So, I will continue discussing the exponential law, it is very important one and anyway there are so many aspects that there may be some repetition also, but does not matter. So, we said that for example, I have been giving the example of a fuse, which does not show the wearing house effect, wearing out effect and similarly, a jewel bearing, you know you have them in watches. So, there is no bearing out effect on such components and they are good as good as new while they are functioning. So, it does not matter how long they have been functioning, they are as good as new and if a fuse has not burnt out, it is like a new one, a jewel bearing does not wear out. So, this is again and again I am trying to give you examples of components for which and therefore, for such components the exponential law is appropriate and is supported by empirical evidence. That means, when you have collected data for such components, how long it takes for them to fail and so on. So, then and then fitting the curve to the data, it turns out that exponential law is an appropriate one for such components. So, another way of saying that there is no wearing out effect is as follows, consider the conditional probability that capital T, the lifetime lies between T and T plus delta T given that capital T is greater than T. Now, the intersection of these two events is simply this because here also T is greater than T and it is less than T plus delta T. So, therefore, the intersection of these two events is this. So, then the conditional probability can be written as probability of the intersection of the two events divided by probability that T is greater than T. Now, this you can see immediately is the probability T less than or equal to T plus delta T minus probability T less than or equal to T. So, this event and since this is 1 minus e raise to minus alpha T plus delta T minus of 1 minus e raise to minus alpha T. So, the 1 1 cancels out and you will be left with e raise to minus alpha T minus e raise to minus alpha of T plus delta T divided by this probability which is e raise to minus alpha T. This of course, I am showing you for the exponential law. So, therefore, this is 1 minus e raise to minus alpha delta T which is nothing but the probability that T lies between 0 and delta T. So, this tells you that this probability is independent. So, this conditional probability is independent of T depends only on delta T that is depends only on the length of the interval that you are considering that means you want to consider. So, that means here from T to T plus delta T. So, the length of the interval is delta T. So, this probability this conditional probability is independent of T and depends only on delta T. So, therefore, this is another way of saying that it is memory less or the varying out effect is not there. That means it is not it does not matter for how long the system has already been working, but now when you want to look at the probability that it will be working in the interval T to T that means it fails before T plus delta T then that is dependent only on delta T. So, this is the whole idea and so we have seen that there are many situations where this is a very appropriate law. Now, see this one to make a note here that even though this probability will all if you would say T less than or equal to capital T less than or equal to T plus delta T this will also come out to be the same as this one. But since we are considering the conditional probability that T is greater than capital T. So, therefore, we have to consider this event and not this event. So, sometimes inadvertently may be one can I may have written it like this, but the when you are looking at this conditional probability then it has to be T strictly less than capital T and here it is less than or equal to T plus delta T. So, that would be the right way to write the event even though because of the continuous case the two probabilities may come out to be the same important part. So, thus as long as the component is working it is as good as new. Now, in this equation suppose I expand the right hand side so expansion for e raise to minus alpha delta T right. So, all of you should be familiar that much calculus everybody has done. So, you can write down the expansion for e raise to minus alpha delta T which will be 1 minus alpha delta T plus sorry I am sure that means 2 factorial and so on powers of delta T. And then when you open up the brackets one cancels out and then we have you have alpha delta T plus higher power terms containing powers of terms like delta T square delta T cube and so on fine. Now, when delta T is small delta T is small we can just ignore these terms and therefore, for small delta T probability of failure in time delta T is proportional to alpha delta T. So, this is what again just reiterating what we have been saying. So, now in fact we have given it a better expression from here this is more you can immediately conclude quite a few things from here. So, that means in a small interval no matter where that time interval is length delta T is the probability of a failure in that time period is proportional to time period itself delta T. Now, this is if you again see I am saying the same thing again which I said. So, this is nothing but your Poisson process this is this is the one of the basic assumptions of a Poisson process. In fact, what you can say now here is that suppose you have a electronic device and you have lot of components which have the same which follow the same exponential failure law and they have the identical distribution that is the same the same parameter lambda let us say and then you are and of course, the components behave independently. So, that condition also for a Poisson process is satisfied that is the you know arrivals are independent and so here the components will behave independently. So, their failures will also be independent of each other. So, that assumption plus the assumption that within in a small interval the probability of a failure is proportional to alpha delta T. So, then in that case with those two assumptions you can then say that if you are considering let us say time period 0 comma T then the number of failures within this time interval will follow a Poisson process. So, you can see that the arrival and the inter arrival times that we will talk in detail later on. So, the inter arrival times and the arrival pattern. So, inter arrival times would be exponential and the arrival patterns would be Poisson and so on. So, we will continue with that discussion. Now, because again we want to say this thing now that since the for the exponential failure law the failure behavior of an item depends only on the length of the time period being considered and not on its past history. So, therefore and for the non exponential just like we have so far considered the normal failure law. So, for non exponential failure laws the past does matter it does matter when you are under you know stress then the varying out effect is there and so it depends on how long the stress has been and so on. So, for non exponential failure laws the past does matter. So, therefore it is important to understand that when you talk of the time T like time you know life length. So, for the exponential failure law T will denote the time in service up to failure because it does not matter when you start counting it is if the component is functioning when you start counting the time from then. So, up to failure T will denote the time it does not matter when you start counting it right, but for other for non exponential components T will denote the total life length up to failure. So, you started functioning from whatever time you you you count your time from that and so capital T will in that case the normal random the random variable will be will denote the total life length up to failure. So, total means that whenever you start service or whenever you start using the item then you start counting your time from here whereas, here it does not matter you start counting from any point and then up to failure. So, the life length will denote that. So, T will denote that time period. So, it is important to understand these two differences between you know how you count the time for exponential failure law and for a non exponential failure law. Let us look at the various graphs connected with the exponential failure law. So, this is a familiar one right at t equal to 0 this will be 1 it will be equal to alpha right and then it will go down this way right as t goes to infinity it will go to 0 and then correspondingly you see z your failure law rate of failure z t is alpha right which is a constant right and so it continues to be alpha value alpha for all values of t this is your t axis this is your z t axis then f t would be of course. So, f t would be what 1 minus e raise to minus alpha t right sorry this function right. So, 1 minus e raise to minus alpha that t equal to 0 this will be 0 and then as t goes to infinity this goes to 0. So, the function finally goes up to 1 and then your r t the failure function sorry the reliability function yes the reliability function r t which is 1 minus f t and therefore, this is equal to e raise to minus alpha t and so here again at t equal to 0 the value will be 1 and then it will go down as t goes to infinity. So, the reliability goes down as t goes to infinity. So, this is the graph for the pdf of an exponential failure law. So, at t equal to 0 it is equal to alpha and then it goes down to infinity as t goes to infinity then we know that the failure rate z t or the hazard function this is the constant right and the constant values alpha then cumulative density function which is f t is equal to 1 minus e raise to minus alpha t would be again at t equal to 0 it will be 0 because this will be 1. So, 1 minus 1 is 0 and then it goes up to 1 the reliability function would be e raise to minus alpha t. So, at t equal to 0 this will be 1 and then again it goes down to infinity. So, these are the four graphs that the four functions that you relate with the exponential law and you have picture of the all four of them. Now, let us look at this example if the parameter alpha is given and reliability is also given that means r t is specified we can find t. So, that means given alpha that means you have specified the failure law and then you are asking for a certain level of reliability. So, you want to know what would be the time required for the equipment or the component to operate to achieve that reliability. So, the number of hours of operation required for the specified reliability level I should say. Now, let alpha be 0.01 and reliability is 0.9. So, you want this to be obtained and your parameter is 0.01. So, if alpha is 0.01 then your mean will be what? So, for exponential distribution the mean is so expected t would be 1 by alpha which is 1 upon 0.01 which is 100 hours. So, if you are talking if your unit of time is hours then this is 100 hours. So, now so therefore, the number of hours that are required is given by to achieve this reliability level. Then you are saying that e raise to minus 0.01 t remember this is the reliability function. So, e raise to minus 0.01 t should be equal to 0.9. So, you want that value of t which will satisfy this equation. So, you take log of both sides and this will then give you minus 0.01 t is equal to ln of 0.9 and remember ln of number less than 1 is negative. So, therefore, this is so there is a minus sign here and so if you now divide by 0.01 then you get the t is equal to 100 into ln of 0.9 which comes out to be if you look up the values of ln 0.9 then multiplied by 100 that gives you 10.54 hours. So, therefore, the way you can interpret this is that out of 100 components all are working simultaneously and 90 what we are saying is and if they all operate for 10.54 hours then our expectation is that 90 of them will not fail. So, after 10.54 hours 90 of them will be working. So, this is what we mean by the reliability level and so on. So, therefore, you know so essentially it is question of given what and then what you can compute. So, sometimes you may be given the time then you can compute the reliability level. So, if you are given t then you will be able to determine this number and if you are given this reliability level then you can determine the time or if you are given time and reliability then you can determine the parameter. You can uniquely determine the exponential failure law because you only need the parameter alpha to determine the failure law exponential failure law. Let us look at another example. So, here you are given the cos c in terms of mu. So, c is 3 mu square be the cost of producing an item where mu is the mean time to failure. So, again we are talking of a exponential distribution exponential failure law and mu is the mean. So, therefore, if mu is the mean then remember the distribution the failure law would be minus 1 by mu t. This is what you have. Now, cos is 3 times mu square. So, which means that if mu is small then the cost is small. If mu is large then your cost would be accordingly large which makes sense. So, may be because if your mean time to failure is small then you expect that the cost is also small and if the mean time to failure is big is large number. Then that means you expect the component not to fail very early or has a long life time and in that case the cost of producing that item would be also high. So, it is reasonable to assume the cost in this way. Now, suppose rupees D are earned for every hour the item is in service. So, you earn a profit of D rupees per hour when the item is functional. Now, you want. So, therefore, profit per item is given by the profit would be D into t if the life time is t hours then D into t minus the cost 3 mu square and t is the number of service hours. So, find the value of mu for which the profit is maximized. So, expected profit. So, certainly because this is a random variable. So, we will maximize the expected profit. So, the expected profit is this because D of e t this is the I mean this is not a random variable this would be some fixed number. So, then D of e t minus 3 mu square and e t is mu. So, therefore, D mu minus 3 mu square. So, exactly what I was saying that. So, this is. So, therefore, to maximize this expected profit I would differentiate this respect to mu. It is a function of mu and put it to 0. So, that gives me D minus 6 mu equal to 0 which implies that mu is D by 6. And of course, only critical value and if but still you need to verify the D square by D mu square is of the function is minus 6 which is less than 0. So, therefore, the critical point is the point of maximum. So, the value that we get of mu here is value which maximizes the expected profit. So, therefore, mu equal to D by 6 is maximizing the profit and the maximum profit is D square by 12 rupees. So, just trying to give you a feeling for the failure law exponential failure law and the kind of problems that can be discussed and that arise corresponding to this. So, again the level is at very basic. The level I have kept is very basic because this is just trying to give you a glimpse of how these probability tools that we have learnt can be used for answering so many questions about day to day operations of systems, service systems and so on. So, this is the whole idea. Otherwise, reliability theory has become very complex and in fact, the next failure law that we will discuss is a complex one and again we will just try to understand the basics of the viable failure law. So, let us now I will talk about the viable failure law and you can see that now the degree of complexity is going up and we have not so far discussed this distribution probability law also. So, let us look at it and the idea here is to because the constant failure rate was only applicable to a special kind of components which were not let us say for which there was no wearing out effect. So, that was a special situation and we have seen that there are so many almost electronic devices or you know behave that way and so the exponential law is appropriate for them. So, now if you want to modify this constant rate then the viable failure law was thought of and this is alpha beta t raise to beta minus 1. So, now you have introduced power of t of the time and of course, two parameters and there can be more than two also. So, we are talking of a two parameter viable failure law and so here alpha and beta are positive and t is greater than 0 as usual because it is the lifetime variable. So, therefore, has to be non-negative. Now, you can look at I have drawn various pictures of z t when for the various values of beta and different values of alpha and beta and so maybe we will just look at it. Let me just first compute your f t. So, remember we said that we can compute f t uniquely given the failure rate function z t. So, then this is z t e raise to minus integral of 0 to t of z s d s integral 0 to t of z s d s right. This is our formula for computing f t given z t. So, then here if you substitute for z t this is alpha beta into t raise to beta minus 1 e raise to minus integral 0 to t alpha beta s raise to beta minus 1 d s right. So, if you just look at this integral let us just compute. So, this will be s raise to beta minus 1 d s from 0 to t and the integral here is 1 by beta s raise to beta 0 to t. So, therefore, this is 1 by beta t raise to beta. So, if I make that substitution here I get my f t as this. So, this is the p d f connected with the variable failure law and the failure law is specified there. So, the way it looks it is little complicated, but just see when you put alpha equal to 1 and beta equal to 1 alpha equal to 1 beta equal to 1 and this is 1 and this will be e raise to minus t. So, e raise to minus t would be your yeah. So, this would be your p d f right exponential with parameter 1 and that is the one I have drawn here right. Then if you look at the value alpha equal to 1 and beta equal to 2. So, therefore, in this case the beta equal to 1 this will be exponential and the failure rate will be constant which will be 1. So, beta of course, here I have drawn it only for beta equal to 1. So, alpha is as it is this one is of course, you put alpha equal to 1 also. So, anyway this is your function for the failure rate. Then when you put alpha equal to 1 and beta equal to 2 then I have drawn this one. This is the 1 for beta equal to 2 of course, not very accurate figures. So, you can always Google search and then you can find nice pictures very accurately drawn graphs. So, beta equal to 2 now you look at this thing here. This is alpha 1 beta equal to 2. So, this is twice t that means it is a linear function of t. So, therefore, you see for different values of beta things are changing. So, alpha equal to 1 beta equal to 1 you got constant alpha equal to 1 beta equal to 2 you get and in fact, any value of alpha alpha does not have to be 1. Then in that case it will be a linear function of t if beta is 2. So, here of course, I have drawn it for alpha equal to 1 and beta equal to 2 the diagram. Then and the corresponding pdf will be 2 t e raise to minus t square. Then for beta equal to 3 for example, I have drawn I have drawn the picture here also for beta equal to 3. So, then this starts taking a bit more bell shape and beta equal to 3 alpha equal to 1 will be 3 times t square. So, that would be that means that t is a quadratic function of t and correspondingly your this thing will be. So, here when beta is 3 then of course, this is t square and then e raise to something right. So, quadratic into a financial function. Now, and for beta equal to 5 for example, it will become more steep like this and then as beta goes to infinity you see you can show that it will simply be a spike. Now, just a spike because beta is going to infinity then this will simply just spike into this thing which you call as a delta function. So, at the point so, here it will become a spike as beta goes to infinity.  So, here beta is a shape parameter therefore, you see beta is a shape parameter and 1 by alpha is the scale parameter. So, I use scale the whole thing right that means when you are drawing the thing. So, failure rate is proportional to power of power beta minus 1 of t. So, therefore, this is the generalization that we have made to the constant failure rate and so, this is the failure rate is now proportional to t raise to beta minus 1. So, you can see that yeah and then this also gives you good feeling. Now, for example, if your beta is less than 1 then this will become negative. So, t will be in the denominator and so, alpha beta upon t raise to 1 minus beta and that will be for as t goes to infinity. So, the denominator will go to 0 and therefore, this will let me so, alpha beta upon t raise to 1 minus beta. So, as t goes to 0 this goes to infinity the denominator t goes to 0 this goes to infinity and so, it should be the other way. I want to show that for beta less than 1 for beta less than 1 this is negative. So, when I take it here it will be positive this power is positive and so, as yes as t goes to 0 this goes to infinity because this goes to 0. So, this goes to infinity as t goes to 0 right yeah and therefore, it is this way and then as t goes to infinity this goes to 0 and so, failure rate decreases with time. Now, failure rate decreases with time that means, see essentially defective items fail early and the failure rate decreases over time as the defective items have been weeded out. So, all the defective items have been weeded out from the population. So, that case the failure rate will decrease with time right. So, all defective items fail early and therefore, as time progresses your failure rate will decrease. So, this is the situation that gets modeled when you are by putting beta equal to less than 1. So, all values of beta between 0 and this thing here all right. So, you take this then this is the situation if you suppose to model and beta equal to 1 we have already discussed thoroughly. Now, here of course, since the failure rate is constant. So, as time goes on the failure rate does not change. So, this is because random external events are causing the failure that could be one of the reasons. So, random external for example, if a fuse will blow out if the high current comes suddenly in the line right. So, therefore, that is the external event and many others can be explained high wind and so on. For other high tension wires you can snap and so on. So, therefore, beta equal to 1 because the failure rate is constant it is understood that external events would cause the failure could be the reason for the failure. And for beta greater than 1 as we have seen failure rate is increasing with time and therefore, this models the situation where aging process has a role to play in the failure of the system. And that is parts are likely to fail as time goes on and this is when the stress part. So, you see this suddenly captures it is a more complex and it will more comprehensive failure law which captures more than one situation and you know you can play around by manipulating the value of beta and alpha and try to get accurate results. So, this is the whole idea and we will continue with the discussion on web distributions. So, let us make this the computations about the expected value and the variance of a viable distribution. So, E t the theorem says that E t is alpha is to minus 1 by beta gamma of 1 by beta plus 1. So, we all know the gamma function and then V t the variance would be alpha is to minus 2 by beta gamma of 2 beta plus 1 minus gamma of 1 beta plus 1 whole square which is we are using the formula that variance is E t square minus expected value of t square minus expected t whole square. Now, so just apply the because we have already computed the f t the p d f for t when t has a viable failure law then this is t into alpha beta t raise to beta minus 1 raise to minus alpha into t beta d t. So, yes so now you can see that this t beta minus 1 and t beta. So, this prompts you to make the substitution that t beta is y. So, we will do this. So, again you are all familiar with this part of the calculus you can do this integration. So, t raise to beta is y that will make beta t raise to beta minus 1 d t is equal to d y the limits will not change they will remain from 0 to infinity since beta is positive. So, for t equal to infinity y will also be infinity and t 0 y is 0. So, now therefore, this thing whole thing gets replaced by d y. So, you have a beta t beta minus 1 and d t. So, this we will replace by d y then you are left with a t and an alpha and then e raise to minus alpha y because t raise to beta is y. So, therefore, this is what you have alpha e raise to minus alpha y and y raise to 1 by beta and there is a yeah. So, y raise to 1 by beta because you have a t here. So, t will be y raise to 1 by beta. So, therefore, this is what you have now you see this looks familiar because you can now relate this with the gamma function gamma p d f. So, here alpha e raise to minus alpha y then you have to have alpha y here as the variable. So, alpha y raise to 1 by beta now y 1 by beta is there. So, alpha 1 by beta I am adding here. So, therefore, I will divide by alpha 1 by beta and then I need a gamma 1 by beta plus 1 for this integral d y to be 1 because this is the p d f of a gamma distribution with parameters alpha and 1 by beta. So, then I am left with this and this finally. So, therefore, the expected value of the random variable t where t is has a variable failure law is given by gamma 1 by beta plus 1 into alpha raise to minus 1 by beta and then the second part should be straight forward. So, you have this. So, therefore, I need to compute expected value of t square and so it will be t square alpha beta t raise to beta minus 1. So, now you see you are again beta t raise to beta minus 1 and e raise to t raise to beta would become this thing yeah I am sorry I mean beta t raise to beta minus 1 d t that will be d y from here right and then you have t square. So, that will be y raise to I mean I have not written the integral here. So, anyway this will this will reduce this will be equal to 0 to I have I written t this is 0 to infinity yeah this is 0 to infinity. So, y raise to 2 by beta and then you have an alpha and then you have e raise to minus alpha y d y right. So, here again I will do the same trick that I did here. So, alpha e raise to minus alpha y is there then this you need to write this 0 to infinity alpha y raise to 2 by beta alpha e raise to minus alpha y is exactly the same thing. And then you will divide by alpha raise to 2 by beta then you need a 2 by beta plus 1 right and you will multiply by 2 raise to beta by gamma of 2 beta plus 1 2 by beta plus 1 and so this whole thing will be and there is a d y right. So, then you will be left with gamma of 2 by beta plus 1 into alpha raise to minus 2 by beta. So, this will be expected value of t square right and therefore, the variance will be this minus the expected t whole square. So, you take out alpha raise to minus 2 by beta common and then you are left with it. So, this is just for your now and the here again we could make use of the gamma distribution computations to compute the expected value and the variance. Again, so we have seen that variable distribution represents an appropriate model for the failure law whenever the system is composed of a number of components right and the failure is primarily due to the most severe flaw among a large number of flaws in the system. So, this is what is happening. So, you have lot of components and lot of parts in the device that you are using and each one of them has a flaw, but then it will be governed by the most severe flaw among all the components. This is what the you know you can say that this is the representation of this is the situation, but which a viable distribution will represent and your alpha beta and of course, you have seen that you know by changing the values of beta you can either have a increasing failure rate or a constant failure rate or a decreasing failure rate. So, this we have already seen right and yeah. So, here you know I am just being able to give you you know short glimpse into the what this distribution can do and one needs to really work at lot of examples to understand the implications of the importance of this distribution. Now, let us just look at this example. So, each of the six tubes of a radio set has a life length in years. So, our time unit is a year which may be considered a random variable. So, the lifetime of a radio tube in a radio set number of years should be considered as a random variable. Suppose, these tubes function independently of each other. So, that is important they are working independently of each other. What is the probability that no tube will have to be replaced during the first two months of service. So, we will have to translate this to years because our unit of time is years. Now, the pdf of the failure time to failure is given by this 50 into t e raise to minus 25 t square. So, immediately you can recognize that this is a variable distribution and since t has power 1. So, your beta is 2 this is beta is equal to 2 because t raise to beta minus 1. So, therefore, if beta is 2 then alpha is and of course, from here alpha is 25. So, this is alpha beta alpha beta into t raise to beta minus 1 e raise to minus 25 t square because this is beta. So, this is a variable distribution. Now, of course, we have not made this computation of the for the for the viable distribution, but certainly you can do it or maybe you can use numerical method. So, essentially yeah it is a viable distribution with these are the parameters. Then, you since the tubes are functioning independent of each other and you do not want and of course, let me say that your t is 1 by this is 2 months. So, 1 by 6 which I have written here. So, t is 1 by 6 you want. So, yeah so we we want their 6 tubes they are working independently of each other. We do not want any one of them to fail. So, therefore, in the first 2 months. So, the probability of let us say the first tube not failing in the first 2 months is t 1 greater than or equal to 1 by 6. So, the time unit is 1 by 6 and then since all of them are independent of each other we do not want any of them to fail. So, then this would be probability t 1 greater than or equal to 1 by 6 raise to 6. So, this we will you know this is not a difficult integral again you know because see you have seen my computations here for e t and various t. So, you can just use those you can use the gamma distribution computations to do the computations here and then you can find out this probability raise it to 6. So, the answer is approximately 0.5 raise to 6. So, this integral you can handle now since I have given you the method of computing e t. So, exactly it just boils down to that for different values of t and so on. So, now this does not exhaust the failure laws I have only as I told you and I have been repeating it that we are only considering very basic failure laws here and my of course aim was to since we have discussed the probability theory and so the various tools you have learnt about. So, I just thought that I would like to show you the various applications also of these tools that we have learnt in the course. So, that has been the whole idea theme across the course that you learnt the theory and then you learnt to use it also and so marco processes discrete marco processes then we will we have talked about continuous marco processes and in the process special cases which are poison and exponential distributions and then birth and death processes and finally applications to reliability theory and here also the basic concepts have been given to you, but as I said it is a very growing large growing area very important and lot of applications of course probability theory and there are many more people have come up with failure laws which probably supplement the theory that has been discussed here.


G'day I'm Wally Lewis and I'm here to exclusively reveal how crooks get into your cars. Is that it? Yes Wally, it's that simple. Most unlawful entries are opportunistic. Thieves try multiple cars looking for ones that are left unlocked. But this isn't exactly a groundbreaking discovery is it? You'd be surprised. Well I suppose it's a pretty simple message. What should we be doing? They can make sure all their windows are up and their doors are locked. So there you have it folks. These are the techniques thieves are using to break into your cars. So don't drop the ball. Lock your cars. Don't drop the ball. Who made that up? You?


Hey, what you doing there? Do you care if I put you on YouTube? You're stroking All right, this is sir stinky schlachs mcgox helping me move this lathe crash Man this guy's a good sport Man the cabinet weighs almost as much as the lathe It does have the motor in it So the shipping label on this said 400 pounds, but it's more like double that Hopefully I got the shipping rate for the 400 pounds a man is definitely heavier than that nice, but it's always nice when someone remembers to Connect the gas line Because on the shipping label it said 400 pounds and it was more like 800 or so So since it was only 400 pounds I didn't take any tools To dismantle the lathe because I figured I'll just take the whole crate. It's only 400 pounds, right? so It was just too too heavy to move We could we moved it a little bit and then we're like, well, we're not gonna get this the whole way so We started taking the crate apart with it with a steel pipe that was laying around and we found a hammer that was just there and Then luckily my friend Was like wait. There was a workshop down the street So he went down there and asked the guy if we could borrow a few wrenches for like half an hour and the dude was super cool and super nice and He let us borrow some wrenches. I mean didn't even know who we were we were he just said, you know Where are you guys going? You told him where we're going. It was like.  I mentioned that a friend was coming to visit potentially to stay and live here And you know this is like the 20th person that this has happened with but I think he's the first one to stand Because he bought a boat. He's he's bought some land. He built himself a temporary house. I'm I'm pretty sure he's staying and Yeah, we went in his boat today to go get the lathe and that was super cool Well, he had he had some some stuff to to move to so I helped him with that It's super cool having a friend to do that stuff with because both of our jobs were easier even though I think I Think more of that work was on my end today, but you know we're friends. We'll we'll even it out at some point all right, I Hope it doesn't rain, but I have everything covered up in the dark here with tarps and whatever that you can't see in the dark Can't believe this lathe is here man is a big blade Awesome, I also gotta say thanks to the guy who sold me this lathe at like scrap metal price like cheap scrap metal price It is worth way more than what I paid for it and and then he packed it in a crate and Got it ready for your shippers and thanks to the guy who sent me the you know, bought me the milling machine, too and You know, I also have to pay extra to get that thing shipped out here to the island Or actually to another island then I have to go get it from that island, but getting things shipped to that island in South Central America you know I have to pay extra for that and That's I just gotta say thanks to Everyone who sends me money on PayPal or on my patreon Super thanks. I try to I try to express that through the through the videos in general But I think once in a while I need to just directly say it so Thank you so much Wow, and thanks to my ankle Let's go clean that up


It is a great pleasure to be here, to see so many smart, bright and enthusiastic people, men and as well as women, who have come together here in Brussels to celebrate Girls in ICT Day 2013 in the US. I would very much like to thank Cisco and Intel. Cisco are here. Please, Cisco, yes, please give them a hand. And Intel, Intel, yeah. I mean, they've made these awards possible today and they have demonstrated their outstanding commitment to seeing women and girls taking up ICT careers and pursue technological excellence. We really appreciate your partnership. We launched the Tech Needs Girl campaign just over a year ago and we have been impressed by the global response we have had from girls and women around the world. We have heard from women who recognize the importance of the core messages surrounding the campaign and from girls who had no idea how dynamic, creative, flexible and indeed helpful and valuable to the community a career in ICT could be. At ITU, the United Nations Specialized Agency for Information and Communication Technologies, we know that ICTs not only affect the lives and work of everyone on this planet, but that they are also one of the smartest sectors to get into. So we have been working hard to encourage girls and women to step up to technology and seize the amazing opportunities ahead. Everyone has a role to play in this effort, whether it's private companies who can involve women in the research and innovation process and processes and spotlight their female tech stars or government who can change the way that science, technology, engineering and math are approached and taught at every level at the school system or the media who can do so much more to change the stereotype way that women and girls are so often portrayed in films and on television and do more to present positive female role models or parents who can make sure that girls not only get the same opportunities as boys, but see that heading into a STEM career isn't dull or geeky or nerdy or simply too hard, but instead it is a smart career move with excellent prospects, not just for individuals but for societies as a whole. So today we are here to honor the achievements of the Techneeds Girls Award winners and so let us move with no further ado into the ceremony.


improve your summertime frame game. Welcome to the channel where fashion meets fragrance. My name is Kevin Samuel. It's style guy father and guys in today's video we're going to talk about one of the three F's frames and how to improve any of your summertime game. If you like these videos cool go ahead subscribe and drop a like down below. Shout out to the CIA what's going on you modern sexy savages guys what are the three F's frames fragrance and footwear and yes in spring and summertime when the sun is out it is a great time to rock great killer frames. Sunglasses are the easiest way from any guy to go from here to cool just just like that whether you're suited and booted or you're just in a white t-shirt and jeans putting on a great pair of sunglasses and change your look. Guys you know your godfather always says do not skimp on what you put on your face. I know I know there are going to be some of you young guys out there that are going to be like hey godfather I'm not quite there yet so what do I do and I get it guys you may not be there but you need to know what you need to get to. The end of the day when it comes down to great frames a great pair of aviators look good on anybody and the question is what do you want to go acetate or metal. Let's take something like this this is a great pair frames from my favorite maker Jacques Marie Bange. This is a great acetate look that can dress down or dress up. Acetate in my opinion looks great as an optical and a much more casual sunglass. This is one of the few pairs of acetate frames that you could actually dress up. This is the felsen and the colorway is noir.  As I have a lot of frames but I'm going to show you some of my favorite newer pickups for this summer. Let's get into it. First up these from Dita right here these are called the System One. Robert Downey Jr.'s iconic eyewear when you see him in the Avengers and Iron Man he's often rocking Dita. This is a System One in matte black with rose gold looks good looks good and dark looks good with dark colors or rose gold. The thing I love about this frame is that top bar. Top bars are making a huge comeback and they give you something else to grab your frames not just the sides and with the and with the detailing with the rose gold out there it these are great. These are really good as a nice sunglass on a day when the sun is really high because it provides a lot of protection. These are frames that obviously really should not wear indoors. If you want to wear something outdoors and indoors let's check something like this out. Oh yeah guys I love this. This is a Dita Flight 007. Yes James Bond 007 in a gold colorway with a nice brown lens that is good for indoors or outdoors and even better guys these are incredibly light to wear on my face when it's really warm outside they feel like you're almost wearing nothing. Guys I get so much use out of this particular frame right here gold is making a real comeback and these are incredible. Now I know some guys say well do you have to match your metals and with frames you really don't unless you choose to meaning if you got on silver jewelry can you wear gold frames of course but it's always better to have more options than less since we said silver let's get into the next one. Love those. Oh yeah Jacques Marie Marge does things right and this frame right here is called the Solar Silver Fox a nice silver matte look with a nice rose tint. Guys it is hard to look bad in a frame that looks this good. Just look at the details I'm gonna tell you right now this particular frame comes in three different colorways and I like all of them.  Next let's go through the Jacques Marie Marge GT. Now you can see the other one what's more a rounder a little bit more casual look this one is straight up sophisticated elegance this looks great in a suit or when you're dressed up these are incredible they have that classic throwback feel that would look good in any decade any season any reason these right here stand to test the time because they're timeless style. Damn I love these oh man I love these. The last but certainly not least guys it's hard to go wrong with something from Cartier. Oh yeah from Cartier is actually a limited edition frame it's silver with leather wrap it's called the Cartier must. Cartier is not for the faint of heart I'm going to tell you right there they're like chrome hearts or anything like that they're on the upper end of luxury but guys all you need is one great pair and the great thing about Cartier is you can customize them you can actually change the lenses out change the metal wear out you can actually get whatever you want etched in there your initials or whatever Cartier chrome hearts are the next step up and here's the thing that I offer young guys these are for the grown damn men out there who are working who want to treat themselves as something really special I'm gonna tell you probably one of my favorite frames to wear because the light blue lens can be worn indoor and outdoor. So gentlemen when it comes right down to it I'm always going to tell you in frames in my opinion are investment level items shoes are investment level items frames are investment level items don't skimp on your frames I know the temptation is to say hey man this pair of $80 Ray-Bans look just like that but no they are not you will know the difference when you put them on your face well I don't want to spend the money what if I lose my break what if I lose them a drop them off but hey man we're growing men over here I expect you to be able to take care of the things that you have I mean you don't use that when you're driving a car do you I mean you don't drive a hooptee because you might get into an accident don't use those excuses when you're talking about something you're going to have on your face when people are talking to you they're looking at your face 80% of the time makes you love what you have on your face again frames fragrance and footwear three ways to make any guy stand out and go from here to here just like that do me a favor hit me up in the comment section let me know what are some of your favorite frames to rock and wear what look good indoors what look good outdoors what makes you stand apart from the crowd inquiring minds would like to know if your godfather is out hey guys whether look style or life whether personal or professional you can level up and be your personal best each and every day if you're interested in any of that do us both a favor follow the link in the description and book your one-on-one session with me details down in the description peace


Navigating the journey, and today's journey is really long. We are going to Rochester, New York in 1852, the 5th of July, 1852. And we are going to listen to Brea Fox, who is, as everybody knows, a great vocalist, and she is going to read the speech that Frederick Douglass gave on that day. And you will understand as you listen to the speech why it was delivered on the 5th of July. But let me tell you a little bit about Frederick Douglass. He was a gorgeous man, he can bring up a picture. This remarkable man was born a slave, self-taught, became a powerful orator and advocate for his people. Always he spoke out with vigor and oppression of the nation. Again and again he wrote of his painful escape from slavery and his lifelong struggle to prevail against all forms of injustice. So, Brea, my dear friend Brea Fox, and everybody in Hawaii knows Brea because of her voice. And so, and then I imposed on her with all 15 pages of this speech. So, Lord have mercy. So it took some time, so if there are any scholars out there, it took some time to edit it down to where we could get into this time frame that we have. So, Brea, thank you so much. Yes, yes. It was an honor and a pleasure to repeat these words from Mr. Frederick Douglass on that day, July 5, 1852. He enters the hall and he says, Mr. President, friends and fellow citizens, the papers and placards say that I am to deliver a fourth of July oration. And so he sounds large and out of the common way, for it is true that I have often had the privilege to speak in this beautiful hall and to address many who now honor me with their presence. But neither their familiar faces nor the perfect gauge I think I have a Corinthian hall seems to free me from embarrassment. Ladies and gentlemen, the distance between this platform and the slave plantation from which I escaped is considerable. And the difficulties to be overcome and getting from the latter to the former are by no means slight. What to an American slave is your fourth of July. And the answer, a day that reveals to him more than all other days in the year, the gross injustice and cruelty to which he is a constant victim.   There is not a nation on the earth guilty of practices more shocking and bloody than are the people of these United States at this very hour. That I am here to say today is to me a matter of astonishment, as well as a gratitude. I will not therefore be surprised if in what I have to say I events no elaborate preparation, nor grace my speech with any high sounding Exordium. With little experience and with less learning I have been able to throw my thoughts hastily and imperfectly together and trusting to your patient and generous indulgence, I will proceed to lay them before you. This, for the purpose of this celebration is the fourth of July. It is the birth of your national independence and of your political freedom. This to you is what the Passover was to the emancipated people of God. It carries your minds back to the day and to the act of your great deliverance and to the signs and to the wonders associated with that act and that day.  I am glad fellow citizens that your nation is so young 76 years, though a good old age for a man is but a mere spec in the life of a nation. Three score years and 10 is the allotted time for individual men, but nations number their years by thousands. According to this fact, you are even now only in the beginning of your national career, still lingering in the period of childhood. I repeat, I am glad this is so. There is hope in the thought and hope is much needed under the dark clouds which lower above the horizon. The sky of the reformer is met with angry flashes, pretending disastrous times, but his heart may well be lighter at the thought that America is young, and that she is still in the impressionable stage of her existence. May he not hope that high lessons of wisdom of justice and of truth will yet give direction to her destiny. As she grows older, the Patriots heart might be sadder, and the reformers grow heavier. Its future might be shrouded in gloom, and the hope of its profits go out in sorrow. There is consolation in the thought that America is young. Great streams are not easily turned into channels, more and deep in the course of ages. Sometimes rise in quiet and stately majesty and inundate the land, refreshing and fertilizing the earth with their mysterious properties. They may also rise in wrath and fury and bear away on their angry waves the accumulated wealth of years of toil and hardship. They, however, gradually flow back to the same old channel and flow on as serenely as ever. But while the river may not be turned aside, it may dry up and leave nothing behind but the withered branch and the unsightly rock to howl in the abyss. The abyss swept land, the sad tale of departed glory, as with rivers, so with nations. Fellow citizens, I shall not presume to dwell at length on the associations that cluster about this day. The simple story of it is that 76 years ago, the people of this country were British subjects. The style and title of your sovereign people, in which you now glory, was not then born. You were under the British crown. Your fathers esteemed the English government as the home government, and England as the fatherland. This home government, you know, although a considerable distance from your home did, in the exercise of its parental prerogative, impose upon its colonial children such restraints, burdens and limitations as in the mature judgment, it deemed wise, right and proper. But your fathers, who had not adopted the fashionable idea of this day, of the infallibility of government and the absolute character of its acts, presumed to differ from the home government in respect to the wisdom and justice of some of those burdens and restraints. They went so far in their excitement as to pronounce the measures of government unjust, unreasonable and oppressive, and altogether such as ought not be quietly submitted to. I scarcely need say fellow citizens that my opinion of these messages fully accords with those of your fathers. Such a declaration of agreement on my part would not be worth much to anybody. It would certainly prove nothing as to what part I might have taken, had I lived during the great controversy of 1776. Now that America was right and England wrong is exceedingly easy. Everybody can say it, the dastard, not less than the noble brave can flippantly discount on the tyranny of England towards the American colonies. It is fashionable to do so. But there was a time when to pronounce against England, and in favor of the cause of the colonies tried men soul. And who did so were accounted in their day, plotters of mischief, agitators and rebel dangerous men. To side with the right against the wrong with the weak against the strong with the oppressed against the oppressor here lies the merit and the one which of all others seems unfashionable in our day. The cause of liberty may be stabbed by the men who glory in the deeds of your fathers, but to proceed. They saw themselves harshly and unjustly treated by the home government your fathers, like men of honesty and men of spirit earnestly sought redress. They petition, they remonstrated, they did so in a decorous respectful and loyal manner. Their conduct was wholly unexceptionable. This however did not answer the purpose. They saw themselves treated with sovereign indifference, coldness and scorn. But they persevered. They were not the men to look back. As the sheet anchor takes a firmer hold when the ship is tossed by the storm so did the cause of your fathers grow stronger. And it breathed the chilling blast of kingly displeasure. The greatest and best of British statesmen admitted its justice and the loftiest eloquence of the British sentiment came to its support. That blindness, which seems to be the unburying characteristic of tyrant, since Pharaoh and his hosts were drowned in the Red Sea, the British government persisted in the extractions complained of. The madness of this course we believe is admitted now, even by England, but we fear the lesson is wholly lost on our present ruler. Oppression makes a wise man mad. Your fathers were wise men, and if they did not go mad, they became restive under this treatment. They felt themselves the victims of grievous wrongs, wholly incurable in their colonial capacity. With brave men, there's always a remedy for oppression. Just here, the idea of a total separation of the colonies from the crown was born. It was a startling idea much more so than we at this distance of time regarded. The timid and the prudent, as has been intimated of that day, were of course shocked and alarmed by it.  Their course, in respect to any great change, no matter how great the good to be attained or the wrong to be redressed by it, may be calculated with as much precision as can be the course of the stars.  Of this sort of change, they are always strongly in favor. These people were called Tories in the days of your fathers, and this appellation probably conveyed the same idea that is meant by the more modern, though somewhat less euphonious term, which we often find in our papers applied to some of our old politicians. Their opposition to the then dangerous thought was earnest and powerful, but amid all their terrible terror and affrighted separations against it, the alarming and revolutionary idea moved on and the country with it. On the second day of July 1776, the old Continental Congress to the dismay of the lovers of ease and the worshipers of property clothe that dreadful idea with all the authority of national sanction. They did so in the form of a resolution. And as we seldom hit upon resolutions drawn up in our day, whose transparency is at all equal to this. I wish your minds and help my story if I read it quote resolved that these United colonies are and of right ought to be free and independent states that they are absolved from all allegiance to the British crown, and that all political connection between them, and the state of Great Britain is and ought to be dissolved unquote. Citizens, your father's made good that resolution. They succeeded, and today you reap the fruits of their success. The freedom gained is yours, and you therefore may properly celebrate this anniversary. The fourth of July is the first great fact in your nation's history, the very ring bolt in the chain of your yet undeveloped destiny. Pride and patriotism, not less than gratitude prompt you to celebrate and to hold it in perpetual remembrance. I have said that the Declaration of Independence is the ring bolt to the chain of your nation's destiny. So indeed, I regard it. The principles contained in that instrument are saving principles stand by these principles be true to them on all occasions in all places against all foes and at whatever cost. From the round top of your ship of state, dark and threatening clouds may be seen. Heavy billows like mountains in the distance, disclosed to the leeward huge forms of flinty rocks, that bolts drawn that chain broken and all is lost. Cling to this day, cling to it, and its principles with the grasp of a storm tossed mariner to a spar at midnight. The coming into being of a nation in any circumstance is an interesting event. But besides general considerations, there were peculiar circumstances which make the advent of this Republic an event of special attractiveness. The whole scene, as I look back to it, was simple, dignified and sublime. The population of the country at the time stood at the insignificant number of three millions. This country was poor in the munitions of war. The population was weak and scattered and the country of wilderness unsubdued. There was then no means of concert and combination such as exist now. Neither stream nor lightning had then been reduced to order and discipline. From the Potomac to the Delaware was a journey of many days. Under these and innumerable other disadvantages, your fathers declared liberty and independence and they triumphed. Fellow citizens, I am not wanting in respect for the fathers of this Republic. The signers of the Declaration of Independence were brave men. They were great men too, great enough to give fame to a great age. It does not often happen to a nation to rise at one time such as the number of truly great, such a number of truly great men. The point from which I am compelled to view them is not certainly the most favorable. And yet I cannot contemplate their great deeds with less than aberration. They were statements, statesmen, patriots and heroes. And for the good they did and the principles they contended for, I will unite with you to honor their memory. They loved their country better than their own private interests. And though this was not the highest form of human excellence, all will concede it is a rare virtue. And that when it is exhibited, it ought to command respect. He who will intelligently lay down his life for his country is a man for whom it is not in human nature to despise. Your father staked their lives, their fortunes and their sacred honor on the cause of their country. In their admiration of liberty, they lost sight of all other interests. They were peacemen, but they preferred revolution to peaceful submission to bondage. They were quiet men, but they did not shrink from agitating against oppression. They showed forbearance, but that, but that they knew its limits. They believed in order, but not in the order of tyranny. With them, nothing was settled that was not right. For them, justice, liberty and humanity were final, not slavery and oppression. You may well cherish the memory of such men. They were great in their day and generation. Their solid manhood stands out the more as we contrasted with these degenerate times. How circumspect, exact and proportionate were all their movements. How unlike the politicians of any of an hour, their statesmanship looked beyond the passing moment and stretched away in strength into the distant future. They seized upon eternal principles and set a glorious example in their defense. Mark them. Fully appreciating this hardship to be encountered, firmly believing in the right of their cause, honorably inviting the scrutiny of an onlooking world, reverently appealing to heaven to attest their sincerity, soundly comprehending the sound responsibility they were about to assume, wisely measuring the terrible odds against them. The fathers of this republic did most deliberately under the inspiration of a glorious patriotism and with a sublime faith in the great principles of justice and freedom laid deep the cornerstone of the national structure, which has risen and still rises in grandeur around you. This fundamental work this day is the anniversary. I eyes are met with demonstrations of joyous enthusiasm, banners and tenants wave exultingly on the breeze. They the din of business to is hushed, even mammon seems to have quitted this grass on this day. The ear piercing fight and the stirring drum, unite their accents with the ascending peel of 1000 church bells. The hymns are made, hymns are sung, sermons are preached in the honor of this day. While the quick marshals, tramps of a great and multi multitudinous nation, echoed back by all the hills, valleys and mountains of a vast continent, we speak the occasion one of one of thrilling and universal interest, a nation jubilee friends and citizens. You need not enter further into the causes which led to this anniversary. Many of you understand them better than I do. You would instruct me to regard to you would instruct me in regard to them. That is the branch of knowledge in which you feel perhaps a much deeper interest than your speaker. The causes which led to the separation of the colonies from British crown have never lacked a ton. They are all been taught in your common schools, narrated at your fireside, unfolded from your pulpits and thundered from your legislative halls, and as much and as familiar to you as household words. They form the staple of your national poetry and eloquence. I remember to that as a people Americans are remarkably familiar with all the facts which make in their own favor. It is esteemed by some as a national gift, a national trait, perhaps as a national weakness. It is in fact that whatever makes for the wealth or for the reputation of Americans and can be had cheap will be found by Americans. I shall not be charged with slandering Americans. If I say I think American side of any question can be safely left in American hands. I leave therefore the great deeds of your fathers to other gentlemen and claim to have been regularly descended will be less likely to be disputed than find mine. My business, if I have any here today is with the present. The accepted time with God and his cause is the ever living now. Trust no future, however pleasant, let the dead pass very extended and act in the living present. Cart within and God overhead. We have to do with the past, only as we can make it useful to the present and to the future. To all inspiring motives to noble deeds, which can be gained from the past we are welcome. But now is the time the important time. Your fathers have lived died and have done their work and have done much of it as well.  You have no right to enjoy a child share in the labor of your fathers, unless your children are to be blessed by your labors. You have no right to wear out and waste the hard earned famed of your fathers to cover your indolence. Sidney Smith tells us that men seldom eulogize the wisdom and virtues of their fathers, but to excuse some folly or wicked wickedness of their own. The truth is not a doubtful one. There are illustrations of it, near and remote, ancient and modern. It is fashionable hundreds of years ago for the children of Jacob to boast, we have Abraham to our father. And when they long lost Abraham's faith and spirit, that people contented themselves under the shadow of Abraham's great name, while they repudiated the deeds which made his name great. May I remind you that a similar thing is being done all over this country today? Need I tell you that the Jews were not the only people who built the tombs of the prophets and garnished the sepulchres of the righteous? Washington could not die until he had broken the chains of his slaves, yet his monument is built up by the price of human blood and the traders and the bodies and souls of men about. We have Washington as our father, alas, that it should be so, yet it is so. Fellow citizens pardon me, allow me to ask why am I called upon to speak here today? What have I, or those I represent to do with your national independence? Are the great principles of political freedom and of natural justice embodied in that Declaration of Independence extended to us? And am I therefore called upon to bring our humble offering to the national altar and to confess the benefits and express devout gratitude for the blessings resulting from your independence to us? Would to God, both for your sake and ours, that an affirmative answer could be truthfully returned to these questions? Then would my task be light and my burden easy and delightful? For who is there so cold that a nation's sympathy could not warm him? Who so obdurate and dead to the claims of gratitude that would not thankfully acknowledge such priceless benefits? Who so solid and selfish that would not give his voice to swell the hallelujahs of a nation's jubilee when the chains of servitude that have been thrown from his limbs? I am not that man.  But such is not the state of the case. I say it with a sad sense of the disparity between us. I am not included within this pale of glorious anniversary. Your great independence only reveals the immeasurable distance between us. The blessing in which you this day rejoice are not enjoyed, enjoyed in common. The rich inheritance of justice, liberty, prosperity and independence, blessing bequeathed by your fathers, is shared by you, not by me. The sunlight that brought life and healing to you has brought stripes and death to me. This Fourth of July is yours, not mine. You may rejoice, I must mourn. To drag a man and fetters into the grand illuminated temple of liberty and call upon him to join you in joyous anthems were inhumane mockery and sacrilegious irony. Do you mean citizens to mock me by asking me to speak today? If so, there is a parallel to your conduct. And let me warn you that it is dangerous to copy the example of a nation whose crimes, lowering up to heaven, were thrown down by the breath of the Almighty, burying that nation is irrevocable ruin. I can say today, take up the plaintive lament of appealed and woe smitten, woe smitten people by the rivers of Babylon. There we sat down and we wept when we remember Zion. We hanged our hearts upon the willows of the midst thereof for there they that carried us away captive required us a song. And they who wasted us required us Murph saying, sing us one of the songs of Zion. How can we sing the large song in a strange land? I ask you, how can we sing the Lord song in a strange land? If you know citizens above your national tumultuous joy, I hear the mournful wail of millions whose chains, heavy and grievous yesterday are today rendered more intolerable by the jubilee shouts that reach them. If I do forget, if I do not faithfully remember these bleeding children of sorrow this day, may my right hand forget her cunning, and may my tongue cleave to the roof of my mouth. To pass lightly over their wrongs and to chime in with the popular theme would be treason most scandalous and shocking, and would make me a reproach before God and the world. My subject then fellow citizens is American slavery, and I shall see this day and popular characteristics from the slaves point of view, standing there identified with the American bondsman, making his wrongs mine. I do not hesitate to declare with all my soul that the character and conduct of this nation never looked blacker to me than on this fourth of July. Whether we turn to the declaration of the past, or the professions of the present, the conduct of the nation seems equally hideous and revolting. America is false to the past, false to the present, and solemnly binds herself to be false to the future. To be with God and the crushed and bleeding slave on this occasion, I will in the name of humanity which is outraged in the name of liberty which is fettered in the name of the Constitution and the Bible, which are disregarded and trampled upon, dare to call in question and denounce all the emphasis I can command. Everything that serves to perpetuate slavery, the great sin and shame of America, I will not equivocate, I will not excuse. This is the severest language I can command, and yet not one word shall escape me that any man whose judgment is not blinded by prejudice, or who is not at heart a slaveholder shall not confess to be right and just. Wow. That's fabulous. Thank you so much, my dear. It's my pleasure is 100 pages more and it's all riveting but I know we have a time. It is, it is, it is just let me say this. I'm going to read from his one of his many writings. It is something to give the Negro religion. It is more to give him justice. It is sometimes to give him the Bible. It is always time to give him the ballot. And we have an election coming up real soon. I want people to remember all that Frederick Douglas said, all he went through all we've all gone through one way. Now, today, the thing we can do today is vote. So, again. Thank you, rare. That was beautiful. My pleasure.  So, again, we are fighting for unity, unity of idea, unity of sentiment, unity of object, unity of instruments in which we shall be. No north, no south, no east, no west, no black, no white, but a solidarity of nation, making every slave free and every man of voter. So, again, thank you. Thank you all for spending this time with us. And with Frederick Douglas. Eric, you want to.


Among the top 100 in the world, we only have one woman and regarding the number of players, we have just one woman for every 10, 12 or 14 men playing chess. In a game or sport where physical strength is not important at all, I mean endurance is important but brute force is not important at all. This is a very big mystery.