Question is from Earthtonina. I've been lifting with no belts or straps. As I increase my weight, should I start to use these devices or continue without? Yeah, no, you don't need to. Now, here's the thing. You can use them if you want to, and if you use them properly. But should you? No. I mean, the only people that I think should use a belt are people who are training to compete with a belt. So if you're a power lifter or a strongman competitor and your competition allows you to use a belt, it's important to train with a belt to learn how to use one. It's basically part of the uniform if you look at it that way. Yes. These are the rules. Other people are going to be using them. You want to know how to use these tools to your advantage so you need to incorporate them in your training. Right. So a belt, basically what a belt does is it goes around the waist. They're very wide and stiff and thick, at least the good ones. And what they do is they increase core stability. And the way they work as you, as you're wearing one, it's really tight, your abs and your core pushes out against it. It creates more stability. That stability then allows you to lift more weight because your spine is more stable. So squatting and deadlifting with a belt, if you use it properly, you should be able to use more weight. But make no mistake, you're relying on the belt because without the belt, you wouldn't be able to lift that way.  And there's a strap that hangs down from your hand that you wrap around the bar that gives you a stronger grip, or at least it grips the bar essentially for you. And for many people, their grip is the weak link. That's what prevents them from pulling max weight or whatever. There may be some benefit for high volume trainers, bodybuilders.  But for most people, there's no value. I mean, you'll see me use a belt when I deadlift really heavy. And to be quite honest, it's because I've done it for so long with a belt that heavy, that I really don't feel like going through the whole process of lifting, you know, with deadlifting without a belt. Now I do go through cycles of not using a belt. But most of the time, if I go above four or 500 pounds, and the truth is part of that is the psychological piece.  I know that with a belt, I get an extra 20 to 30 pounds. And it still counts on Instagram. Yeah, it's right. It counts on Instagram. If you're a client, I've never recommended a belt, a strap, a sleeve, any of these tools, squat shoes, none of those things do I recommend, especially if somebody has been lifting without any of them. Now that doesn't mean that I they're all those tools are in my bag. And I use them all the time. But it's also, I look at it as something that I like playing around with. I never want to become dependent on any of those things. And those things you can become dependent on. If you are somebody who always wear a weight belt, and you get used to that feeling of having a belt for you to push your corgans, which is different than when you don't have a belt.   If you use a belt, you're using the belt as feedback. And then your core is pushing out against the belt to create stability. And what happens when your core pushes out when you don't have a belt? Exactly. You lose stability. So you don't want to be you don't want to use these things so much. And then also with the straps, I mean, there's there's times in bodybuilding. I absolutely use I use my straps a lot more in bodybuilding than I did today. And that would be because I didn't want my forearms and my grip strength to fatigue when I was focusing on a certain muscle group. I'm trying to develop one area. I don't want any other areas to get more developed at all. I'm focusing somewhere. So I wouldn't want them to be fatigued on a day. I get that from a bipolar perspective, especially if you're trying to get a good lat pump. And like a lot of times the first thing to fatigue, what is it?  But, you know, for me, and I probably sound like the purest in the group, but it's just how I've always trained. I've always trained like if I, if I can't pick it up with just, you know, what I have, like I don't like I didn't earn it. Like, and I've just carried that into my squats. I've carried that into deadlifts.  But I just don't want to be dependent on any of these aids, you know, to kind of take me to the next level, whereas, you know, some people, that's really important to them. So I don't, I don't like look down on people for not doing that. That's just like my own mentality. The one that you know that is that is pretty cool is the is the straps. And what I mean by that is your capability to hold on to the weight that your body can lift is actually pretty damn good. I mean, we did evolve from primates and our hands have tremendous capacity for strength. I lifted for years with wrist straps for years. And then when I went off the wrist straps, and it took me a couple years for my grip to get up to the point where it could handle what I could lift to the point now where there's nothing I can't if I can lift it, I can grip it, especially if I use a hook grip or use an alternate grip, you know, those types of techniques. So your hands have tremendous capability for strength. And I really think it's important that we don't, you know, that we allow our hands to get really, really strong because your hands will connect you to the entire world, everything from using a pen to anytime you grab something. But yeah, with belts, I've only used belts twice with clients. There's only two clients I've ever used belt with. And that was Doug was one of them. And that's just because it was fun, you know, Doug was got strong. Well, that's my point. It's an ego lift. I'm very aware of that. Like, I mean, I know even when I've done posts on Instagram where I'm squatting or I'm deadlifting and you see the belt on me, like that belt came on for that lift because I knew I was pushing my max load. I knew that I'm probably going to lift a weight that is getting close to probably PR range. I'm going to wear a belt for safety reasons and I'm going to push that. Is it super beneficial for me gaining, gaining strength or building muscle in the overall journey? Not at all. No, it's it's it's so I know if you're not, if you're somebody who's been lifting and you, you're not using any of these tools, like, Oh, you're staying pure, stay in the purest. Like, yeah, because once you learn how to use these and get used to them, yeah, going back takes time. That's half the that's half the struggle that I deal with is that I, like you, I used a belt and straps and all these tools my entire career and I can feel it's still a difference. I've gotten so good at using those tools that I'm weaker. I'm weaker without them. I'm a weaker on my squat and weaker on my deadlift. I can most certainly strapped up belt it up. I can definitely deadlift more weight and squat more weight than if I was without them.


As Salaamu Alaikum, welcome to lecture number 42 of the course on statistics and probability. Students, you will recall that in the last lecture, I discussed with you the chi-square distribution. I discussed the main properties of the distribution and then its role in statistical inference. You will recall that the chi-square distribution plays an important role in estimation and hypothesis testing regarding the population variance sigma square. In today's lecture, I will be talking about the F distribution and statistical inference about two population variances on the basis of the F distribution. But before I proceed with that, let us consolidate what we did last time with the help of an example. As you now see on the slide, the manager of a bottling plant is anxious to reduce the variability in the net weight of fruit bottled. Under a long period, the standard deviation has been 15.2 gram. A new machine is introduced and the net weights in grams in 10 randomly selected bottles all of the same nominal weight are 987, 966, 955 and so on grams. Would you report to the manager that the new machine has a better performance? Let us first try to understand this problem. This fruit that is being bottled and the desire is that the specifications are not more than that, not less than that, but whatever you try, there is some variability. But, of course, you would like that the variability should be minimal. So, in this, we are trying to test whether the new machine has been introduced or not the mean students, the variability, the variation from bottle to bottle has that variation reduced. So, how do we proceed with this test as you see on the screen? Step one is the null and the alternative hypothesis H naught sigma is equal to 15.2 gram that is the standard deviation is still the same as before and H 1 that sigma is less than 15.2 gram. In other words, the standard deviation has reduced. Step two is the level of significance and we may set it as 5 percent. Step three is the test statistic and students, you will recall from the last lecture that n s square over sigma square or in other words summation x minus x bar whole square over sigma square. This quantity follows the chi square distribution where n minus 1 degrees of freedom. Since we always begin by assuming that H naught is true, therefore we can write n s square over sigma naught square where sigma naught square is the value of sigma square that we hypothesize under H naught. The next step is the calculation and in this problem the sample size is 10. Sum x comes out to be 9713 and sigma x square is equal to 9 4 3 5 3 4 7. Now n s square is equal to sigma x square minus sigma x whole square over n according to the short cut formula and substituting the values n s square comes out to be 1110.1 hence n s square over sigma naught square which can be called chi square our test statistic. This comes out to be equal to 4.81. All right. 4 steps are complete and the fifth step is critical region and students in this particular problem what is the alternative that sigma square is less than what we hypothesized according to the null hypothesis. I hope you will all agree that the entire five percent area should be to the left side and therefore when we look at the chi square table we look under 0.95 because if left side pay five percent area chahiye to is ka matlab hai ke us point ke right side pay 95 percent area chahiye. Or jaisa ke maine last time kaha tha chi square table johana us me aapko jo areas milenge wo hain jo us point ke right pe ho. So as you now see on the screen the critical value is chi square 0.95 at 9 degrees of freedom and this comes out to be 3.32. To jaisa me kahiye ho ke ab hum left side pe jo tail hain a usko critical region maane hain kyunke hain our alternative hypothesis less than sign liye ho hain. But you will recall from the last lecture that the chi square distribution starts from 0 and goes up to infinity to is ka matlab yeh hoa ke yeh jo hain our critical value hai 3.32 uske left side pe jo area hai wo minus infinity tak nahi jaahara students it is going only up to 0. Agar hamari value computed value 0 aur 3.32 ke darmean liye kar jahegi then of course we will say that it is lying in the critical region. Lekin agar hamari value 3.32 se right side pe liye karegi then we say that it is in the acceptance region. So in this problem as you now see on the screen our computed value is equal to 4.81 as we calculated a short while ago and hence we say that it does not fall in the critical region and hence we would not report to the manager that the new machine has a better performance. After all hamara jo alternative tha wo yeh kahra tha na ke the variability has reduced to agar ham us alternative ko accept nahi kar rahe, bal ke null ko accept kar rahe hain because our value has fallen in the acceptance region to humari yeh khahish to puri nahi hui na kyun ke hamara jo data hai wo iss baat ko support nahi kar rahe. Alright students let us now proceed to the F distribution another very important distribution in the theory of statistical inference. I will begin by the formal definition and then I will present to you some important properties of the F distribution. As you now see on the slide the mathematical equation of the F distribution is as follows F of x is equal to gamma nu 1 plus nu 2 over 2 into nu 1 over nu 2 whole raise to nu 1 over 2 into x raise to nu 1 over 2 minus 1 and this whole thing divided by gamma nu 1 by 2 gamma nu 2 by 2 into 1 plus nu 1 x over nu 2 and this whole expression raise to nu 1 plus nu 2 over 2 and this entire equation is valid for x lying between 0 and infinity. This distribution has two parameters nu 1 and nu 2 which are known as the degrees of freedom of the F distribution. Yes another very complicated equation just to make you realize that the F distribution is different from the chi-square distribution because its mathematical equation is different and although just like the chi-square distribution is positively skewed the F distribution is also positively skewed but they are not one and the same distribution. If you do not go into the intricacies of this equation just note one point that the equation that you just saw it has two quantities which can be called two parameters of the F distribution we denote them by nu 1 and nu 2 and students this may do order that is very important I mean if you are saying that our F distribution is with the nu 1 comma nu 2 degrees of freedom then its equation will be what you just saw but if you are saying that our distribution is F distribution with nu 2 comma nu 1 degrees of freedom then it will be completely interchanged in the equation. So, this is a point that you must keep in mind alright let me now present to you formally some basic properties of the F distribution as you now see on the screen the F distribution is a continuous distribution ranging from 0 to plus infinity as is evident from its equation. Number two the curve of the F distribution is positively skewed but it is important to note that as the degrees of freedom nu 1 and nu 2 become large the F distribution approaches the normal distribution. The third property students is that for nu 2 greater than 2 the mean of the F distribution is nu 2 divided by nu 2 minus 2 and this quantity is obviously greater than 1. Similarly, for nu 2 greater than 4 the variance of the F distribution is 2 times nu 2 square into nu 1 plus nu 2 minus 2 and this whole quantity divided by nu 1 into nu 2 minus 2 whole square into nu 2 minus 4. Obviously the square root of this quantity will give us the standard deviation of the F distribution. The fifth property is that for nu 1 and nu 2 both greater than 2 the F distribution is unimodal and the mode of the distribution is at nu 2 into nu 1 minus 2 over nu 1 into nu 2 plus 2 and this quantity is always less than 1. Students, you have just seen that the mean is greater than 1 and the mode is less than 1. So, we were saying that the F distribution is positively skewed. So, it should not be skewed positively. Obviously, if it is positively skewed the mode will be to the left and the mean will be slightly towards the right. So, these properties are according to what we would expect. What is the next property? As you now see on the screen, if X has an F distribution with nu 1 and nu 2 degrees of freedom then the reciprocal 1 over X has an F distribution with nu 2 and nu 1 degrees of freedom. This is a very interesting property students and it is also very useful in certain ways. We are saying that our original variable X that is following the F distribution with nu 1 comma nu 2 degrees of freedom. Now, if we transform or introduce this new variable as we have said that let Y be equal to 1 over X. So, this new variable Y or 1 over X, this new variable distribution that is also an F distribution, but it is that one which has nu 2 comma nu 1 degrees of freedom which I said earlier that nu 1 nu 2 is different for example, if nu 1 is equal to 7 and nu 2 is equal to 9. We are saying that our original X variable that is following the F distribution with 7 comma 9 degrees of freedom. Now, this new variable is 1 over X that will follow the F distribution, but another F distribution that one which has 9 comma 7 degrees of freedom. Having discussed the basic properties of the F distribution, I think I should now share with you the table of areas for the F distribution. Students, in this case may it is a slightly more complicated situation not really, but it is very interesting. Now, in the top row we will be writing the various values of nu 1 and in the first column we will be writing the various values of nu 2. We have different tables, separate tables for 1 percent area on the right tail and for 2 and a half percent area on the right tail and for 5 percent area on the right tail. So, as you now see on the screen the table which is pertaining to 5 percent area on the right tail is as you see in the top row the values of nu 1 are 1, 2, 3, 4, 5, 6, 8, 12, 24 and infinity and in the first column we have various values of nu 2 in a similar manner. If you look at the very first cell we have the number 161.4 and students this is that value on the x axis under the F distribution to the right of wage the area is 5 percent and which distribution are we talking about that F distribution which has 1 comma 1 degrees of freedom. Similarly, if you look at the fourth entry in the row corresponding to nu 2 equal to 1 you find that the number is 224.6 and this is that value of x under the F distribution having 4 comma 1 degrees of freedom to the right of wage the area under the F curve is 5 percent. In a very similar way we have the table for 2 and half percent area on the right tail and also a table where 1 percent area on the right tail. Having discussed the basic definition the basic properties and also the table of the F distribution students I think it is about time that we begin the discussion of the role of this particular distribution in statistical inference. As I mentioned earlier this distribution enables us to talk about 2 population variances and the condition is that the 2 populations whose variances we are wanting to compare the 2 populations should be normally distributed. As you now see on the slide let 2 independent random samples of size n 1 and n 2 be taken from 2 normal populations with variances sigma 1 square and sigma 2 square and let small s 1 square and small s 2 square be the unbiased estimators of sigma 1 square and sigma 2 square respectively. Then it can be mathematically proved that the quantity s 1 square over sigma 1 square divided by s 2 square over sigma 2 square has an F distribution where n 1 minus 1 comma n 2 minus 1 degrees of freedom. Students I A is point to understand kane ki koshish karte hain dekhye aapke pass 2 normal populations. For example the heights of the men and the heights of the women in a particular country are normally distributed. So it is quite an interesting problem isn't it? So now what should we do? We have drawn 1 sample from the first population of size n 1 and we have drawn 1 sample from the other population of size n 2 and now the sample is here. So it is obvious that we can compute the sample variance of s 1 square unbiased. From here we have drawn sample from the women population and we can compute the variance of s 2 square unbiased. Now for a short while you assume that the first population's population variance is known and the other one is also known. So sigma 1 square and sigma 2 square are known. Just for a short while you assume that. Now we have 4 quantities s 1 square sigma 1 square s 2 square and sigma 2 square. Then of course I can compute this quantity that we just short while ago saw on the screen as you see once again s 1 square over sigma 1 square. This whole thing divided by s 2 square over sigma 2 square. The quantity you have computed for these 2 samples that you had drawn one from the first population one from the other. I want to say that again you assume that it is not just one sample that you are drawing from here and one from here.  N1 minus 1 comma N2 minus 1 degrees of freedom. Once again, I would like to say as I said in the earlier lecture, this is the non-mathematical way of doing it, but my point is that you should have some basic idea in your mind about what is going on. Now that we are clear about this, we have this knowledge that this particular statistic follows the F-distribution. After all, sampling distribution, the probability distribution of our statistic, the sampling distribution of this particular statistic is the F-distribution having N1 minus 1 comma N2 minus 1 degrees of freedom. You can also construct the acceptance region and the critical region if you are wanting to do hypothesis testing. Let us begin with interval estimation and as you now see on the screen, the confidence interval for the variance ratio sigma 1 square over sigma 2 square is given by s 1 square over s 2 square multiplied by 1 over F alpha by 2 N1 minus 1 comma N2 minus 1 degrees of freedom. This is the lower limit and the upper limit is given by s 1 square over s 2 square multiplied by F alpha by 2 N2 minus 1 comma N1 minus 1 degrees of freedom. Students, you have just seen the formula. Note two things from this question. The first thing is that it is the ratio of the two population variances that we are talking about. When we were talking about means, I did not construct confidence interval for mu 1 over mu 2. Similarly, when we were talking about proportions, we did not talk about p 1 over p 2. You remember that we constructed the confidence interval for mu 1 minus mu 2 and p 1 minus p 2. Now we are interested in the ratio. Students, instead of that, the underlying mathematics here, which I have said a little while ago, that s 1 square over sigma 1 square over s 2 square over sigma 2 square follows the F distribution. Since we do not want to go into mathematical derivations in this course, you can just see the pattern of the statistic, the F statistic. That tells us that it will be the confidence interval for sigma 1 square over sigma 2 square and not sigma 1 square minus sigma 2 square that we can construct on the basis of the F distribution. The second point to understand is that in the formula that I just presented, you saw that F alpha by 2 N 1 minus 1 comma N 2 minus 1 was written in the denominator and F alpha by 2 N 2 minus 1 comma N 1 minus 1 was written for the upper limit in the numerator. Obviously, there is no reason to be confused. That is the amount of area that we want to the right of the F value that we want to compute. Let me explain this point with the help of an example. A random sample of 12 salt water fish was taken and the girth of the fish was measured. The standard deviation small s 1 came out to be 2.3 inches. Similarly, another random sample of 10 fresh water fish was taken and their girth was measured and the standard deviation small s 2 came out to be 1.5 inches. Find a 90 percent confidence interval for the ratio between the two population variances sigma 1 square over sigma 2 square and in doing so assume that the populations of girth are normal. In order to solve this question of course, we will resort to the formula that is mathematically proved and that was presented a short while ago.  Students, you note that I said 0.05 in the place of alpha by 2 and why is that? Because we want 90 percent confidence. So, the derivation that we did earlier when we tried to construct the confidence interval for mu, you remember that the basic thing was that if you want 90 percent confidence then you will keep 90 percent area in the middle and on the right tail you will have 5 percent and on the left tail also you will have 5 percent. That is why in this problem alpha by 2 will be equal to 5 percent. Now, the rest that is fairly simple as you now see on the slide. We have s 1 square is equal to 2.3 square and that is 5.29. Similarly, s 2 square is 1.5 square and that is 2.25 N 1 minus 1 is 12 minus 1 and that is 11 and N 2 minus 1 is 10 minus 1 and that is 9. Now, in order to find the value of F 0.05 11 comma 9 we will need to consult the F distribution that one which has been constructed for 5 percent area in the right tail and consulting that distribution we find that F 0.05 11 comma 9 is equal to 3.1. Similarly, we also need to find F 0.05 9 comma 11 and looking at the same table we find that this value is equal to 2.9. Abhijo table manai present ki thi that is the abridged version of the larger table aur usme aapne shahid note kiya ho that in the top row we had 1, 2, 3, 4, 5, 6 likin badme the maam values nahi thi kuch values ki spacing ke baad we have some values. To aesi suratme you will be interpolating as you now see on the slide. In the top row after the number 8 we have the number 12 in this abridged table, but in the first column we do have numbers going continuously in the beginning of the table. So, that we have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and so on. To aap agar hum 11 comma 9 dekhna chahathe. To iska matlab ke top row se 11 ke niche ja aana chahiye aur first column me 9 ke agaist hume jaana chahiye. Now agar hum 9 ke agaist dekhne to 8 ke under the value is 3.23 jab ke 12 ke under the value is 3.07. Iska matlab yeh hua ke 11 ke under jo value hogi agaist 9 that will be somewhere between 3.23 and 3.07. Agar hume 11 ke bajaye 10 ke under dekhna hota tap to hum simple average leh sakte thein dono number ka jo 12 aur 8 ke under hain. So, that we would have got 3.07 plus 3.23 over 2 and that would have been equal to 3.15. Lekin agar hume 11 ke under chahiye to iska matlab hai ke 11 to 10 aur 12 ke darmean lai kar rahe. To hum chahiye to 3.07 aur 3.15 ka arithmetic mean leh sakte hain and that will give us the value against 11. So, if we do that 3.07 plus 3.15 divided by 2 will give us 3.11. Students, this is the way we interpolate between two values. Aap yeh assume karte hain ke us range mein jo missing values hain. Wo equi spaced hain aur iss tara se hum average leh ke hum kar sakte hain. Mane aasan tari ke se karne ki koshish ki ke pehle aap 8 aur 12 ke middle mein aajaye 10 ke agaist value mil gayi aur phir aap 10 aur 12 ke middle mein aajaye to aapko 11 ke agaist value mil gayi. So, jais aapne dekhah iss tara karne se humari value aah rahi hai 3.11. Lekin jo value mein e abhi tori deh pehle present ki thi wo kya thi? As you see on the slide, I said that by consulting the F table, we obtain F is equal to 3.1. To aapne note kia students ke manage pehle jo present ki thi value, that was correct to 1 decimal. Agar aap interpolation value ko dekhain, 3.11 to agar aap usko bhi round karlein correct to 1 decimal, you get 3.1. Iska matlab yeh hoa ke agar aap bohot zyada rigorous interpolation value method mein nahi bhi jaana chaate, to aap andaaza lagaasakte hain ke what would be your F value. Correct to 1 decimal jo 12 ke under thi, 3.07 even that is equal to 3.1 aur chuke 11, 12 ke bohot nas dikh hain. Isliye hum kaisakte hain ke 3.1 hi hogi for 11 because it is close to 12 and correct to 1 decimal, it is correct. Substituting these values in the formula of the confidence interval, we obtain 5.29 over 2.25 into 1 over 3.1 as the lower limit and 5.29 over 2.25 into 2.9 as the upper limit of our 90 percent confidence interval and solving these quantities, the interval is 0.76 to 6.81. Students yeh jo answer yeh jo result hain mila iss silsle mein aap do baate note karein. Pehli baat hi hai ke this one is the interval for sigma 1 square over sigma 2 square, yaani the variance ratio. Agar hum interested ho sigma 1 over sigma 2 ke liye interval construct karne mein, yaani an interval for the ratio of the standard deviations of the two populations to hum kaisakte hain. Zahir hai ke we will be taking the square root of the lower limit as well as the upper limit and if we do that then as we now see on the slide, we obtain the 90 percent confidence interval for sigma 1 over sigma 2 as 0.87 to 2.61. Yeh to hui pehli baat ki agar aap standard deviations ke ratios mein interested hain to aap square root liye sath hai. Dhusri jo baat hai that is more important and interesting in a way. Dhe khe yeh jo abhi humne variance ratio ke liye confidence interval construct kiya uski lower limit ai 0.76, upper limit 6.81. Zah la khaur ki jaye ke 0.76 ka kya matlab hai? Iska matlab yehi hai na that sigma 1 square is less than sigma 2 square. Isi liye to yeh ratio 1 se less aaya hai. Yeh thi lower limit. Upper limit ke mutabek the variance of the first population sigma 1 square is 6.81 times the variance of the second population. Isli to unka ratio jo aaya hai that is 6.81. To students yeh kuch confusing nahi hai. Ke aapka jo confidence interval hai agar aap uski lower limit ke taraf chale jaye to aap yeh interpretation aapko mil rahi hai ke sigma 1 square is less than sigma 2 square. Aur agar aap upper limit ke taraf chale jaye to sigma 1 square seems to be much much greater than sigma 2 square. Yes, this is a kind of a problem. Of course, if you lower the level of confidence so that it is not 90 percent, maybe if you bring it down to 80 percent or maybe even less to fir bo narrow ho jaye gana chaya aapko discussion yad ho that the higher the level of confidence the wider your interval is. Lekin iss waak, me uski opposite baat kar rahin ho. Ke agar aap low karein level of confidence ko to aapka yeh narrow down ho jaye gana. It will become narrower to fir ho sakta hai ki us case me lower limit might come out to be 1 point something and upper limit might come out to be 5 point something. To kumse kumse yeh to fayda hoa na ke kha aap lower limit ko dekhin kha aap upper limit ko dekhin. Your number is greater than 1 implying that sigma 1 square is greater than sigma 2 square. Shaaar aap karee honge ki kuch boh jyada complicate hota jaar hai. Students, mera makhse diye hai ke aap iss baat ko realize karein that as I said once earlier mukhtilif mathematical formulae develop kiye gayin with a lot of logic, rationale and very useful formulae. Lekin, har method or har formulae ki koi na koi limitation bhi to ho sakta hai na. So iss traki thodi si problem kisi kisi wak aaj aati hai. Yani interpret karne me shaaar aapko thodi si dekhat ho jaye. But believe me, the more you practice and the more experience you have with this kind of work, it will be become quite easy for you after some time. Now that we have discussed the confidence interval for sigma 1 square over sigma 2 square, which enables us to compare the variability of one normally distributed population with that of another students, let us proceed to hypothesis testing regarding the population variances and I would like to explain this to you with the help of the example that we now see on the screen. In two series of holes to determine the number of plankton organisms inhabiting the waters of a lake, the following results were found series 1, 80, 96, 102, 77 and so on and series 2, 74, 122, 92, 81 and so on. In series 1, the holes were made in succession at the same place. In series 2, they were made in different parts scattered over the lake. Does there appear to be a greater variability between different places than between different times at the same place? In order to solve this problem, the first thing to note is that if x denotes the number of plankton organisms per hole, then for each of the two series, x can be assumed to be normally distributed. Now the hypothesis testing procedure is exactly the same as before, H naught sigma 1 square is greater than or equal to sigma 2 square and H alternative sigma 1 square is less than sigma 2 square. But students please note that H naught can also be written as sigma 2 square is less than or equal to sigma 1 square and H alternative that sigma 2 square is greater than sigma 1 square. Is there greater variability between different places as compared with different time periods at the same place? Now the way I have stated it, it may be more compatible with the statement. In series 1, that is for the same place, different times, but in series 2, that is for different places. We want to know that the population variance of series 2, sigma 2 square is that greater than sigma 1 square. Now note that we have placed this in alternative hypothesis, not in null, because in this statement, equal sign is not occurring. We always have to put that one in the null, which carries the equal sign. So, what we want to know, what we want to test is actually in this problem, it is in alternative. And the equal sign is the complement that is placed in the null. What is the next step? Of course, the level of significance and as you now see on the slide, we may set it at 0.05 as usual. But of course, if we were interested in lower risk of committing type 1 error, then we could also have set it at 0.01. Students, aap jo test statistic hai uspe khas tawar pe gaur ki jie. Maini kushte k pehle aap se kaha tha that if we are drawing a sample of size n 1 from the first normal population and a sample of size n 2 from the second one, then the statistic s 1 square over sigma 1 square over s 2 square over sigma 2 square follows the f distribution with n 1 minus 1 comma n 2 minus 1 degrees of freedom. Agar aap ye 1 or 2 kaapis mein interchange karne, can I not say that the statistic s 2 square over sigma 2 square whole divided by s 1 square over sigma 1 square follows the f distribution having n 2 minus 1 comma n 1 minus 1 degrees of freedom. If you accept that students, the next point is that according to the null hypothesis, sigma 2 square is less than or equal to sigma 1 square. Agar aap equal signa 2 square is equal to sigma 1 square agar aasah hai, toh phir aamaara statistic kya hoga. If sigma 1 square is equal to sigma 2 square, then in the statistic s 2 square over sigma 2 square whole divided by s 1 square over sigma 1 square, sigma 2 square will cancel out with sigma 1 square and we are left with s 2 square over s 1 square. And students, we can say that under the null hypothesis, this statistic follows the f distribution having n 2 minus 1 comma n 1 minus 1 degrees of freedom. Of course, I should not have to remind you that we always begin by assuming that h naught is true. Toh agar aasah aap aasah hai or unko equal money, then they cancel out and we are left with s 2 square over s 1 square. Students, the fourth step is the computation of my statistic and as you now see on the screen, for the first data set, we have 10 values 80, 96, 102 and so on. And therefore, upon taking the square of each value and adding the squares, sigma x 1 square comes out to be 9, 3, 2, 7, 6, whereas sigma x 1 itself is 960. Similarly, for the second series, the sum of the x 2 column is 657, whereas the sum of x 2 square is 63129.  Hence, substituting all the relevant values, small s 1 square comes out to be 124, whereas small s 2 square is equal to 244.14. Hence, the computed value of our sum of our statistic which we can call f is equal to 1.97. Students, the next step is the critical region. Our alternative hypothesis was that sigma 2 square is greater than sigma 1 square or since it is greater than cosine. Therefore, we are going to look at the right tail area. We want the entire 5 percent area on the right of our critical value. Now, in this problem, the number of observations for the second series was 7 and the number of observations for the first series was 10. Therefore, n 2 minus 1 is equal to 7 minus 1 and n 1 minus 1 is equal to 10 minus 1. Therefore, students looking at the area table of the f distribution, the one that is for 5 percent area to the right of our value, we obtain as you now see on the slide, f 0.056 comma 9 is equal to 3.37. The last step, of course, is the conclusion and since our computed value 1.97 is less than 3.37, therefore, we do not reject H naught. Our data does not provide sufficient evidence to indicate that there is greater variability in the number of plankton organisms per whole between different places than between different times at the same place. Students, this is the method of testing sigma 1 square equal to sigma 2 square. Sometimes we might be conducting two-tailed test and sometimes a one-tailed test as you noticed in this example. Now, let us consider another example which is all the more interesting. As you now see on the slide, two methods of determining the moisture content of samples of canned corn have been proposed and both have been used to make determinations on proportions taken from each of 21 cans. Method 1 is easier to apply, but appears to be more variable than method 2. If the variability of method 1 were not more than 25 percent greater than that of method 2, then we would prefer method 1. The sample results are as follows. N1 is equal to N2 is equal to 21, X1 bar is 50, X2 bar is 53, sigma X1 minus X1 bar whole square is 720 and sigma X2 minus X2 bar whole square is equal to 340. Based on the above sample results, which method would you recommend? Students, it is quite an interesting process to have. Now, let us consider the first method which is easier but has more variability. But if the variability is less than 25 percent greater than that of method 1, then we will prefer method 1. So, how we will formulate this mathematically? As you now see on the slide, H0 will be that sigma 1 square is less than or equal to 1.25 times sigma 2 square whereas, H1 will be that sigma 1 square is greater than 1.25 times sigma 2 square. Now, concentrate on the number 1.25. 1.25 means 125 percent or iskai ahima is equal to 1.25. So, it means that 25 percent more as compared with the variability of method 2. Students, I would like to encourage you to work on this particular problem on your own. The second point is the test statistic. In this case, our test statistic is not going to be S1 square over S2 square or S2 square over S1 square. As you now see on the slide, according to what I stated earlier, it can be shown that if sigma 1 square over sigma 2 square is equal to k, then f equal to S1 square over S2 square multiplied by 1 over k follows the f distribution with n 1 minus 1 comma n 2 minus 1 degrees of freedom. Hence, in this particular example, our statistic will be f equal to S1 square over 1.25 S2 square. Students, apne dekha k according to the formulation of the null hypothesis, our statistic changes slightly and once again I would like to encourage you to work on the earlier formula that I presented and the one that I have presented now and see that the two will tally with each other. After that, carry out all the steps and conclude for yourselves what is the conclusion in this particular problem. In today's lecture, I discussed with you the f distribution and its role in statistical inference as far as the comparison of two population variances is concerned. In the next lecture, students, we will be discussing the role of the f distribution with reference to analysis of variance and experimental design. Until next time, my best wishes to you and Allah Hafiz.


My name is Sam Vaknin, and I am the author of Malignant Self-Lover, Narcissism Revisited. In another video on this channel, I describe the concept of Malignant Optimism. The abused victims of narcissists and psychopaths feel the need to be optimistic. They believe that maintaining hope in the face of adversity is the only way they can preserve their sanity. And I understand the need to be hopeful. It may even have some grounds. For instance, there are gradations of narcissism. In my work, I deal only with the extreme and ultimate form, narcissistic personality disorder. But the prognosis for those merely afflicted with narcissistic traits or in narcissistic style, the prognosis for these people is much better than the healing prospects of a full-fledged narcissist, a patient suffering with narcissistic personality disorder. Full-fledged narcissists are merely one percent of the general population, and probably a small percentage of people who display narcissistic traits, behaviors, or style. So there is some grounds for hope. But mostly victims self-deceive. They confuse shame with guilt. They attribute to the narcissist remorsefulness. They say that the narcissist is sorry, that he feels guilty, where actually the only thing the narcissist feels is shame for having failed. Narcissists feel ashamed when confronted with a failure, a defeat, criticism, or disagreement. They feel narcissistically injured. Their omnipotence is threatened. Their omniscience is questioned. Their sense of perfection and uniqueness is in doubt. They become enraged and gulfed by self-reprimand and self-loathing. They internalize their own violent urges. Extreme cases may develop suicidal ideation. And it's easy to confuse this monopoly or phenomena with remorse or guilt. The narcissist punishes himself for failing to be good, not for having mistreated others. The narcissist makes an effort to communicate his pain and shame only in order to elicit narcissistic supply, the same narcissistic supply he needs in order to restore and regulate his failing sense of self-worth. In doing so, the narcissist resorts to the human vocabulary of empathy. He emulates, he imitates emotions. The narcissist will say anything to obtain narcissistic supply. But remember, whatever he says is a manipulative ploy, not a confession of real emotions or an authentic description of internal dynamics. No regret, no remorse, no self-attribution of guilt, no acknowledgement that he had wronged others or had been wrong. Narcissists are infallible. Some victims tell themselves that narcissists is a child. Yes, narcissists is a child, even a very young one, five, six years old, as far as personal growth, development and maturity go. But the narcissist as opposed to most children can tell right from wrong. The narcissist is indifferent to this distinction between what ought, what he ought to do and what he should refrain from doing. He is a law unto himself, there's no right or wrong except as decreed by the narcissist. Yes, it is true that the process of reparenting, or what Kohut called self-objects, that such a process is required to foster growth and maturation in the narcissist. But in the best of cases, and when successful, which is absolutely diminishing minority, negligible minority, even then it takes years or decades, the progress is dismal, incremental and glacial. Yes, it's true, some narcissists do make it. They modify their behaviors, their aggression, control their aggression, they become less abrasive, more pleasant, and their mates or spouses, children, colleagues or lovers rejoice. But people survive tornadoes. Is this a reason to go out and seek one? People survive all kinds of calamities, all types of predators. This is no reason to remain in close proximity with such dangers. Narcissist is a threat, an ominous and venecious danger, imminent. You should stay away, get away and stay away, not try to cope with the danger by somehow assimilating it, modulating it, reforming it and praying to heal or cure it. The narcissist is very much attracted to vulnerability, to unstable or disordered personalities or to people he considers to be his inferior. Such people constitute secure sources of narcissistic supply. The inferior, or those perceived by the narcissist to be inferior, offer him adulation, mentally disturbed, traumatized, normalized, co-dependent, abused, become dependent and addicted to him. The vulnerable can be easily and economically manipulated without fear of repercussions. Personally, I think that a healed narcissist is a contradiction in terms and an oxymoron. There are exceptions, not misunderstanding, but they are rare and they prove the law. Narcissists do not heal and cannot be cured, some behaviors can be modified, and even that, not for long. Healing and not only of narcissists is dependent upon and derived from a sense of security in a relationship. So many spouses or even victims of narcissists tell themselves, I need to provide my narcissist with a secure environment, a holding environment, in which he can safely heal. But the narcissist is not particularly interested in healing. He merely tries to optimize his returns, taking into consideration the scarcity and finiteness of his energy and resources. Healing to him is simply a bad business proposition. He would rather invest his energy in obtaining narcissistic supplies, far more gratifying and far more immediate. Narcissists are very weak when it comes to delaying gratification. In the narcissist world, being accepted or cared for, not to mention loved, is a foreign language. There is no meaning as far as the narcissist is concerned. One might recite the most delicate haiku in Japanese and it would still remain meaningless to some who doesn't know Japanese. Narcissists don't know love. You can love them as much as you want. You can prove to them that you love them. You can repeat, repeatedly tell them that you love them. It's Japanese to them and they are the quintessential non-Japanese speakers. The non-Japanese are not adept at Japanese does not diminish the value of the haiku or of the Japanese language, needless to say. But there you are. Narcissists damage. They hurt others, but they do so off-handedly and naturally as an afterthought and reflexively. They are aware of what they are doing to others, but they simply don't care. Sometimes they are sadistically told and torment people, but they do not perceive this to be an evil act, merely amusing. They feel that they are entitled to their pleasure in gratification. Narcissistic supply is often obtained by subjugating and subsuming others. Sadism equals supply. Narcissists feel that other people are less than human. Near extensions of the narcissist or instruments intended to fulfill the narcissist wishes, to obey is often capricious and volatile commands. The narcissist feels that no evil can be inflicted on such subhumans, on objects, on machines, instruments or extensions. He feels that his needs justify the means and the actions that he takes. This is the kind of partner you're living with. This is the type of thing you're trying to modify. There is no one there under the shell. The narcissist is a shell and only a shell. He is alien because he lacks empathy. He cannot understand you. You don't speak the same language and in many respects, at least in the psychological level, you don't belong to the same species.


and one more. What's up people? Manor here coming to you with a video. This time we're going to be unboxing and reviewing a very useful everyday item that can specially come in handy if you're traveling to a different country which uses different power source. That being 2000 watt voltage converter, travel adapter will do USB ports. As you know these days mostly most of the devices do use USB charging. This is a product UPC code common made uncommon as a saying and these are the three adapters that it can use three different plug types. This is the name of the company. Let's get started with the unboxing experience. Let's open it up. Very satisfying. We have a fine mesh bag which can even be closed these are the different plug types. This one I think can be used in India. This is the other one and also we have the instruction manual. A pretty light read and these are the different countries that can work in actually. So this one that I'm looking at can work in Australia and then we have this adapter. This is British adapter and this is the feast that there is the primary brick. Pretty snappy. This is the conversion matrix. So the top one is 110 to 240 and the bottom one could down converts 220 to 110. So if you have a laptop that can tolerate voltage between 110 to 240 just plug it in here connect the wall outlet and plug it in and it will work without a problem. If you don't have a device that can down convert plug it into here it'll down convert 220 to 110 volts and USB 5 volts to 2.4 volts. So you can plug that in right off the back. Pretty smart packaging pretty ingenious design rather than carrying a adapter and then looking for a voltage step down converter you can just carry all in one device. It has a bag you can carry all the adapters. So if you're traveling you're transitioning from US airport to Europe then from traveling from Europe to Asia all of your charging leads are in one. You can stop over at the airport for a couple of hours plug in your cell phone get on the Insta get on the WhatsApp get on Facebook communicate with people then get to your final destination use the travel accessories at your local location and then once you fly back put it with your luggage use it next time. Definitely a very nifty product I had seen travel adapters before but not a step down converter and a travel adapter all in one. A big thumbs up from my side for sure. Really interesting so when you plug it in the light does come on so there is a light functionality definitely a very neat product and I will highly recommend it to anyone that is planning to travel overseas. As always thank you so much for watching and I will see you guys and girls in the next video. Take care people. Bye.


Hi everyone, welcome to what the F is going on in Latin America, Code Pink's weekly YouTube broadcast of hot news out of Latin America and the Caribbean. This week I am proud to be in conversation with activist academic journalist and my friend Roberto Lovato, whose memoir Unforgetting, a memoir of family, migration, gangs, and revolution in the Americas was released on September 1. Welcome Roberto, I'm so pleased to be in conversation with you today. Great to see you through this medium Terry. So when I first approached you about doing this conversation. I asked we talked about how we want to focus the conversation today and there's so many angles and so many themes that you present in this book and I just want to show the audience this is this is the new book. And you've done many, you've done quite a few interviews prior to the to today, and he said I want to talk about me as a US citizen, which of course you are you were born in San Francisco to Salvadoran parents and and I looked from that perspective as a US citizen was really in a way it was liberating for me to some of the themes that you cover. So one of the, the things that really hit me with this is when you talk about getting your papers and we'll back up for the audience as to how you got to Salvador and needed a new Sedgilla, etc. But you wanted your papers in Salvador to say Roberto versus Robert, which was on your US passport and for me when I read that all this stereotypes and history of immigration to the US just started kind of pouring into my mind as to how, when you come here, you're basically in subtle ways and an overt ways told to just forget where you came from, forget the history of your country or culture your language, whatever violence you you fled whatever economic educational lack of opportunities you fled you're here now. And we become this kind of mix. I wouldn't even call it a culture when when, especially reading your book and you when you when you talk about the richness of the Salvadoran culture. So that to me was a real like strong thing about just forgetting in general. But in the case of your book you are also talking about the violence that that so many people forget on all levels emotional violence, family violence, state violence, military violence, violence in leading to the into forgetting in order to survive. And that seems a lot of what you in this book is a very personal journey and a very personal unraveling for you but getting tapping into the some of the violence that occurred for your family or father specifically. Yeah, I you hit on nail on head I wrote the book. You never I don't think you I don't write with one singular purpose I write with different motives. One of my major motive for writing unforgettable was to simply get my story down on paper that I've witnessed over the last, especially 30 years of my life with the relationship between El Salvador and the United States. It's obviously a personal story and you know tells the story of a family of family secrets, but it's also about the secrets of nations. Nations like El Salvador nations nations like the United States, and the way that these secrets can often have violent effects I mean if you look at for example in the beginning of the book I have a quote by great theorist of nations, Ernest Rennan. And he basically says that forgetting is at the core and at the beginning of nations. It's a fundamental part of it or the way I like to say is if you look under the hood of any nation you're going to find the bones and bodies of indigenous people and others slaughtered to create these ideas and so you know nations are very nations like progress are very genocidal concepts that have material effects and so the material effects trickle downward through the family and what I call my sh i blank theory of state and family violence and so my mission in the book is to link my experience of family to my experience of the states of El Salvador and the United States and the violence between them. And so it's an underworld journey of anything you know I go into the underworld journey of my family history my father's history which is very intense in terms of the kinds of violence that my family lived through in the 1930s in El Salvador during the age of la matanza when the Salvador government killed something on the order of 10 to 30,000 people we don't know in a matter of weeks in one of the most singularly violent episodes in world history as far as the numbers of people killed per day per month per week in a concentrated space according to scholars at Oxford that I've interviewed The book also is a way to look at the present violence of say the governments and the gangs in El Salvador that are perpetrating extreme violence themselves right and I do mean government because often time in the gang equation we leave out the government part and the counter insurgency policing that was brought on by characters like those in my book like a guy named attorney general William Barr of the Bush administration who's back and talking about gangs again he talked about gangs and he deployed massive FBI resources to begin the quote unquote gang war that we now know in the United States in the 1990s after the other riots he's now back and after prop 187 here in California. Yeah, yeah, we were there. So let's talk about let's talk a little bit about the history of these gangs because this is something that is really lost now in the US media and therefore in the US narrative that these gangs particularly MS 13 were created in the United States. And you all in Los Angeles by young people who had no families who had come here either on their own or lost family here. Salvadoran specifically Central Americans in general and already there was a Mexican gang in existence. But this you talking your book about where the term Mara comes from and how it really was about friendship friends gathering families friendship gathering and how that whole term has been bastardized at this point and and and is and refers to a real significant form of violence but let's talk about the founding the creation of them of the Mars in LA just so our audience has a really clear understanding that it is not the story we currently here. Yeah, um, as I document in the book. Um, the get the word models. I didn't even know what it meant I grew up with it. Like in the 70s in El Salvador I was, I was visiting El Salvador my family there. And you know people would call themselves La Mada. Which was basically friend group of friends hanging out on a corner playing soccer or playing Chihuahua's or or or different games hide and seek and it was La Mada. And so I watched as that word suddenly was adopted by young men in Los Angeles in Los Angeles Pico Union area where I work at an organization called cares and what was then called the Central American Refugee Center in the early 90s. And we were serving the Salvador and Guatemalan communities, providing legal services, etc. And we were our clients had these kids who had these tattoos with MS Mada, and we started kind of encountering these gang members who were coming together primarily at that time. Before that like in the 80s, they were, they came together to listen to hard rock music like Metallica, Ronnie James deal and other kind of music that they liked and to protect. And they eventually found themselves having to protect themselves from larger better structured gangs, like what, like the bloods, the crypts, and the Mexican mafia. And so they had to start buying, you know, getting more formal and hardened to protect themselves in this environment. And to name themselves they call themselves Mada they took the word friend and applied it to them because they were friends will listen to, to rock music. Eventually though that word has come to mean the heart of darkness evil quote unquote to everybody from the Obama administration who spent a lot of money researching and trying to help create this image of the evil quote unquote gang member, and now the Trump administration, the Pentagon, the US Southern Command, a number of scholars that I've been tracking over the years who have kind of made an industry out of the creation of enemies, you know that justify militarism in Latin America. There was a drug war in Latin America and drug war and police militarism here and now you have them fused in this thing I call, and that others like Stuart Schrader called counterinsurgency policing. So, you know, as you know in the book I track, and I show the way that the models were used as a justification for this counterinsurgency policing that was brought by Salvadoran US Pentagon trainers who were training desk was in El Salvador came after the 90s after 92 came to LAPD and other police departments in the US to train the local police departments encounter insurgency gang policing. So it's complex this gang equation it's, but it often excludes the police part of the equation and I put it back in. And so it's a really important variable and again it's a very violent variable in this whole physical enforcement of a whole legal paradigm a whole and a whole national paradigm of who and what I would say the United States is, you know when we first talked about, oh, having this conversation I had thrown out I'd like to talk about how those of us in the states are now seeing us foreign policy coming home and of influencing domestic policy. But I would now say having read your book twice now that it really is about US domestic policy being exported that violent expansion of the of the US. Now, as you said earlier the genocide of of a hot and entire race of people is something that's that is part of US history that is rarely talked about, certainly not to the extent of the violence and heinous act that it was. And that's used, you know, and then you go in to talk about this in 1930, 1932 El Salvador but it had already happened here in the States. And so to me it's almost like we're, we're seeing I think I really had it backward when for myself thinking about US foreign policy coming home and talking to you and reading your book it really is more of an exporting of US violence, which you and the later in your book, you know say is necessary for all empires to expand and I really hit me very hard to frame it that way, and I believe it's more accurate. Yeah, it's a it's a complicated culture of violence that is part of the core functioning of states right one of the things that defines a state is the control of violence. Right. According to political scientists and those that are into that. I think that. Yeah, it is an exporting but I prefer to talk about circuits. Because if you look at El Salvador right you have us trainers from the Pentagon going and training the Otlacot battalion that wiped out 1000 people in 19 December 1981. Half of those people were children under 12 half of those children under 12 were under six. I've seen the bones of those kids. I've spoken to people that have witnessed similar massacres. I was there when some of those massacres were happening in the later part of the war. And so, you know I come back from El Salvador to Los Angeles and I see the LAPD starting to get like you remember Adam 12. I don't know if you're. Yes. Your uniform should be really thin. Right. And, and I start button down shirts really thin and suddenly the police uniforms are getting puffier to the point of the Robocop uniforms that we have now. Right, pretty soon they're going to be so puffed up beyond Robocop they're going to be like those inflated. Those inflated you know in the Macy's parade what do you call them balloons. They're giant balloons militarized because that's what they are the inflation is a is a reflection of militarism in of US policing and so when those Pentagon trainers came from El Salvador from training the Otlacot battalion and the death squads. They came to the United States to start training the police. And that's when you start seeing this counterinsurgency policing of what was known for example of the as the crash anti gang units.  And my book is a is a is a personal telling of the way of having witnessed all these different circuits because then remember those police in LAPD went to train El Salvador in some cases in the post war era of the gangs in El Salvador so you have the US gang structures being born with the help of William Barr, and then you have William Barr sending US style policing to fight US style gangs. And then, you know, it's astonishing the way that these circuits work. It's the same. I mean I think you, it's the same sort of circuit with with the arms trafficking from the US into Mexico. And then back and forth. Yeah, and it's, it's very insidious and the fascinating thing with the gangs in El Salvador is that they originated here, many of the members US born and and then all deported to El Salvador. And so there's that exportation again and then how it all, like you said, I think circuit is a is a really brilliant description of it. You just mentioned, you know, in, in talking about all this violence that you've seen, you know, you've seen the phones of victims from 1932 to present day.  And one of the things you mentioned is in your book is how important these forensic anthropologists are. And as far as discovering the grave sites as far as defining, you know, determining how people died, but also in that process, allowing families and friends to recognize the death of a family or friend and to start, or I guess I will say to stop forgetting to start discovering, which allows for healing and moving forward. Thank you for No, I'm sorry, go ahead. Thank you for bringing that up because with all the violence of El Salvador history because it has been one of the most consistently violent places on earth since it's founding in 1821. And all the violence, what tends to get lost in the, in it is, is the tenderness like I like to say the, my journey is one to, to excavate the terror tenderness that survives the terror. And there's a lot of beauty in my book. I try I try to put a lot of beauty in my book I did the best that I could to put the beautiful and the sublime that I've encountered because I already saw what was coming like a lot of us in 2015. And that was the journey of this book, and of writing it that where the world was going and I anticipated that we were going to have to. I was, I wanted to contribute by bringing out whatever Jedi knowledge of transcendent knowledge I had about sustainable struggle. And I've been in it for those that know me since the 1980s, early 90s up to the present, whether it was joining the FMLN gorillas, whether it was as a journalist, whether it was co founding different organizations that have, like presented the work that have done work of solidarity and others. There was always an undercurrent in my work of beauty and the sublime there's a, I like to say the strategic value to the sublime and the beautiful right now that we need to understand. That's why in the content and in the form that I wrote, I try to make it as beautiful as possible. And the beauty is contained in two of the dominant metaphors. It is sewing my grandmother was a seamstress and my grandmother would take disparate pieces of a cloth to create these beautiful dresses for the prostitutes of the shanty town that she lived in in San Salvador, during a great depression that was like a sign bakes, grapes of brass look like a wine festival. You know, and so my grandmother in her mathematical and creative beauty would just size up somebody literally and create a dress for them that gave them some of the after La Matanza, for example, had erased indigenous identity as a public thing in the same way and they were, you know, it's my grandmother was giving that person a piece of the dream that they had in by the same token right the dream of having the dream of being an indigenous princess in the case of one prostitute, my, my grandmother lived next door to by the same token the forensic specialists. So together that story so together the bones of a deceased, this apparecido person to tell the story of what actually happened. What were the final days of that person like to then give to the family. So as I as I narrate the story the bones and therefore the beginning of some closure and the beginning of some unforgettable that I think individuals and families and nations have to undertake right now, if we're to fight the enormous crises we face we have to, we have to have a political vision that doesn't just look forward but that also looks backward in a clear way. And that's I think what the foundation for solidarity and and revolutionary politics of the future are. So I'm thinking about a number of things simultaneously now what is coming I, you know, understanding the understanding the past and coming to terms with it is so important on on all levels moving forward and yes on a global scale more important now than ever, particularly for young people, we older people really need to do the unforgetting to help them create a better planet for themselves and I, I see that in so much of your personal story. Your father because you as a young man really struggled without your, without your father, or because of your father's forgetting quote unquote, because of your father's forgetting that did not allow you as a young man, his son to really understand yourself, your family, your cultural heritage. It was, it was made for a very confusing frustrating and at one point violent youth. And I like you to talk about that because I think it's so important what you just said is for us as nations to come together and to to forget, understand where we came from in order to go forward as peoples, and not just simply nation states and I think that is the experience of your personal life is really analogous to that. That's kind of one of my points on my book is to show the connection between the person on the political. They really always are connected. My first rage against authority was against my father.  You know, tells us that the first entry point for the state in our lives are in fact our parents to their subconscious, the way as the state propaganda education and other things insinuate themselves in the family. Right on our families unconsciously sometimes adopt beliefs and words and beliefs that are kind of messages from the state you can see Donald Trump doing it but you could also see Barack Obama doing it. They're just different forms of the same thing and so I was aware of this and I wanted to kind of show in my own example, the way that I was, I led this kind of crazy life and doing things that I didn't know why I did them, whether it was becoming a violent kid and engaging in criminal activity or joining the FMLN. I didn't know why I did. I just knew that I wanted to do that. And then I go and I discover a secret that I can't share with the audience, Terry, because I'd be giving away the whole book of people that I already have the story. So, there's a big atom bomb of a secret that my dad has that I discovered and that discovery of that secret, I hope and I try to show is the thing that connected my gut, literally my intestines, the tightness and trauma that I contained in my gut to you know it's umbilical connection to state violence, right? That tightness in my gut was connected to the state violence of history that I didn't even know I was carrying. But then I find out I did the excavation. So then that explained to me why I was such an angry kid, why I did crazy things and it's been so liberating for me to write this book because I now have an arc explaining you know myself to myself but also explaining my father and it allows me to be more tender and loving towards my father who I had a lot of anger towards. Because I understand more deeply what it was to live in the Great Depression that made John Steinbeck's Great Depression look like a wine tasting, right? So yeah, the healing is real in the writing. It's a fascinating read and it is a multi-level analogy and the thing that really came through for me you mentioned that you were careful to be sure you talked about beauty and I think in the in the unforgetting we re-encounter our humanity. That the forgetting is kind of pushing you know to heal emotional scars, physical scars so that we can survive. And everybody has different levels of forgetting for very different reasons and the whole nation state forgetting is is causing you know so much of the violence today as you mentioned earlier but that aspect of humanity that you keep bringing back into the book the women you talked to who I think one young student in LA who talks to you about the garden she was sequestered in and climbing the trees and having this beautiful vision that your vista of the countryside the fruit she was able to eat and you just you know those are very human sentiments and experiences among all the physical violence and I think that those moments that you bring out are so important and I love the sewing analogy the creation out of you know pieces which is what so much of society is. Particularly I would argue for immigrants like your parents and my grandparents coming to this country these pieces that they bring with them and what do you do next. You know and your grandmother made beauty made beautiful dresses out of remnants and I just love that whole telling of her and her ability to create out of just remnants and as you mentioned as the bones the bones of these from these mass graves are remnants of physical remnants of human things but also remnants of people's lives their greater lives not their individual lives with their families and society as well. Thank you thank you that's what I was trying to do and I hope to elicit that in the reader. There's a third layer that's kind of unspoken I kind of hint at it at the end. That's what. So what a forensic scientist did do or what my grandmother did in terms of piecing things together. I try to do with words and you can see it at the end of the book where I'm at a table at level in coffee shop here in San Francisco in the mission district and the table is a is my favorite table when I go there people that know me here in the city. And that corner when when we're not in COVID-19 working on my computer on top of a table that is a converted sewing machine that still has underneath the table. It still has the gears and they and the and the and the of the singer sewing machine the iron horse. And so when I'm typing there I'm almost revisiting my grandmother being on my grandmother's lap as she was kind of creating the conditions for our livelihood in San Francisco at coming from the desperate and just devastating history of El Salvador coming here and showing those those close together to make us sustainable. I'm trying to do the same things with our words by taking the fragments of my life and the experiences I have one of which I think is especially important to your audience is the experience of solidarity. Solidarity. I was part of, you know, the solidarity movement here in the United States I was with Karecen with the committee of refugiados, and I actually made a point to try to draw out the beauty of solidarity in it because there is a beauty and kind of connecting with something so far from us and yet doing and committing a piece of our lives like with people like my old friend Don White of committee and solidarity people of El Salvador like this man gave up a large piece of his life before he died to the people of El Salvador and I'll never forget him and others or people that I met in El Salvador who were, you know, guerrillas and guerrillas from Mexico from Spain from across the world I mean the way that you know the way that the way that say Hemingway or Orwell C saw solidarity with of the Lincoln Brigade in Spain, I saw the solidarity in El Salvador in the same way as a heroic act. And so I try to do at least a little bit of justice to that beauty, the beauty of that is his heroic act of of joining a people's struggle across borders, which I think is fundamental and seriously lacking right now here in the United States in our concepts of politics even on the, even on the left. Especially on the left, I would argue lost. Yeah. And if it doesn't matter what race you are whether you're white, black, Latinx or whatever you call yourself. There's a there's many people whose concept of politics is limited to the borders of the United States. And that's already, that's already basically an embrace of empire at a certain level when, you know, when when you fail to see the global context that the United States is in, and the connections, whether it's through immigrants through trade through racism through police models. If we think we're not going to get anywhere, being boarded off in a multicultural movement I, I could care less that Beyonce is somebody's ally, quite frankly, Beyonce is class wise, a billionaire. Who are our class ally, even if they, you know, even though she, she has these black panther things that's a super bolder, you know, I mean she also has, you know, Thai sweatshop labor women, sewing, speaking of sewing, an empowerment for, for sale in the US for big money. So, anyway, I don't want to get distracted by Beyonce and all that but my point is the concepts of politics are, I think are dangerously boarded off and I'm, I'm sharing the experience in my book of solidarity and of revolution in order for people to as an act of political imagination so that people kind of start thinking about politics in the way we did in America Latina. Let's say you mentioned solidarity and my activism interest in Latin America really began when I was in sixth grade my sixth grade teacher introduced me to Mesoamerica and pre Colombian cultures and at that time I was growing up in, in the Catholic or liberation theology which you touch on in your book to as well as evangelical religions and all these years in and out of Latin America and some just touching on work and and and then at other points in my life, you know, it being 100% of my time and work as more now, I have to say and I say this with great sincerity of all the solidarity movements groups of people communities of people that have made the biggest impression on me are the Salvadorans specifically those with a history in the fmln, as far as understanding organizing and being able to come together and not be, I guess, petty about identity and things like that that there's the ability for Salvadorans to organize is impressive. It's rapid it's solid and people just come together and make things happen and I have consistently seen that over the years. And you see it with other organizations as well and other groups of people but with the Salvadoran community, it is consistent and has been consistent for the last 3040 years. It's very impressive and it was really something admirable. I tried to get at a little bit of that political culture that you and I both partook of and I mean I don't put it in the book, but my theory about Salvadorans and politics and why, for example, one of every three people had adopted organized politics at the height of the war. You can read Nakla and see an article in 1989 about how there was a poll that said one of every three people was organized against the Salvadoran state and had adopted radicalized politics. That has to do with some things like the density of El Salvador, very tightly small population. You also have like La Matanza, creating, sadly, a more homogenous culture so that you don't have the organizing issues that you have in a place like Guatemala. We have to organize across different broader expanse of geography and a broader expanse of languages, for example, right? You have all these different Maya Quiche, Maya Canjoval, different identities. Thankfully, thank goodness, I wish El Salvador had more indigenous identity than it does, but it's been forced to go underground. And so, for different reasons, yeah, I bring that into the book to show the spirit of the matter that made Salvadoran organizing one of the most thrilling experiences for many of us to the point where the CIA, for example, said that Salvadoran opposition and people's movement was one of the most effective people's movement in the Americas in the 20th century. And so I try to, in between the lines, I'm doing my best to show whatever Jedi knowledge of revolutionary kind of organizing and spirit I could amass. But I do it through the telling the story of actual people who were revolutionaries and what they taught people like me. So I am thinking about several things simultaneously that you mentioned, you know, the Salvadoran culture being more homogenous since 1932 and that being part of the ability to organize, unlike a lot of the cultural diversity and Guatemala. And when I was reading your book near, you know, you have so many synonyms you use for forgetting. And one of the things that was that I'd heard over and over again in Guatemala, specifically since, you know, the Maya people were given genocide status by the UN and how they were able to after the attempt to completely exterminate them in the 80s. They talk about memory, which I think is, you know, their their historical memory and and not, they had to get to a place as a people the Maya people where they could start talking about what happened to them their women specifically get the men talking about what happened to the women in their in their culture before they had to do this memory before they could actually admit the genocide and then petition for that status from the UN and I just think that's just one more heinous example of of what people suffer. But what has to be done first that unbearing that excavating unbearing that unforgetting that has to be done in order to heal and move forward on, you know, Absolutely, I wish I wish I had the time to do another book on Guatemala. Um, you know, I think we have writers like Hector Tovar and writers in Guatemala who are far better equipped than I am to tell that story as as there are Salva Lorena and other writers. Actually, I want to make that point to is that my mind is just one story. And one of my motives for writing this was to demonstrate in fact that Salvadoran and Central Americans in the United States have the ability to tell compare as compelling and powerful a Salvadoran and Central American story has non Salvadoran and non Central American writers in the US have won prizes for I'm not criticizing any of those writers, but the fact is You can look into your bookshelf. You don't have any books about Central Americans non fiction. This is the first non fiction book by a US Central American about Central Americans published by a major big five publisher Harper Collins. And so we've been here for, since the 19th century, and in large numbers since, you know, the 1950s. And so there are reasons that we haven't been afforded the space to tell our own stories including for example, the fact that 1% of books in the United States are Latino Latinx books by Latinx authors 1%. So, and we're within the margins, because you've got to remember the big groups in the Latino Latinx space are Mexican, Chicano, Puerto Rican, and Dominican and Cuban right I mean those are in the literary sense. Those are the ones that are recognizing and the case of Mexicans. It's a colossal community that has no literary publication record in the US, reflective of its numbers. And that's not the Mexican and Chicano spot. That's the publishing industry fault, because most Mexicans are on this side of the Appalachians rather than on the other side in New York. So, See, I think, you know, listen to you say this, I think that's all part of, you know, of the US nation state quote unquote forgetting, you know, the good part of the Western United States was part of Mexico and Spain at one point in time. And so you, you know, and there's that whole violent history as to how those Texas in particular how you know became, you know, part of the United States and they just you to not have more stories like yours. Or, or, or migrants who just who not even born here don't you know to hear those stories as to what the heritage is why people come I think it's intentional, I have to say it's part of the, it's part of the US nation state forgetting, so to speak. I don't think you can erase a community of 60 million people in film in Sunday news shows in the political narrative of the United States, and in literature and other cultural and media systems with such just totality without it being having a degree of intentionality. And I think it's a, it's an intentionality of a country that doesn't feel it can move beyond a black white narrative of itself. Many scholars of race and identity in the United States, you know, look at what's known as the black white binary the perception that the United States is primarily just black and white and so you know you see this and and and and those of us who are neither black nor white, although Latino is black right after Latinos are a large population and they're not a part of the equation either. So, you know those of us outside of that equation, kind of see this conception that's very obsolete and actually dangerous when you look, for example with the numbers of people identified it under this category of Latino whatever getting coven 19. The children among children the largest group that's getting coven 19 or chill or Latino children of, you know, you know, death by police we're not hearing about the killings of young men here in San Francisco in Fresno and LA, and out of the South West and on the East Coast, we're not hearing about that. It's incumbent upon Latinos to bring that up. And we are but we have to push even harder because the system doesn't seem to want to seem to say there's already enough room. It's the black community for for for for leading the way to abolishing police and and and bringing our awareness of the prison system and what's happening to black bodies. But, but, you know, we're going to advocate for our own dead and our own youth to otherwise they're going to be continued slaughtering our youth with impunity and with invisibility and forgetting and forgetting. And then we just and then we have more young people suffering. You know, a childhood as as you did with the lack of understanding with the lack of knowledge with the lack of connecting any sort of continuum about your, your family or culture and yourself as an individual. That's exciting to me right now because I'm already getting responses from people who like yourself have already read the book. I got these notes from these young Salvadorans and Central Americans and they're on fire for this because if only because they've never seen themselves in on the written page in the English language to read about themselves they have to go read stories like Roke d'Alto and Clarivella de Grilla and Latin American writing but they have no stories, except in in smaller presses and hard to get to spaces like an anthology that I was a part of called The Wandering Song, which is great but you have it's out of print, because it's so out. So there's not a lot about us. So when these kids are seeing a major publisher with publishing a book that's about us and coming out of the United States written by someone born here about us here. Yeah, it's a it's a it's a it's a it's a seminal moment. And that's not even saying if the writing's any good. I mean I don't know. I'll let the critics be the judges. I'll let the reader. All I'll say is that I put el todo por el todo to make it as sublimely sublime and beautiful as I could, because I recognize, not just for those Salvadoran and Central American kids but for those of us on the left, those of us in solidarity. I use my book as an example of what I call the strategic value of the sublime and the beautiful at a time of epic crisis right now. Like I said, we're not going to face what we're facing right now in the world. You know whether it's Trump economic decline, you know, of neoliberalism that's continuation of neoliberalism, the militarization of our inner cities. COVID-19 and then if we deal with that, then we're going to have to go toe to toe with climate change. So we're not going to Democrat liberal or progressive our way out of this. We're going to have to develop something of another order. And I think that that that other order has to include the spiritual power given to us by the sublime and the beautiful that makes for sustainability of struggle. It's a fan. It's a fantastic story and I really I'm so I'm so happy that you wrote this and I think that the message for all of us is really that you share is really really profound and I mean that your story as the analogy for all of us to move forward is just is so important and so profound. I know Roberto I promised you 2030 minutes today and we've been talking for almost an hour and I'm so thankful for that. Is there anything I want to show the audience your book again. Can you say yeah and read it and buy it read it and read it more than once and then share it. Is there anything that that we should add to our conversation this morning before I let you go.  I want to commend you for that and thank you and especially with the work with America Latina that Medea and others have held. I also want to say that I just hope people understand that the book is at its core a very hopeful book. It just takes a very underworld stark dark journey that I took so that you didn't have to to tell the story, but I do it with the intent to bring out the terror that survives the terror the stuff that we're going to need for sustainable struggle. And I guess a lot of folks are struggling right now to to find their way in struggle and in just living. I would ask people to read my book as a, as my blueprint for how to survive an apocalyptic age.  Thank you so much. I'm so thankful for your time I'm thankful for your work and for your friendship. And, and thank you for this lengthy conversation I know you gave me so much more time than, than we had initially talked about. So I want to tell our audience that this conversation can also be heard Thursday on code pink radio broadcasting on WPFW DC WBAI New York City simulcasting on both stations, 8am Pacific 11am Eastern and then re broadcasting again 730pm Eastern. So thank you so much for this wonderful conversation. I'm going to reread your book now with yet more insight and I'm so thankful for the, the, the political analogy that it offers and it's so hopeful for young people, and it's marching orders for us older people. And I think that you know one of the things I'll just say real and closing because you mentioned the underworld and, and it makes me think of the responsibility of us older people which, which indigenous cultures so understand that older people are to leave the world better for the upcoming generations and you talked about going under into the underworld into the dark space but also you tell an indigenous story about that and how the bones of the people in the soil are the fertilizer for the life above, so to speak. Yeah. And I think that's, that's a wonderful story and I think that's what we all need to be now the fertilizer for the future. Thank you. Thank you so much Roberto. Always wonderful to see you and speak with you. My pleasure Terry thank you. Thank you bye bye. Bye bye.