the idea. And then we can study the theories of these hard spin particles by themselves and try to see what are the conditions that they re-sum up correctly and don't spoil the high energy behavior. Let me explain a little bit more why is it related to causality, and what do we mean when we talk about causality and gravity? Because while in gravity, you can say the spacetime fluctuates, so what is, what do I mean when I say causality and here's a notion of causality and gravity, which I'm having in mind, is what is called the asymptotic causality, and this is due to Gao and Walt paper about time delays and the statement of asymptotic causality is, well, the idea is, as we also discussed in the previous lectures, is that far away, so the spacetime fluctuates, but if you go far away, you have a rigid asymptotic structure. For us, it was Minkowski space, and the idea is that we cannot send signals faster than what is allowed by the asymptotic structure, or is allowed by the asymptotic causal structure. So Walt and Gao, they actually were proving theorems but you assume, you start with GR and you add some matter which satisfies our energy condition and then you can show that when you say, let me draw, the simplest, the cleanest thing is to consider ADS, so ADS is a gravitational box, so asymptotic structure is a boundary of the cylinder, it's just Minkowski, it's a flat space, so you have a light cone, and now you can imagine that you added some matter here in the middle of ADS. You can imagine sending signals either through the bulk or you can imagine the signal through the boundary, next to the boundary, and the idea, the theorems of Gao and Walt and the notion of asymptotic causality is whenever you're going through the bulk, it can only slow you down, it cannot speed you up. You can never go faster through the bulk than what is allowed by the boundary. You cannot arrive somewhere outside of the light cone. In the context of ADS CFT, it is especially clear because if you have two CFT correlators, then you know that the commutator would be zero when there's space like separated, that's a notion of causality. So asymptotic causality is this kind of notion. That asymptotic correlators, asymptotic operators should commute, and when you go through the bulk, it can only slow you down. Simplest example, if you take, so you can see that if you take a negative mass Schwarzschild, it will speed you up, but if you take a positive mass Schwarzschild, it will slow you down. And this slowing down, slowing down of signals when going through the bulk, it has a name, and this slowing down is called Shapiro time delay. What is Shapiro time delay? Well, as you know, there are three, yes, and the idea is that we take this effective theory of gravity, gravity plus high derivative corrections, and we impose this asymptotic causality and see what are the constraints on the corrections. What is the Shapiro time delay? Well, as you might have heard, there are three classical tests of general relativity, which is a shift of mercury perihelion, deflection of light, and gravitational red shift of light. And so in 1964, Shapiro posted a paper called the Force Test of General Relativity, and the idea is that if you send the signal to Venus or Mars, and it reflects back when it passes by the sun, it will slow this signal down. And you can measure this effect. It's 1000, so 10 to the minus fourth of a second, something of this order, I think. And this is an example of this slowing down when going through the bulk. So let me compute quickly for you a Shapiro time delay. Let me consider a metric which corresponds to two Schwarzschilds. So I consider the metric, which is Minkowski space, plus I added the Schwarzschild solutions. Of course, it's not an exact solution of Einstein equations for the usual two sources, but it's a good approximation, and we can imagine doing that. And imagine I put, say, I have some transverse plane, and I put one source at impact parameter B, and another source at impact parameter minus B, if you wish. And now we will send the particle from infinity passing between these two Schwarzschilds. So it will go from minus infinity to plus infinity. And because it's a symmetric, it's symmetric, there is no deflection, because there is symmetry. If you put one of them, there will be a deflection. But if you just, if you choose a symmetric configuration, what happens is the light does not deflect, but the Shapiro time delay accumulates. So what we will find is that we will now compute the time, time it takes light to propagate from minus infinity to plus infinity in the presence of these two masses. Let me do this computation. So there are this R i. So R one is simply, say, x minus B, and R two is x plus B, it's a usual coordinates. Now, we can imagine that the problem, we can localize problem in this transverse plane and study the propagation of light in this metric. So for light, this thing should be zero. And say, in this case, we can call this direction Z. Then both this R, R they are equal to B square plus Z square. If I consider a position of the particle, this difference is simply B square and this is a coordinate Z. So we get the equation of the type. If we say that it's a geodesic, we get that one minus two RS over R D minus three. You can get it. Check that this is a correct thing. Easy square one plus two RS over R D minus three. So it's a little exercise to plug this and check that it's correct. And now from this, we can compute the change. Well, we can find the delta T as an integral over DZ from minus infinity to plus infinity. And we have a, well, from this, we get question for DT over DZ. We compute DT over DZ at R minus three. That's AT over DZ when RS is equal to zeros. It's just Minkowski. So this is a relative delay compared to propagation in flat space. Well, and you get something which looks like some numbers, which we don't care about times over B to the D minus four. Here's some number depends on D. So if you consider propagation of light, you get is that it's get delayed and the delay is a one over B to the power D minus four. An interesting exercise, which I will not do here, is to repeat the same thing for the particle which moves with velocity V. So here we've had a particle which moves with the speed of light. That was a photon. If you repeat the change for the particle with the speed V, you will get that it's one over V, one over V. And here, curiously, you get minus delta T of four. Okay, what is this formula again? This is a Shapiro delay or advance for massive particles which move with the velocity of V, which is expressed in terms of Shapiro delay of photons. Notice that there is a one over V square factor in the brackets. So when the particle is very slow, when V is small, the delta T is actually negative. If you take a massive particle, it gets slow, it trails faster and there is a critical velocity after which we can get delay. The fact that these slow particles get Shapiro advance and they travel faster does not contradict our symptotic causality because the symptotic causality is formulated in terms of the fastest signals, which is a light and the light gets delayed here. But there is this curious fact. No, sorry, let me, if you wish, let me write it. That's the right answer. Now if you set V to one, you recover delta T of four things. This is a classic results from the seven case, which is a computation of a delay from a planet. When the light passes by the planet, it gets delayed. If a slow particle passes by this two planets, it gets advanced. But asymptotic causality structure only cares about the fastest signals, which are controlled by the propagation of light. Here we get that this Shapiro time delay is positive, because the gravity is attractive. Now I would like to tell you about the relativistic version of this argument. So imagine that we would like to propagate next to a relativistic planet, which moves with the speed of light. It will, or just some photon. Then we can consider a source in Einstein equations, which corresponds to, let's say we have, as before we have in Kowski space, whatever x d minus one and v plus x d minus one. And now we add the source to this. So imagine we have a relativistic source, which is this. It's some particle which moves along the light cone with some momentum pu, and it's localized in the transverse plane. There is a famous exact solution for this source. You can show that if you add two things, so there is the exact solution is known, and it's usually referred to as a shock wave solution. Or yes, and this h you can find, it's simply the same kind of h, that same kind of Shapiro delay we had. It's a number, which depends on d. It's localized at u equals zero. And instead of rs, which roughly measures the mass of the planet in the units of g, you have now the momentum of the source in the units of g, and you have the same r transverse in this space to the d minus four. Now, two comments. First is that this is the exact solution to find the equation. It's the first comment, not the linear. And the second comment is that actually you can find if you add any type of corrections to Einstein theory, you can write any polynomial terms, whatever you like, this is still an exact solution. That's a peculiar fact, which you might wonder about, but then I will try to explain another explanation why it's, is not so maybe surprising that it happens. In this language, what happens now if we send another probe along through the shockwave? What happens is that here is our particle. So the shockwave is localized at u equal to zero. And find the geodesic and you will find that where this particle jumps through. It's get shifted by some delta v. And if you try to embed it in a global space of Minkowski, you'll see that in the original Minkowski, that's what will happen, but now it's get delayed. It arrives later. This delta v, which simply if you compute is equal to g, pu, and again bd minus four times the number, is a relativistic Shapiro time delay. Okay, that's fine. It's a nice shockwave solution. It's exact, so far, so good. There is something curious happening if we try to translate this computation. This is just, we computed the light geodesic passing through this exact solution. It is curious and instructive to repeat the same computation using the language of scattering amplitudes. Let me do this quickly for you. And let me consider for this purpose and exchange. What is this, what is the physics of this? What is the physics of this geometry? Well, the physics is very simple. This, it's a propagation of one particle on the gravitational field of the other relativistic particle. In the language of scattering amplitudes, what we have is simply, this is a, say, our probe. This is a source. And they interact through graviton exchange. Let's imagine that all these particles are scalars. Then the result for this, not written, but Feynman-Dyger, is simply eight pg s square over t. That's, you can check. And now let's compute the phase shift. As I try to explain, if we, if we, this are wave packets with separation b. Yes, and here, sorry, I had to explain. You could have asked, what is b here? So this is a two plane and this is a, there is a transverse plane. And I consider the source as the origin of a transverse plane and I send a probe somewhere here. It's a distance b. To avoid deflection, I can again consider two shocks, which are symmetric, but I neglect deflection for this purpose. That's what is b here. And this is the same as the impact parameter just by definition. Now we had to do this, we do the integral over the transverse momenta, e i q b. And here we have s square minus q square. Remember that t is equal to minus q square. Well, this integral you can take, it's trivial to do. You will get exactly the same, you'll get exactly the same d minus four times the same number. And if you remember that s is something, p u, which is the momentum of the source, that's the momentum of the probe. And then you can imagine that you start some plane wave, then you add this phase. Then this phase can be recast as p v times delta v. And this formula exactly coincides with this formula. So you can either do the classical geometry computation, or you can take the scattering amplitude, compute the phase shift, and then take a plane wave and propagate it with add to this phase shift. And you can see that the effect of this phase shift is exactly the effect of shifting the wave packet by delta v. So there is an equivalence between this computation as classical geometry and the scattering amplitude computation. However, something you can ask, what is the dual to this fact? Remember I told you that this is an exact solution in any theory of gravity you can check. This geometry is very special. It has some special symmetries, such that it's protected against correction to the Einstein theory. What is the dual of this fact in the scattering amplitude language? And the answer to this is the following, that when you compute this integral, you can see, let me choose some b, some component, b1, q1. You can compute this integral by closing the contour, and you see that the phase shift is controlled by the residue of the amplitude of the amplitude at t equal to zero. However, there is a simple fact that if you have an exchange of the particle, you have a pole, obviously, at this position, say. There is a fact that the residue of the amplitudes at this pole is equal to the square of a three point amplitude. This is an optical theorem for three level amplitudes. The residue of the pole, it's the same as imaginary part. You have something like that. So this is, if you have heard about optical theorem, that is an optical theorem for three level amplitudes. And now, since this delta is controlled by the residues of the amplitude, you can ask, what is this three level amplitude? And the curious fact about three level amplitudes, which I will talk about next, is that they are completely fixed by symmetries, up to a number. No matter what your theory is, of gravity just lowering symmetry fixes them. And in this way, you see that the Shapiro time delay is controlled by three level amplitudes, and these three level amplitudes are fixed by symmetries, no matter how you correct your theory. And this is a dual of this fact that this is an exact solution for any corrections to the theory. And after you realize this, you can ask the following question. Okay, let's now forget about the actions and geometries. We're computing the objects, which is completely fixed by three point couplings. So we can take the general gravitational theory with three point couplings, compute Shapiro time delay, and see what's going on in this most generic case. This is the idea. Here is a little comment. It's probably confusing for those who haven't thought about this problem, but notice that we start with a purely transverse momentum. So it's a Euclidean momentum. Q square is positive in the physical domain. And then we are computing the residue at a point where Q square is equal to zero. And we are computing it because we say evaluate it in a complex plane somewhere. So let me rewrite it as a Q1 square plus Q transverse. And the residue is at where it's equal to zero. So it's effectively Q1 becomes complex. And making a momentum complex is the same as doing a weak rotation. When we go from Euclidean plane to Minkowski space, we say take P naught to IP naught. So here while doing this computation, effectively we switch from say Minkowski signature to what is called mixed signature, which is two minuses and say pluses, effectively it's in quotes. And this is related to the fact that kinematically if you consider say this are three massless particles. If you consider a decay of massless particles in Minkowski space, they are kinematically prohibited. So just write energy momentum conservation. You will see that the massless particle can only decay linearly in Minkowski space. However, in a mixed signature when we have two times roughly that is allowed kinematically. And the moral of this computation is that not on, so the moral of this computation is that the Shapiro time delay is controlled by effectively a computation as a mixed signature due to the simple fact that moreover it's fixed by three point amplitudes. So it's a very clean observable it because it's completely fixed by symmetries. That's why it is so nice to study. Let me explain why is a little bit, why the three point amplitudes are universal. So let me consider now three point amplitude. And you probably will hear a lot about them next week in the lectures by Marcus Sprudlin. University three point amplitudes. Imagine that we have three massless particle which say one decay into two others. So we have momentum conservation and each of them is massless. Well, first you can immediately see by taking square of this equation move P2 or P3 to other side and take a square. You see that PI times PJ is equal to zero. That's a first thing. And now if we have a scattering which involves gravitons as we discussed, let's say we have a gravitons then it should be gauge invariant which is that we can shift this guy. If there's some graviton with momentum P we can shift that P mu lambda nu plus lambda nu. Now let's consider this process which has two scalar particles interacting with the graviton and let's try to write some amplitude. Let's say it's P1, P2, P3. Let's try to write some three point amplitude. Well, the answer is that there is only one thing you can write, P1 nu, P2 nu. This and some number in front. That's it. That's a result in a full quantum gravity. There is nothing else you can have. This just follows from Lorentz invariance and gauge invariance. This lambda is a parameter of the theory. So it's a coupling constant that you should measure in the experiment with its all loop corrections, et cetera. And that was exactly when we were taking residues. We effectively sum over all the states of the gravitons that we exchange and so we get this S square here by taking a square of two amplitudes, of three point amplitudes. You can repeat the same exercise for the gravitons and let me write you the result. If you repeat the same exercise for the gravitons, so now take three gravitons instead. The result is that the three point amplitude for gravitons, it has three structures. One of our Einstein theory, the one was roughly Gauss-Bonne and the one roughly of R-Cube. Riemann-Cube you can add to the action. Yeah, this is two scalars and a graviton. Yeah. Notice that this is gauge invariant because if you shift epsilon by P because of PIPJ zero, it is gauge invariant. And here I can put quotes because it's really what I'm using here is symmetry. I'm not using any particular action. It's completely robust. Just based on symmetry in any theory of gravity, this is the answer. And now as I try to explain to you the Shapiro, this phase shift when we consider scattering for gravitons is roughly given by this A3 square times one over B, D minus four. And write the precise formula. Now you can start playing the following game. Imagine you have the most general three point amplitude and you can, and you, we have a, so if this, if the Einstein theory is one, we have two corrections, alpha two and alpha four, say. So Shapiro time delay is a function of alpha two and alpha four. But it also, it is also, since we are scattering, if we are scattering gravitons, it also is sensitive to the polarization tensors of our gravitons. You can polarize them differently. This was something new compared to the scalars. Now you can ask, what is the condition that it's positive? And the answer, which I, it's a simple computation. You can know the three point amplitudes, you take the same kind of integral, you compute and you see that if alpha two and alpha four are non-zero, then you get the delta is negative, which is a violation of causality. That's the first conclusion. So as soon as you, if you correct the three point vertex of the gravitons and it's, then you get into this trouble. It's the first thing. And a second you can ask, how do I fix this problem? Well, one way to fix this problem is set this parameter to zero. That's fine. But that's a boring solution. And then you can say, okay, let's try to fix this problem by adding new particles, almost done. And then you can show that the only way you can fix this problem is by adding of particles with spin larger than two. Basically, you can repeat the same exercise. You start with three point amplitudes of particles with some mass and some spin. And then you see that unless, if particles have spin two or less, they will not help you. That's the only guys that can help you as particles with spin larger than two. And then by this argument, which I discussed in the very beginning, is that you cannot add one of them. If you add one of them, you violate this bound. You violate causality. Then you have infinite number of them. And then you can ask the following bootstrap question. Imagine you have an amplitude you have an amplitude with higher spin particles which generate phase shift, which does not grow faster than S, according to this bound. And it's a unitary amplitude. What does a class of theories which, what does a class of theories which have this property of higher spin particles? And this is a bootstrap problem. It's completely rigorous mathematically. You should just be able to classify such theories. And the hope is that these theories will be theories of strings and there is some evidence to that. So let me reiterate, we consider this simple extension of this classical general relativity experiment which is Shapiro time delay. We found that if you modify gravity in a very clean fashion, in a very gauge invariant fashion by changing the three vertices, generally we violate causality and then the string modes naturally appear. The same experiment, it doesn't matter if you can run an ADAS or in this theater space in cosmology, it doesn't, it's kind of insensitive to that. If we have these particles, we will have this problem. And this is an example of this warm plant like question where we started with corrections to the theory and at first glance it looks completely fine, but upon further investigation we saw that there is some problem. Of course, it's almost classical. It would be great to get such bounce in a quantum level and probably heard recently about this weak gravity conjecture which is exactly a safe time of question. Thank you.


Hello, I am Adam Navas. I am here with the pleasant as always Liz. Wait. Hello, Liz. Hi, Adam. We are going to have a real conversation between the two of us, two native English speakers. We are going to talk about the program Shoes of the World. I'm very excited to talk about this program. If you haven't listened to this program, you can find it on YouTube or wherever you get your podcasts, or you can check out, if you haven't been to our website, spotlightenglish.com. You can follow along with the script there. You'll also find a lot of other resources and other programs that you might not discover if you're just on YouTube or listening through the podcast. If you're interested, as always, make sure when you're on YouTube, you click that join button.  It really is just a great way to support this channel and all the work we're doing. What did I miss? You can follow us on social media, et cetera, et cetera. You guys know the drill. Like this video, Twitter, Facebook, YouTube. Yeah. We're doing good stuff. Liz, Shoes of the World, this was a program you wrote. I did write this program. The program even begins like this. You think about, well, how complicated does a shoe have to be? It just needs to cover your foot. Even if you take away all of the fashion parts of shoes, because of course there are, I don't know, what are some famous shoe brands. I know there are some in programs like Sex and the City. Jimmy Choo. Yes. Those are the fashion. Yes. We are not high-end. Clearly, I am not in this shoe fashion world, but there's expensive shoes and fancy shoes. Even if you take away all of those shoes, even if you don't think about fashion necessarily, there's still a lot of different kinds of shoes culturally, which is really interesting to me, which is why I wrote this program. This program really, it starts with a very, to me, funny example of shoes. These shoes made of gold. They're literally made of gold and covered in diamonds. There are like 140,000 pounds or something. Now, you mean pounds not in weight, but in blood. Right. Yes. Yes. Sorry. Great British pounds. The program starts like, would you buy these shoes? I wouldn't. Even if I had that much money, I don't think I would buy those shoes. But then it goes into different shoes that are culturally around the world. It talks about clumping from the Netherlands and babushes from, was it Morocco? I forgot. I think that's right. Yes, Morocco. Gaita shoes from Japan. There's parukas from India. I know I'm forgetting one. Well, anyway, that's why you listen to the program, right? Yeah. To find out about those shoes. Really going through all of those shoes and why they are, the Sami boots, the boots of the Sami people, and really finding out how culture has influenced shoes and how shoes maybe have just become part of what a culture is. Yeah. Adam, are you a shoe guy? Do you like wearing shoes? I mean, not wearing them, but collecting them. That is a great question. I have a spotlight program that I wrote about sneakers, right? Oh, yes. Sneakers and collecting sneakers. And around about that time, I am not, here's an English idiom. A clothes horse. Oh, right.  Right. I don't know why it's called a clothes horse, but whatever. I don't have a lot of clothes in my closet. Most, my wife and I share a closet. Most of it, the space goes to her. I'm happy with what I have. But I bought a pair of shoes because I always, my sneakers, so sneakers are a very casual, sporty shoe. They were always old running shoes. And I thought, I'm going to buy a pair of sneakers. Right. And I do think, if you don't mind, Adam, I want to like, this is an interesting English thing because in UK English, these would be trainers, right? So sneakers is the word that is really most popular in the US or tennis shoes, sneakers or tennis shoes. But these could also be, these are trainers in the UK, maybe. So before I show you, are they Air Jordans? No, no, no. Okay, but I'm going to give you a quiz. Okay. Okay. Okay. So there were two brothers who were in Germany. Okay. Yep. Okay. And they had a shoe company. And then they had a fight. And they broke up into two separate shoe companies that are now global brands. Okay.  Well, one is Adidas. Correct. Which is really technically Adidas. Yes, which is what you're going to see from me. Oh, man. If you know, write it in the comments. Write it in the comments. This is a good one. I'll show the shoes. Yeah, this is like a quiz. And then we'll tell you what the other... I mean, I should know what the other one is. All right, I give up. Okay. Well, I'll show you my shoes. So the first pair I got with these gray with the black stripes. Okay, this is the first... They look like vans. They're not vans. Don't call them vans. They look like vans. They're not vans. Okay. And then I decided, you know what, this is going to be my thing. This is not vans. I got maroon. Oh, fancy. Okay. Now I'm going to show you out of order. Okay. Okay. So these are my next... We're getting into really good ones. You did get a lot of shoes, Adam. All right. So we have kind of a gray with the blue. Yeah, I like that one. Nice. Nice. Classy. All right. So this is... I'm showing you... I'm going to show you my latest one that I got for my birthday. And then I'll show you the best one. Wow, this is actually not like you. Whoa! I know. Bright red. Now, the greatest. I've only worn these three times. They are so special. Okay. That... I feel like... Is that like the classic Adidas? I don't know. I feel like that... No, no, no. The classic one is just black. But for some reason, those colors to me feel like they are like the classic like 80s version or something. So there was a children's book called Alexander and the Terrible, Horrible, No Good, Very Bad Day. Yes. And part of what he does, he has to go buy some shoes that are not what he wants, right? He had to buy plain old white shoes. So part of the reason I feel so special in these is because they're white and they will get dirty. So I try to keep them very special. That is true. But of course, the... These are not American shoes. These are kind of a global.  They're not... I don't think people think, oh, this is a German company or, you know, it's a very good company. Right, right. So if you haven't written in the comments, the other shoe company now is Puma. Puma. I don't think I knew that. I mean, I know Puma shoes. Yeah. So they were two brothers and they each... Really? Yeah. In the same city, in Germany. And if you know the city, I don't know the city, but if you're in Germany and you're watching this, let us know. Yeah, I don't know. Was it a big German city like Berlin or Hamburg or something? Probably. I don't know. That's great. So Liz, I showed you my shoes. When you think shoes, do you have a specific... Like if you were a country, would you have a shoe? Would you have a... I feel like probably like me personally or like the US. Because I feel like the US, we might be like a high heel. Don't you think? Yeah. Like just like fancy on the outside, but like super uncomfortable. Is that bad? Yeah, I think you're talking... You're editorializing a little there, but that's okay. Yeah, I don't really wear heels. But yeah, I don't know. I kind of like... I like a plain shoe. Yeah. So I mean, I do actually... If I am going to buy a pair of shoes, it's probably now that I'm older and my legs start hurting. If I walk too long, I buy more comfortable, expensive shoes. So even if I buy a pair of nice shoes, I don't know. They're going to probably be more expensive. Yeah. But I don't think there's like a cultural shoe so much from the US. I have worn a Gita before. Oh yeah. Like from Japan. Those are really interesting. Because you know, I love this from the program that they can go on either foot. Oh, okay. Because it's like a V in the middle of a block of wood. Right. And it yeah, it still goes between your like first and second toe. Okay. But it's just offset a little. Interesting. Well, that brings up an interesting question that if you would travel to a place like Japan, would you bring those shoes back and wear them? Like would you buy them as a functional piece, as a fashion piece or just as a souvenir? I probably would not because they are very uncomfortable for me personally. I mean, it's just a block of wood. This is like the Padukas in this program too. I will tell you what though, I would buy a pair of those boots from the Sami. Oh yeah. I would wear those. Those seem pretty functional. Yes. I love that. Like they're made out of like that because the Sami are from the north. Right. So they have very cold weather and they raise reindeer and then make boots out of the reindeer skin.  And a couple years ago, we went to the Netherlands, which I do have some Dutch ancestry in my ancestry. So it's a little bit like my grandparents, some of them came over from the Netherlands. And so it wasn't necessarily a trip where we visited places like that. But you know, it's always fun. And I'm sure that people know what shoe is associated with the Netherlands. And it is the Klampen or clogs. So I do actually, we came back with a pair. Here, I'll hold them in the correct hands. We came back with a pair of Klampen. And I don't, I mean, I don't have gigantic feet, but these do fit my feet. Yeah. You're supposed to wear them. You should tell people what those are made out of because it's an unusual material. Okay. So this is made out of one solid piece of wood. Usually I think a softer wood. You can hear it. Hello. No, but so we saw them actually make these shoes on a machine that was basically like a spoon that was like on a machine. And it would, it would just scooped them out, like scooped the wood out, shaped it on the bottom. Yeah. And then of course, you know, they dry it out so that the wood is nice and dry. And then they paint it. And this is a, this is a typical sort of paint design or whatever in, in the Netherlands. But yeah, you're supposed to wear it with a very thick sock and have about two fingers of space behind here so that you don't get blisters. And you can wear these shoes like outside. And yeah. I had always heard that they were made of wood so that they would float. I think that might be an urban legend. Or I think that might be like, that is true. But why would they, why would they need to float? Because they're in the Netherlands. They're below sea level. No, I think it's because like they're, they're good for like going outside. And like if you drop a tool on your foot. Oh, it's like a steel-toed boot. But I wouldn't. Right. So maybe it has multiple, if you're watching this from the Netherlands. Yeah. Please. Who's right? Who's right? Me or Adam? In all things. It's you. Yeah. Yeah, exactly. But I don't really typically wear these. So they're more for decorative or? They're more decorative and you know, they're just for fun. Yeah. Well, if you want to let us know your favorite brand of shoe, your favorite kind of shoe, your favorite, if your country has a particular shoe that was not in this program, leave a comment below this video on YouTube or on our website. And we'd love to hear we, we look at all those comments. We try to respond to as many as we can. And I will say, if you are a member, we always respond to your comment. Always. Members, we try to respond to as many as we can, but members always get a response to their comments. Yeah. And yeah, like we said, follow us on social media, check us out on Facebook, on Twitter and the website. And make sure you are subscribed, of course, because we are coming out with new content all the time. We are having new ways of helping you practice your English and you don't want to miss those. So until next time, we hope you listen, watch, practice and learn spotlight out.


Hey! Hey there, Doof Squad, it's Logan here back again with another reaction video. And today we're going to be watching some cute and funny moments from TWICE, and the reason why I'm doing this is because I actually want to get into TWICE, I want to know the members, because I've just been loving their music lately, like legit, their music has been absolutely amazing, it cheers me up, it's cute, the style, and just like everything about it, about them is just absolutely cute and adorable and amazing. So I want to try and know the members a bit more, like I know a few of them, I probably get their names wrong, I know quite a few of them, but I just like can't like get the faces, like I know the names and all that stuff. So what I decided to do was do some cute and funny moments and trying to remember their names through that, and if I get their names wrong, can you please let me know in the comments down below, no harsh stuff, because I know if you get a name wrong people like freaking, like try and kill you with like a pen, they'll like try and stab you like 5,000 times, and I'm just like ah nah dude nah, it's a mistake. So yeah I'm going to try and mention quite a few members and if I don't know one I bet I don't know who this is and all that stuff, so you guys can, so can you guys please help me out by if I get a member wrong by commenting down below, because I actually love the script a lot and I think this will be a good way to ruin their names. But yeah, other than that it gets straight into this, I'm freaking excited to see these cute and funny moments, I hope you guys are too, and let's do this. Twice. What's this? Oh, now it's one on the right, is that Sana? I don't know who the middle one is. Oh, okay, that's Momo right? I'm not too sure actually. Yeah the one on the ground is Momo.   Dayeon, okay so Dayeon is the the rapper and then that's Momo holding the phone and then who's that in the, in the middle? I've seen this. I've seen the script. I indefinitely hear her when it comes to the stretching, I can't, I'll, I bit my knee but man I can't stretch once I'm in it. What happened? I was stretching my leg on a bugfowl on the table. Oh is this like you got to get the paper off? So that was Dayeon versus Mina. All right, it wouldn't be Dayeon, it would be Dahyun or something like that. Momo is amazing. Damn, I don't give people respect, they can do the splits or just aerobic stuff. Is it aerobic or an aerobic, I don't know what it was called. Oh my god that scare attack from before still got me. That's true, you're right. I'm pretty sure I said her name was Zuyu or Tuyu. One time someone had to go in there but Tuyu is it?  I think I'm getting into a good group. Yeah that was good, I'm pretty sure I'm gonna love this group and all. I love their music but I don't know much about their personalities but this was freaking good. It was cute and funny and at the end with the love you, love you and then like stop it and I was like nah I think I'm getting myself into a great group but yeah definitely Momo, she stands out for me. I'm pretty sure she'll be my bias with TWICE. She is absolutely amazing and also let me know if I got the members that I guess write their names right and got the pronunciation of their names right or wrong. Comment down below because I'll definitely love, I'm definitely gonna love getting into this group because they are freaking amazing but if you guys have got any videos you want me to react to for TWICE please comment down below as well because holy moly, coaca moly, I really just want to get into this group but I want to know all the members because from this like five minute video their personalities were amazing so I just cannot wait to see the rest. If there's any other funny moments you guys want me to watch if there's um what is it called like the unhelpful guide to a group like if you guys want me to react to them as well just like comment down below what you guys want me to react to from the script because holy moly, coaca moly, I really want to just get into them. I think I'm about to stand in an amazing group okay other than that this video is gonna be all for this video I hope you guys did enjoy and if you guys did definitely show some support by leaving a like and also comment down below if I got the members right or wrong and also other TWICE videos you want me to react to and also subscribe because I need to channel because there will be more TWICE reactions and it's if you want them but there will definitely be more TWICE reactions to their new songs and comebacks whenever they release those and when that happens so yeah subscribe for those as well and yeah other than that I hope you guys have a great day and just keep on smiling and adios amigos


If you have cats, you've undoubtedly seen one of them spew up at some point. It is usual for cats to vomit, but it is never natural for them to do so. However, it is not always necessary to treat it, nor does the cat need to be rushed to a veterinarian every time she vomits. You'll learn when to take a vomiting cat to the doctor, why cats vomit, and what treatments are available to make felines feel better in this resource. Chronic and Acute Vomiting in Cats Vomiting up can be separated into two broad categories, Chronic and Acute Vomiting. Chronic vomiting means throwing up with some regularity for a long period of time. The cat usually only vomits once or twice with each occurrence. When a cat who usually doesn't vomit starts vomiting, that's the acute type. This is generally a concern for you and your veterinarian only if the cat vomits multiple times. The diagnostic workup and treatments for acute and chronic vomiting can differ, as does the urgency of when to bring the cat to the veterinarian. More urgent care is usually required for a cat with acute vomiting. The exception to this is a cat who is only vomited one to three times and is otherwise normal. If the cat still wants to eat and does so without continuing to vomit, is acting normal, and seems comfortable, she does not need to be brought to a veterinary hospital unless you know that she ate something toxic. If your cat vomits more than three times, cannot keep food down, and seems tired, she should be seen by a vet as soon as possible. She may just be experiencing some passing nausea, but if it's something more serious, treatment should be implemented as soon as possible. Unless the cat is in severe discomfort or does not want to move, she normally won't have to go to an emergency clinic. But if she seems to deteriorate quickly through the night, then an emergency visit is recommended. Cats who are continuously vomiting and not keeping food down are prone to many secondary changes, most notably liver disease, so waiting to get treatment can be dangerous for them. A chronically vomiting cat should still be seen by a veterinarian, but it's not urgent if the cat is still eating and keeping food down, is not showing signs of weakness, and seems comfortable. If these things are not true, a chronically vomiting cat is either an acutely vomiting cat or is having an acute crisis of whatever is causing his chronic vomiting. In the past, a cat who vomited a few times a month was considered normal, but that idea is changing. There is even some thought that a cat who frequently vomits hairballs may have some gastrointestinal disease that does not allow the hairballs to pass normally. Treatment may not be implemented for a chronically vomiting cat, but an exam and a workup should be done to ensure that the cat is comfortable and does not need any intervention at that time. Causes of vomiting in cats. The causes of acute or chronic vomiting can be the same, but there are exceptions. Toxins are generally not a cause of chronic vomiting, unless a cat is chronically exposed to the same toxin, such as eating a toxic plant. Digesting a foreign body is not normally a cause of chronic vomiting, although if the foreign object remains in the stomach, it can be a cause of chronic vomiting. Unfortunately, vomiting is a very vague symptom, and the causes are extremely varied. In fact, almost any feline illness can result in vomiting. In general, the causes of vomiting can be placed in one of these categories, toxins, drugs, diet, including eating inappropriate things, gastric, stomach, intestinal, organ dysfunction, endocrine, neurologic, typically brain-related, infectious, and cancer. In each of these categories are dozens of specific diseases and syndromes. Hello. This video is sponsored by Beemix Pets. Are you looking for high-quality cat collars at an affordable cost? Check out BeemixPets.com. Use coupon code KittenLife to get 20% off. Diagnosing the cause of vomiting. It can be difficult to diagnose the cause of vomiting in a cat. Most cases of acute vomiting are transient and improve with just symptomatic therapy and time. However, a basic workup is often recommended to ensure that a more serious problem is not going on. The starting point in determining the cause of vomiting is getting an accurate history. Here are some questions your vet might have. Was the cat exposed to plants and other toxins? When did the vomiting start? What is the cat's normal diet? Does the cat go outside and if so, does the cat hunt? What is in the vomit? Is the cat on medication? Is there also diarrhea? Is the cat eating? When does the vomiting occur in relation to eating or other activities? Is the cat losing weight? Is the cat drinking a lot or urinating a lot? Does the cat play with string? Based on the answers to these questions, your veterinarian will have a better idea of which diagnostics, if any, to use.  Veterinarian examination and testing. The next step is a thorough physical exam by your veterinarian. The veterinarian can look for things such as abdominal pain, masses in the abdomen or elsewhere, an obvious foreign body, such as a string under the tongue, evidence of weight loss, a heart murmur, an enlarged thyroid gland, and a fever. Again, the exam can help determine which, if any, diagnostics are needed. Barium study, ultrasound, and endoscopy. Often, x-rays do not diagnose the problem other than the presence of foreign bodies and a few other conditions, but they help determine if further abdominal studies are needed. These other studies could include a barium study, which will help determine if there are foreign objects in the intestines or if there are motility issues with the intestines. Endoscopy is a way to look for foreign objects in the stomach that do not show up on x-rays, and it can be used to retrieve foreign objects. This procedure also allows viewing of the lining of the stomach and upper intestines to look for abnormalities and can be used to collect samples of the upper gastrointestinal tract. Exploratory surgery. In a cat with persistent vomiting that is not being controlled by symptomatic therapy, exploratory surgery may be needed. This is true with some acute vomiting situations and some chronic vomiting situations, namely, looking for signs of intestinal cancer, non-intestinal abdominal disease, or inflammatory bowel disease. The surgery is used both to diagnose and fix the problem by removing the foreign object. If no foreign object is found, then biopsies can be taken during the surgery. The intent of doing surgery for chronic vomiting is normally to take biopsies of the intestines, stomach, liver, pancreas, lymph nodes and any abnormalities in the hope of diagnosing the problem. The most common things to diagnose are inflammatory bowel disease or a form of cancer. As a diagnostic tool, surgery is preferred over endoscopy by some veterinarians because the whole intestinal tract can be evaluated, as well as different organs in the abdomen. In addition, full thickness and larger intestinal biopsies can be taken during surgery. Furthermore, biopsies of the liver, pancreas and lymph nodes can be taken. Conversely, endoscopy may be preferred because it is usually less expensive, usually results in a representative sample of the intestines to provide a diagnosis, and is much less invasive. It can take several weeks for a cat to recover from surgery, while an animal who has had an endoscopy at endoscopic biopsies usually recovers within a few hours or within a day. Because some of the diagnostics can be invasive and expensive, endoscopy can run up to $1,500 and exploratory surgery can cost more than $2,000. Many people elect not to do them. There are treatments that can be implemented without a full diagnosis, but those decisions will require communication between you and your veterinarian about the risks of doing those treatments. Treatments for a cat who's throwing up. The treatment for vomiting varies greatly based on the cause, and describing the treatment for each individual cause is beyond the scope of this resource. If the new food controls the vomiting, it was partially caused by a dietary intolerance or allergy or possibly low-grade inflammatory bowel disease. If you enjoyed this video, kindly press the like button. Also don't forget to subscribe with notifications on, so that you don't miss out on videos like this. Thank you for watching.


I found one. The body's uncontested need to devour an explanation. This poem is really, I wanted to write a poem about the natural world, and anytime I try to write a poem about anything I sit down and try and write, nothing happens. So it's always a pleasant surprise when something comes and you're like, oh, this is that. And it was a curious, like, so I read about, I cannot remember the Japanese word, but forest bathing, there's a word for it, and my mind did this kind of mental exercise of going into the forest and then suddenly sniffing spores and sniffing moss.  And so the whimsy of that was like, OK, follow that through. The body's uncontested need to devour an explanation. I am bathing again, burying my face into the great nations of moss. I am leaning in, smelling the emerald mountains and the little inhabitants crossing over rock-like boulders and tree trunks emptied bit by bit. My nose must come to them like a probing spaceship causing a mighty eclipse. They speak in whispers, but do not shriek when gazing into the dim landing bays of my cavernous thoughts. I am grazing like a Dionysian. I come not with religion. I come yearning for first spring and a thirst for spores pooling like mercenaries in the dark. The little gods of the forest live here. I want to ingest their verdant settlements until they carpet my cavities and convert my raptorial self into its own ecosystem off into the green. So when I wrote that first line, I am bathing again, and I listen to it. I am bathing again, burying my face into the great nations of moss. When I repeat I am again, it's almost like I'm cranking. I am leaning in, smelling the emerald mountains and the little inhabitants crossing over rock-like boulders. This is, along with repetition, sentences are a way for me to create music, but also to kind of help follow through on syntactic meaning. I'm also trying to be imagistic. I want a reader to as much see as they hear what I'm saying. So imagery is really, really important to me. And in this particular case, I truly believe that poems are not just merely about witnessing, bearing witness to events that happened in our lives and trying to extract meaning there. I believe we can be as imaginative as any speculative writer or as any fiction writer. I don't believe all poems need to be nonfiction is what I'm trying to say. And so this particular poem contains a bit of truth. All of us hopefully want to connect with, at least in this day and age, want to connect with live things everywhere, plants, trees, rabbits, foxes, ingesting natural spaces is a way for us to kind of widen our humanity. So that poem was fun to kind of think through. I want to ingest their verdant settlements until they carpet my cavities and convert my raptorial self, thinking of dragons, into its own ecosystem off into the green. Have fun writing that poem.


Hey everyone happy Tuesday April 6th here with your day trading recap. Another nice winning day today plus 1,940 on the morning and done by about 10 30 a.m. So nice that's why I like it short sweet take your money and run all right so let's go over these I'll show you what we did a couple mighty 90s in beyond and Tesla both winners beyond for plus 118 Tesla for 405 I had a small pairs trade winner for 105 and then on the runners my only loser on the day was this $60 loss in Airbnb had a biggest winner was MU 676 PLTR plus 106 Roku plus 320 Uber plus 270 total on the runners over 1300 so back to back really nice green days let's take a look at these and I'll show you what we did starting with the mighty 90s in beyond a meat so in beyond had this big push up in fact let me expand this so you can see a little bit better big push up in the morning I was really patient on this getting in and I was waiting really for it to get closer to this pivot so I got short really close to the top here and just caught a nice little down draft there I was really small and then when I was trying to get out it bounced on me pretty quick so I didn't get as good of a fill so only booked 118 on that one but still green nonetheless in Tesla had a nice mighty 90 in Tesla on this push lower I started getting short or I didn't start I just got excuse me it got long right here near yesterday's look I think a little bit below that took a little bit of heat for a few minutes and then it just really fired up ended up closing out my last piece up here so booked a 405 profit on Tesla onto the runners Airbnb so Airbnb was a winner for a lot of the trade I did jump back in and added to it which is ended up what putting put me in the red but had this big spike in volume this pullback got long here pushed up broke new highs I got out of the majority of my position here I think I only had like one contract left when it pulled back I got long again looking for another potential continuation just kind of chopped around chopped around chopped around almost faked me out right there bounce back up I thought we were going to have a chance and then when it just flushed here I ended up just cutting out and and taking that $60 loss overall so not too bad my only loss of the day MU my biggest winner plus 676 an MU had this initial push up big spike in volume and waited for this pullback here got long right in this area and then when it fired up I got out of the majority of it I got out of three quarters of my position up here when it pushed down here I got out of the rest when it broke below this consolidation area I got out of the rest except for I held one contract just to see if we might get another pop higher well obviously that did not happen so when it finally broke down kind of in this area I ended up cutting out of my last contract but still booked a nice profit of 676 pl tr plus 106 pl tr here it is some pl tr is really weak and so on this spike in volume waited for a bounce got short right here got out of half about right here and then another quarter here so I was out of three quarters of the trade I just kind of started chopping around and when it started to push up I ended up cutting out of the last piece and just booked a small profit and then in Roku Roku Roku is a nice one unfortunately I didn't get much size on I had this big spike in volume so I was waiting for a pull back it didn't pull back much but I didn't want to miss it so I just jumped in with a couple contracts I was going to scale into more size if this thing pushed lower it did not just kind of pushed up got out of half about right here and then on this push up I got out of the last piece so if had I had more contracts on I probably would have let one run but still a nice profit 320 and then lastly Uba in Uber I booked 270 and it was just another nice upside volume runner waited for this just barely a pullback actually no I missed it here I missed this first push it came all the way back down and I got long right here and then it pushed got out of some pushed got out of some more and then on this last push I got out of my last piece right here near the top so just small size we still booked 270 so plus 1,940 on the day we'll be back streaming live Wednesday Thursday we'll be offline Friday so look forward to seeing you the next couple days in the live stream room see you then