Hello, welcome to this lecture on Biomathematics. In the last lecture, we have been, in the last lecture, we started discussing statistics, how statistics can be applied in biology. And we took a simple example of a few, a few examples like traveling to your college and number of student, number of mark for an exam and all that. And we discussed the idea of average and standard deviation. Now, how do we, so the basic question we had is that, we get a lot of data in from experiments, large amount of data. And given this huge data, data set or set of numbers, data is essentially a set of numbers. How do we make sense out of this numbers? What we can learn from this numbers? And we learn that, average and standard deviation is some two simple things that we can learn. And that, that has a meaning and there are two numbers. From a huge data set, we can extract two numbers, meaningful numbers, average and standard deviation. What more can we do this? That is the, that is the, that is the, that is what we are going to discuss in this lecture. What more we can extract from the data or how do we present the data, so that we get, we have much more information, we can convey much more meaningful information. So, today again we have statistics as our main title. In statistics, we will have, so this is the slide we, in statistics we will have, we will discuss in specific, specifically probability distribution. So, we will go ahead and see, what is, what do you mean by probability distribution? So, as we said, we, we had various experiments. So, one of the experiment was travelling to the college, but we will discuss a new experiment, a simple experiment that you all can do yourself. We do not need a big setup or anything, just you can do it in your class. So, let us do a simple experiment of measuring height. So, the experiment is measure height. So, measure height of voice in your class. So, this is a simple experiment that anybody can do. You can measure height of all voice, let us say, and or girls. So, here we, we take example of voice, because some numbers that we used might be more suitable here for this example. So, if we do this experiment, let us say you just go on and measure. Now, all the heights of each and every student in your class and what do we get when we measure? We get a, we will be getting a big data set. So, let us look at some, some, something what you will typically get. You will typically get a set of numbers. So, let us say here is what the, let us say in your class if you just look at the numbers. So, you can have 150 centimeter, 171 centimeter, 165 centimeter, 140 centimeter. So, some numbers, these are some kind of reasonable numbers. You know that like, so the many, many of them around 150, 140, very few, 180, this is just 1180. There is nothing bigger than 180 as you see here. There is one person, 180 centimeters and like this one person with like 131 centimeter, very small, short person and very tall person and others somewhere in between. So, you have like large number of such data set, such numbers. So, this is not ending here. This is just a continuous list. So, let us say you do this measurement and how do we make sense of this data? So, we have this huge data here and how do we make sense of this data? So, let us say we have hundreds of, we measure heights of hundreds of students and so we have hundreds such numbers, 150, 160, 130, 140, 140, 122, 135, 100 numbers. How do we make sense of this data? So, two things we learnt are that we can find the average and standard deviation. We can say that average is 155 centimeters or 150 centimeters. That will give you some idea and we can say as standard deviation is plus or minus 20, so standard deviation is 20. So, you can say that average is 150 and the standard deviation is 20. That means, 150 plus or minus 20. So, this is something which we can say if you wish like using the idea that we learnt in the last class, in the last lecture. But the question is, is there any other way we can present this data so that it reveals much more useful information? More than average and standard deviation can give, can we present this data instead of presenting all this many, many numbers here? Can we present this data in a different way such that this reveals much more information by just looking the way we present it? So, we just writing down this numbers is a very bad idea.  It does not make much of a sense. You see lot of numbers. What does it mean? Like many, just many, many numbers. It does not make much sense. But if we present it in a particular way, is there a smart way of presenting this such that it makes much more sense? By just seeing that you should be able to make out lot more information than either average or standard deviation or just by one glance of this numbers you anyway does not make much sense. So, just more than standard deviation and average, we need lot much more information and how do we present this such that, how do we present this numbers in one slide such that it reveals a lot of information? So, the answer to, so this is the question. Is there a way, is there any other way we can present this data so that it reveals much more useful information and the answer is distribution? So, we can, we will discuss what is distribution means. So, but the, just the meaning of the word would tell you we are talking about heights. So, we want to present the distribution of heights. So, how do we present the distribution of heights? So, let us look at this. This is one way. So, we can say that taken presented in different range. So, let us say we can break down the data into ranges. How many students are there having a height in the range of 130 to 140 centimeters? So, this height range is in centimeters. So, if the height range is between 130 and 140 centimeter, how many students are there? Just one student. How many students are there having height between 140 centimeter and 150 centimeters? Let us say there are 17 students. So, this is why this column is number of students having height in this range. So, 150 and 160, how many students are there such that the heights fall in between 150 centimeter and 150 centimeter? There are 35 students. There are 30 students having height in between 160 and 170 and there are 15 students having height in between 170 and 180 and there are 2 students having height in this range between 180 and 190. So, large number of students in the middle and a few students with very short few students and very long few students. So, very tall students, only two, very short students, only one student, like very short. Tall, two tall students and all are somewhere in the middle. So, this is the typical data that you expect and this is what you have. So, this is actually a smart way of presenting the data because this gives you some idea. But if this is just a table and if you plot this table in a graph, this we always like, we always like to present the data in graph as a graph that that can make much more sense. So, one way of presenting such things are called histograms. So, when you have data, this kind of data, if you plot it, they appear as if like a histogram. So, what is a histogram? See this. So, let us say between 130 and 140, this is what I mean by 135. I just put some number in between here. There is one student with 135 height between 130 and 140. So, h is the heights and n of h is the number of students having height h. So, what is the grads, the distribution of heights. So, n of h, you can call distribution. So, this is essentially the same thing that we saw, like if we can draw this in a different way, if we wish. So, we can draw this h and n of h. So, how many students are there between 130 and 140? So, there is 150, there is 160, there is 170, there is 180, there is 190. So, these are the numbers we have. So, 130, so let me write, this is 130. Let me write it little more clearly. So, this is little more clear for you. So, let me draw this little more clearly. So, you have, let us say this is 130, 140, 150, 160, 170, 180, 190. So, how many students, so in this table, if you, they had one student between 130 and 140. So, between 130 and 140, we have just one student. So, we mark it one. So, between 130, just one student, between 140 and 150, there were 17 students. So, between 140 and 150, there were 17 students. So, let us mark this as 17. So, this is 17. Between 150 and 160, how many students? So, this table tells you, between 150 and 160, there are 35 students. So, between 150 and 160, there are 35 students. So, let me mark this as 35, this is 35. So, there are 35 students in this range. Between 160 and 170, there are 30 students. That is what this table says, 30 students in this range. So, 160 and 170, 30. So, this is, let us say this is 30 summer here, this is 30. So, summer here, 30. So, if we, we can mark this, this way, 30 students. And 170 and 180 in this range, there are 15 students. So, this is 17. So, this is 15. So, 15 students in this range, between 170 and 180, 15 students. And 180 and 190, only two students. So, this is 1 and 2 is here. So, this is like two students. So, this kind of a block diagram, if you wish. So, if you, in a block, in a manner, something like a block, like, so it is a block of 130, 140, another block of 140, 150, another block of 150, 160. So, another block here, another block here, another block here. So, such, this kind of a plot is called histogram, if you wish. So, this is called histogram. So, this is distribution. So, this is height in a particular range. And this is number of students having that height h. So, this is what essentially plotted here in the, in this. Exactly what we just drew is plotted here. So, there is, between 130 and 140, I just mark by 135. There are 1 and there is this 30, 35. This is 17. This is just over 15. This is 17. 35. And this is 30. So, again this is 15. And this is 2. So, this is a histogram. And we can call this distribution. But is this an accurate representation? In some sense, it is not very accurate. Why? Because there are students with 130, 130 to 133. We all put in one range. So, we do not actually distinguish between students having 139 height and 131 height. Height 131 centimeter and 139 centimeter, they are all in one range. Like, let us look at here. If a student having 151 and 159, we put them in same range. So, we can actually reduce the range, if you wish. So, instead of writing, instead of writing 130, 140, I, if I wish I could write, how many students between 130 and 132? 132, 134. So, we can range, make this in 2 centimeter. And let us say, 150 and 152. Similarly, 152, 154. So, like, 161, 160, sorry, 150, 160, 162, 162, 164. So, like this, you can write, you can take an interval of 2. So, then, you can make the interval smaller and smaller. Then, that will be a better description of the data. So, essentially, you can make the range smaller to get a better description of the real data. Now, how small it should be? How small the range should be? Let us say that, when you measure this height, you do not have, let us say, this, your tape, which you measure, can only measure this in a, say, in centimeters. You cannot measure less than a centimeter. Let us say, you cannot measure millimeter. You can only measure in centimeters. Then, you can present the data in the range of 1 centimeter, if you wish. So, then, there is nothing better than that. That is the best description of the data. So, then, you can ask the question, how many students having height 131 centimeter? How many students having height 132 centimeter? How many students having height 134 centimeter? How many students having height 151 centimeter? So, each centimeter by centimeter, you can have this data presented. So, let us say, let us say, you have the data presented, such a way that, n of h i is a number of students having height h i. h i height could be like 31. So, this, the height could be 131, 151, 162, any number. In short, you can call this. So, now, let us say, you plot this as a distribution. So, now, if you plot this as distribution, you will have many, many histograms. Let us say, you have a histogram. So, let us say, you have a histogram height this. So, I call this 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So, what are these? These are ranges. You took 10 ranges. So, just like here, in the previous example, we had, we had, how many ranges? We had like 1 range, 2 second range, 3rd range, 4th range, 5th range, 6th range. So, we had 6 histograms, 1, 2, 3, 4, 5, 6. Similarly, let us say, if we are presenting the data of height of students between 130 and 180 centimeter by centimeter. So, you can have 130 here, 180 here. So, how many students having 130? Maybe one student. How many students 131? How many students 132? So, you can have, for each centimeter, so you can have like 50 points. So, you can have 50 points like this. For each centimeter, how many students having? So, this is h i. So, h 1, h 2, h 3, h 4, h 5. So, h 1 is 130 centimeter. h 2 is 131 centimeter. Similarly, h 50 is 180 centimeter. So, you can write this way. So, basically, you can have h i versus n of h i graph, which might look some, which might have some particular shape. So, then let us say, it has this particular shape, n of h i versus h i. If you take for centimeter by centimeter, that means, you ask the question, how many students having 130 centimeter, what is this? This is number. So, this could go from 0 to some particular number, let us say 100. How many students having 130 to centimeter? How many students having 134 centimeter? How many students having 180 centimeter? So, you can ask this question. So, you have two things. You have n of h i, number of students having height h i. Now, if you do this, sum over i, n of h i, what does this mean? If I write sum over i is equal to 1 to 50, there are 50 different heights. What does this mean? What does this imply? So, let us think about it. So, let us expand this. When we expand this, sum over, so this is if I n of h 1 plus n of h 2 plus n of h 3 plus dot dot dot n of h 50. So, let us say h 1 is 131 centimeter. So, this is number of students having 131 centimeter, number of students having height 132 centimeter, number of students having height 133 centimeter plus dot dot dot, number of students having height 180 centimeter. So, this will give you total number of students, right. Because if you, this involves all the students, number of having height 131 to 180, like all the, we are measuring centimeter by centimeter and we are having this kind of a histogram and then we are doing this sum. And at the end, what will you get is the total number of students. So, that is what essentially shown in this slide here. Sum over i n i, by n i I mean n of h i, I get something all n, which is the total number of students. And if I divide this n of h by n, I can define something all p of h. In other words, if you wish, you can, you can write it as p of h i is equal to n of h i divided by n, where n is equal to sum over i n of h i. So, actually in this slide here, it should be n of h i. So, I can write here in this particular way. So, this is the correct way to write it. So, if this is the case, what is p of h i? So, we can call the p of h i as probability. So, we will later come and understand what does this probability actually mean. But let us call this as probability. Probability is essentially sum number between 0 and 1. Probability is sum number between 0 and 1. If you just, at this moment, it is for you to just realize, what is the colloquial meaning of probability, which you all know. When you say something is very highly probable, that means very likely, that is very, very, there is something not very probable, that means very unlikely. So, let us have understand only this much at this moment and let us also understand that probability p is sum number between 0 and 1. So, it can be 0 and it can be 1 or anything in between. So, probability is sum number between 0 and 1 and probability that you have a height h, that is what we actually defined now. Probability that you have a height h is number of students having that height h divided by the total number of students. So, if we have one student. So, let us say, now let us imagine that n is 100. Let us take n is 100. Then let us calculate. So, let us say, there are one student with height 131 centimeter. There are 10 students with height 140 centimeter. Let us say, there are 15 students with height 150 centimeter and there are 0 students with height 180 centimeter. Let us say, there are 0 students with height 180 centimeter. Let us say, this is the case. If this is the case, we can call p of 131. Probability that you have students have a height, students in a class in your class have a height 131 is 1 by 100. So, this is the example. Just by following this formula, this is what you get. p of 140 is 10 by 100. So, 1 by 100 is 0.001. 10 by 100 is 0.1. So, p of 150 is 15 by 100, which is 0.15. p of 180 is 0. 0 by 100. So, probability p of h is some number between 0 and 1. So, p of h is some number between 0 and 1. So, how does, if you typically plot, you take large number of students in your whole school, in your like or many, many schools and take the calculate p of h and plot it. However, it look like. So, it might look like this. So, have a look at this. So, we can call this probability distribution. So, what is this? This is a curve, which has a peak somewhere around 150 and this axis, it is height and this axis is probability to. So, this is the height h and this is probability of having height h. So, very, 0 students have the probability of having a height 120 centimeter is nearly 0. There are unlikely that anybody will have such a very small, such a short person. Very high, like above 190 is also nearly 0. Somewhere in the middle, there are many students, like 150, there are many students. So, the probability of finding students having 150 is around 0.05 in this example. So, this is an exercise that you can do. You can calculate the probability distribution, the way we defined. So, the probability distribution is probability of having students height h. Probability of having students height h is n number of students having height h divided by the total number of students. This will give you the probability. So, now, you have this probability. How do you find the average? Can we find the average from this probabilities? So, it turns out that we can. So, let us say, let us go back to the definition we had. So, we had, we have, we had discussed probability of having students 131 centimeter. Let us say, probability of having students 132 centimeter. Similarly, let us say, probability of having students 140 centimeter and probability of having students 150 centimeter. So, let us say, you have all these probabilities. The average, so basically, you have probability of having students having some particular height h i. So, then the average is defined in the following way. The average height is defined as sum over h i p of h i. So, this i goes from 1 to m. So, if you divide this to m intervals. So, in our example, we had 50, so 130, 131, 131, 131, 132, 133, 134, up to 180 we had defined. So, 50 heights we had defined. If we define 50 height, m was 50. So, this sum over i 1 to 50 h of i p of h y, this will give you the average. And if I calculate this, this will give you the square average. So, we have average and square average h square average and h average. So, there is, this is essentially the same way we had calculated this. So, instead of summing the throughout the data set, we can multiply with the probabilities and sum like this. So, then you get average and h square average. So, do this calculation by taking an example in your case. Do an exercise yourself. If you know h average and if you know h square average, we can calculate h square average minus h average square, which is standard deviation. So, the standard deviation that we discussed before can be easily calculated in this particular fashion. So, now we had this h square average and h average square defined in this particular way. So, we had defined h average as sum over i h i p of h i. So, now let us, this h i we had 1 centimeter by 1 centimeter before. But, let us say we can, we can give h i in a very like 130 centimeter, 130 point 1 centimeter in a continuous manner. So, if h i is a continuous function, so height, so then we, if we plot it, let us say it look like something like this, where every value of h you have a p of h i. For any value of s you take, there is a p of h i. It has a continuous function. In that case, you can write this sum as an integral. So, just by using the idea of, where we learned in this integration, this sum can be written as an integral. So, then in that case, the h average can be written as if h is a continuous function. You can write this as h p of h d h. So, this can be converted to an integral if h is a continuous function. Similarly, similarly if we had h square average can be written as integral h square p of h s d h. So, if h is a continuous function, we can define the averages and square averages in this particular way. In fact, when we did the case of diffusion concentration, we had done precisely this. If you remember, we had defined c tilde, there is something called c tilde of x as c of x by total concentration. So, this is just like we defined today, n of h by n, we defined as p of h. This is exactly the same way we had defined concentration. So, this is, this appeared like a probability. So, here this is probability, we said that this is probability. So, this is also like a probability and we had defined x average and x square average as x c tilde of x d x and x square average as x square c tilde of x d x. So, if you go back to the lecture where we discussed diffusion, we had discussed, we had defined x average and x square average in this particular way. So, the reason for defining this is, as we understand in today's lecture, if you have a distribution. So, c of x or c tilde of x was the probability distribution for concentration. So, the probability of having concentration at a particular distance x. So, what is the problem or the concentration at a particular distance can be defined in some kind of a probability in this particular way and you can define the averages in this way. So, now let us go back to the distribution that we had. So, we had a particular distribution in this particular fashion. So, we had a curve which looks like this. So, now what is the name of this curve which is having in this particular kind of a distribution. So, rough typically most of the things in nature have this bell shaped curve. So, this bell shaped curve or this bell shaped distribution is called normal distribution. So, let us write it. So, the bell shaped curve is called normal distribution. So, many things in nature as it might be the case with height of students or the mark of students or there are many examples that we will come along as we go along. We will discuss as we go along. So, all these examples in all these examples the distribution might look like a bell shaped curve. So, then this distribution is called a normal distribution. What is the mathematical property of this normal distribution? How does it look like? So, the shape of this normal distribution can be written mathematically in this particular form. . So, look at here p of h is equal to a exponential some constant b into h minus h average whole square. So, this is the mathematical formula for a normal distribution where a and b are some constants. So, we will clearly understand in the coming classes what is a and b stands for what is. So, there are some constants. If you wish in a simpler form we can write it e power minus b x square. So, the simplest we can write it as e power minus b x square if you wish in a much more simpler manner. So, this has a particular if this kind of if you have a function of this kind e power minus b x square. So, that is called a Gaussian function. So, if you have a function f of x which is e power minus b x square. So, this is called a Gaussian. So, the normal distribution also has a name called Gaussian distribution and which has a bell shaped curve. Now, what is the meaning of this distribution that we will come when we will discuss in the coming lectures. But, just realize that there are these examples in many examples from nature fall into this category. So, let us look some examples from biology. So, some examples from biology includes n to n distance distribution of long DNA what does this mean. So, let us say you take a let us say you look at the DNA. So, let us say DNA has some particular shape and you ask the question what is the distance of the DNA from one end to the other end. So, this is like a double standard DNA if you wish like it will have all this. I am just showing this double standard DNA as just. So, let us say very long DNA and you can ask the question from this end to this end what is this distance. Let me call this distance as r. So, now let us say that you have let us say that you have the you have in a patchy dish you have a million DNA or Avogadro number of DNA or large amount of DNA. Let us say you have a particular concentration of DNA and imagine that you have this amazing property that you can just take photograph of each of this DNA. You have let us say you have this amazing device where you can take the photograph of this DNA. You freeze the DNA at a particular moment and take the photograph. So, if you do that what do you expect. So, sometimes some DNA will be like this some DNA will be like this some DNA will be like this some DNA will have this shape some other DNA will have this shape some other DNA will have this shape. So, here some other DNA might have this kind of a shape. So, now here the distance between the two ends is very small, here the distance between the two ends is very large, here the distance between the two ends is somewhere in between. So, here the distance between the two ends is this, here you have another distance, here the distance is something else, here the distance between the two answer something else. So, you can just like we did the experiment of measuring height. You can do an experiment of measuring the end to end distance of the DNA and you can write make a histogram and plot it. Then it might look like a Gaussian distribution if you wish. It may look like a Gaussian distribution if you wish. So, it might look something like this, where there can be many of them where the two ends are very close. So, this is r equal to 0 and this is r is r equal to l and this is p of r. So, there can be many of the DNA can have this height, which is very large and very small of them having many the probability that you will find the DNA which is a very short end to end distance. That means, their ends are very close to each other could be large and the probability that you will see their ends far apart could be small. If this is the case, this will this might be look like a normal distribution. So, this is the half of a normal distribution. The other half here, which is a negative part, which is actually meaningless, which we are not plotting. So, this is only one half of the probability distribution of the Gaussian r greater than 0. If you wish, we can plot this is a vector, but we will not come to that now, but you can get such a distribution. This is one half of a Gaussian distribution. That is if you plot e power minus a r square between r equal to 0 and l, this will look like this. So, if you plot this function e power some constant, we define this as b r square for some value of b between 0 and l, this will look like this. So, this is end to end distribution of a long DNA. So, thus look at the slide here. So, this is the first example, end to end distribution of long DNA. We already saw that concentration of diffusing proteins can have a Gaussian distribution. So, when we discuss the concentration in diffusion example, we said that, if you have a tube and if you look at a particular time, how many proteins are here? As a distance, if you go from x equal to 0 to either way, there are large number of proteins at the middle of the tube and a fewer proteins at the end of the tube. So, this might have this kind of a Gaussian like a shape. So, if you plot this, this might also have a shape, which will be like e power minus e power minus some b x square. So, this is another example. You could also think of another example, which is let us say amount of a particular gene expressed in cells. So, let us say, let us imagine that, you can measure the amount of gene expression in cells.  So, you can count, let us say, how much mRNA is produced or how much gene expression has happened. So, then what you might get is something like this. So, let us plot here. Let us plot in this axis. So, let us plot something like this and let us plot some function like this. It should be little more symmetric. So, when I plot it, it does not symmetric. Let us say, it looks like a Gaussian. This is not really like a Gaussian, but it should be very symmetric. Gaussian should be symmetric, but in the case of gene expression, we do not know what should be symmetric or not. But let us say, you have such a curve. So, now here in this axis, we plot amount of protein expressed or it could be called this number of mRNA and amount of protein expressed and how many cells express this amount. So, number of cells. So, amount, let me call this amount as m and this is n of m. So, how many cells expressed very little of this gene? Very few cells. Number is very small. Very few cells amount very little, small amount. Large amount is also expressed like only few number of cells expressed large amount of protein. Maximum number of cells express something intermediate amount of protein. So, if you have this example, this might also look like a normal distribution if you wish, but it will surely have distribution of this roughly this shape. This is the same shape which is at peak somewhere in the middle and dying down to the both ends. So, here this is amount of protein expressed versus number of cells having that particular amount of protein. So, we had many examples in biology. So, to summarize, we learned a few things. What all we did we learned? We learned that probability distribution, the distribution you can show you can present the data in the form of distribution. So, that it makes much more sense like a histogram. So, the distribution is one thing we learned and how do we find averages etcetera from the distribution. So, if you know this n of h, the number of students having height, we can define probability distribution p of h as n of h divided by the total number and we can define averages by sum over i p of h i times h i. We can also define standard deviation in this particular fashion and there are many examples in biology. So, these are the things that we learned today. We learned about distribution, the high distribution and how do we convert this distribution to probability distribution and how do we calculate average and standard deviation from this probability distribution and many examples. So, this is the summary of today's lecture. We will discuss various other distributions and properties of the distributions in the coming lectures and we will discuss many more biological examples. So, with this we will stop today's lecture with this discussion of distribution or introduction of distributions. We will stop today's lecture and you should remember this idea of distribution carefully. Think about this carefully because this is some idea that we will be needing to learn statistics in a better way and this is very useful to present data and to analyze data. So, just introducing the distribution we will stop today's lecture. Thank you.


Hello everybody. I'm Dirk Hollermanns. I'm co-president of the Green European Foundation, and it is really my pleasure to welcome you here at the Green Hub in Glasgow at the start of this very important COP. I don't have to tell you it's really about the future of humanity, and I also want to thank the local Greens here really for this great cooperation. I won't talk about political goals, but I want to emphasize why we as Green European Foundation really thought that this hub here is crucial for the Green family, for the community here. I think this hub is not just a space you can use. We hope it will become a place for all of you the coming two weeks to come together to of course have debates, but also if you had many intensive debates or protest marches to rest to recharge your batteries to come together. We will handle a lot of topics. We will have speakers from academia, of course politicians, people from NGOs, movements, so wide diversity in people, in topics the way we deal with them from classical lectures to really round tables for small groups, and so really to enhance this working well together. There are many crucial questions hanging in the air, and this is the place where we will discuss them. We will have very different topics from eco-feminism, just transition to a future of industry. We will have people from a lot of different backgrounds. There will be a special permanent youth hub, so people looking for capacities to better have a discussion to find the instruments to contribute to the public debate. They can also really find their way here in this hub. There are a lot of new movements in society. There are a lot of organizations that have a message for the politicians, that have a message for the Green politicians, and so also here this hub will be the platform to organize this. Yes, of course it is also exciting for many people to see each other in real life, but I think at the same time it's crucial we organize this hub in a hybrid way. We know that many people, many groups, are not able to come to Glasgow, whether it's for vaccination reasons, whether it's for money reasons or red tape, and so it would really be a missed opportunity just to focus on people in Glasgow. So we open up to the world, and so for me this is not a European hub, this is a global hub, and I'm also very happy a lot of people of the global greens are attending, and so because we are facing here a global challenge for humanity, I think working hybrid, maybe you can also say it's a new normal, but it's crucial and we also have learned the last year that it can work very good. Some years ago, as the Green European Foundation, we defined ourselves as an ecosystem, as part of an ecosystem, and so in an ecosystem the interactions between the parts are crucial, and therefore this hub really wants to intensify these interactions, because with this we build social capital, and social capital is a key part of resilience, and I think this is what we need, and this is what we have to build to common weeks, so I wish you a lot of success in building together resilience for a common future. Thanks a lot.


You are watching people's final moments. Those particular jobs that are totally avoidable are the ones that stick in my mind the most because you could have prevented it. This didn't have to be the scenario.


Myself, Previ Ekhande, working as an assistant professor in Department of Mechanical Engineering at Valjainst of Technology, Sulapur. Today we will see regarding the solving problems related to the planes when the coordinate systems are given. At the end of this session, students will be able to draw the problems of projections of planes when the coordinate systems for the plane are given. Now let us consider the point coordinates are given. Here the example is in which we have to find out the inclination of triangular plane PQR with the vertical plane VP that is a vertical plane and for this the coordinates of the points which are given are PQ and R. Now P for that 3 figures are given in the bracket and these 3 figures are indicating the position of points in the front end top view on the coordinate systems that is X and Y. In this 30 figure indicates the distance in X direction for point P and in Y direction the first point is a 50 mm distance and the second point is 110 distance. Means at 30 mm on X axis, first point is to be completed at 50 mm distance which will give us the position of point in the top view and the second point which is to be located at 110 that is 110 mm that will give us position of point in the front view that is a PF like that the other points can be located. Now we will see how to complete the problem when these 3 coordinates are known to us. Here we have to draw X and Y line X and Y coordinate on that we will be marking the distance. Now here the first point which is given is a point P which we are going to locate on X axis first. Now here on X axis we will locate the point at distance equal to 30 mm and with respect to that then we will complete the position of the point with the 50 and 110 mm distance. Now first point we will complete on this line which is at 30 mm distance and the distance given for first point is 50 mm on Y axis. Now we will locate the point at 50 mm distance which will be the first point and second point is at 110 mm distance. So this point is at 110 mm. So we will have the position of first point pH at this location and that point is to be called as pH because the point is in the top view. Similarly we will have the location of second point that is PF on the 30 mm distance on X axis and the point is to be called as PF because that is a point in the front view. Now the second point which is Q point for that the distance on X axis is 50 mm and the other two distances are given on Y axis that is 20 and 140. So first we will locate the point at 50 mm distance on X axis. So this 50 mm distance on this line will get the position of the points in the front view and top view. Now here the distance on Y axis that is 20 and 140. So 20 will be the first point and second point is 140 mm distance. So this is 140. Now we will have the location of these two points by drawing the line parallel from these positions to the X axis line and the points are to be called as Q with suffix H for the top view point and for the front view point it is to be called as QF. So these are the two points for this Q. Now the third point, third corner that is R which is at distance equal to 90, 70 and 110 that is 100 mm. So on X axis first we will have the location of that point at 90 mm. We will draw the line parallel to Y axis from this 90 mm distance point. Now on this 90 mm distance line we have to locate the points at 70 and 100 mm. So first we will have the location of this at 70 mm distance and the other point will be at 100 mm distance with this we will complete the line in the parallel condition to X axis to obtain the position of RF and RH. So this point is RF and this point is RH. Now once we will complete the three points the next step is to connect these three corners and complete the triangle in the front view and top view where to connect these three points to obtain the triangle in the top view and similarly in the top view in the front view we will have the line connecting these three corners to obtain the position of plane PQR in the front view and top view. Now this is regarding completion of front view and top view when the coordinate systems are given. Now the next step is to obtain the inclination or angle of plane with vertical plane. Now first we will complete the reference line in between these two at certain distance so that that will become XY line or FH line. So that is the reference line FH or we can call that as a XY because F indicates frontal plane the frontal area is on the top side and in the bottom side it is the HRP that is the horizontal reference plane area. We want the angle with vertical plane so we should obtain the edge view of the plane on this side so that the reference line which is to be completed over here will be a F1 line and with respect to that what are the angle for the edge view is obtained that gives us the angle of the plane with vertical plane or frontal reference plane. And for obtaining the edge view the first step is to draw the line parallel in the adjacent view so that we will get the true length of that line in the adjacent front view. So we will draw the line parallel from this P point which will have the intersection at this location so this point will indicate as a M edge. Now we have to project this MH point in the front view so that the true length of that line will be obtained so this point is MF point. Now when we will connect this PF to MF that gives us true length of the line PM and when we will complete the line perpendicular to this true length line that gives us the point view of this point and ultimately we will obtain the edge view on this side. So this is the projector drawn from that and we will complete the line perpendicular to this that gives us the edge view. Now this reference plane which we are completing over here that is the F1 plane and on this side the edge view will be obtained which will have the angle opposite to this F means opposite to vertical plane so that is nothing but the angle made by the plane with vertical plane. So first point we can locate by marking the distance from this side now this distance is 30 millimeter over here or we can have the distance in the compass which can be transferred on this side. So this is a point which is completed on the auxiliary view which is called as a P1 point similarly we have to project the point from this RF and QF, RF and QF from this we will have the completion of projectors and on these projectors we will have the marking of the points R1 and Q1 by transferring the distance from this reference plane. So the distance for this R which we can take in the compass or we can mark the distance 10 millimeter over here on the projector of this so that gives us the position of R point. So that R point is to be denoted as R1 over here similarly we have to locate Q1 point over here by marking the distance of this Q so taking the distance in compass or marking the distance from this side it gives us the location of that point and when we will have the connection of these two points and extending that one it should get the location somewhere here which will be the distance from this reference line. So instead of considering the distance first we will have the extension and later on we will have the cross checking of the point whether that distance is obtained at same point same distance or not. Suppose this is a Q1 point which we have obtained over here at 61 millimeter distance. So this is the edge view which is obtained over here and the edge view makes an angle with vertical plane over here so this angle we can measure at the location R or we can have the extension of this over here and you can measure the angle over here. So when we measure the angle at this location the angle obtained is 50 degrees. So this 50 degrees is the angle of the plane with vertical plane, plane PQR with vertical plane. Here to write the answer as a angle of plane PQR is 50 degrees with vertical got the idea clear regarding obtaining the angle where the angle is to be considered when the angle of the plane is with vertical plane whether it is on front view side or top view side correct you have to obtain that on the front view side. For this the reference second is from the Abaday ML book. Thank you.


Hello, and welcome to the Riff Amonus channel. My name is Pat Schloss, and I strongly believe that you can learn to analyze data to better understand the world around you. Do you believe me? You should! I have found that the best approach to learn how to code is much like how musicians riff off of a theme to make their own music. On this channel, we'll always start with a question about the world around us. We'll answer that question by riffing off on code patterns that were used to answer other questions. Over the past 20 years, I've used this strategy to teach countless people how to analyze their own data. If you would like to develop and improve your own coding chops, please be sure to subscribe to the Riff Amonus channel and join our community.


The cane is a free-read mouth organ indigenous to the people of Laos and northeastern Thailand. It looks similar to a pan flute with rows of long tubes secured together and stacked upon each other. In the middle of the tubes is a wind chest which contains the reeds and serves as a mouthpiece. The instrument is held vertically. It is played by blowing or drawing air through the wind chest and across the reeds. The finished instrument is similar in nature to the Chinese Xiang or the Japanese Shou. Its sound has been compared to a cross between a harmonium, accordion and harmonica. The cane is made of 3,000 years old. The cane is only 200 years old. This is a booby-like cane. The booby-like cane is made of 3,000 years old. The cane is made of 200 years old. It is a Chinese instrument. The cane is made of a Chinese instrument from the province of Sakina Thailand. It is 18 years old. It is the only indigenous person. The booby-like cane is made of 200 years old. It is made of 800 years old. The booby-like cane is made of 200 years old. The booby-like cane is a Chinese instrument. This is a shell. If the booby-like cane is a Chinese instrument, it is the same as a Chinese instrument. It is made of 807. The bell is purified. It means that the people are all the same. We are all the same. About music, we call it can music or bamboo music. So in our country, it's very famous. That is not as hard as how to play. Have to learn first. How to play, but not easy, but not too hard. Some people in the countryside or in the family, man sitting with family, pay for students or for the baby, family for listening to this music. Can music that only so on when they have something special, they have to pay the can. Something special, they have to pay the can. Can come in four types, which are differentiated by the amount of tubes, the six-tube cane hawk, and the 14-tube cane jet, and the 16-tube cane bite, and the 18-tube cane gau. The reed itself is made of thin metal and is symmetrical so that it will vibrate when air is either blown across or drawn through it. For the past 100 years, the metal is typically made from old Laosian coins that are pressed into thin sheets. The cane maker pounds the sheets to the correct thickness using a block of wood into which is set a railroad spike. He then cuts the reed using a small chisel. The traditional cutting surface is an elephant's leg bone. The reed is set into the pipe. At one-fourth the length of the pipe. The placement is at the pressure antinode of the second harmonic, and as a result, the second harmonic is very strong and the fourth harmonic is very weak in the spectrum of the cane. The pipes are made from a specific type of bamboo called miahia, which grows as long as 12 feet and is very thin in diameter. They are cut to the proper length without using any measuring tools. Holes are cut into the side of the tube, which serve to determine the acoustical length of the tube. The reeds are then set into slots in the tube. The reed is partially tuned by adjusting the amount of reed that is in the slot and then fine-tuned by slightly adjusting the length of the tube. Finally, finger holes are burned into the tube using a hot poker. These finger holes destroy the resonance of the tube so the note will not sound unless the finger hole is closed.


What's going on guys? We are back with another episode of the After Hours podcast. This week's going to be something a little different. We are actually, we have Alex back on. He was one of our first episodes and we wanted to kind of get him back on and talk about how he's been in the recent market.  It's been brutal. I hear about it every day and Alex has had some crazy days and then we wanted to kind of hear from him and how he's doing. So kind of just start.   So right now, this is being recorded on July 6, 2021, exactly one year from today. We were at the pandemic, the height of the pandemic. The market was going crazy. The stock market was tanking.  Retirement accounts were going to zero. Everyone was broke. Everyone had no job. All of a sudden, the most lucrative job in the world became the stock market, right? So a year ago today is when we had literally the most amount. I would say it was the peak of the stock market COVID boom. And in 2019, the market was different. In 2020, the market was different. And in 2021, the market was different. You know, what worked in 2020 didn't work in 2019, 2021, etc.  Everything was really easy. On one day, you could buy a stock and it'll go up 500%. The next day, the stock will tank 50%. As long as you make a shitload of money, the short to make a shitload of money. And as long as you pretty much didn't blow up, you could have made money every single day in that market. And that was incredible. I know a lot of people that made a lot of money. I did very well for myself considering just working one hour a day sticking to the MIC process. I think last year, I made a little bit over a million dollars, which is crazy because I only traded one hour a day.  It was crazy. And the reason why I was focused on that is because I started with a $30,000 account and I wanted to prove that every single person that was in our community, if I could do it for one hour a day for $35,000, you could do it the same way and all you have to do is walk away. People don't walk away. Anyway, so while people made a lot of easy money, and here we are at the middle of 2021, and it seems like everything has changed, the first quarter of the year is when cryptocurrency went crazy. GameStop and AMC started running for the first time. And a lot of people that made that easy money in 2020 all of a sudden felt like the king of the world in 2021, the first quarter.  And all of a sudden, maybe mid or February, say March, April time, cryptocurrency crash, GameStop and AMC crash, and all of a sudden the market changed. So this market right now, the current market that we're in, is extremely difficult. The reason why it's extremely difficult at this very moment is there are traps left and right. You think a stock is broken out of nowhere, the zombies. You think the stock is very strong out of nowhere. You get a death handle and stuff. So for me, I found it very difficult in this past couple of weeks to be trading, trading stocks, because I cannot have the conviction and I cannot have the belief that these stocks are going to trade organically, naturally, and follow common price action. Because they're not following common price action, I'm very hesitant and I'm very patient and I'm only trying to look for the best place.  If I could walk away with $1,000 a day or $2,000 a day on a slow day, that's still going to be half a million dollars. So what do you guys think about the market now? I know Harry's killing it. I know James is doing well. So what is your take on it guys? Harry, you can go ahead. Yeah, I think for me, it was just being very, very patient and just making sure that I got a good entry. Because a lot of the times you can get caught up in the chop, especially for me, since I'm logging. And just like today on whatever stock it was that I was talking about with Val, I was definitely going to stuff into $650. I could have probably sorted that if I wanted to. But I mean, as for the most part, it's just really been patient and just sticking to your risk, but also making sure like, because I know that I need to get a good entry in order to feel really, really confident. Like if you get an entry and let's say you're on a seven bucks and automatically you're at 720, 730, right away, you know, like you have a bit of confidence in that trade. So I love trades like that. But when we're potting around like seven, nine, eight, and we're not really bouncing off that level, that's the time for me to be like, okay, this obviously isn't going to work and we need to go lower. And usually I've been like, sometimes I've found myself like looking at stocks, like even on a day like today, where we had like BLIN at like 14. And I was like, guys, I need this at 12, like, I can't be longing this at 14, 14 plus, I need this way, way, way lower. And then, I mean, that's just how I feel like as long as I'm patient, then I'm going to always like do fine in any market. How do you stay patient? What do you, what is it that you do to be able to get these entries?   But if you have the proper entry, that is the difference between walking away profitable or unprofitable.   But for me, I just, I always picture myself like, okay, you lost this way, like a year ago. So why are you, why are you doing that? Like for example, on that burn stock, where I got it at seven bucks, like the old me would be trying to chase, the old me would be trying to get it at like the top of the range, the old me.  That's like, I know that I need to wait, like I literally sit at a chart and I'm like, no, I need to wait, I need to wait, I need to wait. And if it doesn't get there, you don't take the trade. I think that's the most important thing. Yeah, 100%. No, like, if it, if it hits, like, maybe, maybe like, you know, 20 cents, like above where I'm looking at, then I'm like, no, can't get it, like just didn't get to where I wanted it. That's it.  So that's kind of how I feel. Harry, you sent it to me on the phone today. You said there, I forget it was an MRI in or whatever stock you wanted, you were like, I wanted it at X and then I wanted a little bit higher and it would have been okay. But I knew if I started chasing it out of my comfort zone, it would have, you wouldn't have been happy with the trade, even if you won.  I'm just really hard on myself.  You just trade the first hour, right? Harry, after the first hour, you're done. Yeah, I mean, recently, I've been trading the first hour, I've been trading the first two or three hours, I think, because like, sometimes I'll have a line. And it just won't get there in the first hour, because there's just so much commotion and so much action going on. So I'm like, okay, I can wait and watch. And then, but usually, I'd say at around like new niche market time, that's, I'm going to be wrapped up at that time. That makes sense to me, because that's the middle of zombie time. So you're capitalizing on the warning momentum, and you're capitalizing on the zombie. That's awesome, bro. And I'm, I love to see it because, you know, there's a lot of short buys, traders in the room, but whenever I see Harry and Austin agree on something, it's like when me and Val used to agree on short setups, I'm just like, you know, bro, let these fuckers have their fun today, bro. I'll get them tomorrow. That's what I call the Haas indicator.  I'm not even going to look at it for a while. That's the thing, because we want to know what everyone else is thinking, right? Because we have the mindset of a short trader, Harry and Austin have the mindset of a long trader, and knowing as much information as possible, at the end of the day, it's just a bigger edge, man. Yeah. And especially like, I'll read your watch list every single morning or what James or what Tom's looking at, just because I want the information, because there's been times where I've been even in a long trade where, like, I don't know, like a week or two ago, where you said you wanted something at a level and I was in from lower and I noticed that we were having a hard time pushing past that level.  I took it off immediately. Shit, just stuff's lower.  Geez, we're a team, bro. We're a team.  That's sick, man. I'm glad to hear it. What about you, James? How have you been doing in this market? Because I know that you and I have a similar style.  Dude, the reality is I've been very consistent, which is pretty normal for me, which is nice.  I had that sick first red day, and then it was kind of ever since then, I've realized that these traps have been killing us, especially us nail and bail guys for some reason, because we get in and we always tend to have similar spots of entry. We get in, and then the next thing we know, stock's gone. Or it's just we get in at where we always would, and it just goes higher.  And we just say, there's our markets where our style works very, very well. And then there's the markets where we have to take our foot off the gas and kind of just reevaluate. And I think something I made for myself is I've stopped kind of scaling big into any position, like I stopped kind of scaling, like I give myself one to two bullets. But really, I'm only adding to a winner. And that has allowed me that I think I've had like three red days in the past couple months. And it's allowed me to keep my red days like nothing, like dirt small, like nothing, even today I had a trade, you know, I scaled in my 30% and like two bullets. And then I had a break even stop because it was that BSQR. Just once I felt that it was playing games, I put a break even stop. Bro, that break even stop saved you $2 a share, bro. Seriously, it's like, and that's what it's been like.  And I tweeted about today, man.  They can't get their ego out of the way and just say, dude, I need to take the loss and move on.   That's the biggest problem that people face. I don't think it's, I think it's ego, ego definitely matters.  It's like very easy not to do it.   I've seen people fucking, I've seen it all, man. I swear to God, I've seen it all. And the number one thing it comes down to, and we say it too many times, but it's risk management. These guys are not sitting there max size. They're not sitting at max stop. They're not sitting in broker levels. I am a professional trader. I've been trading. I made a million dollars last year. I'm way over a million dollars this year, and I have a max size at the broker level. I have a max loss at the broker level, and I have a time of day that I walk away. So if a millionaire trader is having all these things, someone that's a hundred dollar trader doesn't have any excuse to not have these as well. Yeah, no, definitely agree. And I think like another thing is that I see a lot of people like it's like there's a difference between like being right in the end and like making money, you know, like some people are just trading just to be right.   That's how I see it too, right?  I mean, he's scalping 30 cents, 20 cents, 30 cents, right? Who wants to come in and make money every day? But when you have the people with, oh, well, we have an offering and a fundamental and I'm going to get in at six and hold till four every single day. Those guys are going to learn the hard way, right?  And he's showing you guys that every single trade that he's taking is an opportunity that you could have taken to make money. If he's able to take that trade and make money, that means that you could take that trade and make money. And the thing about bow is in my opinion, bow trades better in a slow market because the channels are easier. So that is something that I try to mention to bow. I'm like, bro, hot markets are not your bread and butter. You are very good in the slow, methodical markets. Whereas for me, bro, slow market, hot market, good market, cold market, as long as I have range, I could pull out money. I can't pull out six figures every day.   So yeah, that was not planned. But I got an Instagram ad about like how you could make your own like, like a plaque and this is my AMC trade. You could input your shares. So I had $30,622 shares at like an average price of $73 and I covered at $50 for a $700,000 win that shows it here. But I have this now as a memory, like my biggest trade power. So I love that.   And I could see you and he's like, yeah, just saying I'm up another 400. So I could tell I literally was in my head. I'm like, this dude's still in it because you're sitting there. You're talking, keep looking back.  I got out of it.    Someone's like AMC is taking, I'm like, I look back, and I'm all of a sudden I'm up another quarter million dollars.  Yeah, I was crying. I was my biggest day ever, bro, $700,000 in one day. And that led up to my biggest week ever, which was a million dollar a week. And the interesting part about that is this. So this year, as of June 6th, I'm up about like 1.6, 1.7 million, which is a lot of money. It's a great amount of money.  So in the market, you never know when that opportunity, when that moment is going to come.  I have nightmares about going to the movie theaters now. But how perfect is that? Like it is exactly how you've kind of taught MIC to trade. You hit you nail and bail every day, you add up gains day after day after day, and then you have those home run days that make your year your month and think about it. Let's say I didn't have that home run day. Nail and bailing, I still cleared 600,000 in here, bro. So I'm on track to make a million by just nail and bailing. And that's the thing, bro. You can make 5 million, you can make 10 million, you can make 20 million, sure. It is possible in the market. We've seen people do it. It is possible.   You are only free when you have free time. Freedom equals free time, right? And for me, if I'm able to trade an hour a day, work on MIC and finish my day early, that is freedom to me. Freedom to me isn't an extra Lambo. Freedom to me isn't a summer house. Freedom to me is being able to leave early, enjoy my day and hey, if I want a day drink, if I want to go to the spa, if I want to go do this, if I want to go do that, you know what, no one can tell me to do anything else because I put in my one hour of the day, I made my $5,000 and I can't literally spend it fast enough. You know? Yeah, 100%. I love that. And I guess this is like a pretty good segue because we just talked about how insane the market was and how much you made.  How do you kind of switch to that? That's a good question, man. That's a good question.  I can make a lot more money with a million dollars in buying power.  It tells me, all right, I got more money in the account. I could risk more money.  But what I've learned based on my personality, based on my personal mentality is the less money I have in my account, the more humble it keeps me because I could not afford to lose a big amount. I'll give you an example. When the AMC trade happened, I was like, bro, it's coming.   So what I did is I wired $200,000 into my trading account. I was like, you know what, my account's 30K. This is the biggest opportunity of the year. 30K is not going to cut it. I need $200,000 in there. I need a million dollars in buying power. Okay. I got my buying power and that's an advance. Someone that's new should not be doing that. I've been doing this for a very long time. So I understand which opportunities require a lot more money. So what I did is I wired in that money.  And they're like, sorry, you could only wire 50K out or 200K out because you got to let the trade settle. So the next day I wired out the rest of the money.  So oftentimes, when all these guys have so much money in their accounts, it makes them very loose. It makes them very lenient, very relaxed. And for me, if my account's $35,000, shit, man, I can't afford to lose more than $10,000 or my account's under PDT. If my account's a quarter of a million, I'm just going to sit here. I'm going to have my hands on my pants.  I'm down 50K. I'm down 100K. I still got a rule. And that's the problem. I did that in the past. And that is what trader maturity is about. You learn the ship after you've been there, done that.  Bro, that's how I feel as well though, because like when we talk about like patience and shit like that, it's like, no, like, I've longed this area before, it didn't work out. I've chased this high before that. You learn from your mistakes. Yeah. And the problem is these mistakes take you five, 10, 15,000 dollars to lose.    And AMC and GameStop took so many motherfuckers out of the game forever.     How do you pack them a loss like that, you know?    That's it. I self get loose.  And for anyone that's struggling right now, for anyone that's not really making money right now, anyone that's maybe bleeding out, you know, my biggest advice to you, what really helps me after a losing day is number one, I size down. So if I'm using 1000 shares max size, on that day, I'm going to be using 500 shares max size. And my goal, bro, I swear to God, it's going to sound crazy is you got to walk away with green by either a dollar or more than just a dollar. It doesn't have to be after commissions. It doesn't have to be whatever.  I could do this because trading, when you lose, you lose your confidence.  So for me, I think my gift as a trader is that I'm able to ignore the wins and ignore the losses. I don't really get too caught up in the highs. I don't really get too caught up in the lows. And that gives me a level of equilibrium, you know. Absolutely. Harry, how do you do it? How do you handle the loss? I don't see you lose too often, but I drink. He drinks out with women. He watches the tape. Well, most of the time, most of the time, see a lot of my losses are, like if I do have a bigger losing day, it's because it's like minus 10 cents, minus 10 cents, minus 10 cents. Yeah, they add up over time. That will be the only time I have a bigger green day. But now, like I've really, really taken a lot of steps to try and like combat like my over trading because like and like it hasn't really been a problem recently, but it was a problem in the past where like either I would get, like I would wait for a line and like it wouldn't quite get there and then I'd see it. So I just start chasing and like that's the wrong way to go about things. And so I guess like what I do is like, like I limit my entries per ticker.  But as far as the long side, like it's more of like, okay, like you're kind of like fishing and then if things work out, like they work out big. So I guess like as far as like losing days, like, I mean, I keep my risk management to like on lower price stocks, like I don't want to be risking more than 20 cents, like that's way too much for me higher price. I don't want to be risking more than 30 cents. That's too much for me too. And so I mean, that's just kind of how I've been been doing it. And as far as like handling it, I'll either like take a small break or I'll just like, like, I'm like, I, like, I, there's a guy who lives down like the road for me who's also in MIC is named Justin Kennedy. And like he records the tape every single day for me. So like year and a half to two to three years worth of tape from this guy. And I'll just watch that.  Like that's literally what I'll do all day is I'll either like my typical day, like, because like Canada has been so like locked down for the past like two, I'd say like not two years, but I'd say for the past year, like I've been putting in the solid like, like maybe like seven, eight hours a day, just like either reading the tape, watching the action, doing something for you're telling me these entries aren't luck is what you're telling me. Well, I mean, yeah, something like that. But I mean, that's what I've kind of been doing. You know, and I mean, that's what's kind of helped me is it's really like putting in the screen time and really just paying close attention to what's going on, you know, losses are funny losses are like funny and trading because I remember you still eat me up so much.  I'm done.  Stupid. And like that was early on and like now it's like almost losing days. I kind of can just laugh about it because I think more traders need to like normalize, like losing like an average green day is like your max loss or like that. Not every loss has to be your max daily loss in the day.   And it's just, it's crazy to me to like, that's why I love trading with all you guys because everyone can have a losing day. Everyone posts about it. Bow, Alex, everybody, and just the way they handle it without going back and like taking it out on the market, taking it out on anyone else. It's impressive. And I think it's, I think it's something that I want to do routine or process after they lose. Like for example, when I lose or when I have a losing day, you know, I shut down everything.  I get myself the biggest chocolate cake I can get.  I sit on, I put on like a nice Avengers movie or like a Marvel movie and I start watching TV. And you know what? All of a sudden, by the time I wake up in the morning, I take myself, you know what? Been here before. And every time that I've been here, I've gone higher. So this is my opportunity to excel again. Because in my opinion, you could tell a lot about yourself and just as a person by how you come back from adversity and how you come back from losses. And I've been in this game long enough to have so many big losses that I keep reminding myself and I keep telling myself our process works. Our process is iron clad. I'm not going to win nine, I'm not going to win 100% of time, but that 90% that I win is going to more than offset that 10% of these losses.  I over-traded. I didn't use stops. I was using my ego. You know, pretty much, bro, like it's been like, I don't know, three days, four days. I'm pretty much 40%, 50%. I made the loss back. So like, doesn't really matter. It doesn't really change anything.   So as long as, like you said, you can keep your losses under control, you don't lose more than a day or a week's worth of work.       I have great amount of money, Bao has a great amount of money. Even if the fucker loses $10,000, he's still pissed. See, we're broke.     If my biggest problem right now is that I have and I'm lost, I'm healthy, my friends are healthy, I'm happy, I have all these amazing things to look forward to, it's not that bad. So try to focus on the positive, try to focus on the good. And remember, come back the next day, be green and you'll be surprised how much your mind suspects. Yeah, I agree. I definitely agree with that 100%. And I think that brings us to the last point as well of like, you know, drawing lines, as far as like tape reading goes, making a plan. Everyone wants to know about tape reading, but I mean, it, I mean, I don't know about you, but that for me, it really goes along with my plan. And it goes along with experience as far as I go, like, I'm not just gonna sit and like, take a- Tape reading is hard, bro. Tape reading is hard because in this day and age, the tape is very extremely manipulated.   So if you're trying to read the tape in this market, jokes on you because it's like hieroglyphics, but the only thing that works 100% ironclad is the lines and technical analysis. So in this market, we should be focusing on technical analysis. Tape reading sure is important, but the tape could be very manipulated. So at this point, focus on technical analysis only. I haven't been using tape at all, to be honest, because I feel like when I get lost in the tape and I maybe that's when I kind of get like maybe a confirmation bias. I'll be like, Oh, you know, there's this is a hidden seller here. There's this where at the end of the day, especially in this market, like you said, the only thing that has been working is my lines where I get in. The hours don't care about the tape, bro.  So if you want to be able to make money, you got to follow big money.   So if they're using technical analysis and they're manipulating the tape, you can't manipulate the tape.  Yeah, I agree. Well, that's it. I mean, I think I think in this environment too, I mean, I feel like people always tend to lean on those skills and they always say, Oh, how do you do this? What do I need to look at the tape? What do I need to learn?  That's really what it comes down to. People love to overcomplicate it, bro.  It's crazy. We're going to do a bit of like, I know there were some people who loved it. Yeah, let's do the audience. Yeah. Oh, yeah. So James texted me a couple. Yeah, I actually have them up right here here. Oh, you have all of them? Yep. Yep. All right. So the first one, we got just like a four right here. How do you stay content with your gains? And what's the best way to deal with greed? That's a good question. That is a good one. Let's start with the first one. How are you content with your gains? I mean, like I said, guys, I don't really focus on the numbers too much. I mean, when I'm trading these days, I look at the P&L after the trade is closed, right? So what I do is I trade the stock, trade the chart, focus on the chart, focus on my entries and focus on my exits. I exit trade, I turn left to look at my P&L.  So that's kind of what helps me. What helps me is I don't really get too caught up in the numbers because the numbers don't matter more than the process matters. If you are focusing on your numbers, you know, you're going to be very emotional.  So for me, I like to trade the chart. I like to focus on my entries, focus on my exit. And then after that is when I look at the money. And additionally, I wire out that money. I put it into my bank account and I let it sit there.  I let it sit there. I let it grow and grow and grow and grow. And the second question, how do you control greed? Well, what helps me control greed is I walk away at zombie times because if not, I'll sit there all day. And because I'm greedy, I try to make a little bit more money. So having a set time a day or a set signal that tells you to walk away is your combat against greed because humans by human nature are greedy motherfuckers. We are greedy creatures. It is in our DNA.    And that's why I walk away every single day. Yeah, I think that's the point. I think that's the point of having that trigger to walk away. And it could be over trading for some people. It could be anything, right? It could be let's say you give back 20% of your profits on day. Have a give back rule. All right, I made $1,000 today.  And that's my punishment. Yeah, that's good. Oh, yeah. We got a couple more here. So do you get performance anxiety while starting the day? Do you get less anxious or how do you get less anxious for trades as you develop? And is there a way around fakeouts or at least a way to get less faked out in trades? You can attack number one first. Yeah, so how do I deal with performance anxiety?  Sure. It does really get to me. It stresses me out a lot. How do I deal with it? I mean, the way that I deal with it is I try to trick my brain and I tell myself that, you know what, even if I have a good day, even if I have a bad day, the members will appreciate me losing money more than me making money, not because they want to see me lose, but because it makes me more human because they can relate to it more and because there's a lesson there. So in the past, I used to get upset.   I mean, beats me. It's really no real strategy. There's no real formula. The only way to avoid fakeouts is to avoid the hot stocks because the hot stocks are the ones that are manipulated.  Yeah, I agree. I agree. Perfect. And then there's just two more. Aside from lines, hard stop and risk management, what are the other key areas any trader should adhere to in every single trade?   That rule, that rule is worth millions and millions and millions dollars that we give away for free. And that's the craziest part about this whole thing is that you could give someone a million dollar strategy to be successful and 99% of the people will not listen.  How many people in the regular stock market are not leaving at zombie times? I am making $1 million by walking away. Walking away is what's keeping that money in my pocket. So the biggest advice, short trader is walk away at $10.30.  Yeah. Yeah, 100%. The golden rod. I just gave it away again, bro. I gave it away. And let's see. The last one we got is how do you guys deal with max losses? How do you set, is it a set number? How did you come up with that number? It should be your day's game. If you're making $500 a day, your max loss should be $500 a day because you're like, all right, I lost $500 on Monday. Tuesday, worst case scenario, I make $250. Wednesday, I make $500 all of a sudden and I'm green.   So your max loss number should be nothing more than a day's worth of work. My current max loss number right now is about $10,000. So $10,000 is what I make pretty much every day. So I don't want to lose more than 10 grand because thank God, if I lose 10 grand, it doesn't mean anything to me.  Yeah, it's perfect. Yeah. Yeah. I think that's, that is all of the Q&A questions. Yeah, man.  Doesn't matter if you're making a week or whatever. The hardest part is finding that process. We made it for everyone. We did it, right? That's the hardest part.   What do you think it is? I think most people don't trust it. I don't think they think that it's like, I don't think they think that it works. I don't think they think that it's as simple as setting your orders and waiting. I think a lot of people have FOMO, a lot of people don't want to miss out on the trade, a lot of people get anxiety, and because of that, they rush their entries, they rush their trades, when if they just waited and followed their plan, they wouldn't be fine. I love it. Harry, you have anything to wrap it up with? Oh, I mean, not really. We got a lot in this little interview.   I'm turning 27, so that means I've been trading for over eight years now. Yeah, I mean, it's just it's someone who's been trading for a while and who's willing to kind of share.   I've been trading for a decade.  Yeah, that's scary. Dude, I mean, I've been trading for three years now and like, I feel like he started yesterday, dude. It's disgusting. I hate it. It's funny, but anyways, Alex, thank you for coming on, man.  So I'm sure this will be one of everyone's favorites. So thank you guys.  No, Bow will come on. Tosh is too busy with the ladies, dude.   All right. Oh, yeah, we got him. We got him.  All right, man. Thank you again, and I'm sure we'll have you back on it soon. Cool. I'll see you guys. See ya.