Sao Borna and welcome back to the YouTube channel to your boy Mr. Ghana baby right here in the kingdom of Eswantini I mean this country is the second smallest country in Africa And I never knew that this country has a lot to offer We are here at the glass factory in Eswantini. You know what we always do? We always travel to discover, learn, educate ourselves and also educate you But as the story goes changing the narratives by telling our own story We always have to find someone who knows more about a glass factory to educate me and you come with me and enjoy this amazing episode Hi Thank you so much Okay, all right Okay Enguena Enguena means crocodile Wow so in Eswantini you guys say in your language Enguena means crocodile. So what is written over there is crocodile glass What come to the crocodile glass in Eswantini? The mountain over there. Yes Beautiful So you can see it from that side from the mountain, from the mining. Yeah, so that is the chain up to here But even the mountain looks like a crocodile That is beautiful Enguena glass, thank you so much We have to go in and educate us So this is Enguena glass Enguena glass was established in 1979 by the swedish people So they came with the idea of recycling all bottles So our all the idea of what? Recycling all bottles old bottles So all our products here as you can see them there are recycled products Yes, we're using all buckles the coca-cola buckles the ginger the mayonnaise buckles and the Tomato buckles tomato sauce buckles all the clear buckles that you can think of we're using all those buckles for Producing our product. We break them into small paddle ships. We put them into the finance They are melted at a temperature of 1,300 degrees Celsius a day. So we use old oil to Furnace for the furnace we use old oil. We use paraffin We use handicrafts and we use electricity and we also have gastronomical panels We're trying to cut the cost of electricity because it consumes a lot of electricity Because it's on Throughout the day we don't switch it off. All right. Yes. So Who is the owner now because you said it was established by the swedish people And who is the owner right now? Is it the same people? No So it was established by the swedish people For two years. They trained the swedish people with the idea. They trained them from there Our government ran it through but unfortunately it has to sit down Production because they couldn't afford to continue. So they closed it down But it was reopened by the fruity John family in 1987 Pretty John family Yeah, no Actually from their from South Africa Basically from the eastern came they came here. It was in Kulu, Gok and their son chess fruity John But unfortunately Kulu passed away. So now it's chess who's running the company Can we see how the presence of the manufacturer? Yes, we go inside and see how it's done Then I'll explain everything to you So we go to switch So this is the old our old measurement that we use That is what I was talking about We take this Why is this So like this are broken bottles that you get from the city Or from anywhere you buy the broken bottles You bring it here So in there It's the panel. It's the melts of broccoli that we get. We call it emulsion class. Okay So the temperature is very very high one thousand three hundred to three sessions. Okay Wow The molten bottle they blow it into a mold it depends on what product They want to make at the moment At that time our production we write it over the board over there. This is what we call juice Everything we write it over the board Then we start making we start working from 10 to 7 in the morning. We end at 4 30 in the afternoon So we have 30 minutes 30 minutes lined and we have 10 minutes So basically the people who work here are all Swans Yes, all of them are Swans All of them are Swans Yes, the training is done here while we work Oh, okay. All right Can we see some of them making the thing? Okay, okay, we can start here Boy is making a wine glass So we call it He shaped and he broke Had this For a wine stalker This one who put it on the top of the stalker. We call it a wine dish From the fire from the ovens we take it out you put them into the different traits like this So when they come in the morning from 10 to 7 they start grinding it and polishing things So they polish Yes, because when it comes out from the oven it comes out wobbly. It doesn't stand properly Oh, okay, because it's happy Yes They have to do it the same day or maybe the same day The same day after this people finish They're gonna It goes into that. They'll do it tomorrow Oh, okay So what we're doing is what we need yesterday Yesterday, okay So they polish something that has been done yesterday They go to the Wow, can we just see their polish process? Yes This wine is Andrea's Cosa This grinding and extra light elephant So this one is a kangaroo It's an elephant kangaroo Elephant what? Kangaroo Oh, okay, wow, it's beautiful This one It's now finished It's now polished because when I took it for the first time It was not that smooth But now, after a few minutes I'm not even gonna say a few seconds Oh, sorry, I'm not even gonna have to say a few minutes But after a few seconds, it's already polished Wow So on this side, on this part We do the polishing of the glasses On this side The sandpaper Yes, that's the sandpaper. We use it for polishing the glasses You see, they're still rough They're still not yet done Yeah I don't have to wait for them to polish it This is the one who does the polishing So is this already polished? It's done already Can I touch it? Yeah, you can touch it But it's still not finished It's still not finished Almost finished Almost done So when it is done They take the clay, they put it in here That's right Then she washes it From the washing We take it to the quality controller On this side That's all the glasses, when it is washed We take it back Now it's finished We have to melt it with a dryer And So now it's a finished product Before you see He's the main guy to finish everything So you see, before It's just fine It's still not yet natural Still not yet finished So now you can take it and melt Because now it's finished It's smooth, you cannot cut it You can't finish it Where do I? What do I do? That's amazing People in this country are so lucky to have their own glass coffee Beautiful We are so proud of when it is washed So this is our finished product Our shop Where we sell our The finished product from the factory We take them through here So this is our animals The pig five animals These are our glasses The drinking wine, the drinking glasses We have a variety of drinking glasses This one You put your wine in here You put your ice in here It doesn't tell you which one Like this And this is our famous glass as well Our whiskey tamela You can use it for juice You can use it for whiskey You can use it for beer This is our new invention So you put your ice in here It doesn't tell you It just keeps your drink cool So this one if you want to buy present I would search that I'll definitely buy it I'm out there I want to say thank you so much for taking us around We really appreciate your time I also appreciate your visit Coming to Switzerland Coming to visit our company I wish you Stay in Switzerland to be very well You are most welcome As well as the people are most friendly people So I wish you stay for long Thank you so much It was nice meeting you You said your name? Maya Thank you so much Thank you so much I hope you guys enjoyed this amazing episode Don't forget to like share And let the world know that Glasses have been made here In S1 TV I am Maya


Don't trust the narratives that you have about yourself, internalize about yourself while you're hurting. So often all there are are the echo of a shaming that you experienced growing up.


In the study I was part of conducting, we explored whether AU employees have any kind of sexist attitudes and whether this causes a problem for gender initiatives in the organisation. We explored this through the standardized questionnaire, the modern sexism scale and that's basically 8 items posing sexist claims and then the employees had to state whether they were in agreement or disagreement with these statements. And 1500 employees answered the full questionnaire and the questionnaire is assessed on a 7-point licket scale so if you score below 3.5 you are non-sexist but if you score above you are sexist and you will express resistance to any kind of gender initiatives in the organisation. Unfortunately the mean for the AU employee was 4.18 indicating that the average AU employee has sexist attitudes and would be resistant to gender equity initiatives of any form. We also found that there was a significant gender difference so that the modern sexism score for male employees was almost 4.6 indicating a high degree of agreement and resistance to gender equity measurements and women scored close to the average AU employee, namely 3.8.


OK. So yesterday, we saw the linear partial differential equations with constant coefficients of the form ut plus b value equal f, where f was a function of t and x. And b was a vector. And we have seen the explicit expression of the initial value problem u equal u bar is at time 0. This is in the half space. And then the regularity was u in c1. So yesterday, we solved this problem, provided that f was c1. OK, also continuous was enough. OK. And also, u bar was sufficiently smooth, c1 also. OK. Let me make just a comment, a geometric comment, on the situation that we have. So assume now that for simplicity, f is equal to 0. So we have here the line, say the time equal to 0. So this is t equal to 0. This is x. OK, so this horizontal now picture is r to the 1 plus n, say.  So your initial condition is defined at time 0. And sorry, this is time. This is time. So this is the x-axis. This is time. And so we have an initial condition u bar defined at time equal to 0. And so this is its graph. So we have a new variable here, so you call it y. OK. And we saw yesterday that at the point here, say, here you have t and x. So x here and t here. At this point here, the value of the solution u was the following. I take the value of u bar here, can you remember? So we have here the vector field b, say. So this is the vector field b. b was transverse to sigma. This was called this sigma time equal to 0. So for instance, in this case, this b is horizontal in the horizontal plane. And the value here, so I have these lines. And the value here at this point, tx here, is exactly the value at this x here when I go backward along the line constructed parallel to b. So you see here, in this picture, the value of the function utx is exactly the same height. Sorry for the picture, it's not perfect. The height, so the value of y, is exactly the value of u bar at this point. OK. And so I can imagine that I have a sort of piece of surface with constant height in the sense that along this segment, the vertical component is constant. So it's like this. I have a curve, and then I have sort of this constant. So what I am constructing here at the end, so given this graph above sigma, I am constructing a piece of surface meeting this graph and continuing a little bit with this property of being constant height. So this graph, of course, this piece of surface, is the graph of the solution u. So this is the graph of u. So I repeat it. So I have any point tx. I look at the value of u bar at this point here, where this point is along the line parallel to b. So I take this point here. Maybe yes, it was called x bar. So I have tx. Then I go to x bar. I look at the value of u at x bar, of u bar at x bar. And then the value of u at tx is exactly the value of u bar at x bar. And so if I draw this segment, I can do this everywhere.  This was the geometric idea of yesterday. And everything was based on a change of variable, say, which was constructed solving the OD x dot equal, say, b. And x of 0, 0, 0 x bar. So everything was based on the solution of this, which gave the trajectories, in this case, lines parallel to b. OK. So the notation yesterday, this was called x bar. But it was also called, at some moment, it was also called maybe pi of tx. This was, I have two notations. Maybe x bar, maybe pi of tx. Doesn't matter. OK. So this is the geometric picture of yesterday. OK. Now, today, let us continue with this sort of PDEs with the linear transport equation with f equal to 0. So homogeneous for the moment, but with non-constant coefficients. With non-constant coefficients. So homogeneous means f equal to 0, but with non-constant coefficients. So and let me generalize a little bit. So now, you have to be careful, because now I change notation as follows. I don't want to distinguish any more time variable from space variable. OK. So I don't want to give a special role now at t. Here you see, it was a special role to t, because, essentially, we had one in front of ut here. OK. And so this system was x dot, more generally, x dot equal 1b, but this allows to identify s with t. But now, I don't want to give a special importance to the t variable. So now, my notation will be x in our n. And that's it. So x in our n corresponds. So x will be x1, xn. And yesterday, our notation was, yesterday, how to pass from one notation to the other was n equal 1 plus n. Huh? And x1 was equal to t. This is yesterday. OK. So now, today, the variable are called x. I don't distinguish between t and other variables. OK. In some sense, this is somehow, at some moment, a more easy notation. OK. Now, let us consider the following operator. So define L of u equal to the sum i from 1 to n bi of x du to the xi, where bi of x in omega. And consider the problem L of u equal to 0 in omega. Open set contained in our n, where bi, bi are, say, c1 functions. Bi are c1 in omega. For any i, now f is not 0. Now f is 0. And bi is for any i equal 1, capital N. OK? So now, my PD is this equal to 0. What is the relation between the notation of yesterday? So yesterday, yesterday was ut plus b dot grad u equal to 0. So this means that notation of yesterday becomes what? Become this when I choose b1 of x. First of all, x is actually t and x. And then b1 of x is equal to 1. And b2 bn of x is the b of yesterday, b of yesterday. OK, so simply, if you put b1 equal to 1, if you think about the first coordinate x1 equal to t, then you end up with ut here. And then plus b dot grad u provided that b2 bn, you identified it with a constant vector b. So it's just a change of notation. This is more general, clearly. Change of notation. This is more general. OK, so let us concentrate on this new notation. So forget the time now. So this is, of course, a first order PD because you have only just one derivative here. It is linear. This is clear. The coefficients now are the bi. They are non-constant because they depend on x. Non-constant coefficients. I assume bi to be c1. And this is a notation. It's just to remember linear operator L-like linear applied to a function u. So the problem is to find the solution of what? So now if I want to reason like yesterday, I have to give an hypersurface sigma and an initial condition. So now this hypersurface, yes, it was very special because we had time in mind. And this was time equal to 0. So it was like an initial condition. But now there is no time here. So how to assign now a boundary condition? We do this. So let sigma be a c1 hypersurface. Yesterday, omega was the half space. So yesterday, omega was the half space. This was yesterday. And yesterday, sigma was t equal to 0. Today, sigma is instead of a hyperplane. It's just a hypersurface. Maybe it is curved, for instance. It's not flat in general. And it's of class c1. And for simplicity, let me assume that without boundary. And then let u bar, maybe the notation was let u bar be a given function on sigma of class c1. So this is slightly more general than what we have said yesterday. This is the setting. The question is, what's the meaning of a surface without boundary? Do you know what is the boundary of a hypersurface? Maybe it's not the case now how to define it. But let me give you some example. For instance, if you have a piece of plane, just a piece of plane, just a sheet of paper in R3. So you have a sheet of paper inside R3. Then the sheet of paper is, of course, a surface. But the boundary of this sheet of paper is just the curve, which is, say, on the border. On the other hand, if the sheet of paper is infinite, it is a plane, then there is no boundary. In this sense, I'm thinking about the generalization of an infinite plane. So an infinite surface may be a little bit curved, but without border. I don't want to define now what is exactly the boundary of a surface, because I need some tools. But so you have to think about this. You have, say, this is sigma, and this is, say, omega, and this is sigma. And I want to work, say, here in omega intersection sigma. So the problem is, more precisely, problem, try to solve the following PDE, say, in omega, or maybe in omega minus sigma, for instance. So say here. And then u sufficiently smooth, say, c1 of omega. And then u equal u bar on omega intersection sigma.  Then you want to solve the PDE, say, here, out of the surface. Of course, here, if you think about time, this is space time, time space. Mm? Omega, now, if you want to remember time, if you like, it's not necessary. But if you like, then we are in time space here. Yesterday, indeed, the situation was this. This was time. This was space. And this was sigma. And omega, say, was the half space. So maybe this is asking too much, maybe. So we will see that we can maybe try to solve the problem not exactly on the wall, omega, but maybe in a strip, in a neighborhood of sigma. Maybe we can hope to find the solution in a neighborhood, not everywhere. Now we will see why. Anyway, this is the problem, generalization of yesterday. So, however, yesterday, there was a, yes, yeah, you're right. Exactly, thank you. So maybe we can do, thank you. Yeah, also, yesterday, you're right. Thank you, omega bar, say, intersection of sigma. And then, sorry, the other question was, yes, maybe yesterday we said, you see one up to the boundary, right? So you see, now, you is, now, because, well, because you are thinking about the half space, but on the other hand, you see yesterday, we construct a solution for positive time. But indeed, we could get the solution also for negative times. So maybe the better is to think about the whole space equal to omega, and now sigma is contained in omega. And I don't need this, OK? Yes, because physically, it's meaningful when t is time, maybe it is reasonable to look for a solution in the future. And so we think about omega half space. But on the other hand, as you see the proof, we can go also backward. So maybe omega is the whole space, if you wish. And then sigma is contained in omega, OK? So sigma, if you want, we can change this. So let me put it like this on sigma. And sigma is contained in omega. So we have a sigma. Now, the new sigma is this. So now, without boundary in omega. So I don't have to worry about these two points. This is my sigma, omega is open. And we are exact in this picture, OK? So now, what I was saying is that yesterday, we observed that one important condition was that the vector field 1b, b was constant. But the vector field 1b was transverse to sigma. Remember, we had the component that was 1. So this was 1 and this was b. And this vector field was transverse to sigma, exactly because of this component 1b. Transverse means that this is non-tangent to sigma. It's not like this. And this was very important for solving our problem. Can you remember? OK. Now, what could be the new condition now that it is natural to impose? So we cannot hope to solve this if we do not impose a sort of transversality. Because this problem generalize what we have said yesterday. And it was clear from yesterday that we need that 1b was transverse to sigma. But here, it is not written anything like that. So we need the transversality condition between the vector field by bi of x now and sigma, OK? So need c yesterday, some transversality condition between the vector field b of x and sigma. And we have to now give this notion now. Maybe I repeat. Yesterday, this was 1b and this was t equal to 0. And exactly because of this component equal to 1, these were transverse, OK? So which is the natural new assumption that we have to do? The natural assumption that we have to do now is we need some definition. So definition. So let x in omega define the set. Let me call it this way. So I take a point in omega. So b of x is well defined because b is defined in omega. And then I define the set of, say, characteristic vectors at x for the operator L, set of characteristic vectors for L at x. As follows, it is a non-zero vector, which is orthogonal to the vector field b of x. So you have a vector field at the point x. You have a vector. And then you take the orthogonal vectors to this, OK? Definition. So this is definition 1, definition 2. So let sigma be a surface of class c, hyper surface, hyper surface of class c 1 as before. We say that sigma is characteristic for the operator L at the point x on sigma if class c 1, c 1. c 1 because I need to talk about the tangent space or the normal vector, if you want. So there should be not coordinates on the surface or casps or something strange like that, OK? So we say, so this is sigma inside omega, this. And I have a point x on sigma. And then I say that sigma is characteristic for the operator L at x if the normal, one of the two, unit normal to sigma at x, where this is a unit normal to sigma at x. So it is simply this. So you have the point x, OK? Then you have the tangent space to sigma at x. Let me denote it by, this is the tangent space. Let me denote it by tan x sigma. This is a hyper plane. And then I have one of the two unit normals, new sigma, this or the opposite. Or this or this, one of the two. It's not important, it's one of the two. So this is new sigma, new sigma. So if this vector, this unit vector, new sigma, say, is a characteristic vector in this sense. So this means that new sigma, that is the scalar product between new sigma at x and bx must be equal to 0, OK? New sigma x dot bx is equal to 0. That is, a new sigma is orthogonal to bx. Or if you want, equivalently, bx is tangent to sigma. So if your vector field here, b, belongs to the tangent space. Say bx is like this, say, this is bx. Then you say that this x is characteristic, OK? Then, definition 3, we say that sigma is characteristic for l, that sigma is characteristic for the operator l, for l. If for any x into sigma, sigma is characteristic at x. So at each point of sigma, b of x is tangent to sigma, simply. If this happens, at all points of sigma, OK? Which is, by the way, the worst situation. Because remember, what we have said yesterday, this is sigma. Vector field was 1b. And the vector field was never tangent to sigma. Was never tangent to sigma. So this condition is bad. And we want to avoid it, OK? So we would say that sigma is non-characteristic, finally. So we say that sigma is non-characteristic for l at x. If this condition is not true, if new sigma of x does not belong to x at l, that is bx is not tangent to sigma at x. Is not tangent to sigma at x. And finally, we say that sigma is non-characteristic for l. If it is non-characteristic for l at any x. Yes. Ah, yes. The l, the question is, you don't see the l on the right hand side. Well, l is identified by the vector field. Because your linear operator l was this. Uniquely identified, you see. Because l was the sum from 1 to n of bi of x du over dxi. So once you know bi, you know the operator l. And this is l. So if you have no l, you have b. So this l is hidden here, OK? So what it is important to remember at the end, OK? So we say that sigma is non-characteristic at x, a point-wise definition. But then we say that sigma is non-characteristic for l. If it at any point x, it is non-characteristic for l. So, and this is what we want. So we continue now our analysis of the problem. So the new assumption that we do is the following. So assume to continue our analysis, assume sigma non-characteristic for l. That is, for any x in sigma, bx is non-tangent, does not belong to the tangent space. So this is now our assumption, OK? So this is an assumption relating sigma and the operator l. Or in other words, sigma and the vector of it b. So this is our assumption. Previous case yesterday, b of x was 1b, with the notation of yesterday, 1b. Always non-tangent to sigma. So it is clear now that this assumption generalizes the transversality condition that we observed yesterday. So let me make an example now. So let me make an example. Assume n equal to 2. And assume that l of u is equal to u over the x1. And assume that sigma is equal to, sigma is equal to, say, x2 is equal to 0. So an omega is equal to r2. So this is x1. This is x2. And we have this operator. So b of x now is simply 1, 0. Is it clear that b of x is equal to 1, 0? Because it is 1 times this plus 0 times the derivative with respect to x2. So b of x is this at any point. So this is sigma. And b of x is 1, 0, which is therefore tangent at each point. At each point of sigma, b of x is clearly tangent to sigma. So it is characteristic at any x. So sigma actually is characteristic for, now assume that I want to solve l of u equal to 0. And u in r2, say, and u equal u bar on sigma. So what I find here? Well, I find the following. If I find the solution, so I find that on sigma, if the solution is smooth, say on sigma, the u bar over the x1 must be equal to 0. Because this is the u over the x1 equal to 0, u bar here. And therefore, the derivative of u bar along x1 is equal to 0. But this is not reasonable. Unreasonable? Unreasonable. Why? Because u bar is your initial condition. And u bar is any initial condition of class c1. There is no reason for which u bar must have derivative equal to 0. No reason for this. u bar is any smooth function. u bar is given in c1, but nothing else. u bar has no condition on its derivative. u bar is given. u bar is given. So in other words, if you have understood this, from now on, it will be clear why we always assume that sigma is non-characteristic. So the question is, do you want sigma characteristic only that sum would be enough, say, or could you allow, say, sigma to be non-characteristic, unless, say, one point or two points? This is the question. No. To be as simple as possible, I will assume that sigma is non-characteristic at any point. This is to make things simpler in this one first-order PD situation. This is the simplest case. So let me comment once more, because this is important to understand. So in other words, we shall assume sigma non-characteristic for L, because otherwise, if sigma, say, is characteristic, at least characteristic in a neighborhood of x and sigma, we would assign a condition on the tangential derivative of your bar, a tangential derivative of your bar, which is unreasonable, which is not reasonable. In the previous example, the tangential derivative was the derivative along the direction x1, which was tangential to sigma. Actually, it was the unique direction of sigma. And we were asking for this to be true, which is not reasonable. So more generally, if sigma is any hyper-surface of c1, asking sigma to be characteristic in a neighborhood of a point x in sigma would mean assigning the tangential derivative of your bar along the vector field b to be equal to something for instance 0, which is not reasonable. So from now on, we will always assume this. Now, the experience of yesterday was going to consider, now consider the following system of oddies, ordinary differential equations. x dot equal b of x. x of 0 equals some x bar into sigma. Now, if you want to be really very, very precise, locally, you have the following picture. This is sigma. This is sigma. Then you have the vector field b of x, which is transverse. Say, for instance, is like this. Smooth. This is b of x. And then you have assigned the starting time, 0, and the starting point x bar. So x bar, what is exact x bar? So to be precise, you should. Since now sigma is a manifold, then you have to parametrize it locally. So you have to find sort of open set here and the parametrization, local parametrization. Let me call this, say, phi. Let me call the parameters here sigma. So phi is a local parametrization, local parametrization of sigma, of sigma. So taking some open set in r to the n minus 1 space of parameters, regularly into rn, and phi of sigma is, say, x bar. So this sigma is going exactly to this x bar. This is a way to describe your sigma. So locally, it is the image through a map, an embedding map, phi. And so any point x bar is coming from one parameter sigma through the embedding. OK, b of x is here. So this is rn. And so x bar, if you want, is now phi of sigma. So now consider the system of ODEs. Fine. Our problem, remember, let me write it here, is just the sum from 1 to n bi of x du over dx i equal to 0. This is a PDE. This is a system of ODEs. How many of these are these? And capital N, OK? Capital N of these, the equations. Because capital X is going into rn, OK? Yesterday, the system, remember, was yesterday was x dot equal 1b yesterday. And yesterday, this allowed to identify the s with time. And so at the end, what was interesting was to study just only the last n components equal to b. This was yesterday, OK? So now, which is the difference between yesterday and today? Yesterday was x dot equal to 1b, where b was constant vector. And now, we have x dot equal b of x. Where is the difference? Well, the difference is that now, well, this is really the E. I mean, it's not so easy to solve it. Yesterday, the solution was explicit. And the trajectories were lines, remember? Yesterday, the important fact was that we found a solution. The trajectory of the ODEs were flat, were lines. Today, there is no reason to say that now, the solutions to these are lines. Because the derivative is not constant anymore. Yesterday was a constant vector. Today, it is not constant. This is the first remark. So today, if we are able to find the solution, the trajectories are not lines in general. The second point that we have to be sure that we have a solution to this system of ODEs. So now, you have to remember the existence and uniqueness and the dependence on initial condition of ODEs. Maybe you already know this. So let me quickly say that. So let me call this point problem 1. So there is a theorem. And if you want to look at the proof for this, one possible reference, but very difficult, however. But anyway, I give you a reference for this. These lectures on nonlinear hyperbolic equations. Well, this is a theorem on ODEs. You can find it in several books. This is a possible book. Please keep in mind, it is a very, very difficult book. So you're not supposed to know it at all. Just if you are interested in, look at the first two or three or four pages. If you like. So the theorem says that theorem, so let me write here, theorem, so there exists a unique solution. Let me call it x, depending on s, which is the parameter to which I'm differentiating as usual. And then also, depending on the initial condition, x bar. Or if you want, if you prefer sigma. Since x bar is nothing else, any unique image of some parameter, sigma, I can make this depending on s or on x bar or sigma as you wish, as you prefer. Yesterday, we had this x bar, and this is a copy of our n minus 1. So the capital phi yesterday was simply, so what is the situation of yesterday? Who is capital phi of yesterday? Well, capital phi is simply x bar into 0x bar. So there is really an identification between x bar and sigma, which is still x bar. So really, so when this is flat, this is a plane, and it was a horizontal plane at level 0, height 0, then the phi was simply this phi, so trivial embedding. And so yesterday, we put the dependence on x bar because it was reasonable. Today, if you want, maybe we can consider dependence on sigma or x bar as you prefer. Let me write dependence on sigma. There exists a unique solution, x of s and sigma, for s less than or equal than some delta. So there exists delta. So there exists delta positive such that there exists a unique solution for short times s of your system of ODE's. So this is a local in time existence. Now, s is time, OK? And since you don't know, you know that B is C1, but you don't know, say, that B has some other magic properties like global lip sheets, for instance. So what you know at the moment is that this has a solution, unique, but just for some time, for some amount of time, but not for all times. Yesterday, it was for all times because the line was globally for any s, for any s. But today, we are not sure about this. We can only say that for some positive time, delta, we have a solution, unique. This is, of course, because the vector field B is of class C1. If B is not smooth like C1, then it is much more difficult. Not only this, so this is the first difference with respect to yesterday. Yesterday, the solution was global and was a line. Today, the solution is not necessarily a line, it's just a curve. Actually, which curve? Well, it's the integral curve of this vector field. You see, if I want to draw the solution for short time, what I have to do is exactly to take those curves such that B is tangent to that curve. So if I draw the vector field B in a neighborhood here, the curves solution to this are exactly the so-called integral curve, meaning that at each point of the curve, B is tangent to the curve, like this. These are the trajectories, is OK? Yesterday, of course, B was a constant vector, and the trajectory was the line, which is tangent to the constant vector. Is it OK? Are there other questions? Problems? Is it clear? So please feel free to ask if there is something which is not clear. I'm making, I'm happy to repeat. So now I'm drawing the integral curves, which are the solution of our system of ODEs. You see? We have a solution like this, OK? So these are called integral curves, integral curves of B. And I repeat, it means that at any point along the curve, B is tangent. This is B, et cetera. You see, what is a big difference now? Well, first of all, we have existence, but just for a fixed x-bar. What happens if I change x-bar to the existence time, delta? What happens? Well, because delta depends on x-bar. So if I am here, say I live for one second. But if I am here, maybe I live for 1 half second. And if I live for 10 seconds, I don't know. The dependence now, the time of life of the solution depends on the previously chosen x-bar. Well, it is possible to show, say at least in this local compact situation, say in a piece of sigma, that delta is uniform with respect to the choice to x-bar. So if I confine myself in a piece, compact piece of sigma, I can say that the solution lives for delta, but for all x-bar. So at any point now, I am sure that my solution exists for delta. And delta is not depending on the point that I am choosing. This means exactly uniform delta. So delta is not going to 0 when I move x-bar. Then, moreover, it is also possible to prove that the dependence of x from s and x-bar is smoothy c1. Actually, it is Lipschitz also with respect to this. So an x is c1, say, well, in the book that I put there, you find also the estimate which says that x actually depends in a Lipschitz way with respect to sigma. And the Lipschitz constant is related to the local Lipschitz constant b. This is not so important at the moment. So we know that this dependence is smooth, say, sufficiently smooth, at least. And next, there is another difference. You see, what happens here? OK, maybe the solution is like this. So it may happen that these trajectories, at some moment, meet together. Yesterday, our trajectories was this. And there were two interesting properties. First of all, that the trajectory was defined for all times. It's a line. Second of all, that this situation does not happen. Say like this. This was not the case of yesterday, because they were parallel, of course. But you see, if you think that what we are trying to do is to define a solution here as the value of your bar here, this is potentially very, very dangerous. Because if two of these objects meet at the point for positive time, then I don't know which kind of value I have to assign to the solution you, if the value of your bar here for the value of your bar here. So this is a very dangerous situation. And it is possible to prove that if delta is sufficiently small, this doesn't happen for delta sufficiently small. So for delta sufficiently small, not only we have existence of a solution, smooth dependence with respect to the initial condition, but we can also say that if delta is sufficiently small, the integral lines say delta sufficiently small implies that integral curves do not intersect. So we are exactly in a sort of situation like this. Here we have sigma. Here we have sigma. Then we are filling a neighborhood of sigma with integral curves, with curves which do not meet each other. And they fill a neighborhood everywhere of sigma. So we are filling a neighborhood of sigma with these curves. Sorry for the picture. It's not perfect like this. So what are these pictures? So this is simply the curve that at s, it associates x of s given that sigma. So if sigma corresponds to this point, so sigma is here. Sigma is mapped to this point here. Then this piece of curve is the image of this map. This is our situation. And finally, this gives us exactly what we like, because then by construction, the solution u at x is equal to u bar x. So now I have to say to make rigorous what I want to say is to say that now there is no f. The equation is homogeneous. So the value of the solution here, say, the value of the solution here, x, will be the value of u bar here. And what is here? Well, I have to take the integral curve passing to this point x, starting from a unique other point on sigma and solving the PDE. So to be more precise, before saying this, I have to observe that there is a change of variable. There is a map from. So let me call this u and neighborhood in Rn minus 1. So there is a map from minus delta delta times u into a neighborhood of sigma. So let me call this object here. This is n, neighborhood of sigma. And the map is the following. I associate to any s and any sigma here the solution x at time s starting from the point phi of sigma. So let me repeat it. I have the space of parameters, capital U, in Rn minus 1. Then I have some time delta. So I can think about this. Fix time s, fix a parameter sigma. Sigma is here. Then I have phi of sigma x bar is here. x bar equal to phi of sigma. And then I can consider the solution of my PDE starting from this point x bar for time s. And this gives me a diffeomorphism between this big rectangle and this neighborhood n by construction. This diffeomorphism between this and its image that I'm called n. I'm calling n the image of this. So given s and l and sigma, I can find a unique point. Conversely, this is invertible. So I can have the inverse object. Now I have a map from the neighborhood n into minus delta, delta times U. So I am the inverse map. The map is invertible with the inverse of class C1. And so at any x, I associate simply s of x and sigma of x. Of course, this diffeomorphism is not always explicit. But this inverse diffeomorphism is, it exists. And so my solution U of x will be exactly the solution U bar starting from phi of sigma of x. This is the solution that we have constructed. U bar of phi of sigma of x. So I remember, I recall once more, given any point x in this neighborhood n, what do I do? Well, this x corresponds to a point s and sigma in this rectangle, delta minus delta. So there is a point s and sigma here going to this point here. So the solution U out of sigma in n here is what? Is the initial condition U bar where U bar, sorry, here, it is even easier, sorry, is even easier, is the initial condition phi of sigma. So it is the initial condition U bar where here, what is this point here? Well, so the point x is going through this, so it's exactly this point here. So this is the parameter. The parameter is mapped to the embedding to this point, exactly the base point, the projection. And so U bar here, so let me recall once more. So I have a point x in the neighborhood. And what do I have to do? Well, I have to find exactly that curve which pass through x of our family. And then this curve which pass through x meets sigma in some point. And then I take U bar at this point. That's exactly what I want to do. So this is x. So this x is coming from one pair s sigma here. OK? In particular, sigma is mapped to the embedding to this point here. This is phi of sigma. And so if I take the solution of our system of these, it starts from here and pass through this x and fill a little bit. And so our U at x will be the value of the initial condition at this projection point x bar or phi of sigma. OK? So what is really important here is the invertibility of this map s sigma into the trajectory solution of the system of all these. OK? Starting from this physical point, phi of sigma leaving for some time. OK? So you see it's a little bit implicit. Anyway, now home exercise maybe would be generalize this to the problem, say, sum from 1 to n b i of x b over dx i of u x equal sum given function f given, say, c 1 of omega given. So the exercise consists in trying to find the solution with the method of characteristics. Yesterday, we studied this problem. But in the special situation, yesterday, remember, we have studied this problem, but with p i u of x equal 1 b. And we found that the solution was the u bar at the previous time, say, but then there was an integral between 0 and t of a function depending on f properly with proper variables. So and here is the same, but you have to try to find to reconstruct the solution. OK? Now, our linear operator that we have studied up to now, you see, is not, I mean, even if this PD is one of the simplest, the solution, a local solution, is not so easy to find, as you have seen. For me, it's not so easy, in my opinion. And of course, a problem is due to the regular, the smoothness of bi. Now, it would be very interesting to study the problem when bi is less smooth than c1, but this becomes quickly too difficult. So we will confine ourselves to this. So what can we do in order to make the problem more general? Well, it's to consider now the following PD instead of weakening the regularity, the smoothness of the coefficients. Let's still take c1, but consider a little bit more general problem equal to f, u, x, x. So now, I have given not only b as before, but I have given also a function c, c1 omega, and f. So this is still a linear operator. There is a new piece, the so-called zero-order piece, 0y, because this piece depends linearly on u, but there are no derivatives. So it's called zero-order term. And so if we define, again, l of u equal to sum, as before, bi of x bi u of u over dx i, we are interested in studying the following problem. L of u equal f minus c times u. So this is usual in PDs. You isolate the principal part of the operator, in some sense. Principal meaning the part where you have the highest derivatives. So here, the highest derivatives are first-order. Here, there are no derivatives. So I isolate this part, and then I consider this problem. And again, we want to couple this with an initial condition. So sigma, non-characteristic for l, for the principal part of the PD, as before, exactly the same definition.  So this is what we want. So slowly, we are coming to more and more difficult first-order PD. We started from constant coefficients and homogeneous, and independent of u without this term. Then we passed constant coefficients, but with f, non-homogeneous. Then we passed to non-constant coefficient and with this equal to 0. Then we passed to non-constant. This is an exercise now for you. Exercise, non-constant coefficients with the non-homogeneous, non-homogeneity. And finally, more generally, any first-order linear, first-order PD with non-constant coefficients, so now there is a new term here. And this is not so, I mean, it's an important generalization. It's not so immediate. So now we want still to use the method of characteristics. So still we want to construct a local solution, local meaning in a neighborhood of sigma, just only in a neighborhood. But there is this more difficult, this new part. What do we do? So which is now the system of characteristics that we have to consider? Do you have suggestions for this? We have to find the correct system of oddies in order to solve this problem. So yesterday I think that we saw something. So you have to want to make an exponential change of variable, for instance, like, ah, this is maybe a good, if you are able to change, so his suggestion, he says, why don't we try to change you into a new variable, let's say v of x, which is sort of, is equal to, say, e to some coefficient times u of x or something like that, a transformation of u into some new v, so that v satisfies something without this 0 or the 10. Well, I think that, well, if you try to do this, if it is possible as a home exercise and try to find the transformation, OK? This would be, this, if this can be done, would be interesting so that you use the previous case to find v and then you invert your transformation and you go back to u, if it is possible. But I want now to, not to do such a sort of trick, because at the end I want to find out a system of oddies, which will be even more general, applyable to more general PDs, more general than this. What I would like to go, what I would like to study would be more general than this, sort going back, now I write it because this is classical, what is a very interesting equation is this. And so for this I still have to find a system of characteristics, which probably is suggested by this problem and which is the difference between this and this and this now is not linear anymore. It's not linear in you because you have the product u, ux. So I don't use the, I don't want to consider the trick because I want to find a system of characteristics that I hope to be applyable also in some nonlinear case, like this. And so, so suggestion on what could be, please if you have some suggestion on what could be now the system of oddies to consider. Remember that yesterday we wrote at some moment a system into in x and also in y. Can you remember? So I think that still we can try x dot equal b of x. And this x of 0 equals sum x bar equal phi of c. This is, I think it's somehow reasonable. But then this is not enough. What could be another equation that we have to couple to this, remembering the discussion of yesterday? At some moment we coupled this with another equation, y dot equal. It was yesterday was f of capital X, right? This was yesterday. And we observed the following. Well, this is uncoupled with respect to this. Namely, first I solve this. I find x, then I put here x, and I find y. This was yesterday. And yesterday this term was not present. Now, what is the reasonable modification of that oddie minus c of capital X times what? Times y. Initial condition y of 0 equal u bar of x bar. Do we agree? It is somehow reasonable to think about to consider this. Now, you see, which is the difference with respect to yesterday? Now these are really somehow coupled together, in some sense. Not so coupled, but I mean still more precisely. Yesterday, given capital X, I can simply integrate and find y. This was yesterday. Today is not so easy, not so difficult, however, because I can find capital X here. And then I have an oddie given capital X. Now this is a first-order oddie, linear first-order oddie in y. It's not just an integration problem. I have to solve another oddie. It is linear in y. So still, this seems doable. Still, I can first solve this and then this somehow, OK? So well, time is over. We will continue from the analysis of this linear first-order oddie. And maybe I can give you a preliminary exercise which is, by the way, maybe if you are not able to do this exercise, don't worry, because still we have to discuss a little bit this. But exercise, and we will do this exercise in the next lecture. So we will do this in class. So the exercise, so consider n equal to 3 and consider the following problem. First-order solve x1, sorry, du over dx1 plus 2, x2 du over dx2 plus du over dx3 equal 3 times u. So it is exactly in this form with f equal to 0 and c constant equal to minus 3 u equal u bar of x1 and x2. Now the notation is clear, because sigma on sigma, which is x3 equal to 0. So try to find the solution to this, OK? Check that the operator is, that the surface sigma is non-characteristic for the operator, of course. Check all assumptions, smoothness of coefficients, smoothness of sigma, smoothness of everything.  The solution that you have to find is the solution that you have to find is u of x must be equal to u bar of x1 e to the minus x3 comma x2 e to the minus 2 x3. If I'm not wrong, the solution should be this one. So u bar is the initial condition given u bar c1. You see, then you have u bar at some points and then there is also this exponent exponential e to the 3 x3 if I'm not wrong, OK?


Dear students, in this topic, we shall discuss the role of genes and environment in the development of behavior of an animal. The genes of an individual provide the instructions for the development of behavior. However, the expression of genes is influenced by many environmental factors. So, an animal's behavior develops by a complex interaction between genetic and environmental factors. Now we shall discuss the environmental factors involved in behavior development. For example, the environment of fertilized egg and animal's diet, animal's social interactions from which it can gain experience or learn something, the environment's conditions in animal's surrounding, temperature, water availability, food availability. These factors influence the development of behaviors. The behavioral ecologists or ethologists use two methods to determine the extent of environment's effect on the expression of behavioral genes. These two methods include cross fostering study and twin studies. In cross fostering studies, young ones of one species are nurtured by the adults of another species. As a result, the changes in the offspring's behavior are determined. The extent of these changes is a measure of how physical environment influences behavior. In cross fostering studies, some mouse species have behavioral differences that suit them well. Dear students, Twin studies are also carried out to determine the effect of genes and environment on behavioral development. Behaviors of identical twins are compared which are raised apart with those twins which are raised together in the same household. Twin studies are carried out on human and human's traits such as schizophrenia, anxiety disorders and alcoholism. When twin studies are carried out, they reveal the effect of different environments on the expression of the disorder. In the development of these disorders in humans proves the contribution of both environmental and genetic factors.


what we're saying is that when we met with them, they said to us, okay, how much of that portion that's left is actually due to the girls. And we said to them, we told them what the amount was, and they said, okay, they'll send that over to us in advance of finalizing all the integrity checks and the documentation. So even after we get that amount, there's still an amount that's going to be due to us. But that is the amount for JFF. And that is really the only amount that we retain because we would have paid everything installed. Has FIFA given a timeline as to when the JFF will get that amount so it can be started with the girls? Yeah, we're hoping that we will settle everything by Friday. In fact, what we've done, we've done all the processing in terms of the banking information. So the only thing we're waiting on is to get the funds in our account, and then we just push the button. And basically it will be done at that time.


All right morning. So everybody ready for their MBA from all the notes from Christie's talk? Did you take notes during Christie's talk? Okay, because that was some good stuff. I think I have probably the worst title just because it's really really really really really long. But and we're not going to diagram it. So it's Managing clients increasing your value thinking about long term Or as I like to call it sort of in the shorthand how to level up as a freelancer Who here is a freelancer? Outstanding. Okay, those who didn't raise your hands. Were you freelancers? A few more okay for those who didn't raise their hands. What do you do? No, I mean just shout out seriously. What do you do? Are we products agencies? hosting companies Okay Business owners, okay, excellent Business owners should be up here. I Think we need to do that. Okay Anybody bowl? Anybody okay. I see some hands doing this.  Does anybody use those other than me? Okay up there. Yep.  You don't want them to go flying off. You don't want to cross lanes It doesn't count if the ball crosses lanes. I I thought I had a strike, but I took somebody else's pins out So you want to keep them going down that nice safe path all the way down to get to where they're trying to go That's what you really want to do You don't want to write code. You don't want to like Have cool images you want them to succeed So that's that's your job if you're working with client services If you're selling products that help people do something that kind of thing once you start thinking about that as opposed to Yeah, okay. I'm a freelancer and I write cool websites or I threw a plugin up on the repo or you know I came up with this really awesome template or whatever Then you're changing your mindset That's the first thing you want to do remember to keep your clients going down that path not just telling them that you write code You're developing a process for increasing your value and what you can do for your customers and There we go to work And you are always thinking about sales So taking those practices those principles The charts that aren't that old from the 80s I Hate having to say that now now. It's not like my dad, but those those principles don't change They're all still good. They're all still important and even if you're freelancing or even if you know you You just started your small business or you just you know hired your first employee. They're still very very valuable And so what I wanted to do is kind of go into that in a bit more of an app of an applied manner using these three sort of big buckets of thought first mindset I Took this from a lot of bullets and I sort of refined it down And I think I'm probably gonna have to like re-upload my deck because I changed it from what I put up there Whatever the last week or whatever Tone and what's the why are probably the best ways to sort of describe at the biggest level possible the mindset shift that you want to do and It don't worry about the order which one's on top which one second we'll start with tone How do you see yourself? How do you present yourself? That's the first biggest thing I Come from a freelancing background did it for a long time just on my own Partnered with some other people. We did a lot of collaboration This open source thing was really awesome. We could work together, but still be competitors We'd still work out of the same co-working space, but you know lean to lean back in the chair and go Hey, didn't you do this last week? Oh, yeah, sure Let me show you this code that I was working on That's awesome. That's that was amazing. It's like old-school business wouldn't do that to be like no get away This is you know, you go to your thing and but I'm gonna try to see what you're doing, but I'm not gonna tell you It was a very Cut throat not really competitive The collaboration and that also, you know, that's all awesome. It's great, you know We get t-shirts at work camps t-shirts are awesome t-shirts are great but When you're going out to the client world you're going out and you're talking to customers You can do that for a long time and be totally happy and totally cool If you want to bring things up to the next notch you want to shift your thinking you're not a freelancer You're a business person You want to present yourself as a business person? You want to present your business as a business? So Little things you can do just starting in your brain That's the first thing is once you start thinking it then you can start acting on it and it does kind of change how you present yourself That plays into all of the dealings with your customers with the what's the why who developers Okay, how many times when somebody says so I've got this problem and I need to come in here I need to get a new site and you start asking them about this, you know, okay We'll tell me what you want to do Gold you have designs. What are you thinking? Oh, yeah, okay? We can build that. I've done this, you know Yeah, the other day we worked on that you might also want to think of this But never in that train of little blurbs that I just said which are things that I've said many times in Conversations with people that I asked what is it you're trying to do? don't start with the You know the code the the what's the the you know, oh, yeah, this is you know, we can do this It's what is it you're really trying to do does anybody recognize this woodcut? It's the blind men on the up and blind men in the elephant This is a Japanese woodcut of a parable that goes back Mid first century BCE the Indian subcontinent. It's in Buddhism. It's in Sufi It's it's the stuff goes back big time You've got an elephant for those who don't know you've got an elephant and the parable is these five blind men come up in each one You know as a different part this guy's got the trunk. This guy's got an ear. This guy's got a foot Every single one of them is like oh, it's an alligator. No, it's a snake. This is obviously a big rock wall This is true throughout life They don't realize the totality of what they're looking at When you're talking to your customers, and you're talking to your clients if you're not asking them What's the business problem that you're trying to solve? What is it? You're having difficulty with what is it? You're wanting this to do If you don't start from there You know you're gonna be over here going we've got this awesome solution You come back six weeks later, and you go hey, here's this great thing and they're like well Yeah, but that doesn't really do what I need to do. I I heard that so many times in my freelance life. This is this looks great. This looks cool But it's not really what I was looking for it's not really this because I didn't ask those questions About what they were trying to solve and I didn't listen to them tell me what they were you know what they really had trouble with So I started in the wrong direction. I had a great plug-in Didn't do anything for them though So what's the business problem? That's the first big sort of mindset shift you want to do if you're doing that You're not you're doing great. I mean if you're starting from this area, you're doing great keep going in that direction. I Did devs in the room?  You're the business owner. You're the marketing department.  You're all that So when you are talking to your customers, you put that account management hat on you put that sales rep hat on you put That business analyst hat on So don't sound like a dev Presentation we talked about that a little bit Sort of going into that, you know not asking them What their business problem is, you know eager and helpful are great if you're a developer We want to solve problems. We hunger for that. We're like, oh, yeah Tell me something doesn't work because I want to get in there like the first thing I want to do is like view source What do you got here? Okay? What does X debug say? I mean, I want to get in I want to like solve it That's awesome. That's why we hire devs because devs want to solve problems. That's that's just amazing But don't jump the gun It's kind of, you know, slow down just a sec, you know, take a breath figure out the right direction then get into it The other thing is are you I Tried to I tried to like write down sort of a script in my head of all the times, you know You're listening to the customer and I say well, I want to do this and as a dev You know, like I don't know if we can do that, but Okay, right there.  I don't know if I can do that or no It doesn't really work that way It sounds silly if you've never thought about it, but just saying things with no, I Don't know that uncertainty that that Negativity even if you're still saying well, yeah, we can do all this stuff, but I don't know about that That little verbal tick is a killer Because remember the customers over here they may or may not be technical but what they are is they're trying to solve a problem and They may be just nervous and the minute you say no Whatever just came after that even if it's an awesome idea. They're still hearing. No, they're absolutely hearing. No and I Was very very very skeptical that if I was like you got to be kidding me. I just said we could do this Well, yeah, but right over here.  My mom was math computer science. So for me. I'm like no wait No, let's I said we could do this these words came out of my mouth.   This guy doesn't know how to do this Okay, we're gonna find somebody else We're gonna have to go over here and the sales gone. That's it. It's it's done. It may come back But that opportunity just got lost because the word no came out or I don't know if we can do this. So Yes, and Cream knows that phrase he's not looking up.  Let's dig into that some more. Let's investigate it never in that Did I say the word? No, it sounds silly if you've never done this. It sounds ridiculous This is like pop psychology. You want to want or some freaking TV show thing where they're telling you You know if you believe it it can be done It's true Just the word shift it's part of that mental shift I learned that painfully the hard way as just a solo dev And it wasn't until somebody I had known for a while and I got to watch them do a call with a customer And I was like, what did you just do there and it took me a long time to figure that out The last part mindset are you a so who's who's a vendor for their clients? vendor Yeah Okay, who's a partner with their clients? Okay way more hands. That's what it needs to be. That's part of that mindset shift. Are you a vendor? To your clients. Is it a client vendor relationship that you have or are you a partner with your clients? And I don't necessarily mean contractually we're partners and whatever blah blah blah blah But you sit on the same side of the table of a problem with your client Not on the opposite end of them saying I'm going to pay you for this and you're like great cool Here you go. Here's your thing.  You don't have to go market to them again So they're there they're there with you and they're there. Hopefully they're with you past the initial project onto more and more Okay, process Process is For me. This was the hardest thing for me to do as a dev Because it was boring. I Hated it. I don't want to be paperwork. I don't want to sit here and like model stuff out.  You don't want chaos Scared clients run away.  I want to write code. Yes. I know I get it This is my voice in my head all those years I was I hated this stuff but do it Because once you do it once you have a process in place you can iterate on a process You can revise it. Don't try to make it perfect out the box, but get something in there and stick to it Documentation as well. That's part of it which everybody loves documentation so process when you're talking with the client and They say okay, I want to do this awesome. Great. You walk away Do you know exactly what it is that you're doing is everybody clear on the next steps? Do they know what they're doing? Do you know what you're doing? Do they know you know? Do you guys have everything clear? Do they have to hosting setup they know when you're getting designed do you know when you're getting the designs? You know, you're supposed to start development here. Did you get those designs? Is that in paper somewhere? Did you get a date? When when did they want to launch when was that? Okay, we got to work on you know, you got to ask all these questions You don't want to be launching over Christmas been there Sitting in the truck going up to grandma's house with the laptop tethered because I didn't get the follow back Follow up from them on when something was gonna happen So The process is that you want to put into there make sure that everybody's on the same page So that's your contracts. That's your development timelines. That's your follow-ups that's Responding back to them in emails by restating the problem by just saying even if you know everybody said the same thing Putting it in that email because that way can always go back and refer to it or they might go Oh, yeah, I forgot all this so that's one other thing gives them an opportunity to re-clarify everything with you. So Getting everybody on the same page. That's the one of the biggest advantages of process and coming up with that So make sure that that happens Are you sure everybody's on the same page?  It's just being look. This is this this is this this is this the sky is blue The floor is brown the trees are green. We're all good here. Yes. Yes. Yes. Okay, boom It's the same way with the process. We're launching win Okay, we're launching here. Okay. When are we doing our QA? Okay, our QA takes us long Okay, what day is it today? That's here. Okay, that's this much time. Does everybody know that it's this much time Does the client know it's this much time? Do you have those five things from the client? Well, okay, when are you gonna get those five things from the client? I mean, it's just you've got to drill it in over and over and over again Clear statements of work That's your lifesaver that sets this Freelancers anybody who has good contracts It needs me more hands than that Who has contracts? Okay, great So that Delta between all the hands that were up just now my hands that were up earlier That's the difference. So that you that's let's bring that closer together More hands came up that said they had contracts that is awesome Start with that make sure that you can Bring those up iteratively over time and improve them a bit by bit because when you get that clear statement of work Delivery item one is this and it's gonna be here. It's gonna come in on this date Every item two is this and it's coming here. It's gonna be on this date all that stuff Just there's no questions, there's that certainty there's that lack of fear clients love that Clients will yell they'll scream. They'll holler. I don't know about this date You know, whatever can we push it back, but you've got something on paper and everybody agrees to it. They signed it Everybody's on the same page. You can work from that things are obviously gonna change I mean, who's ever started a project that at the very beginning and at the end was the exact same throughout nobody did it did anybody go through that and Not get a change order. Did anybody just not get the other stuff. They asked about done. I've done that. I Don't know if we can do that that goes back to that saying no Things should always change It's just how it goes. You start a project something new in Chinese comes out. We want to add it to the project What's who has a good way of addressing that? How how would you address that to your client? Oh, can we do these three things? What's the verbal response I'm just curious if anybody has like a this is how I would answer that You are the man. Yes That's a great idea for phase two You didn't say no The clients like oh cool. I can get that and you just got their mindset for a change order Never ever, you know, give up an opportunity for somebody to give you money So you should underst you should have that anticipation of managing change If you don't have a change order template started make one Okay, if you didn't write it down, it's not real This is gospel Absolute gospel. This is even I think I said earlier, you know Recap the call send them the bullet points in an email thank them for the time all that That's why right here Yes, it's it's friendly It shows that professionalism and you have that extra opportunity to be courteous with your client everything else It's great, but this is right here because in six weeks when they yell at you for whatever whatever Kill them with kindness don't yell back, but forward the email back to them, you know, et cetera as seen here Yeah, we'd love to have a conversation about this, you know, yeah, yeah Most of the time they're gonna be like you're absolutely right Okay. Yeah, I forgot. Thank you for reminding me Every now and then you get the ones that are just it's probably best to walk away from The other part of this is This is that documentation bullet here. This is documentation Documentation is not just formatting the the little notes in your code It's understanding your clients make a dossier on your clients. Who are they? What's their business? What market are they in what's their growth look like I mean some of them, you know You may not you may not know like the the Hoover's business analyst profiles of all your clients They may not be in there None of my clients were when I were from the answers, but you know, we had the the dry cleaning shop They were opening for new locations. Okay, I wrote that down. That was a note because they're growing They've been around for 50 years. Okay, they're not going anywhere. They're stable. I mean these little notes these little details Who are the stakeholders in the business? Who are the people that like who's their head tech guy? You'll go find out who that who's or tech guy tech woman I mean you just you got to know these things so these are those little details of understanding the client because then you Can anticipate the things that they might need That makes you more valuable Know your own stuff too Which projects are most profitable for you which types of projects are the most fun for you. That's hugely important You know know these things and look for patterns because then you can you know kind of go go beautiful On everything and just go. Ah, this is the type of work. We want to do. This is the type of client want to work with When you have that opportunity to learn those things That's that's when you do your growth and that happens because you write things down okay Third bullet sales opportunities never ever ever pass up a chance for someone to give you money Be the snake charmer be the person who can who can have those conversations with clients and instead of saying no and instead of saying You know that's the limit, you know work with them help them through those difficult times because they're gonna they're gonna remember You're the one that helped them solve that problem.  Hate it. Hate it with a passion. It's context switching I'm in my brain space. I'm working through code I'm writing all this stuff down and then the client goes here's a wrench and you got to change direction and That's it. My brain's derailed. I've got to completely rethink the problem I've got a completely rethink the solution all of that that scope creep.  It's the change order It's the that's a great idea. Let's look at that in terms of scope and budget for the project and That's that opportunity to be the partner with your client to sit down and hat when work through them with them What they're looking to have done? Not to tell them no, but to sit there and go awesome. Let's look at it and then Carry them to that realization of okay. Well, yeah, well, let's let's we can do with that that for now But when could we get that in there? And you get that change order template throw it out there retainers and maintenance, this is a another Sales opportunity if you don't do it. It's something to think about doing this You know connecting dots as a freelancer. I had a couple of good years. I had a new one year where it was like It was like being on one of those roller coaster rides where you literally think your stomach liver and spleen are gonna come up. I You know feast or famine for projects committed once I'm one person I'm not sleeping for a while they all launch And I ain't got crap Now I got to go chase more projects and So I'm down here and then I get you know, and so it's just your business cycle looks like this After doing some research on clients after studying them a bit figuring out, you know Who got me the most money who got me the most return projects? What types of clients were they? What type of work was I doing for him? I was like, well Set up a maintenance agreement, you know X amount of Bandwidth a month something like that figure out some maybe you know, I was gonna do the package thing You know all the little plugins have the little three comparison column things that every single bootstrap website has on put that on my website 30 bucks 80 bucks 200 bucks whatever and This you get this many hours of work and this much work and this much work and I update WordPress and you know It's all this stuff and it it worked. I Got three four clients on that You know, I did no contract.  So, you know some of those little things I Had to do some mental mental hooves and sit down with my wife who had her MBA and go Okay, help me out here and she helped me write all that but the point of it is is those roller coaster dips started flattening out Because when I didn't have all those projects come in I had the retainer stuff there that You know, it wasn't the same by all means, but I wasn't dipping down to here and freaking out for you know For however much how long that ramp up to the next projects were It may or may not be you it worked great for me and And I would you know, I would encourage you to look at it as something you might think about You know with managed hosting providers a lot of the basic stuff of I'll update your plugins. I'll update WordPress Which manage hosting providers don't do that these days? So you got to think of more creative things to have that value add to your customers But it's it's worth looking at especially if your customers are coming to you over and over again for Little smaller piddly little stuff. Oh, I want to you know, new page template or something like that Maybe figure out a way that that type of work you can just sort of Push into some sort of you know monthly contract kind of thing if you don't do that yet and this is a You know something that you bring into One of the great benefits of it is you build a portfolio of contracts That is business value So your business value for however long these contracts are you're just you know, oh, I'm worth this much I'm worth this much. I'm worth this much, you know because those are contracts You've got those contracts in place That brings with it a sense of stability. You're in for the long haul You know, that's a promotional thing that you can use that that you know You're not the guy sitting with the laptop in front of the coffee shop Just kind of chilling out writing projects launching websites. No, you've got a portfolio You have a business You have you know professionalism Okay perfect timing This is me Pat Ramsey director of technology crap favorite and I thank you Thank you very much Pat How many years have you been working with the crowd favorite and and how long have you been working in that space? How much experience would you say you have my first version of WordPress was 1.2 beta So so he knows a little bit about a little bit So you're talking to us about asking the business problem Could you give an example of a time that you backed out of a web build? To actually analyze and look at the business problem identify that the question is is there a time when I backed out of a backed out to just kind of say okay, we got to stop and let's look at the business problem. I did there was a social media marketing company in Ten two thousand nine two thousand ten This is this is when all of the the companies would Send like three interns to South by Southwest and say you're the social media managers go and so everybody was getting into that How do we monetize that space? How do we get the numbers for big business in social media? so I was working on a new website for them six weeks into it they Completely just kind of like well, I want to do this and we're also going to do this and when I showed up for a meeting They had one of the the VP's there like we're also going to do this whole new thing over here and We just I just said no we got to stop we can stop we got to step back We can't just keep going this way and and it took two months of kind of back and forth and wrangling with them to Reset all the expectations about what was getting built what was being delivered when? Because they're you know if we hadn't done that there was just no Connection at all between what they were wanting to do and what we had already decided to build It was like these these things will never connect if we don't stop You know and reset everything That answer Absolutely. Thank you very much So you've worked as a freelancer you've worked inside small agencies large agencies you discuss a little bit about presenting yourself And and positioning yourself Is there a particular example that you think freelancers might Find value and how you presented yourself To their they they seem they might seem silly and tiny but they were they were there's a lot of value in knowing these things The first is all the communication is we and it's never I And that's that's big in all your writing. It's we can do this let's do this It's that collective tense when you're when you're speaking in your writing The second one is and he'll of this one is when you're doing these conferences with people and you're not in face-to-face Make it look like you're kind of in an office You know the patio is great. The garage desk is awesome But not when you're on a video call with a couple of directors and business people type stuff with suits on Just there there's there's a disjointedness there So have that sort of professional demeanor in in there If you are meeting them in person put a collared shirt on You know guys don't wear the the sneakers just I work from home. Don't trust me. I work from home It's shorts. I'm lucky if I put shoes on half the time But when I'm in face when I'm in person in that in in person means video to Have that presentation. It's it's just important Thank you very much Pat Ramsey crowd favorite


It's going on everyone Sam here with late sports cards rip in 2018 19 20 21 and 22 bum and chrome baseball through the year 7 box mixer number 4 random team style There's a look again at your random results As always can find those on the website under the results tab as well as the link in chat. Oh really? It's pretty wild actually. Yeah, she lived in Chantilly for like her first 20 years or something like that 15 to go on already gone Good old recon. Let me open this up All the cards ship all teams perfect. All right, we're gonna start with 21 bowman chrome here 21 bowman chrome hobby at one box of that Good luck everybody there for 29. There you go, Steve I thought that was the end of you Show hey, there's Austin Wells Nolan Gorman Matthew Allen Debbie Garcia, there's Francisco Alvarez summer camp JJ Bladet Michael Taglia And here for 22 now you are old illegals washed up, dude Make able baby Shea Langleers Yeah, he's washed up by the way. What may feel before 99 It's called himself old who's he's been in chat. What really? Yeah? Woman Diaz the movie guy is easy. Oh, I know. Yeah. He's been in chat. He's been in chat a few times with me But not recently that sure Alejandro mojica nice one there on the first auto for the Pirates Everybody say bye forest You're not supposed to say bye for Man with another Whitmerfield parallel that's weird 291 Lacey Austin Wells all right. All right out out out. I'm I'm leaving because I want to not because you told me to I Want to go have pizza for the second time today There's Heston Kirstead. Oh There was a right there was Robert. What's on it's very necessary It's about the drugs in summer camp the yearman Mercedes rookie in there the yearminator Green shimmer hunter green nice to 99. That's when they're red Arias Ryan Shoemaker or Braden Shoemaker pretty singer Gabriel Arias They saw the Santiago Flores there you go pirates they saw them my Malvin Valdez Hello Chris Olivares Kate Cavalli nice one there to 299 in the white speckle you look we sespanist and Kate Cavalli again All right, um 21 Bowman chrome choice now three autos in here. It's just super fracter. Why not pop Donald handle the pizza order Still and still not sold on him yet. Honestly Yeah, cuz you had to go out and help too. So yeah All right, we've got base auto is Taylor Dollard I swan there for the Mariners Thank You Andrew B taking a couple of stadium club chrome spots at the end of the night I saw in here is gonna be for the Marlins you de cappy. I swan there yeti. No cappy Nice one there for the Marlins Joshua are yeti. No cappy and Tanner Murray that is to 25 out of 299 white speckle auto for the raise Well, right on to the next one We've got 22 Bowman chrome hobby Mr. Whits and Khalil Watson dollar dollar bills y'all.  We are feeling it Coloss Randon cone your your Donnie de los Santos Please stop looking over here Blue rod, there's a Jared Kelnick to 299 nice one there first Oscar Coloss and Curtis Mead Jeremy Vargas first nice one there for the brew crew First auto of Jeremy Vargas Colton Couser Christian Hernandez see her There's fuchsia Daniel Vasquez to 1.99 for the Royals. We've got Jose Rodriguez Noel V. Marte pre-trade to the Reds pre-trade Noel V Nice that is a Bowman ascension Harry Ford on the short print grads on that Mariners Yonkila Fernandez and Adrian Polincia Josh Lowe say a Suzuki Moreno Vasquez. Yes, sir Mercedes y'all sir Mercedes Top out here. Oh, we need to hit a big Josh Giddy and flawless today. That's what we need We need that more than me I'll get this guy out of here There's shimmer Ezekiel Tovar, please get this guy out of here dandy day in Toronto Leonardo Balcazar Oh, we're keeping the energy up for Rocco all day long. Don't you worry Jay Allen Marcelo Meyer Bets base auto Yissan Morabelle nice one there for the Rangers on the base auto Yissan Morabelle. I asked him if he's an alarm. He says non-Morabelle Over there Gold Joey Vado to 50 nice one there for the Reds Alexis Hernandez and your belt on Hellace. There's a clear Watson shades of greatness Marco Luciano Don't worry, I'll really right back in don't you worry 2020 Bowman Chrome choice next 2020 Bowman Chrome choice. Here's a link again to Recon breaking in just a bit here guys 15 to go Let's get that fellas be on tweet and Facebook in that real quick. Thanks 2020 Bowman Chrome each CH was do the lucky spin right there. I guess the supercracker They were gonna get out of this Three slider that is a Dylan file. It's gonna be our first auto for the brew crew. It's a wahoo's Wahoo's I swung there for the brewers Second auto rookie auto for the Giants Maricio Dubon I swung there Giants Higante's Last auto is a base Luis Matos for the Giants again pretty solid box over there actually Nice one there. Hey, what's up Zach? Zach doing pretty well. I have to say Wahoo's Doing pretty well. All right 2019 Bowman Chrome Two boxes of 2019 It's not one to show Barely Out of an India, Luis your eyes Jake Bowers first or rookies very mookie rowdy Thales rookie I love It's so much fun Fernando Tatsi's rookie nice and Lake Snell Snellzilla Yeah, yeah, they make both. So basically Bowman. So there's three Bowman releases every year There's Bowman then Bowman Chrome and then Bowman draft So Bowman comes in hobby and jumbo Bowman Chrome comes in hobby and choice and then Bowman draft comes in jumbo and super jumbo So yeah, Bowman Chrome will be the next one to come out today. I mean come out this year Green shimmer 299 it's not smokey here at all. No, not at all Peter Lonzo Rookie. Yeah, series two is awesome man. That is based on a Patrick Sandoval going to the Angels nice one there LA Josh Hader, there's T swag purple mark trumbo to 250 Whatever happen to him was they have right but noticeable. Yeah That's what I've been hearing for sure. Alright guys Let's get recon filled up again. I'm gonna drop you guys that link really quick again 15 to go random team style into goo Also have some Crown Royale coming up today. We've got some The other one coming up flawless as well flawless PYTs of contenders to Debbie Garcia. Let's go morale. It's Jonathan India That is 81 of 150 elites farm hands Michael Kopeck Cedric Mullins Nice rookies there for the White Sox in order on her Pilkington Posey Griffin canning rookie Kunya Blake Trinan purple shimmer Corbin Martin, I believe that's not numbered And Machado and Reese Hoskins Slightly ooh nice That is gonna be Jersey auto 32 of 150 Keston here For the Brewers nice one there brew crew. That's gonna be game used. I believe to nice one there from Bowman Chrome Keeps getting pushed. Geez, dude Robbie Ray. All right. Now Corey Ray Joey Bartz that tracker with Merrifield Eloy rookie. Nice. All right next box of 2019 Bowman Chrome. I see a Tati's rookie auto or a Pita Lonzo rookie auto. That'd be pretty sweet You'd be hyped about that. Oh, yeah, I'd be hyped about that polar bear purple first is Robinson Ortiz 250 Blair's Bansley Swanson Anthony Rizzo Ryan Barrochi rookie and a Christian Stewart rookie Yamamoto first Tim Tebow first. There we go For the Mets that's sick Forgot about that. You see kukuchi Ramon Loreano. I forgot that Tim Tebow's got a first in this. Oh, wow. Oh wow Nick Green Kiebert Ruiz purple shimmer the Grom and Lord's Gurriel Rhina Bray There's Austin Warner. That's first base auto for the Cardinals Carter Keeboom and Austin Riley rookie nice for the Braves when I was young That is gonna be Danny Jansen to 499 refractor Rookie Bryce Terang Nolan Arnato And guys got recon coming up in just a bit. That's at 15 to go Let's get that filled on up that is actually at 14 to go Thank you FNH with the spots in Recon that is down like I said to 14 to go Sean's got you on that link there. Thank you Sean 14 to go. Here we go. Let's get on to the next one. Louis Brinson Josh Bell Yeah, Josh Allen got the cover of Madden Kyle Tucker rookie And now it's pregnant. You see that today Yeah Proto Pratomo Josh James Rhino her Tim Tebow refractor first to 499. Let's go Mets Nice one there Taylor Ward. Yeah, make them do Fortnite Durbin Feltman for the Red Sox on the base auto rats on that Red Sox Chris Davis crush Davis Miguel Amaya and John Duplan sir. All right on to our last box here guys. It's gonna be 2018 Bowman Chrome 2018 Bowman Chrome. So, you know, Tony Reese Hoskins rookie Reese Lightning That would be a fun rainbow to do Tim Tebow rainbow man TJ's leak That is gonna be 2150 Keston here on the atomic lot of Keston here up coming out of this this break Test Daddy like Bowman first Otani Otto. Yeah, this is Otani's rookie autos in here one of his rookie autos one of his two Bowman rookie autos Eric Hosmer. Well, Andrew Stevenson rookie nice one there to 250 The Nationals Barlin Castro Aaron Nola. That is gonna be refractor Brandon Marsh. Nice to 499 Congrats on that one there angels. He's having a good year out in Philly now Prospect for a 499 Garrett Cooper and Nick Williams wrong angel, but still very nice Kunia's got rookies in this too Oh Jude Bellingham going to Real Madrid, I didn't realize I know a singer was saying something about that today But that was a track. No, it was Victor Robles Victor Robles, Francisco Mejia there's a Chark Charcer Berks to 655 Mookie Betts and Jake Lamb, but Take lamb Reach on our green labor rookie labor day for the angst rice Harper how Funkhouser to 499 Gary Sanchez and Chris Archer, but base auto for the Padres Michael Bayez on the first Nice one there for the Padres Anthony Rizzo and Michael Fulmer and Michael Fulmer One rookie of the year is a pitcher for the Tigers. All right, here we go recap guys Michael Bayez Brandon March to 499 Durbin Feltman Austin Warner Kesson Hera Patrick Sandoval Louise Matos Mauricio Dubon Dylan Fial Yisan Morbell Jeremy Vargas Tanner Murray Yudi Cappy Tyler or Taylor Dollard Santiago Flores and Alexander Mokica. That'll do it for the break guys. Thanks again for the fill on this one up next We've got leaf best basketball


Dear students, in this topic we shall discuss some basic concepts of animal behavior. Animal behavior is defined as the sum total of responses made by an animal to the external and internal stimuli. The animal behavior is based on its physiological systems and processes. The scientific study of animal behavior in natural environment is studied in the branch of biology which is called ethology. Dear students, let us take few examples of animal behavior. Animals of animals may be simple. For example, moving towards or away from light, blinking of eyes and many reflex movements. However, most of animal behaviors are quite complex. For example, defense of territory, courtship and mating behaviors, liking, disliking, fighting and caring, these are also complex behaviors. Another example of complex behaviors is the migration and navigation seen in many animals. Moreover, the building of nests, hives and dens by different animals is a complex behavior. Similarly, producing meaningful voices and songs by birds and mammals is also a complex behavior. Communicating among the members of species and learning and memorizing the events that is also included in complex behaviors. Dear students, most of the behaviors are essential for the survival and reproductive success of the animals. Such behaviors which are important for survival are substantially subject to natural selection and evolution. So most of the behavioral patterns have been subject to evolution and natural selection. Dear students, nature selection may behavior key development may though major angles contribute to it. First of all, the anatomical development of the nervous system is a major angle or major line on which evolution and natural selection have operated. Secondly, the physiological features of the anatomical development of the nervous system and its physiological features enhance the advancement of the animals and the higher animals. Dear students, study of animal behavior or ethology has certain objectives. For example, to understand the stimuli that elicit behavior. To understand the physiological mechanisms which mediate response. To understand the animals' experiences that influence behavior. Mutlif animals change their behaviors based on different experiences. An ethologist studies these experiences in ethology. Ethology also involves understanding of the role of behavior in survival and reproduction. Moreover, the study of evolutionary history of behavior is also one of an important objectives of ethology.


The latest state high school hockey rankings were released today and despite dropping a pair of games last week the Brainerd Little Falls girls team only fell two spots to number seven. Right on their tails is the Rozo Rams at number eight. Brainerd won both regular season matchups between those teams and you have to think a rematch in the playoffs is pretty likely. Grand Rapids Greenway girls hold steady at 15th in the 2A polls. Warwick remains at the number one spot in class A. The Warriors are 20-0 on the season. They take on Moorhead on Saturday. In boys hockey, Rozo remains at number 16 in class 2A following their tie to World last night while the Warriors remain at number 10 in class A. And despite their 8-13 record the Greenway Raiders have impressed voters enough to keep them at number 12 in the class A polls.


I think among other topics we'll talk about broadband again because it's one of the mean to use ICT applications, especially if you won't have fast connectivity. Also we'll hear about smart society, which is very coming up, like and it's been going on like for quite some time. It's a new, it's an innovation and a very futuristic vision but I think that people should embrace it and take it as their advantage based on a specific roadmap, take into account the environment in which they are, their challenges, what are the pros and the cons and that has been said. One of the consequences or the and also it's a pro, it's the security aspect of it, meaning that we'll also a lot hear about cybersecurity. So people will know how to use the internet but also all applications related to the use of ICTs and security is a key element because everything now it's based on with the development of ICT and new technology everything it's based on technology but we have to take into account the fact that if people don't have confidence and or doesn't know how to use wisely the internet is very risky. So it's very important to educate people that we can use new technology and ICTs to our own benefit but we should know how to use it so we should have secure platform. We should put in place more secure data center which should take into account personal data protection, so consumer protection on the use of internet with more focus on child, so meaning child online protection but also with vulnerable people such as disabled or people with special needs who doesn't necessarily have some of the tools or means to better use those application in their own favor in their own use. So I think those are some of the element that we'll hear about a lot and also we'll also have to take into account the environment meaning climate change, e-waste, contraffit products etc etc so all that is kind of embedded together they're kind of a synergy among all those topics so I think that we'll have an interesting study period for the next coming years. Collaboration it's key so collaboration among all sectors whatever is within the ITU but also with private sectors, government, academia, institute because we have to share experiences for the benefit of all users so I think that they've been doing a lot of research you know experimentation so it can help us save time but also avoid duplication of the work and which can imply whatever is financial or means or budget issues so and the fact that is they know what's happening in their sector they know what are the issues they're facing so I think we should all come together because at the end of the day the benefit is beneficial for everybody.


Welcome back to Kids Fun Science. My name is Ken. Today's experiment is the holiday spec holographic lenses. As always, adult supervision is required. What you need for this experiment is holiday spec glasses. I picked mine up at the local Christmas store, but I'll show you in the description where you can find those online and order them yourself if you desire. Here's what they look like. They're made out of paper. They're very cheap around a buck fifty and look in the description where you can get them. When you look up close through these diffraction glasses, you're looking through a piece of material called the diffraction gradient. This gradient is a piece of plastic that has small openings, which usually is narrowed through the closing space of each other. When light passes through these openings, it bends in the amount of the dependent of the type of light. For example, red light bends more than yellow light. When the white light enters the diffraction gradient, it separates into a fundamental color. These colors are the same as the spectrum of the colors that you see in a rainbow. Here you can see I put on the glasses and you can see it turns into candy cans. You pull them down and you've got your white, red, and green Christmas lights. I'm sure you still have them around. So we also have different glasses. So we have here we go. We pull it up. We got the Santa's face and you pull them down and it's kind of cool. It's doing every individual light on the glass because of the way it's set up on the lens that each turns into that image. And here's a snowflake. So basically the science behind it is the as I showed you earlier, the micro etchings into the plastic lenses causes the light to diffract the shape that is etched onto these glasses. Hence like this one is a snowman, right? So understanding how it works isn't easy. It's an interesting property of nature of light that's going through these glasses and diffracts, in turn transforms that image. One thing is it doesn't matter where the light moves through the glasses. The glasses will always show you the image that you have no matter how many lights are out there. It will refract that many, which is pretty cool. I hope you enjoyed this video. Remember to click share or like and thanks for watching.