Okay, so now we are on week 5 and we will be discussing tutorial 5, okay. So let us do a quick recapitulation of what was done in week 5. We discussed about the commutator operators. Going from the classical picture where we have portion bracket from portion bracket how one talks about when you go to the quantum mechanical analogy, you obtain the commutator operators. So these commutator operators when you talk about them, if the two operators say A and B commute that is A and B commutator is 0, then one can do the simultaneous measurement of these two operators. And if A and B do not commute, then the simultaneous measurement of A and B is not possible. That is what resulted into what you know now as uncertainty principle. And then once you talk about the commutators, you talk about compact and non-compact observables. And this tutorial will cover all these topics which will include commutators that is compact operators, non-compact operators, determination of eigenvalues and eigenvectors. Is it possible to do a simultaneous measurement when two operators in the form of matrix are given to you? Then we will talk about the time evolution operator and then how the eigenstate is evolved in time. So when you go from time t is equal to 0 and when you find the eigenstate or eigenvector in the evolved state using the unitary operator. So this choice of the basis we will talk about that, then we will talk about from the commutator relation how one obtains various observables or various terms like for example in problem number 2 you can see or in problem number 4 and 5. So these 3 problems out of 5 you will be using commutator relation obtaining certain observables or for example in the fourth problem you can just see here in the fourth problem you have to obtain the mean momentum of the state using the commutator operator. So I hope you will enjoy this tutorial. So let us just start with the first problem which talks about a two state quantum system as the basis state plus ket and minus ket and these basis state are not the eigenstate of the Hamiltonian of the system. So at time t is equal to 0 the system is either in state so to start with it is in plus ket state. Then as it evolves in time the state is going from t is equal to 0 to t to t etc then the system is in plus state and then when you are in time t by 2 sorry t by 2, 3t by 2 etc you are in minus ket state. So you have to construct a Hamiltonian which will describe the above physics plus and minus ket are not the eigenstate the Hamiltonian this is what is given to you because the system is either in state plus or minus at different time. So when it is evolving in time so what is given to you is that at in this state plus ket for time t is equal to 0 t to t that is to say that nt that time the system is in plus ket state and the system is in minus ket state for t by 2, 3t by 2 that is you can write this as 2n plus 1t by 2 so the system is in minus ket state. So now there are two ways to go about this what I can do is I can start with the basis which will be the eigenstate of the Hamiltonian and use a special case that is I can use a special case where in I know the eigenstate of the Hamiltonian and using that I will obtain the Hamiltonian. So first thing would be we choose a basis state or the eigenstate choose the eigenstate of Hamiltonian that is to say that I would choose these states 0 and 1. Now these are so called you can say that as conjugate basis state. So let me rewrite this conjugate basis state. So that is to say that we already know that these definitions we already know right 1, 0 and this is nothing but this state. So you can define these in this form. So what you have is you have these eigenstate which you can actually write in terms of these plus and minus kets. So how will you do that? In this one more assumption we make that the eigenvalues thus in this case what you have is the eigenvalues will be 0 and E. So one of the eigenvalue I choose it to be 0 and that would not affect because the global phase will not change. So the choice I make here is 0 and E that is the eigenvalue one of the eigenvalues 0 and the other is E. So the Hamiltonian will look like so my Hamiltonian will take the form. So Hamiltonian will take the form this will be the form of the Hamiltonian. So we know this okay. Now the thing is the question was that we have to obtain a relation between these time evolution I mean this time with respect to the energy. So how will you do that? First step would be I would again just a reminder that this plus and minus ket are not the eigenstates of the Hamiltonian but it is possible to have a linear combination of plus and minus ket such that they are the eigenstate of the Hamiltonian. So what I will do is I will define plus state. So this is how I define plus state it is a linear combination I will write again it is a linear combination of plus and minus state and ket 1 is a linear combination. So this is the two possible combination I can have. So one has to invert it. So when I invert this would give me the definition of plus and minus ket in terms of the defined what you call the defined 0 and 1 state this is what we have right. So this would be I will write this as after inversion I will have 0 plus 1 this you can do it easily. So I have ket plus and ket minus in terms of the kets 1 and 0 and 1 I need to change this okay. So the next step would be now I have these kets in terms of plus and minus eigen ket. Next I would do is so this was step 1 next step what I will do is I will have a so since you can see this is a evolution in time. So now the unitary time evolution operator take me from time t is equal to 0 to time t is equal to some time t. So here we know that initially to start with at time t is equal to 0 the particle is in or the system is in plus ket state. So you have to go from so let me write a general expression first. General expression for time evolution operator is nothing but if you have n such eigen states or eigen basis then you can write a general expression as this is nothing but a complete set of state.  So in this case we have 0 and 1 as the ket. So this would get modified as so basically when you write t, 0 it will mean that I am going from t is equal to 0 to some time t. So that will be nothing but so here we actually do not need this summation sign because I am writing term by term. So this would result into one of first eigen state is 0 I have eigen value is 0 which I have chosen and the second eigen value let me write it values. So second eigen value is E. So that would result into state 0 plus I will have e raise to i minus i t upon h cross 1 1. So this is my time evolution operator in terms of my complete set of state that is ket 0 and ket 1. Now using this time evolution operator I can evolve the wave function or the eigen state, state vector from time t is equal to 0 to another time t and this we need to do to find out the Hamiltonian. So the next step would be next step would be I will write the state as the unitary operator that is t, 0 which I had defined in terms of so at time t is equal to 0 you will evolve this from time t is equal to 0 to t. So this will be the time evolution operator or the time evolution equation for the eigen vector. So at time t is equal to 0 the system is in plus state. So let me rewrite this as t, 0 this is plus state again now we have this this is nothing but you had written let me go back. So here we had 0 and 1 as the ket 0 and 1 as the ket. So coming back here let me write this as psi of t now will be I will write in terms of the plus state again the plus state or the plus ket can be written in terms of 0s and 1s. So this in turn this would be so this is what I have now the wave function or the eigen state Schrodinger time dependent equation. So let us go to the Schrodinger time dependent equation. Let me write here Schrodinger time independent equation using Schrodinger time dependent equation what we do is we obtain. So this is the special case we have considered for obtaining the relation between the time and the energy eigen state. We will also discuss a general case after this. So this will be dou by dou t. So this is the e part and that is nothing but h psi of t that is. So this will be a time evolution of the eigen state and using this we obtain the Hamiltonian. So now we have to calculate the left hand part this can be easily done and you can do it as diy one step. I am leaving this space for you you can just obtain the Hamiltonian from here which will be of this which will be of this form if and only if your energy e is holding this relation to pi h cross upon t. So let me quickly go back to the question once again. So what one need is to construct a one parameter Hamiltonian which produces this above physics that is system is in plus minus state plus state and then minus state and then plus state at a regular periodic time of t by 2 and what we have done is we have constructed that Hamiltonian which depends on t. So coming back here this is what we obtain. Now I also want to discuss a general scenario. So apart from this what we have done I will discuss a general scenario in which so let me write this here as a general case. So as I already said you all that this plus and minus state are not the eigen state but it is a possibility that a linear combination would give us the eigen state. So let me just write general expression general expression eigen vector what I do is I start by writing a general eigen vector which is nothing but the general form that is psi of some t. So previously we tried to evolve this eigen vector from psi is equal to 0 I mean psi at t is equal to 0 to psi of t. Now here what I am doing is I am starting with a general expression for the eigen vector. So the eigen vector of the system the system which is the system the system we are talking about which is periodically is either in state plus ket or in state minus ket. So let me write a general expression. So let me define some alpha of t plus beta of t minus. So this general case I am starting with this general case wherein the wave function or the eigen state vector is either in plus state or minus state. So how do we understand this? So actually my alpha of t is nothing but cos pi t by t. So you can easily see this because when I have alpha of t as cos pi t by t that means I am for the case if I say psi of 0 what will sorry this has to be. So psi of 0 will be alpha of t that is I am talking about this cos pi t the system will be in the plus state with some constant. There will be some constant. Similarly I have this beta of t. I am defining this beta of t as sin. So this will satisfy this relation. So I will check for this. This will be again a constant times I get the eigen. So this C constant C which I am writing here can be plus or minus 1. How? So let us just see an example wherein when t is equal to 0 for the first case when t is equal to 0 or pi also t to t etc. For these values of t you will see that alpha of t becomes plus or minus 1. So always the system is in plus ket state and beta of t becomes 0 and when I take the second condition I mean the second step. So when t is equal to t by 2 3 t by 2 etc. So this goes up to n t and this goes up to 2n plus 1 t by 2 which we have already seen in the previous general case when we talked about the general case. So I am sticking to the same color and then here what you will see is alpha of t is always 0 for this condition and beta of t takes the value plus or minus 1. So from there you can see that C will always take value plus or minus 1. So now what I do is let me go to the next step. Now it is easier, now you just have to use the Schrodinger time dependent equation and obtain the result. So the wave function or the eigenvector which we have defined let us write in the matrix form. So when I am writing it in the matrix form how will I write it? I will write this as psi of t will be I am trying to write in the matrix form. So the plus plus component will be alpha of t and this will be beta of t. So this is the eigenvector or the eigen basis which we have used. So this will be nothing but cos sign. So once you define the general eigen basis or eigen state the next step what you will do is use the Schrodinger time dependent equation time dependent. So that is nothing but ih cross dou psi of t that is equal to h or when I am writing it in this representation wherein I am talking about just let me write it in this form that is what I want to this state. So from this to be very quick I will just put this terms and you must verify this by yourself. This will be I will have a factor of ih cross pi by t. So I have a i coming from the exponent.  So this will be sin pi t upon t cos that will be h of cos pi t upon t sin. So I have sorry there is a ih cross coming from here this pi t when you take the derivative and the signs will change.  So basically when you try to write in terms of E the energy will be the same as what we obtain in the previous expression 2 pi h cross upon t. So E what we obtain here will be similar to you can see the relation. So if you want to write h in terms of E so basically you will obtain the energy as 0 minus E E and 0. So we have obtained Hamiltonian in terms of a single parameter t. So you have I think already done some relations like x. So there are commutators like x, p. So famous commutators like x, p and then you have you can check whether a Hamiltonian operator commutes with the momentum operator, the position vector. So let me put a cap here. So x cap, p cap where x and p are the operators and operators are represented by a hat or a cap. So this is an operator representation. And this is called as a commutator brackets. 2 operators commute operator a and b commute that means that a and b when you put in the commutator bracket it is 0. You will see in coming lectures that why do we check whether 2 operators commute or not. So when 2 operators commute they form a simultaneous eigen ket. So the measurement of a to not affect the measurement of p that is what it would mean. So when you operate an operator a, b on a eigen vector this will be equal to, so interesting part of these 2 operator is that the measurement of a and b are independent. And hence you can form a simultaneous eigen ket for this vectors. And this will be useful for coming lectures. This is a slight background. And as we know that operator x and p gives ih cross. This is the relation we obtain. And I think you might have proved some time or if you have not proved this please try your hands on prove this. I will not discuss the proof in this tutorial but you must try out x, pn. You can also try this is 1. You can also try what do you obtain n operator p. So x raise to n on p. So x on pn this I will give you this result which you can use in the problem. But it would be I would suggest that you must prove this identity. So this we are going to use in this tutorial too. So in second question you are given 2 operators position operator x hat and the momentum operator p hat. And you have to write this operator evaluate the commutator of these 2 operator. So let us try evaluating the commutator bracket or the commutation relation of x and alpha e raise to alpha p. e raise to alpha p cap I can write this as 1 plus alpha p hat plus alpha square upon 2 factorial p hat square and so on. You can write the exponential series. Now when I do this would be commutation of the position operator with these terms of the exponents. This is a simple way to do plus dot dot dot. So the first part this is the first term. Second term would be this third term would be x hat p square plus all the terms. So remember the operator times a number will always give you 0. First term is 0 plus alpha i h cross. Now second term you will use this here it will be square this square n is 2. So you have 2 i h cross p.  So what will be the result of this alpha i plus you have the other terms alpha i h cross plus you have 2, 2 will get cancelled. You have alpha square h cross p hat I have not missed anything okay. I have a factor of i also. Plus n terms. So in general form can I write it as i. So this I can take i h cross alpha and I have 1 plus second term would be alpha p hat plus so on. So this is nothing but again you get an exponential series. So this would be x e raise to alpha p hat is nothing but i h cross e raise to alpha p hat. So this is what I get after performing the and I have missed the alpha which I put here. So this is the expression I obtain for commutator of x e raise to alpha p. Now if I replace alpha by my question is i a upon h cross.  So this is what I have obtained after finding the commutator of these 2 operators. Remember a is a constant and it is having the dimension of length dimensionally it is the dimension of length you can see from here it is very simple to see from here. Now the second part of the question is show that x is the eigenstate of this operator. The eigenstate of this operator I have a exponent e raise to i a p hat upon h cross I operate on x. So when I operate x hat on x I obtain x times x. So x is some eigenstate of a positive operator you have to evaluate that. So now if I operate this on e raise to i h cross so now we have the commutation relation. So if I write x hat as this operator I define as commutator of x i a operated on x minus or plus let me see this is x e raise to i then I have a minus so I will have a plus e raise to i a p hat upon h cross on x. So this is what I have this would give me this relation we have seen gives this commutator gives minus a e raise to i h cross and operating x on the vector will give me x. So I have x minus a e raise to minus e raise to i a p hat upon h cross. So the final step is e raise to i p hat upon h cross x will be x minus a e raise to i a p hat upon h cross x. This is what I had correct. So what do we observe this is some another vector x. So what do we obtain here is that e raise to i p upon h cross x is an eigenstate this operator let me call it as some capital X. So this capital X is an eigenstate of operator x with eigenvalue x minus a.  So if this operator is operated on x it should give me same x and then get x capital X back but here it does what it does is it gives me x minus a that means it translates the particle to minus a. So this is a very good exercise wherein you understand the operator how the unitary operator comes into picture for this particular problem in the previous problem also you have seen a different flavor. So with this we stop here.


we've got our tools ready there's where we're at so far we should be we should really be home now but we've lost two hours cleaning the cavity and an hour and a half going to warrington so there's half a day that we've lost that's ready for building up the padstone going in i'm going to do this side next right we're set up we've got our tools ready we've uh i've got that part set up kindly for the dust sheet set up for me on the other side 10 blocks well nine brick then slow to demolition what a pad yeah it's 10 o'clock so we're having a good break yeah so we'll catch up to break let's go so you're coming to see this so there's the socket you'd imagine like a normal place yeah i can hear that you'd think normally you'd just go up wouldn't you well not this one i don't know what the hell they would they were slushed on when they started doing this but pardon yeah but they obviously must meet up at the socket so if they're on an angle they're legal you care them to go vertically or horizontally they're not supposed to go up on an angle oh there you go well it's just coming sense as well look at that one of them's not even in the this that's probably going to the socket that's pathetic that yeah i don't get how you you do that right right you want your music now then you want his music so put your time lapse good news is it used to be a door here what was that the clock fell off the wall get a strap on that oh no i can hear them o'clock good yeah anyway yeah good news is there's a door in the middle it's been bricked up with the fact the thermolites so that's going out a lot easier the thermolites are nice and loose as well yeah i'm just trying to get the plaster off see where this winkle stops so there aren't much i can get out best thing you need to do is work your way along the top and pop that top course off even use the bar to prize them off okay and i'll get over here get this so um that's just on my wall so we'll film this picture now yeah it's just blocked in no ties it's just shoved in yeah so the doorways like a like a video game so it was like the mystery door oh yeah off color you just smashed through like a mario something yeah well i've just gone to stop the camera and it wasn't going so sorry about that you missed that so brickwork complete inside and outside just need to tie up a little around this area and then i'm going back there to help Alex spinning around after something almost no battery left i left this on during lunch there's where we're at so far we should be we should really be home now but we've lost two hours cleaning the cavity and an hour and a half going to warrington so there's half a day that we've lost but um hey ho no no unfortunately that isn't on the fly can i talk carry on thanks unfortunately that's not the finished product it looks like it but no carry on no i'm on the toilet i'm on the toilet so basically that's ready for building up the padstone going in i'm going to do this side next because this side goes past that wall because it will run right up to the nib we left this nib on to give the extra bit of strength here because you've got the steels going across here and yeah that's it basically Alex is going to see how it's taking this lot down clear it all out got the spear hacker already to get the steel in and propped and then i'll put the padstones underneath that so i'm going to change the battery and put you back on timelapse you're going to get a little surround shot of the inside in a sec i'm just going to do the outro out here and then we'll pan to the finished footage but i can show you this side as well though so there's the window new lintel there to match the new window length all break up a nice brick match there's the finished result of that uh little awful patch with the bricks we picked up this morning god that does not feel like it was this morning that feels like i feel like the other day now was it hell but and in a minute you'll see this the results of the seal work but for now i'll just say thank you all very much for watching if you enjoyed be sure to give us thumbs up and if you're new to the channel you want to see more be sure to subscribe and tap on that bell that way you'll always know when notified that's always a massive help and we greatly appreciate the support very much appreciated this has been bricklaying with steve and a very dry alex rainproof and we will see you in the next one cue the steel


I hated that video so much, IT SUCKED SO BAD! Ah, what's up wobbly boys? In today's video, we are going to be doing a Q&A about a certain topic regarding these two videos. Recently, here on the JellyJest channel, I kinda dropped the big bombshell. I have actually been making content on this platform for over 12 years now. The 28th of February is actually my 11th year anniversary. Now if you haven't seen those videos, I highly recommend watching those before this one. Today, I'm going to be answering your extra questions that you wanted to know about the whole situation. Let's get to it! What inspired you to pursue an animation channel rather than anything else? To be honest, I just really liked watching a bunch of animation channels back then and yeah, it kinda inspired me to make my own. On this channel, you can expect to find some story times and some other random bids along the way. All in form of...animation. I always knew I wanted to do something sort of artsy or craft-related because I have always been obsessed with those videos. Like if someone has to customize something, boom, I've clicked on that video already. How did you come up with the idea for Dazz with Dopey? Okay, Dazz with Dopey was like my main series on my channel about this little hamster doing some dares. Clearly, that was only meant to be like a filler series, but it stayed. It stayed for a couple seasons.  No, I mean, I haven't watched a series in a very long time, so I would probably cringe a lot if I go back on it. Something I did watch recently though were my two LPS McDonald's videos and I filmed my reactions to post over on my second channel, Jolly Jazz. The video is out now, so be sure to go check that out. It was a fun one. What did you feel, Slash, do when your first channel got 1K subs? Sorry, I didn't know if that said subscribers or subs. Man, when my first channel got 1K subs, honestly, I probably peed myself because that is such a milestone. And from what I remember, I think I did a contest because contests were like so big back then. Yeah, it was, I guess kind of wholesome. I remember more of my 500 subs special compared to the 1K special. There were so many specials, OK? Don't even get me started on the specials. Will you ever return to the channel? I think that answer is kind of obvious. Moving on. Why did you not make a video telling your fans why you stopped? They would have supported your decision. So why? When I decided I didn't want to make LPS videos anymore, I honestly just didn't have the guts to confront my audience and be like, hey, I'm up and leaving this channel because for a long time I really wanted to juggle the two and, you know, make everyone happy. But sometimes it's just not possible, OK? Who inspired you to start an LPS YouTube channel? OK, so there were a lot of creators I watched when I first started out, when I was like 10. Fantasyland Films. Man, I binged that Rapunzel series in one day. LPS Hannah for sure, she is such an icon and she was my friend on LPS Tube for a very long time. Of course, Sophie GTV. Sophie GTV was like the queen of LPS Tube. Like everyone knows about her LPS popular series even if you weren't part of the LPS community. That's how iconic it was. So this person has two questions. First one is, did anyone ever talk about your channel not knowing it was you? No, I never had that in my life and I'm very fortunate about that. I don't think anyone in my friend circle or anything was on that side of YouTube. With the Jelly Jess channel, someone where I used to work kinda watched my videos and talked to me in real life and kinda got the idea of, I think this is the same person. Yeah, she was all cool about it. We're friends now so literally the weirdest thing that's ever happened, honestly. And second, did anyone treat you differently when they saw either of your channels? No, all my friends and people have been very supportive and yeah, much, much love. Have another secret account, I'm curious now. If there has to be a secret account, I will say I did make a craft channel back when I was like 12 and I didn't upload to it. So there goes that secret. What happened to all the littlest pets you had? So those clips that you saw in part two of those videos, they are only from a few weeks ago. I still have the whole collection. All the pets, I mean. They have been packaged up since I quit and in the cupboard not doing anything. I will say I did downsize on a lot of all the accessories and the houses. Did you watch Sophie G TV? Of course I did. I used to binge watch LPS Popular numerous times. It was great, I loved it. It's very much like mean girls if you haven't seen it. I really love the sayings. Oh my dog, what the tail? Classic. Did anyone try and stop your journey throughout your early days on YouTube? No, not really.  What I was doing off camera anyway. What do you think is your cringiest video? There are actually so many videos I hate with a passion.  One of them when I was really not enjoying LPS 2 when I tried to make a comeback, I think that was the Lego movie parody. Papa, help! I've got you son. It sucked so bad. Even the Boss Baby parody, I hated that video so much but Boss Baby was like such a big thing back then. I really felt like I needed to do a Boss Baby parody but I was so uninspired by anything in the trailers to come up with anything. And the fact that I had to explain a joke from the trailer and add it into the parody just proves how bad that video was. Please don't go and watch it. If you never stopped and still had motivation, do you think anyone would recognize you and would you still be hiding your identity, AKA face? Well, the identity part, I mean I'm still hiding my face so I don't think that would have changed. People recognizing me, I really don't think anyone would. It kind of blows my mind that I have definitely, at least in my lifetime, I've walked past someone that watches my content but I don't know and they don't know and that's just life at the moment. There was always an ongoing joke in my family that someone would recognize my LPS pet world's hands. No, it hasn't happened yet. What's your favorite video you've ever made on any of your channels? Okay, I will start off with Jelly Jess. I probably would say the marrying a stranger online as a nine year old. That video was really fun and for LPS, that's a hard question honestly. I would have to say the two McDonald's kids that I mentioned before, they were fun to make and full of crazy characters. What was your favorite pet that you owned when you were younger? I don't know, honestly there's probably a good handful that I will say I really like that sort of pet.  I also really liked the deer shapes. I'd probably say the snake. If you didn't decide to become a creator, what would you be doing? YouTube isn't the only thing I'm doing, I'm actually doing a couple other things outside of this. I don't know, it would be awesome to be a full time creator if that's ever possible, but I'm doing multiple things at the moment. Got a crazy work schedule, but I'm loving it. But I'm done, did you ever do stop motion for those videos? I feel like I did, but I can't think of anything. If it was something, it was very short because I just didn't have the motivation or time to do that. But some people made like really big ones and they were crazy. What was it like to be a child in the content creating business alone? Okay, so when I was a younger child, I didn't really have much of an audience. I was literally just playing with toys and you know, if someone was watching it, they were watching it. I remember the first time my first ever video got a hundred views and that was mind blowing. Like I didn't even think going into this that it was going to be a job. I just really liked, you know, LPS and I found a whole community online who also liked LPS and it kind of just worked out. If you could go back and tell your younger self something, what would it be? Stop stressing so much about people not supporting your decisions in changing content. I'm glad things have kind of worked out, but I don't know, I was really scared of what people thought about me or I didn't really express my opinions well on the internet back then. Or I made it out to be like happy and fun videos when I'm on the other side of the camera being like, when can this end? Have you always enjoyed making art? If so, could you make a video showing your old art? Love your videos by the way. Thank you. And second, I have actually been thinking of doing a video like this for a while. If you do want to see it, let me know in the comments below. How much of an influence did LPS have on your art style? Honestly, I have never thought about that, but if you're looking at my character, if you look at the eyes, I can kind of see LPS vibes there. Okay, do you still have your littlest pet shop toys and how are they doing if you know? How are they doing? I haven't asked them, but they've been stuck in a cupboard for years now since I quit, kind of like Toy Story 3.  I imagine it must feel pretty good. Oh, I tell you what, it feels amazing. I feel like there's a whole level of trust going on now. We can all talk about everything. LPS words aren't blocked in the comments. It's great. But to be real though, I have been loving it. Just having this whole connection again with you guys and people that have rediscovered me from their childhood, it's been great. It has been such a journey. And you know what? I love every second of it. Did you join any cringe LPS fan sites? I remember seeing a lot of them from my cringy Amino days. I wasn't a part of any of those websites, except for LPS Amino. It kind of flopped after everyone started promoting it though. But it was good for maybe like a month. And I got to talk to a lot of people and see what everyone was up to. It was great. RIP LPS Amino. What was the hardest thing you dealt with during your YouTube career? Just kind of not having the passion for it anymore. I feel like that was the hardest thing I struggled with. I really just didn't want to disappoint anyone. But I was disappointing myself. Okay, next question. How was it like? Did you enjoy it? Which characters were the most fun to act out? Ooh, that's a good question. The crazy cat lady. She was always great. Honestly, Dopey's family. Dopey's family had a bit of everything. And I will say those videos were also pretty fun to record as well. Just Dopey's mom. I really, really liked Dopey's mom. Family meaning! She was just so oblivious to everything going on. Did you get a YouTube play button for the Ops channel? The Black Ops LPS channel? Nah, she's in Vinnie's somewhere. It's on my shelf down there. You can't see it, but it is down there. And since that was so long ago, it's actually like the old YouTube plaque. How many LPS do you have? And by the way, I love your vids. Thank you so much. I think before I quit, it was over 400, but I can't say a number. It's 400-ish. I'm behind you. Looking back, what was your best video quality wise? I would probably say this was a movie split into two parts. It was called Terrible Things, which is very different for me because this was a very serious video topic, all of that, which I was never really known for on this channel because I was the comedy. Definitely gotta do that with that. I will say though, there was always a series I was working on behind the scenes and my computer would wipe the actual clips and I would lose them so many times that I eventually just gave up. But I had this whole series going on where it was about a ghost town and it was really spooky. Will you do more LPS stuff on Jelly Jess? I'm not too sure if there's anything. And again, if you guys want to see this, maybe some reaction videos. Might not be here on the Jelly Jess channel. It could very well be on the second channel. Jelly Jess, check that out if you haven't already. I'm probably gonna be in a lot of cringe pain, but if you wanna see that, I guess the show goes on. What was your least favorite LPS? Definitely this thing. This thing is ugly. Can you just make one more that's really stupid? Honestly, that unboxing in part two, that was the end. That's the end. That's the last one. Oh, oh my God. Oh, come on. I hope it made Hasbro proud. How did you come up with your storylines for LPS? Some of them were like real life experiences or like childhood storylines I made up with the characters and all that. Some I actually did do lengthy scripts for. Most of it was made up on the spot. I am just gonna be honest. A lot of it was made up on the spot. How did your experience as an LPS Tuba help you with your animation channel? Ooh, good question. I would probably say talking into a microphone. That definitely helped. I was still in that American fake accent though, but definitely I had that experience of talking into something. Do you regret anything you did? Absolutely not. I really don't think I would be on this platform if it wasn't for some plastic toys, which is really crazy when you think about it.  Was it an easy or hard switch? I would probably say easy in a sense that, you know, experience with a microphone and a hard switch. It was kind of hard trying to come up with a design. Like we all know Jusica. Will you ever come back to the community? Again, being honest, no LPS isn't for me anymore but it doesn't mean it's not for other people. There's many other creators still doing their thing on LPS Tube. I have found my new thing here. You know, I'm just really thankful that people still watch my content. And hopefully there's many more years to come. We're doing so. Well, wobbly boys, that was a journey and a half. Thank you so much for all the questions. I hope I answered them good. No, but honestly, the amount of support and love you guys have all shown, it's amazing and I am forever grateful. I'll see you in the next video. Catch you later, wobbly boys. Damn, she done.


عود بالله من الشيطان الرجيم بسم الله الرحمن الرحيم السلات والسلام على أشرف الأنبياء وسيد المرسلين حبيبنا ونبينا وشفيع نفوسنا أب القاسم محمد المصطفى صلى الله عليه وآله وسلم وعلى آله الطيبين الطاهرين الغر الميامين المظلومين ولعنة الله على عدائهم أجمعين السلام عليكم ورحمة الله وبركاته ما بي love it brothers and sisters and respected viewers welcome to yet another t3 teach talk and thrive إن شاء الله as always your host for tonight علي البرجي and we are blessed and honored to have with us سيد شبير كرماني from the united states of america السلام عليكم سيدنا وعليكم السلامة how are you inshallah everything's all right الحمد لله وشكرا i'm actually quite excited today we will be discussing a topic of leadership very crucial important topic now with regards to leadership how important is it in development بسم الله leadership it's extremely important in development a leadership and a leader has to basically get people tell people their vision inspire them and bring them all together to move towards a common goal and that goal could be either in a business and success towards that front that could be in an educational institution or university or a college or something of that like that could be on a personal level even within a family structure and indeed that could be at the level of a religion a global religion such as the one that was established by our holy prophet رسول الله himself and it requires a tremendous amount of strength of will it requires a lot of a lot of good communication and also clarification of vision رسول الله was someone who had a tremendous amount of influence on the world and if there's any one word that can probably define what is leadership it's actually the ability to influence now people can be good leaders or bad leaders it really depends on them meaning that somebody can use their skills and their talents of being a leader for negative or they can use it for positive of course أهلبي تعلي مسلام always use it for the best of intentions but if we look at books like for example 100 the most influential people in history that was written by michael h heart in which he listed the most influential people that he thought in history existed in the top five he puts confucius bouda jesus christ he's be upon him isaac newton and also at number one he puts the holy prophet رسول الله at number one he says there's been no person in history that's been as influential as the holy prophet in the global scheme of the world the global global system of the world and they asked him why you know he himself says that you know people would be really surprised as to my decision of choosing Muhammad is the most influential person now influence as i mentioned can be positive or negative and we take on board that رسول الله had a tremendous amount of influence michael h heart says everyone else on the list brought either a secular system or a spiritual system one or the other so for example confucius is known for his spiritual system or bouda is known for his spiritual system jesus christ peace be upon him is known for the spiritual system that he brought isaac newton interestingly is known for the secular system that he brought an interesting side note of isaac newton is that although isaac newton is known for his contributions to physics and mathematics and science in general he actually wrote extensively on god in particular on monotheism newton newton was an adamant monotheist meaning he rejected the trinity to the point that he was affiliated and associated with cambridge university not too far away from here and he had the lukezian chair of mathematics the lukezian chair was also the chair that was held afterwards by individuals like steven hawking in any event he at that time the church relationship with cambridge university was very strong to the point that you needed to for example تدخل ايزاك newton لا تعتقد في هذا to the extent that he went and got special exemption to not have to do this because he had to be a priest ordained as a priest to be able to be a professor and he said i don't believe in the trinity i only believe in that one god because jesus himself never said that he was that there was a trinity this happened after various things that happened in the history of of christianity and we need to be mindful that anyways isaac newton wrote a lot about religion but was known for his secular contributions and number one is that contradicting though sorry to interrupt sure what what do you mean for example secularism secularism basically removes the law of god and allows man to place his own laws so if you're a believer in monotheism how can you then go and write um the secular system or contribute well in in this context when we say secular we mean not having directly to do with religion it doesn't necessarily mean anti-religion secular just in the sense that you know he's known for his science and mathematics now someone who's involved in science and mathematics they can be either religious or not religious up to them that's so we mean in the sense that secular meaning in this context not relating to a religion but not anti-religion at the same time so number he said number two was newton and the man the author may be a little bit biased because he was a he was in his he's an historian and a astrophysicist that's his day job his primary job is astrophysicist anyways number one on the list the most important person he said the most influential person he said was the holy prophet was muhammad according to him and he said the reason for this is he's the only individual on my list who brought a spiritual system and a secular system and had influence in both of them الله مصلى الله عليه وسلم and now having said that some person may critique and respond and say you know but this person says the use of the word influence influence can be good and bad and i'm saying that from the beginning that i accept this notion that influence can be good and bad and maybe this person did not have the same spiritual relationship with the prophet but that's okay well we'll leave it at that now at least he recognized him as an intellectual and for the achievement what he achieved during his era some people may try to dismiss dismissal صلى الله عليه وسلم by say he was god forbid god forbid a warmonger and things allegations that have been made on on him over time and over history and anyone who's studied the man in depth صلى الله عليه وسلم would realize that he is far from that and he was someone who could actually lead the modern world and i'm not the one to say this this is people like جورد برناد شا who said محمد i've read the man and i believe that had europe taken over his was the leadership was of europe was taken over by this man it would succeed and thrive and things like this what i'm saying is رسول الله had it was a leader of the highest caliber the holy prophet was a leader of the highest caliber and the notion of leadership was exemplified by by رسول الله رسول الله you know and to go a little bit more extensively on that what system should lead the world today you know we talk about democracy and democracy is there but what were ancient philosophers saying about democracy was democracy and is democracy the best form of government well play dough didn't think so in his republic he argued otherwise uh and and other philosophers said the same thing even modern leaders have said the same thing we're told that Winston Churchill has said this as well that you know democracy is the worst form of government except that everything else has been tried so what is the right form of government according to play dough in his republic the right form of government is where you have a philosopher king where he said the world will not see justice until all philosophers become kings and all kings become philosophers now philosopher was a place holder for an intellectual intelligent person a person who was well read literate and someone who used their mind and rationale this is important to note because over time philosophy branched out into different fields and became science and history and different fields and political science and economics and the likes but philosophy was just knowledge at that time and so he said the world will not see peace and justice until all philosophers become kings and all kings become philosophers and he said that means that those people who are in power they must also be intellectually enlightened and those who are intellectually enlightened need to be in power unfortunately that's not the case because what's the problem with modern democracy what's the problem with democracy today well there's a voting system and the goal and of and the achievement of the democracy in the voting system it seems to be good but it has injustice embedded in it how and this is what play dough argued he said that in the in the democracy system that we have you have a person who is not an expert in a field voting on a particular matter that they may not have knowledge about exactly so meaning that you may be a medical doctor you may be a physician for example and i'm having you make a decision and voting on economic policy that's not even your field of interest that's not even your field of expertise how do you make that decision exactly and vice versa you may be an economist a phd economist and i'm asking you a decision on medical systems and how it should be done and operated and how society should deal with it it's unfair and unjust and therefore he said that democracy everywhere is mob rule you have these gangs who basically form in these clusters and they begin to rule so what is the solution how do you get proper leadership that is successful he said you need a philosopher king a philosopher king who is able to take complex ideas simplify them explain them to the masses and then take action by himself meaning in the sense he has total power but he is the he is just and fair and equitable that he does not abuse his power in any way this was the view of plato and then Aristotle after socrates plato Aristotle this line and Aristotle was in in in our books of philosophy or Islamic philosophy Aristotle is known as معلم الأول the first teacher many years after Aristotle came a man by the name of farabi or al farabi who is known as a معلم الثاني the second teacher he came forward and said that this philosopher king that was being spoken by Aristotle for example and Aristotle came from that line of thinking from socrates then plato then Aristotle Aristotle was talking about this philosopher king and the likes al farabi says معلم الثاني he says that this person that was being talked about by the former the greek philosophers was none other personified in the life of the holy prophet he says he was that philosopher king that the greeks were talking about that's what i was going to tell you that through their intellect and logic they came to the conclusion because what what you described is the attributes of an infallible leader because only an infallible leader who always act righteously justly and never basically have any faults absolutely absolutely and this is exactly what resoula did he took the complex notions the divine inspirations the thoughts of allah subhanu wa ta'ala simplified them for humanity expressed them to the world and then he took action on them the problem is every other time in history besides two instances what then those two instances being very particular everyone who has gotten absolute power has abused has abused that absolute power the only exceptions are رسول العظم and امير المؤمنين علي ابنة بيطارد these are the only two individuals that when they were given power they did it acutably fairly justly and established the system that the whole world could actually follow it's unfortunate that the world was not able to take advantage unfortunately however this is what يهل البيت علي مسلام exemplified in terms of leadership being fair just equitable with the people telling them this is what this is what we are going to do explaining it in a way that they understood it and then taking action on it and actually mobilizing a movement to implement it it's not easy to do what رسولة did in a span of 23 years to change the face of the world it takes leadership of the highest caliber to be able to achieve what he achieved and then followed by امير مؤمنين this level of leadership the world has never seen where امير مؤمنين is ruling over كوفا he's moved his capital to to كوفا four and a half years can you imagine a leadership and a governorship that there was not a single person who would go hungry under the state of امير مؤمنين can we say that in a modern world today can we say that we can't say that today there are many people many people in many places in america in the uk people going hungry in our backyards in this modern developed world how and that's really what يهل البيت علي مسلام they try to decrease the economic divide bring people together maybe the people who are living luxury although many of them were living very well maybe they weren't living as extravagant and as luxurious as they may have wanted to but at the same time there was no person going to sleep hungry without food in their stomach this is the the the miracle of the leadership of the اهل البيت علي مسلام and at the end of the day we pray every day مام الحجر الله تعالى حجر شري to come back and inshallah re-establish that system and that's the only third time that the world will ever see that's the third time and the only last time the world will see true absolute justice because what happens is humanity or people who become leaders sometimes the ego gets in the place sometimes other things happen that they're not able to see the good of the people at large and they begin it begins to become about the eye as opposed to the weak the problem with us normal human beings power it's like a curse it does it does affect us it messes with our minds and then you have the whispering of shaitan as well is is for us it's illogical irrational to have a leader without being infallible because having a leader like one of us then it's a recipe for disaster it's meant to have is a time bomb that's why the only possible way for us going forward is having an infallible leader and inshallah one day will happen inshallah with regards to leadership if i were to try and identify one what traits would i be looking for very good question in terms of the traits of leadership many of them are actually exemplified by the أهل البيت better than anyone else and this is substantiated by much research in the model modern world the first trait that the أهل البيت عليمة سلام taught us about leadership is the leader themselves must have a certain level of credibility in terms of their character they must have integrity in this character this is the same way رسول العظم himself established as we mentioned previously in episodes this character of being صادق and عمين being someone who's honest and trustworthy he established this and he this was 40 years though his lifetime before announcement of profit he established this character and people trusted him and believed in him the same with أمير المؤمنين علي ابنى بيطالب سوات الله وسلام وعلي people knew that this علي ابنى بيطالب i had the highest position after رسول الله that رسول الله they knew that امير المؤمنين was exalted to such a level that there was no comparison that even Muslims throughout the world شعا عا نان شعا doesn't matter whenever the name of علي ابنى بيطالب would come up they would say علي ابنى بيطالب كرم الله وجه may Allah illuminate his face may Allah brighten his face why because this was that person who never once in his life bowed down before an idol at any moment in time and he was the first of the first with رسول الله in the battlefield in every war and every time whenever Islam needed assistance علي ابنى بيطالب was there from the beginning to the end of his life from one house of Allah to the other this was the life of علي ابنى بيطالب he sacrificed his entire life for Islam and there was no companion greater than علي ابنى بيطالب that رسول الله himself says that علي ابنى بيطالب whoever whoever is مولا i am علي ابنى بيطالب is his مولا فان كنته مولا فهذا علي مولا this مولا it means master that is the definition of the term contextually so this is رسول الله's leadership reflected in the leadership of علي ابنى بيطالب they mirrored each other علي ابنى بيطالب did not learn from any teacher except رسول الله himself so the greatest معلم the greatest teachers رسول الله and his greatest students is علي ابنى بيطالب and in terms of those traits so number one they had character number two humility you'd say how a humility علي ابنى بيطالب and رسول الله had the highest level of humility a leader must be humble now رسول الله could have had the ability to be very arrogant he is much above these terms but what i'm saying is رسول الله could say that i am divinely appointed prophet of god you must listen to me and if you wanted he could have descended the worst of calamities on people but this was the prophet who when he would go to طايف for تبلغ to give the mission to propagate the message they would pelt him with stones to the point that he would become bloodied and فاعتمت الزهراء his blessed daughter would would clean off the wounds but رسول الله even in that circumstance when people were pelting him with stones and five he would raise his hands and would say يا الله oh my lord forgive them for they do not know who i am they do not know my position this was the رسول الله this was the humility and this this was the level that they went to to protect their people the same with امير المؤمنين and this is how they operated امير المؤمنين امير المؤمنين is too high امير المؤمنين's deputies let's go to امير المؤمنين's deputies his commander his right hand command مالك الاشتر we're told that he is walking in the streets one day when somebody a young youth begins to harass him and bother him he was wearing the cloak over his shoulders we're told and he began to he wanted to pull it off as as an insult and he pulled it away and when he pulled it away someone addressed him he said do you know what you just did and who do you just did that to he says i don't care he's like do you know who it is he says he says that's مالك that's i leave him with us commander and chief he can have you finished in one second he became very shaken he followed مالك to the point that he went to he went to the mosque and when he got there he noticed that he began to pray and when he noticed he was waiting for the prayer to end when he finished the salah he was reciting salah separate went for the salah finished he went up to him and he said that i i beg your pardon please forgive me i'm the one who pulled your cloak i'm the one who troubled you i'm the one who bothered you forgive me please i didn't know who you are he said الله is my witness god is my witness the only reason i came to the mosque at this time was to recite to raka'a salah that الله سبحانه وتعالى forgives you for your action this was the level of this was the level of humility of the deputies of amir further humility رسول الله in the battle of خندق he's giving a lesson to the muslims on leadership he says does anyone have any ideas or strategy for to protect us from the enemy for example he's asking all the people one person speaks up salman he says يا رسول الله where i come from in persia or he says we dig a trench around us to protect us so that no enemy can come does رسول الله not know this of course رسول الله knows this he's saying and he's giving a message that when you come for strategy military strategy or other strategy business strategy take advice take an advisor on board so even while he was the leader he was teaching us how to lead so what did they do all the muslims they began to they began to dig a ditch to protect themselves against the other side this was the level of humility that existed in رسول الله and this is the level of humility that exists in amir al-mumine and his deputies and this is how the أهل البيت عالم السلام operated number one character number two they had the utmost of humility the other was in terms of explaining they they understood human psychology better than anyone else they understood how the mind operates they understood how people actually be able to function and how they think and they would explain things that sometimes are the most difficult of things in the most simple ways on the level of the people i remember a story that comes to my mind about رسول الله and how he tackled some of the most difficult issues those of youth were told who once came to رسول الله and he had a sincere difficult issue and a difficult scenario and the companions are surrounded and sitting there and that moment this this this young man comes he says he says you have a problem can you help me now islam is a religion that says there's there's no shyness or shame in religion in the mattress of dine that the the principles must be laid out as an individual i must have shame and modesty and integrity of male or female doesn't matter we must have modesty and and shame and hayaa but islam must lay out the rules in the foundations this young man comes to رسول الله we're told he says yeah رسول الله i have a vice i have a problem and in my heart i want to commit adultery at that moment all the companions get very upset they said this is رسول الله you're talking like this what's wrong with you رسول الله says hold on i'd like رسول الله the leader the demeanor of a leader to not jump to rash decisions very calm very cool very collected okay let's go for a walk you tell us come on you stay here let me go with a walk with this young man let's go for a walk so you go for a walk do you go separate away from the people we're told that you say this is my issue he says let me ask you something what do you accept that someone would do this with your sister I said no never so would you accept that someone would do this with your mother like this is what we're told this is no never he said then why would you want why would you accept yourself to do this with someone else isn't that someone else's daughter isn't that someone else's mother couldn't that be someone else's mother in هل لم يكن هناك شخص أخرى؟ هذا حقاً لذلك إنه قلت في نظاره أنت بخير ولكن الآخرين يريدون أن يساعدوه يريدون أن يقتلهم يريدون أن ينقذهم ويكونوا جيداً رسول الله مع الأدب والأخلاق من رسول الله كانت ذلك تستطيع أن يكون able to calm the hearts at such a level هذا هو ما يهل البيت عليهم السلام لقد كانت محاولة لهم لقد فعلت معهم ويخبرونهم بهم على أمورهم أذكرت أن هناك أمور who came to رسول الله and said يا رسول الله my son he eats too many dates can you speak to him can you tell him not to eat so many dates رسول الله says come the next day he said okay he came the next day رسول الله said don't eat too many dates he said يا رسول الله you could have told me this yesterday why did I have to go back and why did I have to come again رسول الله said because when you asked me yesterday I had just eaten some dates myself and I didn't want to tell him something that I myself am not practicing the level of integrity and they inspire us to have in our lives to implement that in our lives every single day أميل المؤمنين did he not implement this أميل المؤمنين on his dinner table while he's ruling he's ruling an empire the Muslim empire that would spread over maybe 57 countries today and he is ruling and what is he eating he's eating some bread and some salt some dry barley bread and some salt and they ask him يا علي why such a simple food you're the ruler of this entire entire governorship this entire kingdom the Muslim empire is under your rule you're eating so simple he says that I have a wish I have a desire and that desire علي ابنة بيطالي that desire of mine is to meet my lord in a state in which I am hungry further he أميل المؤمنين says I do not want that in my entire regime that I am ruling over from the north to the south from the east to the west I don't want a single dinner table to be spread tonight that is simpler than mine there should be no one eating in this entire kingdom or this entire empire or this entire Muslim state or this empire that is eating food that is simpler than mine if I am ruling I must eat the simplest food I must live the simplest life I must be the simplest leader to the extent that أميل المؤمنين's own shoes he would patch them up to the point that he would say bear witness that I have not forsaken this shoe but it has no more repair left for me to give it this was أميل المؤمنين this is how they are in the house of peace operated yet they question us how can we love أميل المؤمنين to that to such an extent yet they do not know Allah is great it is beyond comprehension أميل المؤمنين was such an individual that just as followed أميل المؤمنين not the other way around truth followed أميل المؤمنين not the other way around that Ali ibn Abi Talib was the essence of truth رسول الله Himself said if you want to see truth see Ali ibn Abi Talib that's where truth is doesn't matter what people say we have traditions they are very clear in this regard that Ali ibn Abi Talib status as a leader as a status as the representative and the vice-gerent of رسول الله is there is nothing to come against it there is nothing to oppose it it's absolutely clear do more traditions tell us this to the extent we're told that there is a tradition that أميل المؤمنين is present one day in the vicinity of رسول الله and أبو بكر enters upon them and عايشة is there as well عايشة is narrating this in the tradition and رسول الله is there present and Ali ibn Abi Talib is there at that moment عايشة says I saw my father was staring towards the face of Ali ibn Abi Talib and grilling his face in a state that his face was frozen on the face of Ali ibn Abi Talib after أميل المؤمنين after Ali left عايشة says I asked my father oh father why were you staring at the face of Ali ibn Abi Talib in such a state that you were not looking away he says my daughter have you not heard from رسول الله نظرو إلى وجه Ali ibn Abi Talib عبادة that to look towards the face of Ali ibn Abi Talib is worship these are clear narrations that tell us the position of Ali ibn Abi Talib beyond the shadow of any doubt to the extent that رسول الله says أنا مدينة العلم وعليه بابها that I am the city of knowledge and Ali is his gate Ali is his door if you want to enter into the city you go through the door بعد ذلك ، بعض الناس ، وهي جميلًا أثنانًا من أخرين أسكولرين من أسكولات نانشعة الذين أثنانًا ، أن هؤلاء هؤلاء تصميمون وإضافة كثيرًا أنهم يقولون أن شخصًا هو فاودي وشخصًا هو دور وشخصًا هو فاودي الألوك هل تعلمون ما هو المشاكل؟ ويأتي إلى أسكولر من أحل السنة لم يكن لديه شياس كولر who said do you know what the problem with this tradition is that where they add on and they say so and so is the foundation you know what the problem is that is the problem with that is that when you say that someone is the foundation of knowledge the foundation is primary over the building so you're saying that person has a higher position than Rasool Allah himself that person whoever wrote this did not have a clear understanding of how a building works and did not have a clear understanding of how the world works to the extent that this person wrote an individual wrote that the lock on the door is Muawiyah this is the extent that people have gone to try to lower the position of Ali ibn Abi Talib for 90 years Ali ibn Abi Talib was cursed in the friday's ceremony why such animosity why such hatred towards the personality of Ali ibn Abi Talib why such hatred towards his children people must wake up and ask these questions the reality of the matter is people understood that they could not aspire and rise to the level of Ali ibn Abi Talib therefore they tried to bring him down envy drove them mad envy drives a person mad and this is the tragedy of the world in which we live human nature throughout times has caused people to do some of the worst of things Ali ibn Abi Talib yet Ali ibn Abi Talib strived and hoped for the best for everyone that went on the 19th of Ramadan when he struck on his head Amir al-Mu'mineen in the masjid in the state of Sujood with that sword that has been soaked in poison over time Ali ibn Abi Talib when he sees the person who struck him Abdulrahman ibn Muljam and he sees him in that state and they bring some water or they bring some milk for Ali ibn Abi Talib for Amir al-Mu'mineen he says give it to him give it to the one who struck him on his head I can't stand to see him in this state Allahu akbar Amir al-Mu'mineen Amir al-Mu'mineen is not a light title Amir al-Mu'mineen is only for Ali ibn Abi Talib because he exemplified leadership at the highest level Allah سبحانه وتعالى chooses his leaders and no one selects leaders better than Allah سبحانه وتعالى أحسنت إنديد أحسنت وحضلا رب العالمين أم بيت سبيت لس to be honest with you after listening to a beautiful speech on one of the best leaders this planet has ever seen and that may Allah سبحانه وتعالى bless us with the leadership of Imam Al-Hujja and I truly wholeheartedly hope that that time will not take too long to come because we've been for too long orphans we've been for too long orphans from Ahl al-Bayt and I hope that your words have pierced through the heart of every believer as done to myself especially tonight will be and it's the night where Amir al-Mu'mineen was struck in the masjid by Ibn Mu'l Jamal and I hope this incident will help us contemplate and reflect upon the life of Amir al-Mu'mineen this personality as you could not have explained better and insha'Allah I hope that I hope our brothers and sisters throughout the world can use this inspiration Amir al-Mu'mineen to bring that fire, to reignite the fire the love of Ahl al-Bayt and reignite the fire of willaya in the hearts and also use it to penetrate through the destruction of the world insha'Allah so we can eventually built that foundation that is required for their mom's return with that being said unfortunately we've come to an end of this program I would like to thank you all for being with us insha'Allah I hope this show has been as beneficial to yourselves as it has been to us with that being said I would like to wish you all a splendid and joyful and this night if you start with family and friends and remember us all in your du'az and most importantly Imam al-Zaman عجل الله تعالى خرج الشريف please do pray for the hasting of his reappearance and insha'Allah we'll see you next Saturday with that being said thank you all so much for being with us and Alhamdulillah رب العالمين واصل الله على محمد وقاله طيبين الطاهي


So, let's speak a little bit about how hard is it to compute a Nash equilibrium in a normal form game. So, let's start with a little history. John von Neumann, one of the founders of modern game theory, when he investigated zero sum game, we proved the existence of equilibrium there, and he used what's known as the Brouwer fixed point theorem for that. And that led directly to algorithms for computing fixed points in such linear programs. First, there was Dante's algorithm that really equivalent to what in modern days is called LP duality, and it's an exponential procedure, although in practice used widely. Of note is the Hacciatin polynomial time approach to solving linear programs, although in truth in practice it's not used as widely, it's not as practical a procedure. And when you go beyond zero sum games, so when John Nash approved the existence of equilibrium for general sum games, he used the same fixed point theorem of Brouwer. And that also informed a series of algorithms, and they're noted there on the slide, and we will be looking at two of them, the Lemke-Hausen algorithm and a much more recent algorithm due to Ryan Porter and others. I will note that all of these are exponential in the worst case, and I will get back to that later. So let's start with the Lemke-Hausen algorithm, and let's start with a formulation of the natural equilibrium for two player games. It looks as follows. This is a busy slide, but I'll walk you through it and all will become clear. At heart are two sets of variables, the S's and the R's. The S's will capture the mixed strategy used by the two players, player one and player two. S1, for example, of S2K, for example, would be the weight of the probability with which player two plays action K in his mixed strategy. So the S1's and the S2's capture the mixed strategy of the two players, player one and player two. R's are what are called the slack variables. And to understand their roles, let's look at, for example, this equation right there. So this applies to any action of player one. For any action of player one, we look at the value that it, the value that it gives with respect to the strategy of the other player. And so we look at all the actions available to player two. We look at the payoff to player one given that he is playing a particular action J and looking at that action of player of the other two and normalizing it by the probability that the player two attaches to that strategy A2. And so if we look at this sum as a whole, this is the expected payoff for player one when playing strategy J given that the player two is playing a certain mixed strategy S2. And it is what it is. And in general, if you look at all the actions that the player one plays, they will give different payoffs. What we want is for player one to best respond to that strategy of player two. Because in equilibrium, every player is best responding to the other. And so let's call u star one to be the payoff to player one in the natural equilibrium. So in general, the payoff for player one when they play AJA will be no greater than the best response, but in general will be less. So we're going to add this slack variable as it's called that will say this is how much player one is missing relative to their best response when they're playing strategy J. Those are the slack variables. And so now that will also give us a sense for this condition here. So the slack variables are always non-negative. And in the natural equilibrium, they will be exactly zero, except when you speak about strategies that are actually played with zero probability by the player. So now we talk about the S's. S's, as we said, speak about the weight in the mix that each player gives to each of their actions in the mixed strategy they play. And so when player one plays strategy J with non-zero probability, it better be the case that he's best responding, namely that the slack variable is zero.  And you capture that by requiring that the product be zero. This is exactly the condition and this is what makes it a linear complementarity problem. So I hope that's clear and you can see now similarly for player two. For player two we take each of their actions and we say if they're going to play it with some probability then and we look at their best response here given whatever player one is going to play their mixed strategy and we're going to look at the slack variable here and again we're going to require that the product be zero. In other words, the probability that they play J is non-zero just in case the slack variable is zero. So this is the nature of this mathematical optimization program and of course I forgot to mention but of course we want the S's to be a probability distribution. So they sum to one and they're all non-zero. Alright so this is our linear complementarity program and now come Lemke-Housen who suggests to find a solution in a particular way and we won't go over it but the flavor of it is to initialize the S's and the R's a particular way in fact to artificially initialize them all to zero and then one by one take them it's called a pivoting procedure take the an S and an R in turn alternating between the two taking them out of the set that has the current value and replacing it with a complementary variable if it's an R replacing with an S and with an S replacing an R until you get an equilibrium. That's the general flavor of it and in this lecture we won't go in more detail into the Lemke-Housen procedure but it is a procedure that looks very deeply at what a natural equilibrium is sets it up as a mathematical program and then searches the space of variables in an informed way. Let's now look at a very different procedure one that doesn't look in as much detail at the structure of equilibria but compensates by performing heuristic searching in a certain way. So let's look at it and we'll look at it at two stages. The first step is to note that when you fix the support of a strategy profile finding out whether there is a natural equilibrium with that support is an easy problem. Remember that the support of a strategy is consists of all the actions to which the player is giving non-zero probability in that mixed strategy. So let's look at this formulation. Let's look and this will be limited to two players and so let's look at all players in turn for example player one and let's look at every action of that player for example A sub i. We'll be looking for some mixed strategy P, mixed strategy profile for one for each of the players that will give us a natural equilibrium namely each agent will be best responding and so for all actions in the support that we're considering we'd want the agent to be best responding so let's assume that the best response value is V sub i just call it that number then we want A i in fact to be a best response to the rest and what we want is all other actions any other actions not in support to give us a value that's no greater than the best response and we want it for each each of the two players and each of their actions in the support so that makes sense and we want these to be a probability so we want the probabilities in the support to be non-zero we want the probabilities outside the support to be zero and we want it indeed to be a probability distribution this all makes sense so this is a linear program it's solvable in polynomial time that is theoretically there's a polynomial time procedure in practice the procedures used are not polynomial in the worst case but but nonetheless effective by the way notice that we actually use the assumption that we're fixing the support here superficially you might look at it and say oh i could do the same thing but simply ignore the support part where are we using that really well we're using it in the assumption that that when we're best responding inside and don't have a profit profit deviation we're actually playing these p i's with probability with positive probability because if we playing the remaining strategy with zero probability in fact doesn't matter if we're best responding to it or not and so this is where this assumption is hidden so now we know that when we fix the support we can solve the question efficiently the flying the ointment is the fact that there's an exponential number of support to explore and this is the second part we need to simply now start exploring the set of support and i won't go into details about how we do it but the basic idea is the following we will bias the support to supports that are close in size to one another that is we will not start by considering one agent looking at only two strategies among which is his randomizing and the other agent looking at 17 strategies we'll look at a strategy profile that's similar who support is similar in size we'll also start with small supports and gradually move to larger supports if we do that and we involved and we we use another trick called conditional domination that is we look at certain thing we can ignore along the way then what turns out that although the procedure is in the worst case exponential as is the Lemke-Housen in fact it performs in practice quite well and in fact better than essentially all other procedures tried including the the Lemke-Housen these procedures do have exponential worst case and so the question is can we do better are there procedures that are less than exponential in the worst case and that takes us from the realm of complexity algorithms to the realm of complexity analysis so let's first remind ourselves a little bit about what complexity analysis looks like we're looking at classes whole classes of problems such as the class of all games and the problem of determining a sample natural equilibrium those games and we look at the how hard is that class as a whole and so here are it's a small part of complexity hierarchy the class p as it's known is the class of problem for which a polynomial time solution is is known the class np is the class of problems for which a class a solution can be verified in polynomial time but not necessarily found in polynomial time the class np complete is the hardest among all the np classes that is the classes to which all np problems can be reduced and perhaps the biggest unsolved problem theoretical computer science is the question of whether np is different from p it's widely believed to be but has not been proved so this is the general background we need to keep in mind and now we can ask well where does where does the problem finding a natural equilibrium reside in p in np what can we say well first of all strictly speaking we can't quite speak about it being in p or np because we know from Nash's theorem that a natural equilibrium always exists so the question does it exist in natural equilibrium is trivial the answer is yes so we need to look at it a little differently one way to look at differently is to ask for natural equilibrium with specific kind of properties so for example we can say does it have a unique natural equilibrium or does a exist a natural equilibrium that's strictly Pareto efficient or does is there a natural equilibrium that guarantees a given player some minimum payoff or can we guarantee some minimum social welfare in a natural equilibrium does there is a natural equilibrium that includes some pure pure strategy some action of the player in it or conversely that does exclude it all of these and others are examples of questions that are provably np np hard okay so that tells us something about the hardness but still we still ask about it just finding a sample natural equilibrium how hard is that so we've seen the algorithm people have tried very hard to find algorithms computing a sample natural equilibrium and it does seem hard the question is can we somehow capture that formally within the complexity hierarchy and and and for that we need to introduce a new new concept the essential concept is that of the new class of problems called ppad for polynomial parity arguments directed graph introduced by Christos Papadimitri in 1994 we weren't going to detail but just so you know the chronology ppad is a specialization of a class called tfnp which is in turn was a specialization of a problem called fnp going in detail here is is beyond the scope of of what we want to speak about but it does help us now position the complexity of finding a sample natural equilibrium in the complexity hierarchy and again we have the class of polynomial time problems of problem that can be verified in polynomial time with these being the hardest among them and given that ppad turns out to reside somewhere within this class now again we don't know whether this entire class does not collapse and all become one of the same it's why do you believe that it does not but proof doesn't exist however we do know that ppad lies someplace in between p and np now what does that have to do with the problem computing a natural equilibrium well that's where the the following theorems come in originally it was shown that the problem computing a natural equilibrium is complete for this class ppad that is it's the hardest among all problem that class initially proved for four players then for all four games with three or more players and then finally in 06 for all all class of games and so we widely believe that the problem is not polynomial cannot prove it but we do know where it resides and within the complexity hierarchy that we are familiar with


Alright, in this video I'm going to be talking about the best sites to sell your photography for 2023. I'm going to do this by going back and looking at my revenue from all the different sites I've got my photos on from 2022. Well, and then we'll also take a look at some of the trends that I've seen. So we'll go back and we'll compare 2022 to 2021, see which sites increased or decreased. And then we'll also go take a look at all my sales and all the sites over the past four years and see how they all rack up together. Through this, I think you'll get a pretty good understanding of which sites are increasing as far as the revenue goes and which ones are decreasing. So you know which ones to focus on over the next year. After that, I'll go through and we'll talk about what my plans are for this year and how I'm going to be trying to make some more money selling my photos online. Now I know it's been a long time since I posted a video. I want to apologize for that. First off, thanks to all of you who reached out to me and asked me how things were going. It wasn't that anything was going badly. I actually had a really great year last year, but it was just that I just got really busy. Unfortunately, making these videos is one of the things that kind of gets cut when I'm too busy doing other work and items related to my photography as well as my software development. Again, I'd like to say that I'm going to try to post more this year, but I said the same thing last year. It didn't really work out, but I am hoping to be able to carve out more time to do these videos more regularly this year than I did over the past year. Also, another thing to note is that I did not upload a lot of photos last year either. That was another thing that I just didn't have time for. When we're looking at these stats, for the last couple of years, I haven't been uploading as regularly as I used to. When you look at the stats, think that there's not a lot of new photos being added. These are my old photos that are getting sold. You can kind of see if a site went up, it wasn't because I put more photos on there. It's probably because that site is more popular or that site is better for selling your photos. First, let's look at the revenue by site. My best site or my highest revenue by site was Pexels and Pixabay. I put them together this year on the list because they are kind of owned by the same company and they are free sites. Now, I get asked this a lot, so I'll kind of go through it. Pexels and Pixabay, I've uploaded my photos there and anybody can download them from free. However, when they download them, they're prompted to give a donation. And a lot of people do give donations. And if I take a look here at almost $600 worth of donations, I got in 2022. And that was actually my highest site, so I made more money giving my photos away for free. Then I did selling them on Shutterstock or Adobe stock. Now, one of the things to note about these free sites is that you need to get a lot of downloads to get a small number of donations. So to give you an idea, I went and checked and I'm getting about 100,000 downloads every month. Okay, so every month, my photos are getting 100,000 downloads. Now, that was only on Pexels, but I get most my donations through Pexels. So that's probably the more popular of the two sites. And so every month, 100,000 people download. And I maybe get five to 10 different donations. So it is a very small percentage. So I know some people have mentioned, oh, I uploaded 10 photos and they got a couple hundred downloads and no donation. So I take them off. Well, you're not really getting to scale when you do that. You need to kind of, if you look at me, I'm getting about 100,000 downloads. What you can actually do is Pexels, one of the things about Pexels is they'll show you the stats. So you can actually go, I'll put a link down in the description to my, you know, my Pexels profile, and you can go in there and take a look at the stats for yourself, right? So again, I've got a very large number of views. I'm actually, I think, 44th all-time on Pexels. So because I started early, I got my photos up there earlier, I'm kind of high on the list and obviously take a lot if you were starting today to catch up to that. But that being said, I don't have a lot of photos up there and there aren't as many, as much competition on Pexels as there is on a site like Shutterstock or Adobe Stock. So, you know, I think you would be better off uploading your photos to Pexels now. Typically, then you'll be for Shutterstock and Adobe Stock. However, I do upload the same photos to most, right? To both of them. Now, you might think that people, you know, if I upload a photo to Pexels, then nobody would buy that photo on a Shutterstock. That's definitely not the case, okay? Pexels and Shutterstock have very different markets and the people that go to Pexels aren't typically, you know, going to Shutterstock.  If they have a subscription to Shutterstock, they go to Shutterstock. I don't think there's a lot of people out there going, oh, I see this photo on Shutterstock. I wonder if it's on Pexels. People just don't have that amount of time. So, I don't think it really hurts my other sales and it just adds up. And again, it was my largest site and it has been increasing year over year for quite a while now. Now, the next on the list is Fine Art America. Most of my photos I take during vacations and a lot of them are like landscape photos. So, I have them on Fine Art America where basically people can go through and buy prints. And I do make a fair number of sales and that was my second highest site of the year. It's just selling prints on Fine Art America. Again, some of the other sites, I haven't uploaded there recently, but I've got some photos up there. I think what happens with those is people go traveling someplace, they come back, they want a photo to remember their travels and they find them. Some of the photos that I sell up there, they're not great photos, I don't think, but they're unique photos, right? Photos that maybe they don't have a lot of other content there. So, if you're looking for a specific place, they can find it on Fine Art American, they can purchase my photos and they purchased them as prints. And I get a fairly large sums, 10 to 60 or $70 as opposed to Shutterstock whereas normally a couple of cents each sale. Next is Shutterstock and Adobe Stock there. That's pretty normal for them. Typically a number of years ago, five, six years ago, Shutterstock and Adobe Stock would be the top but they've definitely been going down over the years as they get more and more saturated and there's more and more competition on those. One of the things to note about this is I had a really bad year from my website. If you take a look at my website, I didn't make very many sales. Compared to last year, we'll see on the next slide more. I typically make a lot more. So that was one thing that I found that I saw a pretty big drop and it's probably because I haven't been focusing on my social media. Most of my sales on my website come, people see me on social media and then I'm coming over to my website but if I don't post on social media, I'm not getting the coverage. So I'm not gonna get the sales on the website. Next, let's look at the revenue change between 2021 and 2022. Now the first thing that jumps out is just what I mentioned. My smug mug website, a huge decrease. However, one of the things to note is that in 2021, I got a sale that was like $1,100 from one company. So although I did see a decrease, it looks a lot worse than it is because that was one sale, one less sale, lost $1,000. And I typically don't get $1,000 sales each year. So I would have expected myself, you'd ask me at the start of 2022, I probably would have expected to get maybe about $400 in sales from my website. So it did still go down a lot more than that, but it wasn't as bad as it looks here. One of the things to note too is you can take a look, Pexels and Pixabay went up. Although I didn't upload photos, again, they are increasing and I've seen that for a while now. And you can see Shutterstock and Deposit photos are decreasing by almost exactly the same amount. So although I'm making less money on the paid sites, I'm actually making more money on the free sites. Next, let's take a look at my sales from 2019 to 2022, okay? So this is four years worth of sales stacked on top of each other. So the way you can read this bar chart is you can just kind of see green is 2019, yellow 2020, red 2021 and blue 2022, right? So what you can see is the total over those number of years. And it's actually quite interesting because you can kind of see that Final America, Shutterstock, Smugmug and Pexels and Pixabay are all around the $2,000 mark, right? You can see like, for example, Smugmug, although I had a really bad year this year, last year I had a great year and other years were average, right? So over the four years, those sites have been about the same. And you can kind of see from the trending that I would expect that if I did a five-year trend next year, probably Pexels and Pixabay is gonna be a couple of spots up, probably pool pass, Shutterstock and Shutterstock and Adobe Stop will keep moving down. Final America has been pretty consistent over the years, okay? So this just kind of gives you an idea of, you know, what it would look like as far as your sales go if you were starting out today. Now, obviously most of the photos that were sold up there, I shot in between 2012 and 2016. So a lot of them have been up there for a while. It's much harder to get into selling your photos online today than it was back then. However, you know, I still think I would still focus on these websites, right? So I think of my own website to sell, selling Final America, Shutterstock, Pexels and then Adobe Stock. Obviously there's some of them here that just have been over-declined which I probably wouldn't upload as many to anymore. One to three or half can stock photo, you know, 500 PX. There was a time where 500 PX, I was making like a thousand or $2,000 a year back in, you know, 2014, 15 around then but they really went downhill. They changed their business model and now it's like a really small amount. So I definitely wouldn't spend a lot of time selling my photos on 500 PX or some of those ones on the end down there. One of the things to note too is that I have never had much luck with Alamy but I think, but I've heard that a lot of other people do. I think it depends on the type of photos you shoot and it's just the type of photos that I shoot don't do well on Alamy. I mean, the types of photos that do do well are more journalist or, you know, editorial type photos and people look for them more there. So just because I haven't done one Alamy you may want to try it out because it may work a lot better for your type of photography than it did for mine. So now let's talk about my plans for 2023. Now, if you go back and watch the same video that I did last year, my plans haven't really changed. I really want to focus selling photos and helping others monetize their photos too as NFTs and incorporating blockchain technology into my workflow to sell my photos with blockchain. Now I know over the past year crypto hasn't done great, but I've seen the headlines, NFTs have really plummeted as well too, but I haven't, you know, the technology hasn't changed. I am as optimistic about NFTs and crypto as I was this time last year before the crash. And the way that I see is what's happening right now in the crypto market and NFT market is very similar to what happened to the internet market back in 2001, 2002, okay? The internet was this great new technology and I was a web developer back then, right? I was in the software industry so I kind of like had a front row seat to watch all this happen. But what happened was the VCs got very enthusiastic about investing in the internet. Internet stocks went way up, right? And there's a bubble, bad things were invested in, money was put where money shouldn't have been put and eventually that bubble, bubble collapsed. However, if you look back at the majority of the gains of the big companies like Facebook, Amazon, Google, they all came after that internet crash, right? There wasn't a problem with internet technology. It still was a game-changing technology, right? The internet has incorporated itself into every aspect of our lives now, right? However, it didn't look that way back in 2001. There's people calling for the internet dead. It was a fad.  And it's the same things happening with the crypto and the NFT market right now. There was a huge bubble. Maybe NFTs and blockchain technology, the best use case, wasn't to have monkey profile techs. Maybe that's what everybody was fighting over, right? So there were some bad use cases, but the technology is sound and it is a transformative technology. It is a technology that I believe in. And I believe that this 20 years from now, just like we're kinda 20 years past the 2001 internet bubble crash, the blockchain and NFTs will be incorporated as much in our lives as the internet is today. And I don't think that's gonna change. I also still strongly believe that there is a place for NFTs and blockchain technology to really change selling your photos and licensing photos online and licensing all creatives online. And as I did with selling my photos online early on, when a lot of people said you'll never make any money doing it, and obviously I have and I'm glad that I got in early, I really do wanna get in early on the NFT technology. So although again, the market isn't as mature, the technology isn't mature. I just spent a lot of time doing research, trying to get things to work the way that I wanted to or the way that I thought they needed to for me to be able to make a profit as well is kinda share some of the learnings with all of you through this channel. And I have made some progress. I've got a prototype up now for an NFT marketplace that I plan on releasing my photos on within the next couple of months then hopefully opening up to other people later this year. But that's something, a little progress has been made, nothing's been released. Follow the channel though, there will be definitely more on that going forward. And as I go through and kinda get through the technical glitches of the technology, trying to figure out the best way to do things and the best way to license your photos online, I'm gonna be posting them all on this channel. Anyways, hopefully you found this useful. Leave me some comments below. I'll do my best to post more videos over this next year. And best of luck selling your photos online.