So I'm just going to start by recalling some things that we said from last time. So we defined this notion last time of this like blocking coding where we said that we have a unitary U which was a blocking coding of matrix A. If we can write U in this form where U has like an A and it's like top left block or top left as a sub matrix in the top left and then the one way I wrote this was I defined this like I sort of had this like selection operator that like went into this like top left corner and I said that this was equal to A or alternatively like if the dimensions match up you can write it in terms of like selecting the Q bits. And here the Q is like the gate complexity of U. And what we wanted to where we left off was I had this statement that I sort of asserted and I didn't prove which is that if you have a blocking coding sorry if you have a okay so we're looking at like polynomials applying polynomials to blocking coding. And we had some polynomial that's even or odd and it's bounded by one for all x in minus one one. And in this setting I stated that we can take a Q blocking coding of A and then we map it to something like I'm going to write something here it's like maybe D log D plus Q blocking coding of the polynomial applied to A. So recall that here this polynomial just this PSV just notes if you have x cubed it gets converted to like A, A dagger A and like if that's x squared it gets converted to like A dagger A. So what I'm going to do in this lecture is try to just prove this theorem. So yeah that's a great point. So here I might make this mistake more but so just keep that in mind if there's any more issues with this. But P is degree so I'm going to I made this mistake here so it should be like okay so I'm using I think I'm going to use D for the dimension and N for the degree yeah okay so I'm going to prove this. So it might be a little bit tedious at times so hopefully it'll be illuminating because I think it's a it's a what we're going to do is we're going to sort of analyze the expressivity of some types of quantum circuits and I think that's a useful exercise okay any questions before I before I begin B is a blocking coding yeah any other questions so how this is going to work is that first of all I'm going to consider this notion of quantum signal processing which is basically if you're looking at a unitary that's like two by two and my and it's blocking coding something that is just like a real number and I'm going to show how you can basically so here it doesn't make sense to call it a anymore I'll call it like X and then I'll show how you can get something that has X in the top left to something that has like pfx in the top left or something like this and then there will be some like lifting to get this to work for arbitrary matrices and this lifting will basically it'll show that the same protocol will work but if you just define it in the right way okay so first off I'm going to discuss quantum signal processing and the idea here is that we have some matrix that we can apply as a black box but sort of we think about it as like a blocking coding so like we know it's a blocking coding this X here but we don't actually know what this X is okay so I'm calling this R and what we can try to do to interact with it is sort of interspersed other rotations other single qubit rotations that are going to look like the form here and the idea is that like okay this comes from like signal processing intuition but so I don't know if this is like exactly right but like maybe R of X is their signal and then we're somehow like controlling our signal and then getting something that's like able to transform without necessarily knowing what the signal precisely is okay and so we're going to define a QSP circuit which is it has a bunch of has a bunch of individual real numbers which are going to be our phase factors I guess I should say we're gonna denote these 5j okay and how we define our QSP circuit is it's going to be equal to basically I'm going to interleave these E these rotations with these R of X which happens to be reflections you could also think about it as rotations in the X poly X basis in the rotations in the Z and then you interleave these here this is 5j and this is 5 0 and the sigma Z is okay here we're taking a rotation with respect to the Pali Z basis okay and okay where this is like a product we're imagining the product is being like going from and on the left-hand side to one on the right-hand side okay and so the question is what you can achieve with these sorts of circuits and so based on this we can say that a polynomial is QSP achievable if there exists some phase factors such that QS the corresponding circuit is going to give me something with like a P of X in the top of corner okay and we want to figure out which kinds of polynomials are QSP achievable and and the way that you can do this is if you sort of just look at the first few terms and then sort of keep working your way up you can do it as said there's some recurrence that my entries of the QSP circuit satisfy and what this is in particular is that if we consider if we consider QSP of some of let's say k plus k phases or something like this okay so if we only consider performing our QSP up to the case phase factor like this I guess the application of R then we can write this in the form so p of X so I'm gonna so it's gonna take this form so basically I have and here so I'm just saying it has some form where these p pks and qks are all polynomials qk this bar means conjugate so it means I'm taking the coefficients of the polynomial and conjugating all the coefficients and so I'm going to say that it looks like this and then these pk satisfy the current recurrence that I'm going to write down here and we have some sort of base case that comes from right with QSP of we only look at one phase factor this is going to look like e to the i phi e to the minus i phi because we're just we're not applying any R it's just one of the it's just this this final term up here and so we can get stats we get that this is the base cases like what is it p0 is equal to e to the i phi and then q0 is 0 yeah okay and then you can see that it does indeed like take this form if I plug in these values this is precisely this okay so to prove this is just some annoying calculation but I'll go through a little bit of it and the idea is that just that like if you wanted QSP like you just want to compute what happens when you add another phase factor another piece of your circuit so I'm considering up to k plus one and then this is going to be I'm gonna peel off the the first the first element of the product and then I'm going to have some the rest of it okay and then we know that it takes this form from sorry we know that it takes this form from here I'm just going to copy it so it's this guy and then there's also this e to the i phi k plus one times R and what this guy is is it's yes I'm just gonna do the multiplication okay and here you can see that what happens when I multiply things together is that okay so I have like a term here this e to the i phi k plus one times px this gives me this like first term of my pk and then this second term the square one minus x squared they they multiply together and then so you don't get any root terms in my polynomial here I and if you want us to check you could see that like if I look at this like bottom corner term I have the same thing but instead I have this like one minus x squared e to the minus i phi k and then q bar of k of minus x so that's what you get if you take this px pk and then take the conjugate and then a sub in minus x so you're so in this bottom right corner you're getting like in this bottom right corner you are indeed getting something that looks like pk plus one bar okay so hopefully they should just confirm to you that this is like indeed what I'm what I'm saying it is and so now that we have this recursion we can sort of see what is happening to our polynomials and so one thing to there's a couple things to note here first of all it how it starts off is that at p zero at at k equals zero my p is even and q zero is okay it's a zero so it's even or even and odd but I'm gonna say it's odd and whenever you compute this pk plus one and qk plus one if pk is even and qk is odd then pk will flip the parity then you know so if this is if pk is even then x times pk is odd if qk is odd then one minus x squared times qk is odd so what's happening is that if p zero q zero are even odd then p one q one will be odd even and you can keep going and then see that for example you know like you know pk here if it's even and qk is odd then x qk is even and so the whole thing is even and so on okay so you can see that basically what's happening is that we're building up these polynomials so these polynomials are increasing in degree by one each time is the other thing to notice because we start off with p zero being degree zero q zero we're saying is degree minus one and here we add one degree to pk and then we add two degrees to qk minus one but because qk is one degree lower then they'll be degree they'll be degree k or pk plus one will be degree k plus one or at most k plus one so there's like some things that you can notice about this recursion and okay so what you can actually show is that the sort of set of requirements that you need is essentially like what you can just visibly see from these recurrences so if you have some degree polynomial it's qsp achievable so we can find phase factors for it if and only if the following holds if and only if there exists some q so here this is like the q from above such that first of all q has degree at most n minus one secondly p and q are like either even or odd or odd or even more precisely right because we said that p is degree n p will be whatever parity that n is and q will be the opposite parity from that and the final thing that we need is that this equation holds okay well where does this come from if we look at our lemma we can see that what this is is we're saying that this column has norm one that's what this equation means and so this is immediate so like if you have a qsp phase sequence then the polynomials the implements must satisfy this because this qsp thing is a product of unitary so it's unitary okay so so this has a norm of one for these qsp achievable polynomials and this is the constraint that we see that we see showing up okay so hopefully I've argued that this direction at least most of this direction so if you have some qsp achievable polynomial then you can look at the source corresponding p and q that you get from this above recurrence and then see that it satisfies okay that you have your q that's degree one lower at least one lower and if they're opposite parities p and q are opposite parities and that you have this property that this has a unit norm so this should just follow from the lemma and like unitary of qsp okay now in the reverse direction where we have p and q that satisfy these properties and we want to show we want to show what we want to give like an explicit construction for what the phases are or just show that some phases exist okay so how we can do this is we can do this by induction by the way are there any questions so far about what I've talked about it's like a little technical yeah so here I even odd this basically means p is odd or and q is even or p is even q odd and here by even I mean that p of x is equal to p of minus x and by odd I mean p of x is equal to minus p of minus x does that make sense yeah yeah I guess like the recursion is what's occurring like every time I do my reflection operator and then my rotation operator so like I'm imagining I'm doing these in in in sound however however many steps well your quantum walk operators well your I think I think typically the quantum walk operator is defined for two of these time steps I'm not I'm not sure though like the typical one that you might see for like rover or something that's what you mean right I think that's typically like two of these time steps but it's like the same principle I guess yeah so so what I did was I I defined this notion of achievable which means if polynomials achievable and I can get a blocking coding get from a blocking coding of a to a blocking coding of p of a so what I did as I constrained this to look at scalar guys so I now I'm looking at there are two by twos with like the top top left being a scalar and so you can still define this notion of achievability here but only for like scalars I'm looking at a subclass of this which is which polynomials are achievable with these particular kinds of circuits so we're going to prove which ones are QSP which polynomials are QSP achievable this will all of the QSP achievable polynomials will turn out to be achievable and furthermore yeah I guess this is like not this is this will follow by some like lifting argument and there's some additional extra step what we what we want is actually some things that are like slightly outside of this achievable QSP achievable class and I'll show how you get those okay okay any other questions okay so arguably I have one more annoying sort of matrix computation to do but the basic idea is that like okay I have my p and q and I want to figure out how do I construct phase factors from this and so how I start is I suppose I suppose p and q satisfy he's like one two and three then what I can do is I can sit I can try to figure out I can try to work backwards and try to see like if I have some degree n polynomial can I pull off one of my steps of my quantum walk and then be left with an n might degree n minus one polynomial and so if I can do that then I can sort of apply induction to say that my whole set of my whole polynomial can be described via phase factors and the thing to note is that like there's like a base case is like a base case of n equals zero and as I mentioned before what this what this what this corresponds to is like p being like e to the i phi some like root of unity and q being zero so this is so so this is this is my base case and so then this corresponds to sort of as I might have alluded to you can just look at the look at these p and q and then you see that this is a qsp with a phase factor of like phi where you where you're just not applying x at all okay so what did I say I wanted to do I said I wanted to take like sort of pretend that I could implement my function and then I would get some some matrix of this form and I want to peel off one layer of like my supposed qsp circuit so that's one layer and I'm taking the inverse so I'm peeling off one layer and then what I want to say is that this with this for particular choice of of var phi that I can get this to be equal to some I'm calling it p p down arrow and q down arrow here but these guys hopefully will be one degree lower and so the thing to notice is that if these p down arrow and q down arrow if these are one degree lower and however I define them if they happen to be like the opposite parodies you know even an odd or or respectively or like vice versa then then I can imply my inductive hypothesis to get that this is equal to qsp of some phi so here I'm okay so here this case is like so inductive hypothesis I'm taking p to be degree n plus one here okay and then I'm looking I my inductive hypothesis as I can find face factors for this degree n thing okay and the reason I can do this is because it'll satisfy all the criteria so the main thing to check here is that your your equation here satisfied for the p and q down arrows and this will follow because by my assumption here that p q satisfy three this matrix is unitary and so I'm multiplying unitaries by unitaries and so this matrix is unitary and so you'll have that this column satisfies your equation and so you can apply the inductive hypothesis and then you'll get like then that then this will imply that that PSP is a qsp achievable and the face factors will be well it'll be phi zero through phi n and then there will be this additional var phi if I can find what it is okay because I like I take this qsp and then I I move this this piece to the other side and then I'll get an additional factor of face factor of phi or phi okay right so what is this expression well I'm going to what this is is I'm going to what you end up doing is to do this is you just do the computation you like take this e phi of r phi I see you take this one step of my qsp circuit I use that ours a reflection so it's its own inverse and so this will look like the following okay and if you multiply these guys together you'll see that what you need your what these expressions are or what you what these p down arrow and q down arrow if you like pattern match between the two you'll see that they need to be the following okay so this is like I guess pretty similar to the recurrence relation from before if you remember that but the question is like can we choose some phi so that these two have degree lower than the degree or this p down arrow has a degree lower than the degree of p and this q down arrow has degree lower than the degree of q or at least like lower than degree and now the way that you can see this is so by my assumption I know that p is some degree and plus one thing and it is has parody the same as parody the parody of n plus one so namely this means that I can write this as a n plus one x to the n plus one plus I just basically I just want to look at like the highest monomial like sort of the leading coefficient and seeing if it can become zero and so on and q of x is going to be equal to some bn x to the n and so on and okay what's going on here is that if you look at the leading coefficients of p down arrow and q down arrow the leading coefficient so it's like this is like degree this would be the degree n plus one thing for for the p and then this would be the degree n coefficient for q these turn out to be the same and this is e to the minus i phi of n plus one plus e to the i phi of bn there's a minus sign okay and so the question is can I find some var phi to make the zero and the answer is yes the thing to use is that what you can just say is that a n and a n plus one and bn have the same magnitude and the reason to see this is that in this equation okay if you look at the leading coefficient of here the leading coefficient is a n plus one squared and the leading coefficient here is minus bn squared and we know that they cancel out right so there's a term here that looks like x to the 2n plus 2 and this will have a term that's x to the 2n plus 2 and because this is equal to one it's equal to one as like polynomials so you know that these two cancel in so that you know they have the same magnitude and so you can just choose just choose e to the i phi to be like like square roots of bn over a n plus one something like this and this is going to this is going to be some root of unity and so or not root of uni but like some something on the unit circle and so you can actually cancel okay um so that's like the proof um yeah where yeah yes um yeah I think that's a typo in my notes okay yeah yeah thanks any other questions yeah so what I want to do is I want to take some my degree and polynomial I want to find some degree n minus one polynomial such that they're the same properties such that if I apply one more step of my qsp thing I get to p and q and so I just want to find some value of phi that will achieve that'll achieve this and I sort of like worked in reverse a little bit but this will show you how you get this value of phi and you know about that if you wanted to at the top of the statement you could say we choose this phi to be this this particular value based on the monomials and this will give you like then you could like you know if you wanted to actually do this which you shouldn't because it's not numerically stable but you could then like you could take your p and q and then you could work backwards work all the way down you get to down arrow and then further down any other questions okay so there's one more characterization that I wanted to say which I'm not going to prove because of time and what this says is that so I know what my p and what p and q are that are like what my p and q can be such that these are p is qsp achievable achievable but this is actually like pretty constraining it's not clear that if you give me a polynomial p that I can find such a q that satisfies this but it turns out if I relax if I allow myself some more room if I like give up control over the imaginary part of my complex polynomial then I can actually get any real polynomial to be essentially achievable so I'm going to consider two polynomials to call p real and q real and these are going to be real valued polynomials so so I'm going to say given this there exists some p and q that are qsp achievable such that p the p real is like the real part of p so so here these two can be complex valued or have complex coefficients and so basically I can find a comp like complex I can I can sort of take these real polynomials I can add some imaginary part to them and when I add my imaginary part they'll be qsp achievable that's why I'm saying I can do and I can do this if and only if well first of all like there'll be two properties but the two properties will be the same as these two properties up here so the properties will be q is degree and most n minus one secondly you'll have pq are you know even or odd or odd or even and the final thing that you need is that you should all be the real parts it should be the exact same thing as before exact same equality but instead of being an equality it's an inequality so I'm just saying like I have my p real and my q real they satisfy everything that I want except they're maybe not something to one and then what I can do is I can add imaginary parts to make it some to one and if I don't really care about what my value of q is I can just set this q to be like zero or yeah and so this will give me some p that's qsp achievable and the real part of p is this p real of my choice provided that it is a most one okay so this is like how you get so that you think from this you can get like sort of how you get that p real is a cheat is a achievable in this like two by two setting is that you get some p that's qsp achievable such that the real part of p is this p real and remember that this the only constraint that we really needed is that this is even or odd and also that this is bounded by one so this is okay this is for all x and minus one one by the way okay and then what we could do is we could just say that like so p is going to be equal to some p real plus like some imaginary part help p imaginary and so I can achieve this with some phase factors phi I can also achieve the conjugate with the phase factors minus phi so I don't know if that's obvious but and then once you have that both p and p conjugate are qsp achievable you do like the linear combinations of unitaries to get that one half of p plus p bar which is your p real is okay well you're doing a linear combination of unitaries of a qsp circuit so it's not like strictly qsp achievable but it is achievable and so this is how you get that any real polynomial you can achieve at least in this two by two case where you're like doing a blocking coding of a scalar guy are there any questions I'll show how to lift this okay right so I don't have much time but I'll try to explain so recall that what we had is we had some in the setup for the beginning we had that you is a blocking coding of a which means that we can write you is some block matrix where a is in the top left corner and we have some other matrices in the other parts and how can we and what we have is okay I'm going to define a couple operators so I'm going to define pi r as being the identity so here this is r by c and so pi r is just gonna be the projector onto the part the a part of the right-hand side and I'm going to define pi l to be the projector onto the left-hand side and the way that I define this is so that pi l u pi r is equal to a zero zero zero so I'm going to define these operators and so what I was doing before is I was sort of taking my original matrix or start taking my scalar x and I was doing some rotation sort of between x and these like other parts of my matrix and so you can sort of pattern match and try to figure out what the right thing is in the more general setting I'll just tell you so if we have some phase factors we can define this quantum singular value transformation circuit as being basically the product of I'm going to write it as the following there's some now some issues of like parity so I'm I'm just gonna try to write it for the even case here so again I'm I'm like interspersing I'm interleaving my applications of the u with applications of some rotation and what this is going to be is it's going to be with respect to the projectors so so here to pi l minus identity this is a reflection across the subspace defined by pi l same for pi r and we're sort of applying you and then we're doing this rotation and then we're applying you dagger and then applying another rotation and so on and this pi is actually a product here so I this like it should be like J and it's like should be like J from 1 to n over 2 or something okay and okay how should I be looking at this yeah question this is Phi 2 J minus 1 this is Phi 2 J is that what you are asking okay if I remember writing and it's confusing they're also the lecture notes which I'm copying off of any other questions what's the goal of which one yes I'm defining this u Phi to get a blocking coding of polynomials of a yeah so right the hope is like I can pick some value of Phi such that what I get is p of a and there's a result that you can show okay first of all you should notice that okay if indeed I'm looking at my you and my you is r of x blocking coding x then this u Phi is precisely the same thing as the qsp circuit you can stare at this and like see that this is the case and the main result here is that if p is qsp achievable with these phase factors Phi then u Phi is going to be a blocking coding of p of a so I'm saying that if p is qsp achievable then it is also achievable in the blocking coding sense right okay so how am I going to prove this I'm just going to show you what happens when I write everything out in terms of block matrices and you should hopefully see sort of what's going on okay so I'm gonna take specifically I'm gonna look at what's happening with this qsp t this u Phi that I just defined and something I'm going to notice I'm just first of all I'm going to write down what these these guys are okay and I'm going to not really I'm gonna sort of be a little bit loose with defining dimensions here because when I define these they're all gonna be different dimensions but the products are going to work out so it'll be fine in the end what this is is it's e to the Phi 2 j times I e to the minus I if you just look at what this guy is it's a block matrix where you have some it's basically if you think about it it's sort of like the same thing as my rotation from before except I do it on a large subspace all at once okay similarly I can say that e to the I with the sorry this is like this is in the exponent just to be clear 2 pi r minus I and what I'm getting is it's gonna be exactly the same picture but the dimensions are gonna be different so hi Phi 2 j plus 1 times identity okay and the final step here is what I'm going to say is like okay I'm gonna call okay for the final step I'm going to use this decomposition called the CSD composition and what this states is that if we consider a block matrix of the form if I have this like blocking coding that I mentioned before then we can actually write it in terms of a bunch of simultaneous singular validity compositions okay so what's happening is I am taking this so V what I'm doing is I'm getting a an SVD for every block and they sort of pair nicely together in the sense that my left singular that vectors of a are also my left singular vectors of d1 of like you want to like my I have the same left singular vectors for both of these matrices and I have the same right singular vectors for both of these matrices that's what's happening there and now what I can do is I can notice that if I look at what this guy is this V so what I have here is I have this matrix you okay my matrix you I'm sort of interleaving with these polynomials here so you and then on the left hand side is going to be one of these pi L's right so you have a U and then a pi L and then a U dagger and then a pi R the thing to notice is that to make it simpler what's happening is that this V can actually commute with this they're saying this pi L and if you look at what's happening and you compute this times this versus this times this they will commute again I'm being messy with dimensions but if you were trying to be formal this a here is this this these blocks are the same as these blocks in terms of sizes and then here V1 and V2 are square W1 and W2 are square and then these have the same dimensions as these so they're actually commuting genuinely okay and similarly W and my pi R commute and so if you look at what's happening right I had this expression that's sort of like U and then this e to the i phi pi R or pi L and then U dagger and then e to the i pi pi pi R okay and then I'm writing this as VDW dagger and then WD dagger V dagger this is the conjugate transpose I can see that these terms are in fact cancel out so U phi is going to be basically the same as like D phi up to some change of basis and then finally the thing to note is that what this guy D is if you look at what it is it's going to be a bunch of entries and the entries are going to be of the form sigma 1 and so on they're going to be of this form and so on so so I guess a way to write this is that it's going to be CSS minus C or S square root of 1 minus C squared so C and SR diagonal matrices and then if I look at every particular 2 by 2 block it'll be of this form of like a reflection of the corresponding sigma i where the sigma i's are the singular vectors of a singular values of a right so here my D11 which I'm calling C now are my singular values of B of a and then I'm doing this rotation operator with effective sigma i so if you work it out what's happening is that when you're doing this QSVT you're doing simultaneous QSP on all of the sigma i's all of your singular values at once so that's like the most important thing and if you want to actually prove this what you would do is you would go back up here so you would notice the CSS minus C you would go back up here look at your proofs and then saying tactically replace all of the X's with C's and all of the square root of 1 minus X squared with S's and then it would everything would go through immediately so that's like how you would actually prove such a thing more than the lecture notes that I don't have time to cover but that's going to be it thanks


What's up everybody Jason for jazzy's case race comm we're giving away five mixer spots in 2020 mosaic football cellar one-pack break number 56 So again 32 total spots no better in commons will ship out of the cellar pack and the way this works guys is first We're gonna randomize customer names and teams distribute the hits out of the cellar and at the end of the one-pack break We'll randomize all 32 customer names again and Customers top five will win a spot each in the mixer. So good luck guys Let's roll the dice and we got ourselves a four and a five nine Times so good luck nine times. Let's do the break first One two three four five six seven eight And nine Cory done a cow iron nine times One Two three four five six So eight nine Tennessee Titans down to the Kensington chiefs and again stick with what you got guys Which go through the couple of big quarterback teams, of course, I've been all been playing extremely well So bangles Jason Dolphins amber Chargers cow Call done with the chiefs as well. So there you go So stick with what you got guys again, and then we'll come back after the pack break and see who wins spots in that mixer flee Flaker JK Dobbins Jamal Adams Jerry Judy and Jacob Eason Sweet so now let's switch scenes guys and Roll the dice and Customer names there six and a two I changed this one here Six and a two eight times. Good luck one two three four five six seven and Ethan final time guys good luck Boom top five get in guys Kyle Mark Michael Drew and Kyle last spot mojo. There you go top five get in Congrats guys, so I'll post up another one of these guys. We do need to do a couple of them So number 57 will be on the website soon guys. Appreciate it. Jasper's case breaks calm


Hello everybody, welcome to Wednesday. Good to see you here. What is our date today? What is our date, the eighth? Yes, June 8th, 2020. Welcome everybody. We're gonna have a good session today. I'm gonna talk about PaperClick and Shopify. However, this PaperClick will work on any website you've got. It's pretty cool stuff too. It can make you money like within hours of you starting it. So stay tuned for all that. Don't forget to subscribe if you haven't done so so far. Hit that subscribe button down there. Turn it from red to gray. Don't forget to ring the bell. Turn on all notifications so you're notified each and every time I go live or if I upload a video. Man, oh man, we're gonna have a fun session today. But you make it fun. And the way you do that is you start using that chat box.  Tell me where you're at. Tell me what time of day it is, wherever you're at. I don't know, tell me what you ate for breakfast.  But make sure you use that chat. If you have any questions about starting, running and growing an online business, you wanna use that chat box. And also, even if you're not watching this live, let's say I record this, you're watching it a week later, use the comments section below because I go in there and I answer comments, I talk to people, we meet each other. We get all kinds of cool stuff going. So make sure you do that and invite your friends to these two guys. But I really appreciate you being here. I really do. Like I said, this can be a really cool session today. I think you're gonna enjoy it. Paul, finally you have shown up. Where have you been? My man, Paul. He says, coming in loud and clear brother. I appreciate that. I miss Monday. I apologize for that. We had so much stuff going on. I will be here again Friday. We had a decent day yesterday. People like to know sometimes what I've made in a day. I think Oprah on survival came food yesterday. We did a little under $28,000. Not a big day for us, okay? We've had $100,000 days. But I want you to understand that selling online is not always the same amount every day. And that doesn't include JR Fisher training, which we have all kinds of subscriptions coming in there and people buying courses and all that good stuff. So over there, we made some more money and I'll be honest with you, I don't know. I know it was in five figures. I don't think we hit six figures there. But KMI, KMI, I think you're new to us. I don't know if I know you or not. Paul, do you know KMI? Say, tell us about yourself. Tell us where you're at, what you do, all that good stuff. I'm gonna jump into this pay per click advertising thing that you use on Shopify. But you can use it on any website. You can use it on Magento, you can use it on Wix, you could use it on WordPress, it really doesn't matter. So you can use that. Let's see here, what else we got going? By the way, how's the new book coming? Pretty good, actually. I'm about halfway into it. If books take some time, guys, you can write a book real quick.  But I've got to kind of fit that in between all my other endeavors and what's going on. And Paul calls me out, he says, hey, where's the book, where's the book? It's coming, it takes time. But that is gonna be coming out. The first course I did took me over two years to do. One course, and that was, what was that course? Guys, I can't think of it now. Oh, Digital Cash Academy. Yes, Digital Cash Academy, it slipped my mind for a second. But that first course took me two years. And that was all I was really working on at the time. I mean, I had my duties over at Survival K Food. But let's jump into this pay per click thing, guys. Let's talk about it and how it's gonna benefit you. Because the cool thing about it is it can start really fast. It's one of the fastest and most effective ways to generate traffic for any type of e-commerce store. And actually any type of stuff, even if you're selling services, these are pay per click advertisements, okay? They appear like on websites you'll see them, social media. They're highly targeted to individual users as the ads they see are mostly based on their browsing history and interest. So you could really focus in on people, which I think is really pretty cool in using pay per click. This means that people are coming to your store and they may be interested in what you're selling and might become a customer. So you drastically increase your chances of selling them something. General media advertising of the past and still around today, like a TV ad or something like that is kind of like a scatter approach. It's kind of like getting the word out and generating interest with ads running on like mass media, TV, radio, newspapers, magazines, billboards, all that kind of stuff. But with these, you can really target it. The aim is to advertise and when you were doing that mass media stuff to a big audience as possible in hopes that some small segment may be interested in what you have to sell. But the thing is they don't work that well. You really couldn't tell what you were getting out of your ad with pay per click you actually can. So when the internet came around and advertising was really, I mean, reborn to a much different, more efficient practice. We kind of cut out all the wasted money we were spending and we were able to target audiences instead of those who may have no interest whatsoever in our product. So that's why it's so cool about pay per click. Plus pay per click you only pay when somebody clicks on your ad. So you could have an ad out there and tons of people could see it and it could be embedded in their brain but it doesn't cost you anything.  Cause they're gonna charge you for that billboard no matter what. Let's see here, Paul's got a comment. Let me pop him in here in between everything going on here. He says, okay, I'm on the same boat pushing it target to get my book done. I really like your formula for testing ads and getting best bang for your dollar. Oh yeah, you have to do that. I mean, that's just, that's a given man. I mean, really running ads online is more just testing and figuring out what doesn't work and continuing with what does work. And that's a whole other training but yeah, thanks for calling me out on that. Once people arrive on your site and perhaps for the first time, it's then up to you and what you have in your store and how it looks and functions to make sure they complete the buyer journey by choosing some items and checking out and paying for them, okay? So you still gotta have a good site and all that. Now, when you first set up your pay-per-click campaign also known as paid search, it's one of the most popular elements of any digital marketing campaign because of its immediate results. There's practically no waiting around before the traffic starts to come in and sales, right, hopefully start to rise. But you need to know what you're doing even though the most popular PPC networks and platforms such as let's say Google or Facebook or Instagram all have these automated systems that allow you to set up ads. You still need a degree of planning and exercise to get you going, okay? You gotta do that. So the key to good results is Google, let's say pay-per-click ads appear in people searching history, okay? They're gonna see it on their page when they go and type it in. So what you wanna do is, you wanna do extensive keyword research to find keywords that are most relevant to your niche. That's really important, okay? You can use a variety of online tools. You could use, let's say, Moz, you could use BuzzSumo and those tools will help you out a lot. These tools will also let you see the demand, okay? Which is really important. How many people are really interested in that? The competition for specific keywords. And like anything in business, the more popular something is, the more expensive it's likely to cost you, okay? So if you put a really expensive thing out there, let's say camping equipment, okay? That's most likely a very expensive search requiring a budget of thousands of dollars to get a campaign going and sustain it. That doesn't mean you need to spend it though because they're fairly general keywords. That's why they cost so much. To get a lower price, you need to try variations which are called long tail keywords in consider adding a location to them or a combination of all three such as best camping equipment, San Diego, California, okay? If you do that, then of course you're gonna get better results and more targeted. You can also add negative keywords that exclude various terms people are searching for that can help really boost your return on your ad. All right, so you wanna work out your budget and how much you wanna spend per day of your campaign.  I mean, you could spend five or $10 a day, that's all. And then you can scale it up as you get some good ads that work. That's what you do. Let me see here, Paul's got some comments in here. Let me pop them in here and I think this is a really good one I wanna cover too. Do you advertise every day or are some days better than others to advertise? Can you pick the hours of the ad to run? Yes, yes, yes. Now, keep in mind, when you start getting more and more particular, let's say the hours it's gonna run, like I wanna run it from 9 a.m. to 9 p.m., but not during the night, it's gonna cost you more money, okay? It doesn't allow the algorithm to work as well. Now, some people are gonna argue with this, but I've experienced it myself. As far as days of the week, yeah, I would advertise every single day because what happens is, sure, you're gonna have some days where you're gonna get more clicks than others. However, the reason you're gonna get more clicks than others is because you have more people out there now searching for that. Let's say on Mondays, everybody searches for survival food. Monday mornings, they always search for survival food. Now, if they're not searching much Tuesday, Wednesday, Thursday, and people see those ads and they're disinterested, in other words, they don't care about it, not gonna cost you anything because they're pay-per-click. So if people are seeing your ads and they're not interested, they just don't click on it. And if they don't click on it, it doesn't cost you any money, but you still get that visibility out there. So I would say advertise every single day, and you don't wanna really do breaks in your campaigns because as soon as you do a break, let's say I advertise for a week straight and then I drop it for a week and then I advertise for a week straight. The algorithm has to relearn all over again. And when you do that constantly, you're gonna get worse results on your ads. So you don't wanna do that. You wanna tell yourself, well, I wanna advertise for three months and I'm gonna spend $10 a day for three months and then I'm gonna look at the results. That's a way of doing it that works. Don't have any breaks in it. Don't have any time breaks. Don't have any day breaks. Don't have any of that stuff in there. Now what you wanna do is you wanna add a landing page or pages to your website and link your ads to them. There's little point in advertising a product or service and then directing traffic to your homepage because they don't wanna have to go to your homepage and start to find the products and look at your dropdowns and all that. They wanna get exactly to the product. So you really need a landing page if you're gonna do ads. You don't wanna drive them to your homepage. I know I did this in the beginning. Back in 2010, I would run an ad and send them to my main page and nobody bought anything. It's because when they got there, there was nothing to do. It just told them about our company and all that, okay? So we don't want that. We want a page that you're gonna take them to that is actually something they can buy, some action. They can download, they can attend a webinar, whatever it is. Really important that you do that, okay? Once you've done that, then you can do upsells, all these other things but you wanna get straight to the point with a specific webpage about the product or service that you're advertising and you want to sell. And I gotta watch my time here because this is really interesting stuff to me. I can talk too long. All of this sounds, I know, overwhelming, okay? And time consuming. And you may think you should get a degree in pay-per-click before proceeding but don't worry, as you can always outsource these tasks to specialist pay-per-click agencies and stuff like that. Just make sure you get a good one, okay? There's a lot of good ones out there. One of the first things you should do when you're figuring out how to increase your clicks through, your pay-per-click conversion so that people do something you want when they arrive at your store from ads and not immediately leaving is to look at your site and see if it's responsive, okay? What does that mean? What that means is, does it work on a range of different devices? Super important, guys, because you don't know where they're coming from. Are they coming from their mobile device? Are they coming from an iPad? Are they coming from a computer? Where are they coming from? Let's see here, Paul's gonna have another comment and pop that up there so everybody can share in his wisdom. If you sell digital products, can you target English-speaking countries and is there a cultural difference between English-speaking countries to worry about? Let me think about what you're saying. If you sell digital products, can you target English-speaking countries? You may be, maybe you mean foreign-speaking countries and the answer is yes, you can target. But whatever you're selling, if it's a digital product, you're gonna have to offer it in Spanish or you're gonna have to offer it in German. You're gonna have to offer it in Greek. So if you're targeting a different country, yeah, you can do that, but you've got to change your campaign for that particular country. If you just want to target English-speaking people in Germany, you could just run it to Germany and the people who don't speak English, they're not gonna really notice your ad anyhow because they can't see what it's saying or they don't understand what it's saying, they can see it. So yeah, you can do that. Let's see here, are there cultural differences between English-speaking countries to worry about? You know, between English-speaking, and when I say English, I always think of the big four, which is Australia, the UK, Canada and the US. There's not a lot of cultural differences there, okay? We've kind of overlapped there. But if you get, let's say, to a Muslim country versus an American country, there's gonna be some differences and you gotta kind of look at your ad copy, you gotta look at what you're saying, you gotta see what's going on because if you don't, you could offend somebody or you could miss a sale because of it. But mobile devices, and that's what I was saying, you gotta look at where these things are showing up, are really, it's growing so fast, guys, people almost doing everything on mobile now. So you gotta make sure that when they see your ad on a mobile device, it works and it works out. And your landing pages work, okay? It's not just your ad, it's your landing pages. Paper clicks and finding the PC only that doesn't display or work on mobile devices will lead to an enormous bounce rate, okay? As a hefty portion of your paper click generated traffic, please the minute they arrive at your site, so you gotta make sure it's gonna work. If you're using something like, let's say Shopify, they have an extensive range of responsive themes, but some may not be or they may not be responsive on certain devices, okay? So you gotta look at that, such as those that run on Android operating systems, for instance, a quick check to see if your store's responding will put you in the picture. So you need to check these things before you run them, okay? Next, you need to make sure that your product pages are clear and clean and compelling. Some companies, okay? Now some companies put a lot of effort into their landing pages, but they neglect their all-important product pages, which is a real shame. And it's here that the browsing and the buying actually happen. So they may go to your main website after you've run this ad to a landing page, and you gotta make sure your products are optimized. Photography's gotta be really high quality. It's gotta be professional. When they see this stuff, if it doesn't look well, like especially our company, Survival K Food, the food's gotta look appetizing. It's gotta look delicious, okay? Even the best products won't fly off the virtual shelves because poor quality images may give the impression that they're poor quality products. You've gotta make them look good.  When you get there, your Big Mac or your quarter pounder is not gonna look like that picture, but they've made it look delicious. That's how they get you there. So make sure you make your products look really appealing too. Give people a better look at your products. It could be the first time they're buying them, and the photos, after all, are one dimensional and therefore flat, okay? So you may be able to install a display plug-in from, let's say, the Shopify app store or the WordPress one and add another kind such as a smart product viewer, which offers a 360 view of your products or WooCommerce 360. Imagine an app that does the same thing, okay? So that really, really helps a lot. Let's see here, let me see, Paul's got something. He just put it in there. Gotta get the man up there. He's working, typing stuff out. He says here, nothing worse than an ad on a mobile device that doesn't work well. Your landing pages are great looking as well as the copy for the ad. Thank you, Paul. And it is important that you do that. Super important that you do that. And I want you to think about this. Another way to increase your pay-per-click conversions is to add a live chat feature to your store, okay? If they see they can get in touch with you, that's really, really important, okay? You can also use something like TrustPilot when your Shopify store or your WordPress store or your Magento store. And then seeing those reviews on your product can really sway people. A Shopify app store has a lot of live chat choices, including WhatsApp, you got Facebook Messenger, you got Shopify Chat, and it lets your customers get in touch with you with ease. And what do you do about customers who are passionate and just can't decide whether to buy now or later? Give them what a product with time limited discounts or offers. Do this all the time. If they like something and ours really is time limited because we have shortage of supplies right now, but if they like something and it's price and they see that there may not be a good price later on down the road or it's gonna go up in price like we sell canned meats, it's gonna go up in price, that offer will expire in a few hours and more likely to actually buy your product than if there was no expiration date. You can't just put a price out there and go, here's the price because the human mind says, well, that's the price. It's always gonna be that price. It's never gonna change from that price. You've got to make it urgent for them to do so. Why should they act today versus tomorrow? Why should they do that today? It can also be an inventory thing. Like we have inventory shortages right now. We can't get chicken or turkey. We do beef, chicken, turkey, pork and ground beef. Ground beef is taking too much time to put in the can since we have such high demand and I can't get chicken and turkey. So I'm down to beef and pork right now. But those are two of my most popular ones. So that's a good thing. And I'll get back to having chicken and turkey. It's just a delay right now. But if they know that there's big delays and shipments, if they know that you have limited inventory, if they know that price could change, those are all reasons for them to buy now. You've got to give them reasons, guys. You can't just put a price out there. You've got to do something that is going to spur their interest. Get them going. Now, if you guys are nearing 10, 19, I'm gonna stop a little bit early today. The only reason I'm doing that is because I got to record videos. I was supposed to do it yesterday. I got one done.  So I got nine more to do today. So bear with me a little bit. I'm gonna stop a little bit sooner than a 30 minute stay. So if you have any questions, if you wanna know anything, if you wanna just say something, put it in that chat box now. Also, guys, I was watching a show last night and there was this guy on there and he's the number one agent in Atlanta, Georgia. Young black gentleman, very super intelligent. He has already made $8 million so far this year. I'm like, this is June, guys. That's his commission so far, it's $8 million.  I did too. I grew up in a really bad area. But he said the one thing he did is he got negative thoughts out of his mind. Just got negative thoughts out of his mind because he realized he had this hood attitude where he was down on people and this stuff doesn't work out and that stuff doesn't work out. You gotta take what you want. And he says he changed it to a love attitude. He says he started caring about people. He started loving people. He started being kind to people. And when he did that, all of a sudden people started responding to him differently. He was getting different results. And the one thing he said, which I thought was really cool, is he says it doesn't mean you've gotta work your butt off constantly. That's not what it's all about.  That's gonna come across. You would do better to work half as much time and have a super positive attitude. Be super kind to people. Be nice to people. Help people out. And when they see that, they're gonna be more likely to do business with you. What he found was just changing his attitude. Just being nicer to people. Just being kinder to people. Genuinely caring about their situations. When they wanted to buy a house, he really cared about their wants and needs and desires. And he expressed that. And when they saw that, they wanted to do business with him. Nevermind now that he's got this penthouse mansion, he was showing he had a Ferrari and he had a Maybach and he had his Rolls-Royce. He had all these fancy cars and all this stuff. But he said he got all that because he changed his attitude. So it's not just about hard work. And I talk about hard work a lot. Hard work is very important. You can have the best attitude in the world but if you never work, you're not gonna make any money. But you gotta have both. I had a sale yesterday, a pretty large sale. And it's from a guy who's been buying from me for about three or four years and he's over in China. And man, every time he does business with me, I totally thank him. I'm like, thank you so much for your business. You don't know how much you're appreciated. And he's like, what? What are you talking about? He doesn't get that feedback from other people. And I do totally appreciate him because he spent hundreds of thousands of dollars, maybe into the millions with me now. And he keeps coming back. And I don't know, I take really good care of him. I keep him updated on his orders. He puts in really big orders. So it takes weeks to make his orders. But I always let him know what's going on. I always let him know I appreciate him. And here's what he does. He's a nice guy. He pays me upfront, which I do require, but it's a large sum of money. So there has to be a certain amount of trust there for somebody to just wire you money. Because when he wires me money, his money's gone. How does he know that I'm gonna fulfill all my promises when getting him a product? Well, it's pretty simple. I've done it in the past. But he trusted me in the beginning and I've always gone through and done what I needed to do. I've had people who put a huge order in and for some reason we couldn't make it or we couldn't get the supplies or whatever. And I would send the money back to them. They know I'll do that. There's no risk in dealing with our company. How risky is it to deal with you? How do you treat your customers?  Are you positive? Are you kind? Do you really, really care about your customers? Do you really care about other human beings? Because if you don't care about other human beings, you're not gonna do well in business. You're just not.  What's the point? Be kind to people. Care about people. Genuinely help people without any agenda and your business will grow. This is some of the best advice I can give you. And if you've got negative people around you, you need to get rid of them or change them. It's really hard to change them.  I'm really trying to, you know, succeed in life. And what I found is being positive is the best way to do this. So do me a favor.  But while you're around me, please, please, please just talk positive thoughts. Only be positive around me if you don't mind. Now he said, some people will be taken back by that. They say, oh my God, you know, how offensive is that? And if that's how they take it, that's how they take it. But some people will stop and go, wow, I didn't realize that I was being negative. I'm sorry about that. I'll be more positive around you. You need to have that positive vibe. Let me see here. Paul's got another comment I didn't put up yet. What other sites are good besides Shopify and can you push some ads on all sites or are you paralyzed for doing the same ad on other platforms? Now, you can do any ads on any platform you want.  It's just a website address. So if you wanted to send some to Magento, some to WordPress, some to Shopify, you could do that. What I like to do is if I'm testing different pages, you know, now in Cartra, I can automatically do it. It's built into Cartra. And guys, if you don't know what Cartra is, look below the description, click on the video to watch Cartra. It's really cool. What I can do in Cartra is let's say 1,000 clicks come in, I could have three different landing pages or I could have two different landing pages. Each one could have one difference in it and that would tell me which landing page is better. It's not really the platform it's built on. It's your landing page, okay? So I can build a landing page in Cartra and put it on Shopify, put it on WordPress, I can put it in Magento, it doesn't matter. But I build it all in Cartra and then I can use any one of these other platforms or I can send them directly to Cartra and they don't have to go to the website. So yeah, you can certainly customize this stuff all you want. The ease of use of Cartra is why I can do this, okay? I can literally make a landing page and click duplicate and then I duplicate it and change one sentence and boom, I've got two landing pages. It's really that easy in Cartra. That's why I like it so much. So I lied and I'm almost at 30 minutes, look at that. 26 minutes. If you haven't subscribed yet, what the heck is going on on your side of the computer? I see you over there. Make sure you subscribe. Hit the subscribe button, turn it from red to gray. Don't forget. It's a long ring, it's worth it. Ring the bell, turn off the notification so you're notified each and every time I go live or if I upload a video, I'll be live again on Friday. We got videos coming out this week, Tuesday, Wednesday, Thursday. I don't know if the ones hit yet this morning may have also got one tomorrow hitting. So every week, every week, unless I miss a day like I miss Monday, you're gonna get six trainings. You're gonna get three that are prerecorded and edited and you're gonna get live ones like this where I kind of wing it and talk to you about stuff. It's all derived to help you make more money online to start running, grow online businesses. Paul says have a blessed week, dang. See you later. Thank you so much, Paul for being here. If you haven't liked this video, weird thing at YouTube, they like it when you click that like button and you do a thumb up, okay? Just a thumbs up, that's all you gotta do. Let's see here. Any new cooking videos? I have some, Paul, they're on the back burner. That's a little play on words right there. They're on the back burner and I'm gonna get them up soon. I've got really a cool one from the Austin, Texas barbecue thing I wanna get up there. Gotta get it done. That's all there is to it, I gotta get it done. A lot to do, a lot going on. The worst thing to kill your motivation is making a lot of money. What? Yeah, we have been making so much money from Survival K Food that I haven't put as much effort to other things. We are doing some cool things though, I've actually taken some time to go places. We went and watched Joe Rogan the other night. He plays at some small club in downtown Austin and I guess he just likes to try out new material. He was awesome. He was there with Ron White and three other, four other comedians. They were awesome. So we're going to that this weekend. We're gonna be at Jimmy Buffett.  Then we are going to Bill Burr. Bill Burr's gonna be on the 1st of July. If you live in Austin guys, I gotta tell you, the entertainment choices are unreal.  So I've been spending some time actually just having fun. I had my mother-in-law here for about a week. She was hanging out here. We did a lot of stuff with her. So we're kinda enjoying life. That's what we're doing. We're enjoying life. But I have to work too. And I don't have to work to pay my bills. My bills are paid. I have to work because you gotta contribute guys.  You gotta put something out in the world. It's really important. Whether you think it's gonna be good or not, it doesn't matter. Do your best, that's it. But make sure you contribute. Spend more time creating content than you do consuming content. Think about that. How much time do you spend watching YouTube videos, watching Netflix, watching, you know, whatever you're watching and how much time do you spend creating stuff? You've gotta spend more time creating than you do spend consuming. Today, I will create. Today, I started this morning early this morning but as far as creating, I started at 10 a.m. And I'll probably go to four or five this evening. There's no way in heck I'm gonna watch eight or nine hours of videos online just to watch for entertainment. I'm gonna create more than I consume. That's my word for you today. Guys, you have a great day. I will see you on Friday. Don't forget I have videos coming out today and tomorrow on this channel. Check them out. Subscribe, notification, thumbs up. I'll see you later. Treat each other kindly.


a fiery horse with a speed of light, a cloud of dust, and a hearty hyal silver, the Lone Ranger. When the western United States was first opened to settlers, many criminals traveled to the new territory in the hope of finding easy wealth. They soon realized, however, that wealth could only be purchased by hard work, so they turned to robbery and cattle wrestling. It was these men that the masked rider of the plains fought so tirelessly, and was only through his efforts that law and order was finally established on the frontier. And our return with us to those thrilling days when the West was young, from out of the past come the thundering hoofbeats of the Great Horse Silver, the Lone Ranger rides again. Our story opens in the town of Prairie Grove, a typical frontier settlement in southwestern Texas. It is late afternoon, and Clem Barton, a rancher, hurriedly enters the small post office on the main street. Fred, hey Fred, I'm in a doggone big hurry. You got an email for me? Might have. Well, then give it to me quick. I'm looking for something special. I'll just hold your horses. I'll have a look. Oh, man, can't exactly recollect whether there was something for you or not. Don't be so horrified slow about it. Just a second, just a second. Yeah, here's something. This is yours, I reckon. What do you mean so blame hasty about? I got to meet Bankershaw at five o'clock. That's why, and it's just about five now. Oh, here, give me that. You're meeting Bankershaw? I am, but this is what I'm looking for. Yippee, this is it, all right.  He's getting ready to take that stage. What's that? Look for yourself. You don't believe me. There's a stage just across the street. Well, of all that, it looks to me like he kind of forgot about you. I'll catch him. Hi there, Bankershaw. Hey. You're calling me, Clem? Gosh, Mr. Shaw, what are you doing with your bag all packed and everything? You ain't forgot our business, have you? Yeah, business? What business? You know, the ranch, the mortgage. Mortgage? I thunder claim it Clem slipped my mind. Gosh, I was hoping we'd get things cleared up today.  The stage won't be leaving for a couple minutes yet. Well, come along. Well, what is it? It's a dog-gone secret. Well, it's like this, Mr. Shaw. I just now got the cash I sent for it to pay off the mortgage. And I'd sure hate like blazes to take the risk of keeping it on me. Well, that's a shame, Clem. I'm sure sorry I forgot about our appointment. I wasn't going to Gold City. You could give me the cash now, and then you wouldn't have to worry about it. But can't you put off your trip till tomorrow, Mr. Shaw? Sorry, Clem. My business there is a sight too important for that. But then how about leaving the cash in your bank for the night? Now, Clem, you know better, Nat. The bank's closed up tight this late in the day. Of course, you could have him take care of it over to the cafe. After all, the hold-ups has been not by a blame sight. Then I reckon you'll just have to take it home with you again. But when are you coming back? When? Oh, I'll be back tomorrow evening. I'm just staying overnight. Could I see you tomorrow night, then? Yes, I suppose you could. Of course, the mortgage ain't due for another week yet. But I won't feel real easy keeping $5,000 out to the ranch. And I don't blame you, Clem. Well, let's say you meet me tomorrow night at 10 o'clock, then. That good enough? Oh, that do just fine. Get aboard, folks. We're set to travel. Well, the stage is ready to leave, Clem. Sorry I couldn't do no better for you. Oh, we'll make out, I reckon. So long, Mr. Shaw. Tomorrow at 10, then. Good day to you. Good day, Mr. Shaw. We're near to five minutes late. Getting started already. I'm ready, driver.  Huh, Sophie? Well, what time is it? Most 9 o'clock. I'm glad you had to be to meet Mr. Shaw in town at 10. Oh, gosh, I was near forgetting.  I'll have to make tracks. I'll get it. My hat. Where in blazes is my hat? Your hat's on the chair where you put it. I declare when you get fussed you never know what you're doing. Well, I reckon I'm just feeling good knowing the mortgage is gonna be paid up, honey. It was mighty nice of your brother Ned to give us a lend of it. You'd better be careful with it. And what he says, things bein' the way they are back east, he won't be able to send you no more. You bet I'll be careful. Here it is, Clem. Now, you put it to a good safe place. Yeah. It won't fall out of that inside pocket, I reckon. Now, where'd your same hat was? Oh, here it is. Oh, you're hurryin' to town. The horse is all saddled outside. It's a nice moonlit night to ride. Well, you take care of yourself. Who in the blazes is that? Whoever it is, don't you stop to talk to him. You just keep going. If you want red skin, don't stand there, Clem. I'll deal with the engine. I'm a-going, honey. All right, engine. Whatcha say you want it? Me want food. Me pay you. Well, landscape, we got a whole lot on hand, but you're welcome to share. It's just for yourself. No, me got friend. Oh, there's two of you. Another red skin, huh? Him, white friend. White friend? Then why don't he come up mask for the grub instead of send a ninja after it? Well, I can't stand below in the shadows. Well, I reckon they don't matter, though. You just wait till I have a look in the kitchen, and I'll see you. They are sharp. That's the way Clem rode. Something's happened. Me, come. Stranger, don't let nothin' happen to Clem. Help him. Hurry, tunnel. Hit me ready. Come on. That's right. Sounded like a rifle. Hurry, tunnel. There's a horse. And there's a man lying on the trail. What's the matter, left the ranch house when you knocked on the door? He has the same power. He's not dead. Will it cut cross-head? Yes. Didn't wound him seriously, but it was enough to knock him out. He'll come, too. He'll be conscious in a moment. Look, channel. The shot must have come from behind that cut bank. It's the perfect spot to hide it if he wanted to drag out some man on this trail. The man who fired the shot could follow down the ghost and make his escape unseen. The cash. You'll be all right, friend. The bullet only scraped your scalp. Wait a minute. I gotta look. The cash. You were carrying money? It's gone. It was stolen? How much did you have? $5,000 in stolen money. $5,000 in all of it borrowed.  You're the fellow that shot me. Easy, Clem. Your wife can prove we were at the ranch house when the shot was fired. And we didn't know you were carrying money on you. Here. Feel well enough, ride back to the house. Just let me rest a minute, stranger. Can you answer some questions? What questions? How many people knew you had that money? Nobody. That cash come from the east and I never told nobody about getting it. No one at all? Well, I did tell Bankers Shaw. But he don't count. What I mean is, it was him I was taking the cash to. So he'd have just as much reason as me for keeping it secret. I see.  A mortgage for $5,000? Uh-huh. But from what I've seen of your place, it isn't worth that much. Well, as a matter of fact, stranger, it ain't. But when I asked for that $5,000, I needed it bad. And if the bank was willing to lend it, I wasn't going to put up no objections. Then Shaw would be more anxious to have you pay the mortgage than to take over your ranch. Shucks. I ain't suspecting him, stranger. You just asked me who knew about the cash and I told you. Of course, he might have been careless but Bankers Shaw don't ever say anything careless like. And besides, he couldn't have told nobody. We fixed up our meeting tonight just when he got on the stage yesterday. He's been out of town ever since. The stage is only due in now.  Say, do you mean that? We do. Gosh, you're sure a strange sort of fella to be wearing a mask and riding with a red skin. We're not crooks, Clem. You think you can make it back to the house now? Your wife will be worried. Your hand, will you? My head's like to split. Here, of course. Thanks, engine. I'll help you, Clem. Golly, I sure don't know what I'm going to say to Sophie when I get home. I'll sure get a tongue lashing with the cash gone and no way to borrow more. Steady silver. How soon does the mortgage have to be paid, Clem? Well, there's just six days left. A lot can happen in six days. You ready, Tello? Say, which way are you heading? Aren't you going back to the house with me? Not now, Clem, but we'll see you later. Hail, silver! They ain't the blamest fellas I ever seen. That night, the Lone Ranger and his faithful Indian companion, Tonto, made camp. But the next morning, they returned to the dry gulf to search for some trace of the man who'd robbed Clem Barton. Oh, hold this over. Hold this over. Too dark to follow the trail last night, Kimosami. The moon night didn't help any of this, Golly. But we may find something today. There. Empty shells. Yes. Look. Here's where the man kneeled to shoot. You can see the mark of his knee in the soft earth. That... that's right. And there are hoof prints. Of course, got broken shoe. The broken shoe on the left forefoot. There was a small horse. You can see how light the prints are. That's right. I'm afraid we can't trail him, Tello. No. Him ride on hard ground. Him not leave trail. Yeah, but I knew what he was about. Now what we do? Some things I don't understand, Tello. The outlaw must have known Clem had that money. That's right. Clem says the banker was the only one to know. If he'd loaned more than the ranch was worth, he stood to lose if the money wasn't delivered. Here's a loan, Tello. We're going to town, Kimosami. You've got plans? Yes, but there are things I want to find out. Two hours later, the loan ranger disguised, but without his mask, sat at a table in the cafe with Thoughto. They watched a hard-faced man call Pete as he talked with the banker. Hello, the hoof prints left by Peace Force are exactly the same as those we saw in the ghost. Oh. I wonder what business he could have with the banker. It looked plenty strange. Too bad we can't hear them. At least we can stay and see what happens. Well, I was telling them about it before. Yeah. Well, Mr. Shaw, I better be on my way. Even already? Yeah, I got it. But I'll be seeing you again. Uh-huh. Maybe there'll be some more business we can do together. I sure hope so. What happened to your head, Clem? Get in the shooting screen. Hey, hold on and tell us about it. Not now, boys. I got to talk to Mr. Shaw. Howdy, Mr. Shaw. Can I sit down? Thank you. Maybe you'll let me know what you've got to say for yourself. You kept me waiting last night till after midnight. Mr. Shaw, I was shot at. That's how I come to be wearing this bandage. Shot at? And the cash stole from me. Well, um, who done it? That's something I don't know. The only fellas I've seen was a masked man and an engine that rode up when they heard the shot. The bullet knocked me out cold. A masked man and a red skin? Why, there, the crooks have stole your cash. Well, that's when the shot was fired. Then they had a partner with them. Don't you see it? Their partner could have shot you and then rode off. And other fellas talked to Sophie so they'd have an alibi.  You know why you were still out? And it worked because you was injured enough to think the same fella that shot you must have got the cash. See, do you really think that?  I look over there. That's the same engine. And that fella with him, he's got a lot of money for this. Man, grab that red skin this friend. Get a hold of him. There they go. After them. They're heading for their horses. Grab your guns. There they are. Man, this is a job for the sheriff. Tell him claims you said $5,000 stole and those are the fellas that stole it. The curtain falls on the first act of our thrilling ronranger drama. Before the next exciting scenes, please permit us to pause for just a few moments. Now to continue the story. The ronranger and Tonto, suspected of the theft of Clem's money, made their escape from town. Their great horses carried them safely beyond pursuit. But that night, they returned under cover of darkness. That's Pete's place up ahead, isn't it, Tonto? Uh-huh. And there, like in Captain's. That means he's still at home. Now that we've got to make him talking, right, a man who would fire from cover must be a coward. I think we can persuade him to confess whether he planned that robbery alone or whether someone else gave him his instructions. Uh-huh. Someone must have told Pete about the money. Maybe Banker told him. Sure, no more money than the ranch was worth. Clem forgot that the banker could have hired someone to steal the money, and that's why he got the ranch too. Not right. Tonto, you saw Pete through the window.  Come on. You may not be alone. All right. We're going to have a talk, Pete. Don't slap, Mother. Get out of here. I need my suit now. What's your idea? Good. Throw the fire. Now, Pete, you're going to tell us about your holder. You shot Clem. He stole the cash he was bringing to town. You can't lie out of it, Pete. You shot him from the dry ghost next to the trail. We found the Prince of your horse. My horse? No way. Who was your partner, Pete? Someone told you Clem had that money. I have a good idea of who that person was, but I want the information from you. How are you going to talk? Talk, I said. Talk or take the beating of your life. Quit shitting me.  That's only a start.  Stand by the door, Tonto. It makes a break for us to stop him. You can save yourself by telling me what I want to know. I don't know nothing about it. Stand back. Don't. I'll talk. Just don't beat me up. It was this way. I was down by the cafe the other day. We found out the name of the man who gave Pete his information, Tonto. But there's still more to do. We've got to trick him into returning the money. It won't help Clem to get the guilty man of the money. You've got a plan? I have. We're going to call on the banker. Open that door. Open that door. Come on, Tonto. Close the door, Shaw. You didn't think we'd be back in town, did you? The sheriff's looking for you, fellas. You're not leaving the house. If you try to reach that rifle hanging about the fireplace, you'll never make it. I can draw before you've taken another step. We'll see about that. I know who's responsible for the theft of Clem's money. You ought to know you took it. That accusation won't stand, Shaw. Tonto and I can prove we're innocent. What's more, you're going to help us prove it. I meant exactly what I said. You a friend of Clem's? And you want his money returned to him? Then listen to me and stop looking toward your gun. You'll listen whether you like it or not. The following day, Shaw, the banker, entered the cafe. Looked around a moment, then made his way for the man standing at the end of the bar. Come on, Mr. Shaw. Howdy, fellas. Hello there, Jake. Good afternoon, Fred. Howdy, Mr. Shaw. Have you ever heard something that settled the dust in your throat? Don't mind if I do. Have one with me, Fred? Glad to. Hey, what are you so pleased about?  Just had a stroke of luck, that's all. Yeah? Come on. Let's sit over that table here and I'll tell you about it. Hey, Barkey, two of the usual. Bring them to our table.  There. Now, what in blazes is it all about? I suppose you know I'm holding the mortgage on Clem's ranch.  No. Give them 5,000 for that mortgage, didn't you? Yep. When you got the cash together to pay your off or what's stole from him, won't it? It wasn't a pay you with, can it? No. And if you can find anything in that to make you happy, I'd admire to know what it is. It was me I wouldn't give half the size of that mortgage for Clem's place. If you can grin about losing more than $2,000, you must be off your head. You're just Postmaster, Fred. Nobody'd expect you to understand these things. And you mean to sit down as much as say you want Clem's place? I ain't said it yet, but that's the fact. It beats me. I reckon you're needing to drink worse than I am. Just set them down, Barkeep. This'll pay for them. Thanks, Mr. Shaw. There you are. You can keep the change. You want a thing more, Judge Pollard? Look here, I've been taking over what you just said. Yeah? I've got a notion why you want Clem's ranch. Maybe I'm wrong, but I'm bitten I eat. There's something on that ranch that makes it valuable. Now, what would that be? I don't know, but whatever it is, you know about it. Maybe it's coal, maybe it's oil, but that don't matter. I don't want to re-in that ranch with a heap of cash. Something that's got nothing to do with the cattle. Because the rain of cattle men alive would pay you $5,000 for that measly, dried-up ranch. Oh, come on. Tell me what it is.  You haven't even tasted your drink. Change my mind. I don't want it. Good day to you, Fred. I savvy while you're living. I came to blame close to the truth, didn't I?  See you later. Now, I wonder. Bye, heaven's tourist hunter. I'm going to find out. Hey, Fred, what's the matter with you? Huh? You look as though something bit you. Something did, just about. You saw me talking to Banker-Saw just now, didn't you? Of course I did. Didn't I bring you your drinks? Barkeep, there's something blame-funny going on. Huh? You know what Banker-Saw told me? He wants to foreclose on claim. He was laughing about it. No. I'm telling you the truth. But he'd be losing money. Barkeep, I'm just wondering if he would. Nobody, I said it. But he's got a reason for foreclosing. And just between you and me, Barkeep, maybe that same reason would make him keep Clem from paying off.  But it seems to me it's a mighty strange thing. Mighty strange. Alice? The Banker's aim to make himself rich with Clem's rights. What's that? There's oil or gold. Oh, just what's the Banker up to? I don't know. I don't know. It was Banker-Saw had Clem robbed. He aims to get his range. We must have barely done the Banker-Dunnett. Why else would he want to foreclose? All right. You know what, we ought to set the sheriff up on you. Banker-Dunnett sure is shooting. He can't get away with a thing like that. Hanging's too good for a polkaid like this. Shaw, you're in a heap of trouble. Yeah? Ain't you been uptown? Not since the last to talk to you. Well, everybody's talking about your full clothes, none of them. They're saying that if you're so blame-anxious to get his ranch, maybe you took steps to see that he didn't pay you. Nonsense. Yeah, if you think I'm lying, you just go over to the cafe again and see what happens. You mean they really think it was me rob Clem? They don't think nothing else. But they know better, Ned. I'm no crook. Why, I wouldn't take a penny. I didn't come by, honest. You didn't even tell me that, I believe you. But it ain't all the folks in town knows you as well as I do. There isn't going to be trouble, is there? Shaw, you and me have known each other since we were young. Sure we have. And we've been good friends all that time, too, haven't we? I reckon so. Well, then you can believe what I'm saying. I've seen some mighty mean crowds. I can recollect the time the folks in town raided the jail and hung their crook who shot the other sheriff in the back. What I did. Just you wait till I'm through talking. What I'm getting at is this. In all the time I've lived in this here town, I ain't never seen a crowd that meant business anymore than uptown tonight. Shaw, they're fixing to hang you. They put two and two together and decided you're guilty. They haven't any evidence. That's just why they're going to hang you themselves instead of waiting for the law to do it. They can't do that. They show her blazers are fixing to do just that. And you got just one chance to save your skin. I got a chance, you see? I got it all figured out. The only way you can keep from being hung is to show them you don't want Claims Ranch. What's that? It's not the ranch, then they'd never got the notion you was responsible for the holdup. Ain't that so? Hey, I guess so. Now, if you do something to prove your will and to give it up, maybe the crowd will change its mind about you being guilty. What can I do? I said we've always been friends, didn't I? I heard you. Well, I'm willing to buy that mortgage from you. Then I'll go uptown and tell the folks you sold it. After that, they'll have to figure you wasn't a bling. I'll take my chances, Fred, before I'll lose my $5,000. You won't be losing it.  I will. But just because we're friends. There you are. $5,000 even. Now make over the papers in the hurry so I can get back and head off to mob. That won't be necessary, Fred. For what? Where'd you fellas come from? We were hiding behind this other door, and just waiting for you to show us whether you had that cash on you or not. Well, Sheriff... The Sheriff has already told the townspeople to bring him in. He tried to escape last night. Had we forced the truth from him, the townspeople and I brought him back. Then the mascot had brought him around to my office and made him tell me who his partner was.  Fred, even without Pete testifying in you, that $5,000 you just put on my desk would almost prove it. Where could you have saved $5,000 on the salary of a postmaster? It's a mistake. You'll frame early on. It's no mistake, but we nearly made one without his receiving the money. Clem forgot that he opened the envelope which contained it in front of you in your post office. But the mask fella found out the truth, all right. And it was a mask man's scheme to make you think there was gold or oil on the ranch, Fred, so you'd hand over the cash you stole. If I get my hands on him, I'll... You ain't, Fred. You're going to jail. And, Clem, we might just as well take care of that mortgage right now. The mask fella cleared up the first robbery, but there's no sense in taking chances on another. The story you have just heard is a copyrighted feature of the Lone Ranger Incorporated.