Hi there folks! Sorry about that. My internet has decided to die exactly at 8 a.m., which is super fun. Okay, so I'm doing this on a data plan. Hopefully this won't cut out at any point. Yeah, just maybe let me know if there are any thankful issues during the interview. Just let me know in chat or just feel free to shout out. Alright, so let's jump right into things. I will share my screen. Cool, so just some quick announcements right to the pre-classes sort of going on as usual. Just laid out an order pretty much for the rest of the semester so you can just work through those. They're all sort of available on Gradescope right now. So if you want to try to work ahead a little bit on any of them, if you have extra time, then you can do that. Just kind of clear as many out as you're able to. The rest of the semester is really just everything we're doing now, all of this trigonometry. I think the last section is 5.2 or 5.1 or 5.2. I think a lot of that is simplifying trig functions. So really, I think you're probably equipped at this point to do all of these kinds of problems. It's just a matter of practicing some specifics. Sorry, I just realized my volume is super low. Alright, so pre-classes, yep, just have a number of them left. Let's see, in terms of the project, I think I kind of sent out sort of a status summarizing where you should be. I think what we want to do is go ahead and have some kind of rough draft due, I think I said at the end of this week, maybe Friday. Let me just pull up the announcements so I can double check the exact dates. But just as a rough idea of where you should be at this point, hopefully you've met with your partner and at least kind of discussed your understanding of the project and sorted out if there are any parts that you don't understand. This would be the week to get any questions that you have answered. So I'll be in office hours later today and I'll try to hold some extra office hours throughout the week. And this would be the best time to just clarify things. Hopefully you've read the project handout. Just see if there's anything outstanding that you don't understand about the project at this point. Sort of what's required and what needs to go into it. So we'll talk about it today more in more detail in Thursday. So hopefully you've already met.  So please do try to meet with your partner ASAP just to avoid missing easy points on the project. If you end up behind on these kind of things, then it's hard to absorb the finer points we get into in these later. So get closer to the things that we discussed. They're meant to be more fine points on things you've already looked at. Hopefully I want to discuss the structure with your partner a little bit. Just going back to the announcement on ELC here. Just how many overall sections do you think you want? You definitely have to have an intro section, some kind of middle piece and some kind of conclusion. So there should be some kind of like macro structure to your document that you've sorted out so far. But you might want to also decide like in that introduction, do you want to combine this like explanation of the physical situation and just make it one sort of introduction that covers everything. You want to break it down into two pieces. Some people have done this for previous projects where one of them is an introduction and discussing kind of what the goals are and what the mathematics you'll be doing will be. And then there's a separate section for like the actual physical situation. You want to discuss a little bit how you want to break up this middle analysis. So we're discussing some stuff in class. So there's some stuff from last class, some stuff from today and some stuff from Thursday. These will definitely need to be in the project in some form or another. And just a quick disclaimer, if you're doing the derivations for stuff that you have to include in the project, you really do have to walk through these steps yourself. So that's really not super great to, you know, if we just like go through something in class, we just get to the final answer. Like in your project, you don't want to just like start with the initial thing and then say, okay, and here's the answer. Like last time we did some like derivation of solving for M and this kind of stuff. And I think a lot of people for Project 2 just said, okay, here are the initial equations. Here's what happens when you solve for M. But this being a math class, that's kind of the part that you really need to show or like that's, you know, that's one of the more important parts. The analysis is important, but being able to walk through these derivations yourself is also really key. But yeah, so discuss with your partner how, you know, how much of that analysis you guys understand and make sure to try and get to office hours. If you don't discuss how you want to break up this intermediate analysis section. So in our case, you know, we at least have two things to look at. We have like one situation is where this leaf is stationary in one situation where the leaf is rotating throughout the day. So maybe you want to do one now one analysis of both together, maybe you want to break this into two subsections. Maybe you want to do one and your partner do that's the other that kind of thing. Definitely have have these discussions. So ideally that's where you'd want to be at by today, having met with your partner, having discussed the structure and having discussed your understanding of this analysis in the middle just based on what you've read in the handout which hopefully you've read at this point. By Thursday, I would aim to have some kind of rough draft completed based on just what we discussed today will go through a lot of the analysis you need for the stationary leaf case. But there are some decisions you as a group have to make. We talked a little bit about this there's going to be coming up with some kind of angle function, some sort of periodic trigonometric function that models this like energy density throughout the day. I'll say a little bit more about that when we're talking about these details. But there's some choice here that you have to make. It's kind of a difficult choice, I think. Like you have to now turn all over the math that we've been doing on its head and you have to like yourself come up with a function to model this thing. And I think that's that's a little bit tough. Yeah, by Thursday, you want to have some of this analysis for the stationary leaf at least copied down written out. And make sure you understand it and then make sure you get to office hours feed help with the derivation.  I usually recommend writing these last, because you kind of don't know how much you need to introduce or what the summary is until you've already done all the work. I think in this case, it's maybe easier to have an abstract or an intro or both to have a rough draft for them. I think they're pretty easy to write in this case, just describing the situation overall, there's not really too much to say about those. It's complicated as project to a project one, in terms of the physical situation. But maybe just have a rough draft of those and then after you're done with the project come back and do a final final draft of the intro abstract sections. And then by Friday, go ahead and turn in something on great scope should just be some version of your project which hopefully includes abstract introduction. And this analysis of the stationary leaf. And some indication that you've started looking at the rotating leaf, which is what we'll be talking about on Thursday. And I think that's pretty much it and then we'll try to go ahead and have the final draft you next week. How are you going to have an actual sort of fall break of some sorts anyways. Alright, so that being said, I think that's pretty much it for announcements. I'm going to say stuff about office hours a little bit later too. Okay, so. Professor Garza. I saw in great scope that there was like a pre class and like work sheet do like Thursday of next week and I was wondering if that's still, if we still have those assignments to you. Right because we have holiday break starts Wednesday, I think. Yeah, that's why. Yeah, I'll probably go ahead and move those. Okay, thank you. You know which, which assignment it was off end. No, but I'll look it up right now. Okay. Yeah, if you want to just drop it in chat or something that's, that's really fine. And so whatever the pre class and whatever the worksheet was for that I'll probably just push it back to the next week. It was the 4.5 b worksheet. Yeah, it was like the pre class and I think the worksheet too. Yeah, so I'll try to just push everything back. Make that do the following Tuesday. Yes. Okay. And so we see what we are looking at today. So I think today is probably one of the more, more fun days we just get to look at a lot of a lot of demonstrations which is, which is nice. I just want to remind, set out some reminders of things that are kind of important at this point. So maybe want to review. So things that are coming up on pre classes are these special angles. And I just remember that there were a few, maybe like a handful of these that we want to know. Maybe it's actually better to say special like reference angles. It's kind of the best way to think about them. So these were all of these angles in the first quadrant. I won't list them out. I'll just say in words you can kind of go back and look at the notes from a previous lecture, if you want to see a discussion of them. And the important point is that there is huge complicated diagrams on Google where they list out like every single special angle on the circle. And there's something like a 69 plus four 13 of them. And the important point there is do not memorize that circle. I think that's something that's pushed in a lot of trigonometry or other pre calculus classes. The idea here was that we had this sort of flipping process where you kind of pick any angle you want, you find this reference angle. And this reference angle is going to tell you what triangle to look at in the first quadrant to sort of determine sine and cosine and all of that. And then you can just kind of flip things around change the x and y coordinates between plus and minus to get the right thing. And I think to memorize, I think it was six angles, you can go back and look at the table but it's essentially in the first quadrant, you know, something that's like zero radians. And then you have by six by fourths by thirds. And so I guess that's only five to zero by six by fourths by thirds, and I have. I have to emphasize that we really do want to memorize what the values are for these or have a way of like easily remembering how to come up with them. And just remember we had this table trick where you can kind of list out sine and cosine and kind of do like square root of one over four square root of two over four, kind of work your way up for the the sine values and work your way down for the cosine values. How do you remember which one is up or down we have this.  It's not exactly true unless you're on the unit circle it's not that cosine of theta sine of theta is the x y coordinate. It's taken to account the radius for this like polar transformation. But loosely this is kind of how you want to think about these things. And then so when you're trying to remember these angles you can just remember that if you're at, you know, zero degrees or something, the sine is starting out at zero. It's the y coordinate. And as you're, you're kind of going through this quarter rotation up to I have radians, the y coordinate is increasing. So the sine is the one you want to increase when you're doing this table process. And the cosine is the x coordinate so the cosine is the one that's decreasing. Okay. So yeah, just remembering the special angles and remembering this demonic about signs and cosines corresponding to y and x coordinates. Maybe I'll just say remembering polar coordinates. This is one of those things where coming to class is kind of useful, because this is not necessarily the way Torian approaches it in her videos and it's not really the way it's approached on the worksheets. But I think that this is worth doing a little bit of extra effort up front to understand these like this this back and forth process between x y coordinates and polar coordinates are theta. I guess somehow you can just do all of this trigonometry. Most of the stuff in in chapter four with this like one single idea. So it's kind of a hard idea to think about internalize just how do we do these polar coordinates. But I think it's definitely worth the effort up front because it makes the last five to six units. It's much easier. Just as a quick reminder of how this goes. We kind of choose our little reference frames we've sat down. We've decided that someplace in the real world is the origins we've marked that we've picked two orthogonal directions y hat x hat. And let's say we pick a pair are in theta. The first thing I do is I measure theta. So maybe it gives me something like this. That's the angle theta. Remember that data determines the rate. This is an important idea. But if we choose an R, then we choose a point on that rate. So now we get a line segment of radius R. See if I can switch to a different research. Okay, cool. Once we've done that. It's a line segment or another way to think about this is as a maybe I'll make this polar coordinates slash slash vectors. Sorry, I just saw that something was in chat. So let me just double check 4.5 p. Oh, from the pre class. Okay, so we are starting to switch the switch the eraser back here. Okay. So we are thinking about our theta determining a vector in the plane. So it's an arrow with a direction in the magnitude, the direction of the state of the magnitude is R. And we get some coordinate out of it x, y. And the formula for that coordinate is given by following x coordinate is our cosine of theta. And I guess I should mention here there is a way to kind of go back from this. So if you this is kind of like going from this is like going from our theta to x, y values. And there's a way to go backwards, which we didn't talk about. I'll just tell you what the formula is. If you're given x and y, and there's a formula for our name, the R is just square root of x squared plus y squared. And hopefully I'll go back up to the triangle in a second. I'll just tell you what the theta is. And the theta is a little complicated. It's the best way to put it. Instead, when I can say. So everyone has an easy description is telling you what the reference angle theta is. And this is the arc tangent or inverse tangent of y over x. Okay, so hopefully we try to point out why it's hopefully believable that the R thing would work. We try to point out why it's hopefully believable that the R thing would work. So right if we had this coordinate x, y, we could drop a perpendicular. Down to the axis. That would be a right angle. The length of this segment would be x. The length of this segment would be y. So we would just be doing the Pythagorean theorem to get R. This is just R squared equals x squared plus y squared. So no real funny business there. Except that we've kind of gone through this process of breaking a vector into components kind of without explicitly saying so. We've broken it into a horizontal component and a vertical component and the length of the horizontal component was x and the length of the vertical component was y. And so, okay, we do Pythagorean theorem to get R. No big deal to get theta. Well, we can just note that if we pick this beta here, we have an adjacent opposite and I bought news in this triangle that we found. And tangent of theta. It would be equal to the opposite over the adjacent side. And for us that's y over x. These are just lengths. And so if I apply, so maybe apply arc tan to both sides. And the key thing to remember here is that just like the exponential in the log and arc trig function in the original one so arc sine and sine or cosine and cosine and so on.  And so we're not really like we're not multiplying them we're actually taking tangent of theta and plugging it into arc tan as a function. The other thing about functional inverses is that they, when you compose them together like this it's like you did nothing at all. So it's the identity function it just gives you the argument back. So the argument, full argument there is just theta. And so this would tell you that theta is arc tangent of y over x. And the side here, kind of motivating this stuff. But well, the problem this is that this only really works in the first quadrant, just because of the way we've drawn our picture. So here's kind of a warning here is that up here is to always draw a picture. This goes for virtually everything in this unit trying to find some way to draw a picture. This is a sort of a sanity check. The algebra we're doing at least makes sense, saying like the first quadrant or something. The problem is is that we can't actually use this picture for proof. It's just one of the tools in our tool bag. And what goes wrong is that if I'm in quadrant two or three, I think our problem areas is our tangent is going to come back with an incorrect sign. So if you just plug this into your calculator, you're not going to quite get the right thing. So we aren't going to have to worry about this too much because we're never going to do this direction of it. We're not going to start with an XY and go to an R theta. They'll usually be the other way around. The kind of the thing to keep in mind here is that if you ever do need this comes up in engineering and physics.  And so you need to actually play this flipping game to figure out. You have to sit down and draw a picture to figure out what quadrant to put it in and maybe you have to. What happens here is that theta is equal to a ref reference angle. But you might have to adjust it by pi. So what'll happen is that whatever you get out of arc tan will either be pointing in the correct direction, in which case you're fine. Or it'll be pointing in exactly the opposite direction of what you want. So it determines the same sort of line segment, the same way it's just pointing in the wrong direction. I shouldn't say so it's not the same way, but it's determining the same line. So you just need to flip the X and Y coordinates a little bit. I guess this is useful like if you ever end up doing like computer science or something to you have to do this all the time because your computer monitor is a two dimensional plane.  Okay, so there's a little bit of how to go back and forth between those two representations. Just keep in mind, we won't need this one much. Another important concept was vectors and breaking into components. Just because we're pressed on time we have to say a lot about the project. I won't say much more about this, but we want to look through a little bit the notes from last time where we had one vector and we broke it into an X component and the Y component. And you'll need that for the project so try to make sure you understand that or if not, bring it to the office hours. Oh, and I see somebody's asking a chat if this was the method we were supposed to use for question 12 or sorry quiz 12 on the first question. And the answer there is not quite. Sort of, I mean you can use this process to do it. What you kind of wanted to do and in that question was to essentially if you just draw a picture, like what's happening here, then you can just reason about these sign links. And if you think what happens there is if you plug in these side links, you get something that's like a standard angle. So maybe you do the inverse tangent of one or something like that. And then you know that just from like this geometric ratio of business and that's like a sign over a cosine. So you need some angle where the sign is equal to the cosine. If the tangent is going to be equal to one. So maybe just like what I'm saying here is like an easier sort of general way to go about this but you can always kind of go to this kind of picture and draw the triangle and reason about the actual ratios. So, you have this business about breaking a vector into components. You know just do a quick sketch of what this is supposed to look like something like this and like this. So the vector. Very important we've chosen a coordinate system so we should tell a reader. The details of the system. The idea here was that we could break this into horizontal piece by kind of projecting it down. And we could break it into a vertical piece by projecting it onto y axis. We can kind of move vectors around freely as long as we keep your links. And so if we had some, let's just say this is a vector, be with a little arrow is just telling you that it's a vector. Then there are the red one is a V sub X. And the blue one was a B sub Y. And there were kind of formulas to determine what the like how do you actually express these vectors. Like if you knew that this vector was given by a point X, Y, then you could find coordinates for these and it essentially boils down to using polar coordinates to get the VX and the VY. Okay, so that being said, we're hopefully ready to talk about something slightly new. Let me see if I can pull this up. Okay, it works. Okay, so hopefully this animation is visible to everyone. Just one sec here. So this is kind of a new situation we want to think about. Not really so new. But it'll be something new that comes out of it. So we want to think about sort of what's happening here is, let me see if I can simplify this a little bit. So this is a new situation to start out with. And it's just like a little particle traveling around in a circle. Over time right now it's just on the unit circle. And so what I'm doing here is these are literally just, I'm plotting cosine of theta and sine of theta as data ranges between zero and two pi. This is giving you a little point on the circle as data increases from zero to two pi. This is kind of traveling in a counterclockwise fashion around the circle. And this is kind of the basic model of periodic behavior. And so we want to use this to model other things that are periodic in the world. So there's sort of two things that'll be important here. One of them is that you will measure if I can here. This one. And that one. Okay. So there are two things that we could measure on this particle. One of them is that we've chosen our origin. And we can measure the height of this thing. So this is just the Y coordinate as we go around. And you can kind of see that if you're just thinking about the height, it's starting out at zero. It's increasing to one and then it's decreasing back to zero. And then it kind of continues decreasing once you're all the way over on the left-hand side. Sorry, let me do it like this. So we start here at zero as we travel from, for just increasing theta from zero to pi halves. The Y coordinate is just getting bigger and bigger until we max out at one. And at which point starts decreasing again. And so this is going from pi halves to pi. At some point we hit zero again. After we increase past pi, then now we have a Y coordinate's decreasing. And eventually it minns out. And then it increases again. So that's one thing that we could measure. It's just the height of this particle over time. And then another thing we could measure here. I turn these two off. These two on. It's not the greatest way to see it. But we could measure the, so hopefully you can see the kind of blue thing swinging back and forth from left to right. We could measure the X coordinate as we go around. And we remember that the X coordinate literally was cosine of theta. So what we're trying to do is understand cosine is like a function of time instead of a function of theta. So change the domain a little bit. And so you can just see that as the X coordinate, or sorry, as we go around the circle, the X coordinate is just changing in sort of a similar way. It is starting out at one. And as you go over time, just following the blue dot on the projection down to the X axis, it is decreasing. It eventually hits zero, continues decreasing and hits negative one. And at some point it starts increasing again and goes back to one at the end of the day. And then starts over. So these are kind of two phenomena we'd like to understand. Just as we vary this coordinate around the circle, we want to measure the X coordinate and the Y coordinate separately. Okay, so let's start off by looking at what the sine function looks like when you do this. And so hopefully this is, hopefully everybody can see the animation here. What we're doing again, this is just the sine function on the unit circle. And now we're thinking of it as a function of time instead of theta. So if you think about the Y coordinate as a function of time, all I'm really doing is just measuring the height as I left this particle sort of run around the circle over time. And I'm just measuring the height at every, every point in time. And what I'm getting out is some kind of graph. And the XY plane that looks like this sort of thing where you can tell there's there's some kind of periodicity to it, right? Because as soon as I've done two pi revolutions, right, I'm just now back to square zero, right? I can just start. You know, I've kind of measured all the possible ways the height could change in that full revolution. This is the kind of animation to keep in mind. We're just measuring the Y coordinate. Now let's think about what happens when you measure the X coordinate. This one's a little bit trickier to keep track of. So let me maybe walk through this one a little bit slower here. So if we're starting off here at zero, at time zero, we're just measuring a height of one as we increase from zero to pi halves in terms of theta. And just at each time we're just recording the height of the Y coordinate. You can see the graph here is just measuring that height and it's maxing out. The exact same behavior. As we continue past pi halves to pi, we're getting a decreasing of the Y coordinate, decreasing of the height until it zeroes out, continues. It mins out at some point. At two pi comes back to zero. And then we're just playing the same game again. It's periodic. So it's periodic with zero to two pi in this case. And we just measure the heights again. So we're doing the same thing now with the X coordinates instead of the Y coordinates, which you end up with is something, right? So if we're starting at time zero, you just maybe let this run a few times first. Theta is increasing. And then over time we're just asking you each point in time. So let me just run this forward. At each point in time, what is the X coordinate of that particle on the unit circle? Well, the X coordinate literally is just cosine of theta. How is that varying over time? Starting at one, we are here. So it's a cosine starting at one there. As we go up to pi halves, we're decreasing to zero. And because you're just pointing straight up, there's no X coordinate next to zero. As you go, continue on to pi. The X coordinate goes all the way out to negative one on the unit circle. So we're minning out in terms of this cosine graph. Again, the cosine graph is really just measuring the X coordinate. And then as you go past pi radians into the third quadrant, the X coordinate starts decreasing again down to zero. So eventually it's increasing again. And then in two pi, we're periodic. On the project, are we only looking at zero to pi or something because of like the sun? Like it rises. Yep. Yep. It sets or something like that. Yeah, it's a little bit complicated because. Yeah, you'll be looking at angles between zero. And pi. And what you'll want to do is come up with what it'll be is the angle theta as a function of T. So it's going to be a little bit weird. So you won't necessarily get a cosine graph like this out. Yeah, maybe it's easier just to say what that'll actually be. Yeah, so essentially what'll happen is that when you do this kind of thing, you'll just be starting at zero. You'll start at pi in terms of angles. But what'll happen is that for the this like function you're coming up with the angles will be the range of your function. And instead what you'll want to do is have a T going from zero to 24. And it'll go and your thing will go from like zero pi. And then it'll stay zeroed out for a while for the rest of the day. And then back at the start of the next day, you'll start back at angle zero. So yeah, it's it's essentially the right idea except for the the angles are the the outputs instead of the inputs and what you're doing in the project. Okay, so hopefully that takes things and microphone went out for a sec. Okay, so these are the sort of things to keep in mind for these trick functions that you really want to think of sort of a particle moving around the circle. Cosine is measuring the x coordinate over time. And sine is measuring the y coordinate over time. And that's kind of where these these usual these other graphs you've probably seen elsewhere have come up. Yes, I'll say a quick word about sort of the the general form for these things. The general form. So what I'll just say is of a wave. So there's an identity, like somehow I think it just suffices to think about cosine. It's kind of the easiest way to approach it is that every wave is just a cosine and a sign is just like a shifted cosine. If you think about that. Using the one of that your identity or something so if you understand cosine really well, and it's not too difficult to transfer all of your knowledge to a sine function. What works is that if you have so a sign. So start with the picture. So it's a little bit tricky because we're graphing things now where the dependent variable isn't really an x, but it's a like a time or something as we're thinking about this particle moving around as a function of time. This will be kind of you can call them really anything you'll just call them w's or something. And if we're thinking about like some kind of wave, the general form will be f of t was a cosine. I guess W wasn't great here. Let's call this L or something. The general form is a cosine omega t minus five. And what does this correspond to essentially extend this down a little bit so we have some room. There's a plus a minus a. So if you have a cosine I guess this is starting at one in general. So you get one for like the parent function cosine here. This would be starting in a where you've shifted over by some phase shift five. And I'll just roughly sketch what this does. It's something like this where the there's a period here of since that being two pi over omega things called the period. And that was the phase shift. So we're just looking at one period but this is a periodic function which just means that if we just know this one little region we kind of know it everywhere because it just repeats itself. After that continues in essentially the same way. And I think that's pretty much it for this. So there's just three important parameters one of them is to say amplitude. It's very important to recognize that your amplitude is not just the height of the graph or anything like that. It's, you have to take the midpoint of the heights. So it's like the average height or something like that. So, yeah, so it should be going plus a units above the the sort of you just draw this line in here. And one one analogy here is that electricity for example is modeled by waves and the red line would be like a like a ground current or something like that. But the ground current doesn't necessarily have to be zero. It could be like, you know, you'd have like something shifted up by 12 or something, just some baseline.  So we don't have to worry about this for the moment. This like amplitude business but you'll see this on later free classes. So some sort of common mistakes there. Okay, and you may need this to as you're doing the modeling of your function for the project, something like this may be useful, but you may want something like a sign instead, depending on how you set it up. But the sign really just works the same way, except for you might have to change this would not start at, you know, one there and said it would start to help. Okay, so let's say some stuff about the project. So number one has to see. Here's an uploaded video from Cal who designs the project. You know, he sort of does this for all of the pre calculus classes. So he sees put up a video where he kind of walks through the example calculation in the project handout. And I think that's that's worth going through. See a lot of the same stuff I'm saying today showing up there. I need a reminder of kind of what's happening. It's probably one of the best resources. Let's just kind of remember what was going on. Let me grab a screenshot here to save us some time writing. Okay, that's visible. Remember, we had this kind of situation. It is we want to sort of the goal for this is to we have we have some kind of leaf sitting on the earth, absorbing some sunlight over the day. So how much sunlight could theoretically possibly absorb throughout the entire day. And so eventually this will, you know, we were going for like the theoretical maximum is kind of a phenomenon here where only these light rays that are hitting the leaf in a perpendicular manner contribute to the energy that it absorbs. So we have to do some business about fiddling with how do we break up this light ray into components and find the component that's hitting this in a perpendicular way. So what we'll do first is analyze this in a stationary way so the leaf is in the same place. The sun is moving over it. And so that'll give us some amount of energy that we can expect. But then you can also imagine, you know, if leafs were if leaves were trying to, you know, or trees were trying to optimize the amount of energy they absorb in a given day, you know, they might like shift their leaves a little bit so that they're always perpendicular to the sun to maximize that energy. So that's kind of the behavior we want to understand for this is like, if tree was doing everything in its power to keep itself flying with the light rays at all time. What is the total possible energy it could absorb over a 24 hour period. Okay. And yeah, maybe this will help answer that question from earlier if I just drop this picture in something like this. This is kind of our simplified model. What's happening? She didn't preserve the ratio, unfortunately. Okay. So the model was that this yellow line was like an incoming light vector. And what'll happen is that this light vector will also is like an energy density or something coming coming from the sun. There are two phenomena to keep in mind here. One of them is that this yellow vector depends on time. So time zero, it's, you know, sitting out horizontally. As time increases, it's, you know, kind of sweeping out the horizon and ranging from zero to pi. And then, you know, once the day starts again, it kind of resets and goes goes back to zero. One of the angles to think about here, one of them was this angle that the light ray was making with this plane of the leaf. And that's the, that's something that's changing over time. And the other one, the one that's important for us is one angle is this light ray making with the, we've kind of made this green kind of vector and pointing out of the leaf sort of sort of indicating what the orthogonal direction is. The component of the yellow vector that's lining up with the green vector, once we do this decomposition will be the component that's being absorbed. So you can see that that's, you know, here in this first situation, it's not maximized because some component is kind of lost in the horizontal direction. This yellow breaks up into something that goes that way a little bit, something that goes that way. So if it's a fixed amount of energy, some of it's getting lost because those rays are more parallel in the situation in the middle. All like all the right light rays. It's exactly lining up to the sort of the agreement of these angles is maximizing the amount of the energy density there. And then we kind of go back to them in again. Okay, and what's happening here is that we want to think of as a function of time L of t. So it's a little bit weird to think about but this is something. If you give me a time bill value I tell you what the vector is. So I'm telling you what the full yellow arrow is. That's, that's a little bit hard to think about. So just simplify things. Maybe I'll just write Theta sub L as a function of time. Theta sub LN as a function of time. I haven't labeled these super well but let's call this angle. Theta sub LN, so just the angle between whatever orthogonal you have on the leaf and the light ray coming in. I'm just remembering that this changes over time because the sun is moving. And then Theta L, which is this angle here. So you get two angles that depend on time. And maybe it's actually, maybe it's helpful to kind of think about what these look like in terms of graphs. So you're going to have to be a little bit careful with domains and co-domains. What we're sending into these functions will be T values and what we're getting out will be Theta values. So what happens here is that there's going to be some, let's say we're doing Theta L of T. And the first thing I would say to do is like let's determine the domain of Theta L of T. And this is just asking like what are the T values we should be expecting. And these will be from zero to maybe 24. You just include one of the endpoints to make sure you get the full day. What is the range of Theta sub L of T? And this is, if we go back up to this picture, this is exactly the, so all of the possible values this angle could take. And so we'll kind of artificially restrict this to say zero to pi. And I'll just mention there is a way to make this work where you don't have to make this restriction to where like it would more naturally model the fact that you know that at some point the sun is kind of, or kind of the earth is turned away from the sun or something like that. So this angle, if you think about this light angle coming in. Okay, let's go to the last picture here. At some point the angle is pi. And if you think about just what would happen if you continued rotating, while at some point this would be coming in like that. And you would get some kind of like negative angle or some obtuse angle between the light vector and the perpendicular vector. And you could kind of make that work with equations, but for us, since we have a choice over the function, it's maybe easier just to say it's zero. Or to say it stops at pi or something like that. So you could have this be zero to pi, it would just be more complicated to work out. And so what this graph will look like is if we just go back up to this picture, we know it's something that should start at zero. And you'll mark off where 12 noon is and then I'll mark off where 24 hours will be. So what I want is that as in this picture I want when the, let's see, so we're looking at theta sub LFT. So this should be something that increases from zero to pi will be the max. And so we know we have two points on this graph, something at zero zero and something here at 24 hours and pi. And okay, I'll just draw one possible function that might make sense here, which would just be a linear function. So this is an angle that increases over time and it just increases at a constant rate. This is just a linear kind of growth. And let me just indicate really quickly, we've only specified one period but we want this to exist for all time. So what you can do is just say, okay, this function is going to be periodic. So it's just going to repeat itself there. And it's going to repeat itself there. And you can kind of work with it this way. But you can see this is a little bit of a problem, right? Because we can't have, for it to be a function, we can have two outputs for one input and sometimes zero is going to be a little bit of an issue, time 24, time 48 and so on. So you kind of need to delete a point somewhere. So maybe you delete this point. So you're saying that theta of 24 is equal to zero. It's also equal to theta. Sorry, this is theta L times zero.  Maybe delete some points to make sure you get a function. And you just make it periodic everywhere. But actually, you get to choose what this function should be. So maybe you might think that there's, you know, is it, is it true that the sun just sort of gradually increases angle at a constant rate? Maybe that's true. You might think that, you know, maybe it's something more like this where sun increases. I'll just draw another function in here randomly. You might think it's more gradual like this green thing. And you could have something kind of more like that. It increases really quickly in the early part of the day and then kind of levels off. The angle doesn't change as quickly later in the day. So you have a lot of choice over what function to use for this. But in any case, you'll have at least two points to model your function on. And so you can, you know, go into Desmos and do a fit if you want, kind of mess around, see what kind of functions you might like there.  And maybe make these match up a to t plus a one to a to t squared plus a one t plus a zero. You might fit it to like a, some kind of parabola or something in this, this range or maybe you shift it around a little bit. You might do data. These are all theta L's of t. Maybe you want to do a one of t plus a not, which would be this like linear function situation. Maybe you think it's an exponential change.  So this is, we've looked at theta L of t. Let's look at theta L of t. Just remembering what these are in the physical situation theta L is just the angle of the sun where we haven't even talked about the leaf yet. L is the component. So the angle between the light ray and this normal vector for the leaf. So we'll need to model this as a function of time to. Again, we have to be a little bit careful with domains and ranges. The domains are again time values. The outputs are angles theta. And now we have to kind of fit this to our intuition from the picture or at least start there to figure out what kind of function to use. So we're examining the this kind of angle here between the green and the yellow vector. And if we like plot this on Desmos and just sort of thought of this like particle running around the circle sort of thing. See that the angle starts off being big.  This angle closes up to zero. And as L continues past like 12 noon. The angle is opening back up to something like pi halves. So maybe you get something like, there's pi halves. You're at time zero. Think about what happens at 12. What happens at 24. So it seems like we're at zero. Or sorry, we're at pi halves at time zero. We're at pi halves at time 24. Let me just double check something here. Yeah, should be fine. So the angle between these two start something like this. Maybe you think it's just kind of linearly increases if you chose the linear function for this one. You might think it's something more like this if it sort of changes the rate of change changes over time. Maybe it's something more like a parabola or something. You might think it kind of changes more gradually to something like that. So all of this is you have to choose sort of what function to use here. And okay, once you have all of this done, you are essentially ready to go for the last sort of the last part of the analysis for the stationary relief. So what will happen here is that you've come up with these functions theta ln of t, theta l of t. And these could be related in some way like you can maybe just do theta l of t and then do something to it to get theta ln of t. If you use some geometric considerations from this picture here, you might expect that these angles are related somehow. So maybe their functions over time are related to. But whatever you end up doing, what will happen is that you found out and see if I could find what we concluded from last time. Okay, so I can paste this in. Okay, so this is, I'm sorry, it's super blurry, but it's a little bit about what we talked about last time we were talking about. So f and g you're talking about here, these are corresponding to our theta, theta l of t, theta ln of t we're talking about today. The point is they can just be any functions. We concluded somehow that there was this energy density that depended on the vector, this light ray vector l. We found that it was proportional to the sign of theta one. We kind of did some derivation to get there. So you'll want to try to reproduce this sort of derivation when you're writing up your analysis. So you'll need some way of drawing geometric pictures and kind of arguing about, you know, why is this, why is this sign showing up? That should really be something you explain in the project. So once you have this, I guess I should say something a little bit more about what happened here. We found that E of l was proportional to sign of theta. And then we came up with this function that just gave us the vertical component. So I'm saying call that function g of t. And we made an assumption. This was assuming at some point we assumed that the vector had radius one. And this kind of made the analysis a lot simpler for us. The reason we did that is because we can actually go through. And at the end of the day, scale up that vector by whatever we want and we can scale it up by a function. So this function E of t is going to be something else you figure out from. You'll find energy density function. Sorry, realize we just have one minute left here. So I would look at the video for some more details on how this part will go and we'll talk about it more a little bit later. But the idea here is that the energy density hitting it. So this is energy density, say E on this axis as a function of time, it will max out like 136 or something. And you want some kind of function that does this kind of thing, probably more symmetric. And this will depend on time and should just, yeah, so you actually get to choose this too. So you have to kind of argue about. So the energy density kind of depends on this angle.  So theta ln was measuring the angle between the light vector and the plant. So this should be somehow related to the energy density.  So these two analyses should be tied pretty closely together. And what'll happen at the end is that total energy, let's say in a time period, delta T will be equal to essentially E of T times G of T times the area of belief times a little delta T. This is getting into a kind of a more complicated part of the analysis. So I'll say more about that. But kind of what you want to have to, you know, started on is definitely finding these angle functions and then starting to choose a synergy density function. Okay, so that video is up in. You'll see right now on your projects, definitely try to look that over and then I'll be in office hours, department office hours of four to five. Yep, that'll let you go. I'll post these notes up online. So to find like the light intensity, you do just like, could you use your time on your, as you're like kind of your X and your angle, because the angles change constantly right on the first part. And that could you like find the like vector or the, I don't know, it'd be like the hypotenuse, I guess. Would that be your light intensity? Essentially, when you go back to this picture here, the yellow vector coming in. In the first part we kind of assumed it was length one so we could find out what the component was. And then this EFT function you're doing is making this vector longer or shorter based on time. Okay, it's a little bit complicated. I'll try to have a demo for next time and hopefully make it a little bit more clear. Also my partner, like for the, we met on zoom and he found the leaf and stuff, and he was going to use, like the project says to you divide it into rectangles or something and then, but he was going to just do it like some sort of other way, I don't know, like some sort of other way to find the area that's more accurate. Like, and I was going to like ask, because I was like maybe we should ask if that's like, I don't know if maybe like they want us to use the rectangles, I don't know. Probably. Yeah, I think that's that's the intended way for this project. If you look at the video part of this. Part of what Kelly has lined up for people is to put this info in a spreadsheet. Yeah, so what this is is this is doing an approximation of something from calculus where we're measuring like little rectangles instead of doing something called the integral which does that precisely. Yeah, I remember like the Ramon sums or something like that from when I took calculus in high school, but I don't remember. Yeah, like I don't remember much of it, but I remember the Ramon sums. Yeah, exactly that same thing. And then at the end of the day what you're going to do is chunk up the day into like little two hour blocks, and then just evaluate this function at every two hours. And then we'll approximate it and if you imagine if you chunked it up into one hour blocks or like 30 minute blocks or 15 minutes, the approximation would get better and better and better. But we're just doing kind of a very rough approximation. Okay. Thank you. Thank you.


Hey guys, John Wise here with another Comigetting review this time it's going to be a Thor Ragnarok Which officially debuts today at your local theaters check it out I got a chance to go to one of the advanced screenings yesterday that would play last night at various theaters I went to the Avan theater here in Decatur, Illinois They were doing a five-dollar special On 2d or 3d with no upcharge So if you're in Decatur, Illinois, Central Illinois area and you have a chance to hit up the Avan theater on one of their special showings special Facebook showings Which means you'll have to like them on Facebook. That's the Avan theater Then you'll can Go and five dollars go see 2d or 3d Just FYI anytime you go see a 3d movie at the Avan theater. There is no upcharge So always happy to plug a local business But let's get on the topic at hand Thor Ragnarok the highly anticipated Marvel movie of the year For me it was Spider-Man So Thor Ragnarok Everybody's saying the best Marvel movie to date. I Strongly disagree Sorry, it's not the best Marvel movie Iron Man any Captain America movie Spider-Man homecoming Doctor Strange Not for Ragnarok So far to me as far as movies go, Thor has been the weakest of all I enjoy I really liked the first one the second one not so much the third one I like better than the second one but still It's it's just not Something wasn't right with this movie. I think They tried to go to Guardians with this movie. They really did they tried to they tried to go to Guardians of the galaxy with this a Lot of a lot of the things that you've heard about a lot too much a lot of humor Too much humor It tried like I said tried to go Guardians of the galaxy when I just should have stuck To the formula the first one had which took a Thor a little more serious But has some humor in it as opposed to too dark like a second And this one's just I think it really missed Missed was it funny? Of course. Yes. It was funny. They were very very funny moments in the movie And since at this point I should probably sit earlier. There's gonna be spoilers so for those of you Hulk fans who are we're hoping for a Decent Planet Hulk movie Sorry Is there a planet Hulk story here ish? kind of But don't expect this to be Thor Ragnarok with Planet Hulk B story line since it's not there Death goblum Don't look for the collector 2.0. He's not good. Is he related to the collector?  It's not goatee.   I love Jeff goblum. Well goblum is amazing But in this movie he just didn't fit Was he funny? Yes Hulk Hulk might have been one of the shiny moments of the movie honestly Yeah Was he funny yes And of course His alter ego Bruce Banner he was there he funny. Yeah, you're gonna hear me say this is over this person funny Yes, yes The only person that really wasn't meant to be funny and wasn't funny was the main villain Which is hella the queen of death the queen of hell Who in this movie plays Thor's Sister the firstborn of Odin who is released when spoiler spoiler spoiler Okay, I'm warning you ahead of that lots of spoilers in here Odin dies and then because he is holding holding her captive Captive and then he's released when he dies And why does he die? I'm not gonna go over that but we do find out what happened to Thor Or we do find out what happened to Odin At the end of ends of Thor Dark world the second Thor movie that was dark world I was called Thor 2 but yeah Loki's role in this movie Tom Hiddleston nails it as Loki another high moment of the movie is Loki Thor Chris Hemsworth He he's Thor And this this whole thing is moving. I apologize. My laptop screen is just moving. He's too He's not I don't know the something seemed off about his for this time around So yeah, I just I don't know I'm trying to I'm really trying to figure out what is wrong with uh Hemsworth's Thor he was Thor but I know it was almost like he was trying to be too much star lord. I guess would be would be the proper explanation Characters that were should have been taken more serious like Uh, the character of the executioner because they have a scourge um, again places a conquer leaf character but Um, Carl urban does a good job. Um, I've never known Carl urban to do a bad job. So Uh, and it's almost unrecognizable Uh with the bald head he's beefed up and everything So there were moments that I forgot Honestly, I wouldn't see the movie. I totally forgot he was in it. I kept seeing this guy. I was like that looks like Carl urban and it is so good job on on that um The character of sulter The flaming demon thing that you see In the trailer I know he's supposed to be taken more serious in the comic book Again, he plays kind of like awfully like a like a comic relief character between back and forth Thor It's just I don't it seems like a mess to me This plays out more like a sci-fi flash gordon Movie than it does a Thor movie to me And I get why they're doing it. They're trying to set things up for Thor To meet up with the guardians of the galaxy In the avengers movie So they're trying to get him more feel it more familiar with that type of air, you know environment But I just came off Uh, just it just there was something that was really weird about it. I just I don't know Um, my big beef was there was too much humor speaking of cameos This for me was the highlight of the movie. Yes Dr. Strange does appear in the movie. He does cameo And it was it was it was that that that whole thing was also very humorous We see a lot most a lot of the scene that takes place in Thor Ragnarok is a scene we already saw at the end of Dr. Strange So not only was that kind of a teaser, but it was also the main scene of the camp his cameo in Thor Ragnarok Um, but there were various events that took place before and after that were quite humorous But yeah, and he does still wear the yellow gloves, which freaking I geeked out over the whole thing Um I apologize. Should we look this way or look this way? I'm at work So I kind of have to keep out an eye out for customers so Um, overall was it an enjoyable movie? Yes. Did I like the movie? Yes Did I have issues with it more than I would like? Um, is it the best marvel movie? No Um, not the best marvel movie Like I said, um the captain america trilogy um Avengers iron man Uh spider-man homecoming dr. Strange Um Guardians of galaxy all these Uh, I would sit down and watch multiple times even at the theater Thor Ragnarok for me is a one time view at the theater. I'll see it again when it comes out on blu-ray I don't know how many times I'll see it when I get it, but I'll get it on blu-ray. I'll watch it and um Yeah, that's that's my thoughts on Thor Ragnarok Um If you've already seen it or you've seen seen it say today or tomorrow You've seen Thor Ragnarok. Let us know what you think. Let me know what you think Do you agree with me? Do you disagree with me? Let us know down in the comments below Also, please make sure you like subscribe and Tune in for more come again reviews here on come again tv on youtube Thanks for watching


I really want to thank India and Indian Presidency for hosting us and being such beautiful kind hosts and we've appreciated the discussion with all of the delegates and look forward to future discussions on promoting decent work and social justice. The hospitality is amazing, it's tremendous, it was wonderful food, wonderful people, everybody is very very friendly, very very friendly and to be honest I think the prettiest for me is the colours, it is a very colourful country and a very colourful society and culture. The Presidency is deploying a lot of efforts to welcome us here and the hospitality is amazing. We have not only great hosts in the room, facilitating the discussion making it very smooth and easy but also outside giving us some social programs, inviting us for social events in the evenings and this also creates team building in the group and improves our outcomes in the deliberations. I think there was progress, a lot of discussion, most importantly there was dialogue and I think we have made some steps forward which is very important given the subject. Yoga plays a really special part in that part of your life, being so healthy. So yoga in Brazil is very popular and I think we all acknowledge the benefits and the gifts that India gave us as giving us yoga.


Live from Las Vegas, it's theCUBE! Covering AWS re-invent 2019. Brought to you by Amazon Web Services and Intel, along with its ecosystem partners. Good afternoon. Welcome back to theCUBE's coverage of AWS re-invent 19 from Las Vegas. I'm Lisa Martin, a co-host as Justin Warren, the founder and chief analyst at Pivot9. Justin, great to have you. Great to be here. Thanks to be in the hosting chair today. Yeah, yeah, always fun. Let's have a great conversation next, shall we? Shall we, well. All right, please meet a couple of our guests that have joined Justin and me. I've got Dan Hubbard, to my love, CEO of Lacework, and Ilan Rabinovich, the VP of Product, a data dog. Guys, welcome. Thanks for having us. For having us. Our pleasure. Good to be here. Love, anytime we can talk about dogs, even if there's no relation to the actual technology, two thumbs up from me. So, but let's go ahead, I know that you guys have both been on or your companies have, but give our audience, Dan, we'll start with you, a refresher, an overview, Lacework. What do you guys, what do you do? Yeah, Lacework, we wake up every morning with a goal of trying to help our customers secure their public cloud infrastructure and or any type of cloud native technologies, such as Kubernetes or containers or any microservices. So, a security company for the cloud and cloud native technologies. Awesome, and Ilan, give us a refresher about DataDog. DataDog's a monitoring and analytics platform for your modern infrastructure and applications. So, microservices, containers, cloud providers like AWS were here at re-invent. Our goal is to help teams collaborate and to understand the health of their business and their applications and their infrastructure. So, how do you guys work together? So, we recently announced a partnership and an integration of the intelligence and the data of all the risks and the threats that Lacework is identifying, being sending those automatically inside of the DataDog platform. So, we're putting the data from our platform directly into obviously the monitoring, the metrics platform of DataDogs. Yep, and so, we're pulling that intelligence from Lacework into our platform for our new security monitoring platform in addition to enriching it with metrics from our infrastructure and application monitoring. We find that a lot of times the first signs that something's going wrong might be a change in how your infrastructure or your applications are performing or a request that came in. And so, if we're able to marry the two together, it's a better together story, give people much clearer insights into what's going on. So, security's been a really tricky thing to solve for as long as I've been in computing, which is longer than I care to remember. But walk us through, what does this extra visibility actually provide to customers? One of the big issues, it seems to be that security's just too hard. So, how does this make security easier for customers? So, one of the big trends that we're seeing is that security and infrastructure were, in the past, very separate groups. Silo's didn't, many times didn't know each other or talk to each other. But DevOps is becoming a unifying force of data, intelligence, and infrastructure. You know, it's infrastructure as code, it's a little bit different, like AWS for example, but it still is infrastructure. So, the combination of security and infrastructure comes together when you get DevOps. Some people call it secure DevOps, DevSecOps, SecDevOps, whatever you want to call it. But really bringing those two together is finally the first time really where there's a meaningful connection at the data level that allows you to actually combine both. Exactly, and so as all of these teams are taking advantage of infrastructure as code and other DevOps best practices, the security teams are looking at this and saying, how do I get earlier in the cycle? How do I make sure that code is enforcing this? So, I'm scaling with automation, scaling with code rather than with people. And then, as they start to do that, they realize that the data that's in the security Silo and that's in the application or infrastructure Silo is actually very relevant to one another, right? If a crypto miner shows up on your systems, the first thing it's going to do is spike your CPU. Something like Lacework will detect that as well. If we both look at both those signals, we'll detect it faster. Go ahead, Justin. This is a bit of, that's the reactive side of security, which is there's a threat happens and you react to that, but part of DevSecOps or whichever term you want to actually use, part of that is to actually shift left and try to get rid of these security flaws before they even happen in the code, which is a lot of software development. I like to say that the first 80% of software development is putting the bugs in and the second 80% is taking them out again. So, how do you help developers actually remove all of the security vulnerabilities before they even make it into production code? So, just like metrics and monitoring allow you to look at the quality of your infrastructure or very early in the pipeline. Security needs to go there also. And it's really, there is no time. It's just a continuous cycle. Early what we allow you to do is to look at your configuration and check to see if your configuration is changing in a way that is leaving you at risk or an exposure. What's particularly interesting about this partnership is that quite often security people don't know enough about the application or the infrastructure to know if it's a risk. It's actually the DevOps people that know. So, security people, when we send an alert many times to a security person, they scratch their heads and go, I don't know if this is good, bad, or indifferent. The DevOps people look at it and go, oh yeah, this is definitely okay. That's the way our infrastructure should work. This is the way our application should work. Or they say, oh no, this is a big problem. Let's get security involved. So, doing that early is really critical. And again, it's all about breaking down. I mean, if DevOps was all about breaking down silos between Dev and operations and other parts of the business, DevSecOps or SecureDevOps or whatever we want to call it is just bringing more people into the fold and helping security join that party and get at things earlier in the cycle so we can catch it before it. You know, before there's a breach that's in the news. Right, to be able to be predictive, which is, and then prescriptive, which is what a lot of businesses would love to be able to be. I'd like to get your opinion, Dan, on how cloud native, cloud, and the transformation of cloud technologies is changing the conversation within the customer base. One of the things Andy Jassy said yesterday is that transformation has got to be driven from the top down, like true business transformation so that a company isn't Uberized, for example. Are you seeing that, are these, for example, what you're talking about with enlightening the DevOps folks and SecureDevOps bringing them together so that they can be more collaborative? Are you seeing that come from more of a top down approach in terms of how do we leverage our data better, make sure that we have security and are able to securely extract insights from the data or is it still kind of from both ends? It depends on the company, it's very diverse. What we see a lot is in large companies that are migrating to the cloud, that weren't born in the cloud, every company they're buying is a cloud native company. So they buy these new companies and everyone looks at the new company and goes, wow, that's amazing, they can move so fast, they are super forward thinking and they're pushing code and they're more efficient than us, we want to do that also. So it just kind of breeds the innovation and the speed from an M&A perspective. In the cloud native side, what we see is it depends on your tenure as a company when you really want to take security seriously. Usually B2B companies take it more seriously than B2C for example, but it's usually, when your customers start asking you how secure are you, is when people start paying attention. We would like it to be before that, but it's not always before that. Yep, I think it's from both directions. It depends on the size of the company and the culture, but you can't dictate culture, right? So, and a lot of these silos and a lot of these camps and fiefdoms that start to exist within organizations that have caused these groups to be separate, they weren't necessarily top down, it's just, it's human to human interactions and so you can't just walk in and say, you must now be collaborative. The executives have to beat that drum and help people understand why that's important to the business, but the folks on the ground have to actually want to be friends, want to talk, want to collaborate on projects, want to pull people in earlier and once they have that human connection, it's a lot more successful, so you have to do both. I mean, what we're seeing is as IT becomes more distributed and security is more centralized, you run into problems. So, the people that are getting it right are distributing security as close to those teams, whether it's a scrum team, a weekly get together, you know, whatever it is, to get that human interaction together, because if you don't understand the application and what people are working on, how are you going to understand the risks and the threats and the models, so distributing it is really key. And it's important those security teams understand the business requirements as well. Sometimes the most secure answer isn't necessarily the answer that actually serves their customers. Sometimes, and sometimes app teams don't understand the trade-offs that security people may understand, so it has to be a partnership, yeah. But you mentioned cultural change is probably harder than anything else, especially if there's a legacy organization and Dan to your point, a lot of the acquisitions they're doing are of cloud native companies who are presumably much fresher, maybe have a younger workforce. That's hard to do. Ultimately, though, what a business needs to look at is the legacy business. There's probably somebody in my review mirror is a lot closer than I might think that is more agile, more nimble than we are, has great technology, and the aptitude and the culture to be able to move faster. How do you see some of these enterprises that you work with together? Let's put them in the context of they're an AWS customer. How are you seeing these enterprise organizations that are adapting and acquiring cloud native businesses, how are they able to pivot at the speed they need to use cloud technology, understand the security issues that they can remediate, and really take that data to what it should be, which is a business differentiator. Yeah, I mean a lot of the times you run into the DevOps people say security slows us down, they're getting in our way, and security says developers are insecure, we're totally going to get breached. So one of our models is you got to move with speed and safety. As soon as you get in the way of anything, typically the developer and the application's going to win. So you got to figure out where to get involved in that. In really big companies what we've seen that are very acquisitive is they're moving this as security to a central governance role and maybe have tooling and some specialty teams, and then they're distributing security baked as deep into the development infrastructure as they can, and then they have groups which kind of work together broadly across that. So you can structurally set it up that way, I think. And if you have the incentives right, nobody's looking to create a security breach or a vulnerability, they're going, well, I mean engineers and your employees have the company's best intentions at heart, otherwise they wouldn't work there. So they're looking to do the right thing. You just have to make it easy for them with, and some of that's tooling, some of that's culture, some of that's just starting the conversation, not the day of the release. Start it when the first line of code's being written, what would it take for us to solve this problem in a secure fashion, and then everybody's happy to work together. They just don't want to redo things the day before the launch and have to be slowed down. Well that technical debt becomes a real problem if they have to do that. I think one of the great things about our technical partnership and integration here is, security in the past has always been just very binary. Are we insecure or secure? That's it. There's all kinds of nuances around it, and that's what lends itself to metrics. What are our metrics? How are we doing? What's our risk? What's our exposures? Is it getting better over time? Is it worse over time? So there's always the doomsday scenario, but there's also the what's happening over time and are we getting better at what we do? And metrics really lends itself to that. And that comes right back to that, some of those DevOps philosophies of continuous improvement and continuous learning. Bringing that into the world of security is just as critical. So you mentioned culture, you mentioned transformation, you mentioned metrics, three things, very close to my heart. We keep hearing that security is becoming a board level conversation. So a lot of this is very technical, and DevSecOps is down here with the technical people, but that structure of the organization that you referred to and changing that structure and setting the culture, that tends to come from the top level. And we heard from Andy in the keynote yesterday that that is very, very important. So what are the sorts of conversations you're having with senior management and board level from what your products do together? What does that look like from the board's perspective? So learning to manage risk, looking at how are we doing, how much of what you do is actually available to the board for them to make their job easier. I think one of the exciting trends is that compliance is cool again. Right. Compliance is never a cool thing, you know? Compliance is kind of a boring thing. The auditor's coming once a year, you know, you get stuck with it and away you go. But now compliance is continuous. It's always running. And it's more about risks and exposures. And am I adhering to compliance via the risks and exposures? Executives, it's very challenging to explain things like Kubernetes and pods and nodes and all this technical acronyms in Mambo Jumbo that we live in every day, you know, in this world. But compliance is real. Are we PCI, SOC, are we applying best standards and best practices? So the ability to pull that in either via a metrics dashboard or through measurable things over time I think is really key as part of that. And similarly, as folks are moving, you know, whether they're moving new applications, existing applications from, you know, a legacy or on-prem environment into the cloud or building something from scratch. It's, you know, visibility on compliance is important. We can bring that into our dashboards and sort of into the tooling that executives can look at over time. But also just understanding, am I done with the migration? Is my application there? Taking this nebulous thing that is a cloud and making it a tangible asset that you can look at and see the health and progress on over time in Datadog has significantly sped up many of our customers' cloud migrations. They often get stuck in a sort of analysis paralysis. Are we performing the same as we did in the data center? I don't know. Are we as secure? Can we move this workload? And tooling like Datadog, like Lacework and the two together helps them put that into something concrete that they can say, actually, yes, we're ready to go or no, there's these three things we need to do first. Let's go do them. It's really challenging for traditional security people in this new world order because it's very ephemeral. Things change all the time. It used to be like I got five racks, I got 22 hundred servers, these are the IPs, and that's it. Now it's like, what time is it? I don't know what I have, so invisibility is key. You used to be able to have a server that you might have monitored throughout your tenure at a company, now you probably can't monitor it through the tenure of your lunch, yeah. How much, last question for you guys, how much do you see of a lift or an impact from something like the Capital One data breach that happened a few months ago? You talked about B2B being more on it in terms of B2C, but we see these breaches that, and many generations that are alive today, understand to some degree, is that, in terms of getting insight into where are all of our risks and villain bills and needing to get that visibility on it, do you see some of these big breaches as catalysts for businesses to go, whoa, we have a lot at stake here. We don't really try to understand what the heck's going on and what we own. I mean, security has a very bad reputation of fear, uncertainty, and doubt. I've been in the industry for a long time. That said, those moments do get up very high, especially somebody like Capital One, who's known to be one of the most sophisticated cloud security organizations on the planet. So it certainly piques people's interests. I think people get carried away, maybe on the messaging side of things, but in order for a security market to get really big, you have to have a big IT, transform a trend, you have to have a very diverse attack surface, and you have to have the beginnings of breach. If you don't have the beginnings of breach, you spend all your time convincing people there may be a problem, and because there is problems that are happening almost every week and are getting published, many of them are being acknowledged publicly, it does help, it definitely helps the conversation. I don't think that, there are a lot more breaches in the news off to some extent because there's a lot more tech companies using, going through these digital transformations having tech news. I don't know that this is cloud versus not cloud. What cloud does however, introduces new concepts and new workflows that security teams need to understand and that application teams need to understand, and so this is where the new breed of tooling and education comes in is helping people be ready for that. And yeah, of course, anytime there's a headline on any of the big news shows, of course the first thing we're going to do is say, well clearly they're going to bring on Dan, one of our security experts of some of the industry to talk about how you prevent that in the future, and so it does bring some attention our way, but I think that's great, it's reminding people of what's important. And one of the conversations we have with our prospects is have you ever had a breach before? They're always going to say no, of course, but then you ask, how do you know? How do you really know that? And then let's walk through how you would actually find that out if you did know, and that's a very different conversation than, oh my traditional data center, I would know this way. So it's just very different. Interesting stuff, guys. Thank you for sharing with us, and congratulations on the integration with Datadog, and Lacewick, we appreciate your time. Thank you for having us. Our pleasure. For Justin Moran, I'm Lisa Martin, and you're watching theCUBE live from AWS ReInvent 19 from Vegas. Thanks for watching.


Drink two cups of water and you get a surge of the adrenal hormone noradrenaline in your bloodstream, as if you just smoked a few cigarettes or downed a few cups of coffee, which boosts your metabolic rate up to 30% within an hour, which, when put to the test, your randomized controlled trials appear to accelerate weight loss by 44%, certainly making it the safest, simplest, and cheapest way to boost your metabolism. Now, if you're on a beta-blocker drug, this entire strategy may fail. Beta-blockers are typically prescribed for heart conditions or high blood pressure, and tend to end with the letters LOL, such as a tenolol, natolol, or propranolol, sold as to Norman Korgard or Inderal, respectively. So, for example, if you give people the beta-blocker drug Mentoprolol, sold as low pressure, before they chug their two cups of water, the metabolic boost is effectively prevented. This makes sense, since the beta that's being blocked in beta-blockers are the beta receptors triggered by noradrenaline. Otherwise, though, the water should work, but what's the best kind of dose-type temperature and timing? Just a single cup may be sufficient to rev up the noradrenaline nerves, but additional benefit is seeing them at two or more cups. Caution, one should never drink more than three cups in an hour, though. Since that starts to exceed the amount of fluid your kidneys can handle. If you have a harder kidney failure, your physician may not want you drinking extra water at all, but even with healthy kidneys, any more than three cups of water in an hour can start to critically dilute the electrolytes in your brain with potentially critical consequences. In How Not to Diet, I talk about the first patient I ever killed in the hospital as an intern. I was a guy who drunk himself to death with water. He suffered from a neurological condition that causes pathological thirst.  Anyways, doesn't have to be plain straight water? Shouldn't seem to matter, right? Water is water, whether flavored or sweetened in some diet drink, but it does matter. When trying to prevent fainting before blood donation, something like juice doesn't work, as well as plain water. When trying to keep people from getting dizzy when they stand up, water works, but the same amount of water with salt added doesn't. What's going on? We used to think the trigger was stomach distention. When we eat, our body shifts blood flow toward a digestive tract in port by releasing noradrenaline to pull in blood from our limbs. This has been called the gastrovascular reflex. So drinking water was thought to be just a zero calorie way of stretching our stomach. But instead, drink two cups of saline, basically salt water, and the metabolic boost vanishes, so stomach expansion can explain the water effect. We now realize our body appears to detect osmolarity, the concentration of stuff within a liquid, covertly slip liquids of different concentrations into people's stomachs with a feeding tube, and you can demonstrate this by monitoring sweat production, which is kind of a proxy for noradrenaline release. This may be a spinal reflex, as it's preserved in quadriplegic, or picked up by the liver, as we see less noradrenaline release in liver transplant patients who've had their liver nerves severed, whichever the pathway our body can tell. Thought we only had five senses? The current count is upwards of 33, so maybe the Bruce Willis movie should have been called the 34th sense. In my Daily Dozen recommendation, I rank certain teas as among the healthiest beverages after all. They have all the water of water with an antioxidant bonus, but from a weight loss perspective, plain water may have an edge. That may explain the study showing overweight and obese individuals randomized to replace diet beverages with water lost significantly more weight. This was chalked up to getting rid of all those artificial sweeteners, but maybe instead the diet drinks were too concentrated to offer the same water-induced metabolic boost. Diet soda, tea, asked about 10 times the concentration of dissolved substances compared to tap water. So plain water on an empty stomach may be the best. Does the temperature of the water matter? In a journal published by the American Society of Mechanical Engineers, an engineering professor proposed that the secret of a raw food diet for weight loss was the temperature which the food was served. To bring two cups of even just room temperature water up to body temperature, he calculated, the body would have to dip into its fat stores and use up 6,000 calories. Look, just do the math, right? He says calories defined as the amount of energy required to raise one gram of water, one degree Celsius. So since two cups of water is about 500 grams, and the difference between room temp and body temp is about a dozen degrees Celsius, 500 times 12 equals 6,000 plus calories needed. Anyone see the mistake? In nutrition, a calorie is actually a kilocalorie, a thousand times bigger than the same word used in the rest of the sciences. Confusing, right? Still, I'm shocked the paper was even published. So, drinking two cups of room temperature water actually only takes six calories to warm up, not 6,000. Now, if you were a hummingbird drinking four times your body weight and chilling nectar, you could burn up to 2% of your energy reserves, warm it up, but it doesn't make as much of a difference for us. What about really cold water, though? A letter called the Ice Diet, which was published in the Annals of Internal Medicine, estimated that eating about a quart of ice, like a really, really big snow cone with no syrup, could rob our body of more than 150 calories, the same amount of energy as the calorie expenditure in running one mile.  I mean, what your body does is just crowds more of the waste heat you normally give off by constricting blood flow to your skin. How does it do that? Nor a dremel. If you compare drinking body temperature water to room temperature water to cold water, there's only a significant constriction in blood flow to the skin after the room temp and cold water, and neither the warm or tepid water could boost metabolic rate as much as cold fridge temperature water. So, your body does, after all, end up at least indirectly burning off more calories when you drink your water cold. So, two cups of cold water on an empty stomach a few times a day. Does it matter when? Yes, watch my evidence-based weight loss lecture to see how you can add the benefit of negative calorie preloading by drinking that water right before your meals.


The Williams & Spookfest is returning for 2023 with a twist. It will be held indoors at the Williams & Field House. Spookfest will include pumpkin carving, trick-or-treat, costume contests, and more. So Spookfest is an annual event that the CBB hosts and basically kids get to come out and trick-or-treat. It's free for families to attend. We have vendors that set up. We have music. There's a costume contest that's going to be happening. We have a pumpkin carving contest. And then new to this year, we have a fire performer that will be there the entire evening. And also new this year, the King Cole premiere was supposed to be happening in conjunction with the King Cole Parade last month. But due to weather, we have decided to move it and we're going to host that earlier in the day at around two o'clock on the same day as Spookfest. You want to save money and Appalachian Wireless gets that. Right now you can get up to $650 off select devices, including the latest and the greatest on the Advantage Unlimited plan with a trade-in. Did y'all hear me? Up to $650 off select devices, including the lightest and greatest with a trade-in. I'm not a math whiz, but this deal it's amazing and you'll be on the region's premier network. We are you. We are Appalachian Wireless. The festival is free to attend and begins at 5 p.m. Saturday, October 21st. We just we really want to see everybody get out and have a good time. I think everybody is still recovering from being indoors so much with COVID. So any chance that I know my family has to get out, we definitely want to get out and it's really important to host for events for the community as well, so that everybody's got an opportunity. You know, if you can't travel, you can come down the road or trick-or-treat is not happening in your town on the same night. It's really nice to see that there's a bunch of different options for the kids to come out. And as a mom, I really like having my kid be able to wear their costume more than more than once. And I know my kids love it too. So we just love getting the community out. For more information, go to Williamson Spookfest on Facebook. Reporting for Mountain Top News, I'm Breonna Robinson.


What's going on everyone Sam here with late in sports cards ripping one box of 21 Bowman Sterling baseball for Chris L It's a good luck here Chris. See what we got 21 Yeah, Creed Humphrey is a good example like Zach Martin back in 2014 was always a great example Quentin Nelson another good one Trying to think who else is big good rookie o-line man Rashaun Slater was a good one when he's healthy Mackay Bekdon used to sell extremely well Andrew Thomas sells very well now But yeah, I mean it's it's pretty solid honestly, man three crews again This is this is 21 so there won't be any alley, but there'll be some other nicer Nice guys in here too like Torx got it in this. Yeah, Penne Sewell is another one who sells fairly well Still haven't redeemed it All right first pack for you here Chris. Good luck, buddy Same here all of your rookies and stuff will be sleeved in top load I'm not gonna sleep him at this very point in time Debbie Garcia. There's an Andrew Vaughn rookie Pache rookie first auto Nick York. That's going for the Red Sox nice one there definitely a very solid solid prospect for Boston unfortunately It's a wander and a G rod Yeah, Joe Thomas is another classic one. Yeah, Joe Thomas always sells really well Bro, then I don't really Yeah, dude I bought like for I bought like a creed Humphrey certified rookie to like 499 for like a dollar And I sold it for like 25 on eBay.  We've got Emerson Hancock That is going to the Mariners Nice Mariners auto for you there Chris congrats again, buddy Got Luis Patino and Tariq school.  I'll be get I'll be picking those up Dane Dunning there's another Alejandro Kirk. We've got nice Jason Dominguez 12 out of 25 There you go, Chris. Nice one there, buddy. We'll take a Martian 12 out of 25. That'll work on the blue You've got that's Alexander Ramirez for the Angels on the prospect auto We've got Louise Garcia and Xavier Edwards Yeah, that'll the Dominguez will work for sure that'll play that'll play big-time Hessem Kirstead Thomas Christian Robinson. We got Justin Foscue for the Rangers nice one there as well on the prospect auto Justin Foscue Austin Martin nice one there and a Mackenzie Gore Nationals legend Mackenzie Gore now All right last box or last mini box. I guess I should say Empty O'Neill cruise would be pretty awesome out of this for sure. I'd be I'd be in on an O'Neill cruise for events Nate Pearson Is that gonna be an insert auto? Oh That's sick 84 out of 199 6-dose Sanchez Dude, this is so cool Chris how about an insert auto 14 out of 99 Joey Vado on the on-card Nice one there man. That is all that is so freaking cool Giant Joey Vado signature on that one too a gorgeous gorgeous parallel And 14 out of 99 on the Vado auto and we've got Nick Gonzalez and Matthew Allen That'll do it for your break there, Chris. Thanks again for jumping in buddy. We appreciate it. We'll get them right out to you