from San Jose, it's theCUBE. Presenting Big Data Silicon Valley, brought to you by SiliconANGLE Media and it's ecosystem partners. Welcome back to theCUBE's continuing coverage of our event, Big Data SD. I'm Lisa Martin, joined by Dave Vellante. And we've been here all day, having some great conversations, really looking at Big Data, cloud, AI machine learning from many different levels. We're happy to welcome back to theCUBE one of our distinguished alumni, Ron Bodkin, who's now the technical director of Applied AI at Google. Hey, Ron, welcome back. Oh, it's nice to be back, Lisa, thank you. Yeah, thanks for coming by. Thanks, Dave. So you have been a friend of theCUBE for a long time. You've been in this industry, in this space for a long time. Let's take a little bit of a walk down memory lane.  Sure, you know, so I first got involved in Big Data back in 2007. I was VP Engineering at a startup called Quantcast in the online advertising space. We were using early versions of Hadoop to crunch through petabytes of data and build data science models. And I saw a huge opportunity to bring those kind of capabilities to the enterprise. We were working with early Hadoop vendors. Actually, at the time, there was really only one commercial vendor of Hadoop. It was Cloudera, right? And we're working with them and then others as they came online.  Why was Hadoop an open source Big Data interesting? What did it mean to build a data lake? And, you know, we always said, look, there's going to be a ton of value around data science, right? Putting your Big Data together, collecting complete information and then being able to build data science models to act in your business. So, you know, the exciting thing for me is, you know, now we're at a stage where many companies have put those assets together. You've got access to amazing cloud scale resources like we have at Google to not only work with great information, but to start to really act on it. Because, you know, kind of in parallel with that evolution of Big Data was the evolution of the algorithms as well as, you know, the access to large amounts of digital data that's propelled, you know, a lot of innovation and AI through this new trend of deep learning that we're invested heavily in. I mean, the epiphany of Hadoop, when I first heard about it, was bringing, you know, five megabytes of code to a petabyte of data as sort of the bromide. But, you know, the narrative in the press has really been, well, they haven't really lived up to expectations. The ROI has been largely reduction on investment. And so, is that fair? I mean, we've worked with practitioners, you know, all your Big Data career and you've seen a lot of companies transform. Obviously Google's Big Data company is probably the best example of one. Do you think that's a fair narrative or did the Big Data hype fail to live up to expectations? You know, I think there's a couple of things going on here. One is, you know, that the capabilities in Big Data have varied widely, right? So if you look at the way, for example, at Google we operate, you know, with Big Data tools that we have, they're extremely productive, work at massive scale, you know, with large numbers of users being able to slice and dice and get deep analysis of data. It's a great setup for doing machine learning, right? That's why we have things like BigQuery available in the cloud. You know, I'd say that what happened in the open source Hadoop world was, it ended up settling in on more of the subset of use cases around how do we make it easy to store large amounts of data inexpensively? How do we offload ETL? How do we make it possible for data scientists to get access to raw data? I don't think that's as functional as what people really had imagined coming out of Big Data, but it sort of served a useful function in complimenting what companies were already doing at their warehouse, right? So I'd say those efforts to collect Big Data and to make them available have really been a, they've set the stage for analytic value both through better building of analytic databases, but especially through machine learning. And there's been some clear successes. I mean, one of them obviously is advertising. Google said a huge success there, but much more in fraud detection, you're starting to see, you know, healthcare really glomm on, financial services have been big on this. You know, maybe largely for marketing reasons, but also risk, you know, for sure. So there's been some clear successes.  Your thoughts on that premise? You know, I mean, I definitely think there is a lot of truth to that. I think some of it was, there was a hope that a lot of people thought that, you know, Big Data would be magic, that you could just dump a bunch of raw data without any effort, and out would come, you know, all the answers, right?  There's always a level of, you have to at least have some mobile structure in the data. You have to put some effort in curating the data so you have valid results, right? So it's created a set of tools to allow scaling. You know, I mean, we now take for granted the ability to have elastic data, to have it scale and have it in the cloud in a way that, you know, that just wasn't the norm. Even 10 years ago is like, people were thinking about very brittle, limited amounts of data in silos was the norm. So the conversations changed so much, we almost forget how much things have evolved. Speaking of evolution, tell us a little bit more about your role with applied AI at Google. What was the genesis of it, and how are you working with customers for them to kind of leverage this next phase of Big Data and applying machine learning so that they really can identify, well, monetize content and data, and actually identify new revenue streams? Absolutely, Lisa. So, you know, at Google, we really started the journey to become an AI-first company early this decade. You know, a little over five years ago, we invested in the Google X team. Jeff Dean was one of the leaders there, started to invest in, hey, these deep learning algorithms are having a big impact, right? And, you know, Fei-Fei Li, who's now the chief scientist at Google Cloud, was at Stanford doing research around how can we teach a computer to see and catalog a lot of digital data for visual purposes, right? So combining that with advances in computing, with first GPUs, and then ultimately we invested in specialized hardware that made it work well for us, and massive-scale TPUs, right? That combination really started to unlock all kinds of problems that we could solve with machine learning in a way that we couldn't before, right? So, it's now become central to all kinds of products at Google, whether it be the biggest improvements we've had in search and advertising, coming from these deep learning models, but also breakthroughs like, products like Google Photos, where you can now search and find photos based on keywords from intelligence in a machine that looks at what's in the photo, right? So, we've invested and made that a central part of the business, and so what we're seeing is, as we build out the cloud business, there is a tremendous interest in how can we take Google's capabilities, right? Our investments in open source, deep learning frameworks, TensorFlow, right? Our investments in hardware, TPU, our scalable infrastructure for doing machine learning, right? Where we're able to serve, you know, billion inferences a second, right? So, we've got this massive capability we've built for our own products that we're now making available for customers. And customers are saying, how do I tap into that, right? How can I work with Google? How can I work with the product? How can I work with the capabilities? And so, you know, the Applied AI team is really about how do we help customers drive these 10x opportunities with machine learning, partnering with Google. And the reason it's a 10x opportunity is, you've had a big set of improvements where models that weren't useful commercially until recently are now useful and can be applied, right? So you can do things like translating languages automatically, like recognizing speech, like having automated dialogue for chatbots, or, you know, all kinds of visual APIs, like our AutoML API, where engineers can feed up images and it will train a model specialized to their need to recognize what you're looking for, right? So those types of advances mean that all kinds of business processes can be reconceived of and dramatically improved with automation taking a lot of human drudgery out, right? So customers are like, that's really exciting. And at Google, you're doing that. How do we get that, right? We don't know how to go there. Well, natural language processing has been amazing in the last couple of years. Not surprising that Google is so successful there. I was kind of blown away that Amazon with Alexa sort of blew past Siri, right? And so thinking about new ways in which we're going to interact with our devices, it's clearly coming. So it leads me to my question on innovation. What's driven, in your view, innovation in the last decade and what's going to drive innovation next 10 years? I mean, I think innovation is very much a function of having the right kind of culture and mindset, right? So, I mean, for us at Google, a big part of it is what we call 10X thinking, right? Which is really focusing on, how do you think about the big problem and work on something that could have a big impact? You know, I also think that you can't really predict what's going to work, but there's got a lot of interesting ideas and many of them won't pan out, right? But the more you have a culture of failing fast and trying things and at least being open to the data and give it a shot, right? And say, is this crazy thing going to work, right? I mean, that's why we have things like Google X where we invest in moon shots, but that's why throughout the business, we say, hey, you can have a 20% project, you can go work on something and many of them don't work or have a small impact, but then you get things like Gmail getting created out of a 20% project, right? It's a cultural thing that you foster and encourage people to try things and be open to the possibility that something big is on your hands, right? On the cultural front, it sounds like in some cases, depending on the enterprise, it's a shift in some cases, it's a cultural journey. The Google on Google story sounds like it could be a blueprint. How do we do this? You've done this, but how much is it a blueprint on the technology capitalizing on deep learning capabilities as well as a blueprint for helping organizations on this cultural journey to be actually being able to benefit and profit from this? Yeah, I mean, it's absolutely right, Lisa, that these are both really important aspects, right? That there's a big part of the cultural journey. You know, in order to be an AI first company to really reconceive your business around what can happen with machine learning, it's important to be a digital company, right? To have a mindset of making quick decisions and thinking about how data impacts your business, right? And activating in real time, right? So there's a cultural journey that companies are going through, right? How do we enable our knowledge workers to do this kind of work? How do we think about our products in a new way? How do we reconceive, think about automation, right? There's a lot of these aspects that are cultural as well, but I think a big part of it is, you know, it's easy to get overwhelmed, right, for companies, but it's like, you have to pick somewhere, right? What's something you can do? What's a true north? What's an area where you can start to invest and get impact and start the journey, right? Start to do pilots, start to get something going. What we found, you know, certainly I found in my career has been when companies get started with the right first project and get some success, they can build on that success and invest more, right? Whereas, you know, if you're not experimenting and trying things and moving, you're not, you're never going to get there. Momentum is key. Well, Ron, thank you so much for taking some time to stop by theCUBE. I wish we had more time to chat, but we appreciate your time. Oh, it's great to be here again. See you again, thanks. We want to thank you for watching theCUBE Live from our event, Big Data SV in San Jose. I'm Lisa Martin with Dave Vellante. Stick around, we'll be back with our wrap shortly.


Hi, I'm Zor. Welcome to Unizor education. I would like to spend some more time and talk about the higher-order ordinary differential equations. Well, higher order actually means the second order. Don't want to go any further than that. That would be kind of pure theory, which actually I'm not interested in right now because I would like to demonstrate the higher order differential equations as they are applied to physics. Now, the previous lecture was about acceleration and I had a primitive second-order differential equation which looked like this. Some kind of function. Now, I will just do a little bit more difficult in this particular case. So, that equation was just a very simple one. You integrate twice and you will get function x of t. Now, I would like to apply a little bit different logic and the application is a very physical problem, which is related to the law which is called Hooke's law. That's about a spring. So, I will have a little bit bigger picture here. So, let's assume that you have a spring which is fixed on the left end and here you have some kind of a point mass m. Now, let's assume that this particular string is horizontally stretched and this mass is lying on the table, frictionless table. So, the mass can move left and right along this line, which we will assume this is an x line. Now, this is a neutral position. So, this will be x is equal to zero and what our experiment is, we stretch this particular mass to another position, let's say d. So, this is length d. We stretched it by d from its neutral position. So, question is what happens next if we will just let it go from this point. Well, first of all, we know the equation force is equal to mass times acceleration. Well, acceleration, we know what this is. This is second derivative of the time of the x-coordinate by time. Now, mass is fixed. That's fine too. But the force f is not a fixed force and it's not dependent basically directly on time because we don't really know how it depends on the time. We do know the experimental Hooke's law, Hooke-Hook's law, which says that the force actually by its value proportional to a distance we have stretched our spring. Well, obviously, this is an experimental law and its approximation, obviously. Obviously, it depends on the material the spring is made and it depends on how much we stretch it because sometimes we can really overstretch spring in such a way that it will not return back at all. It will deform completely. But within certain reasonable limits, our spring obeys the Hooke's law and we can say that our force is actually proportional to a displacement of its end from the neutral position. Now the real law states that this proportionality has some coefficient k, which is dependent on the material the spring is made of and it should be assigned minus here. Now, why minus? Well, because if d is positive, force goes back, right? Force is trying to push the mass back to original position. So whenever my displacement is positive, force is negative. Whenever my displacement is negative, which means we are compressing the string, force should be is directed towards positive direction, right? So it's always opposite to a displacement. So that's why there is a minus sign and k is a positive coefficient, which depends on the spring basically. How big it is, how strong it is, what kind of a material, steel, non-steel, whatever it is. And again, that's just purely experimental kind of a coefficient. But what's important is that for a given spring and whenever I'm saying this is a given spring, it means I have certain value of k given to me. Force depends on the distance you stretch in this particular way. Now, if my distance is actually a function of time, then that would be my force as a function of time. So it's a function of time because it actually depends on the distance I'm stretching. Now, doesn't really matter whether I stretch it to this particular and in this particular case, my force is equal to minus k times d. Or I let it go and at any moment my mass is going back to the original, to a neutral position. Force is still acting on this particular point mass, right? So and the force is equal to exactly this minus k times whatever my position, whatever my displacement from the neutral position is. So at half the distance, my force will be half the force minus k times d divided by 2. And at any given time, wherever my mass is, my force would be exactly equal to this, where x is a coordinate of my mass because my zero coordinate is a neutral position. So this actually represents a function force as a function of time and I can substitute it here. And what will I have? My Newton's second law would say minus k times x of t equals to mass times acceleration, which is x second derivative as a function of t. So from the Hooke's law and the second Newton's law, I've got this differential equation of the second order because it's the second derivative. Now what's good about this equation? I mean, what's easy about this equation? Well, it's linear. You see, all x's, all the derivative, second derivative and the function itself are linearly related to each other. And that actually makes this particular type of differential equation both soluble. We can really approach this in a relatively standardized fashion. So let me just rewrite it in the form x second derivative of t plus k divided by m x of t is equal to zero. So this is my equation. And I'm going to show you how we can very easily solve it. All right. So let's forget about our pictures. We know everything about this and let's consider just an equation itself. So the whole preamble that I was just talking about before was to put some kind of a physical sense in this particular linear equation. Because I can start, okay, let's consider we have a linear equation of a second order. That's how we can solve it. That's not very interesting. This actually represents some practical situation. And to be exact, the whole physics is about different differential equations to be exact. Sometimes we are kind of masking this. If we are not teaching physics the way how it's supposed to be taught. I mean using this mathematical background which we have. But physics is about mathematics and differential equations to the very, very deep part of it. Okay. So let's consider we have this particular equation. And I will generalize it a little bit and I will tell about, I'll talk about how to solve it. So what's my generalized differential equation of this type? A linear differential equation. Well, I can always put it this way. Where p and q are some kind of constants. In this particular case, my p is equal to zero because I don't have the first derivative. And my q is equal k over m. All right, fine. So whatever it is, I have this particular type of equation. Now, let me start with this one. Let's just for a very short moment assume that we have this. So k over m is equal to one. Just for one brief moment. Do you kind of have a hunch, a guess what the solution might actually be? Well, recall that the derivative of sine is cosine. Derivative of a cosine is minus sine, right? So the function sine and its second derivative, which is minus sine, are together equal to zero, right? Sine of t goes to cosine of t goes to what's the derivative of this? Minus sine of t. So I'm differentiating. I'm differentiating d by dt. d by dt. So differentiating one, I get cosine differentiating. The second time got minus sine. So this is x of t. This is a second derivative of x of t. And obviously the sum is equal to zero. I guess the solution to this not very difficult equation. Now, what if I have some kind of a coefficient here? Well, here is how we can do it. What if I will put sine of alpha times t, where alpha is some kind of a number? Then the derivative is cosine of alpha t times the derivative of inner function, which is alpha. Now, if I will differentiate this, I will have minus sine of alpha t. And I will have here alpha square, right? Minus alpha square. So if this is true, then alpha square sine of alpha t plus a second derivative, second derivative of alpha t would be this alpha minus alpha square sine. So if I will add it with this, I will have basically here. So if my alpha square is equal to k over m, then this is an equation which has a solution sine of alpha t, right? So the solution to this one is sine of square root of k over m t. My first derivative will give me cosine times this square root. The second derivative would be minus sine times again square root. So I will have two square roots, which is k over m. And that's exactly what I have here. So I have guessed a solution. Now, are there any other solutions? Well, you know, I might actually think about something on the top as the solution which I can really think about guessing. Now, think about different signs between p and q. Do you remember, you see, what's the very interesting kind of a part about trigonometric functions? Because after derivation, they sometimes convert into themselves. Maybe a sign will be different. Like we have to twice differentiate to convert sine into minus sine. And then we have to change the sign. So with proper coefficients, we really can manipulate these trigonometric functions. What other functions actually allow similar things? Well, exponential function, remember? If you have a derivative of e to the power of x, we get e to the power of x. So even the first derivative actually converts into something. And then we can manipulate with different coefficients. So we have exponential functions and we have trigonometric functions. Now recall the Euler's formula. e to the power i t equals cosine t plus i sine t. Remember, when we were talking about complex numbers, we were talking about how to use complex number in an exponent. And that's where we were discussing this famous Euler's formula, which basically combines trigonometry and exponential function. So it looks like trigonometry and exponential functions are somehow related in the complex world, in the world of complex numbers. And all of them have this specificity that the function is transformed into itself after differentiation, maybe once, maybe twice, but in any case. So my very intelligent guess looking at that thing is, what if I will try to basically look for a solution to this particular equation in the form e to the power of lambda t, where lambda is any complex number. So lambda can be anything, a plus bi for instance. Now, differentiation of this function, which is not really a function of real argument, which takes real values. We were only talking about differentiation and integration, etc., of the functions which are real functions, real argument and real values. Now, this argument is real, but the value is complex, right? However, we can very easily expand all our theory. Everything whatever we did talk about in the realm of differentiation is actually absolutely true if lambda is a complex number. And that includes how to take the derivative. I'm not going to prove this because the proof is really very easy. Let's just consider that it's true and whatever I was discussing as a proof that the derivative of this is equal to whatever it was in the real world, in the world of the real functions. Exactly the same line of arguments can be applied to this because manipulation of the complex numbers is absolutely similar to manipulation of the real numbers. They have the same operations of addition, multiplication, division, etc., etc. So, what if I will differentiate this function couple of times and substitute into this equation? What will I have? Well, my first derivative is lambda times e to the power of lambda t, right? My second derivative, I will have one more lambda square. And by the way, again, notice since lambda is a complex number, it basically, this number e to the power of lambda t, it generalizes the properties of both trigonometric functions and exponential functions. Now, if I will substitute these into this equation, what will I have? Well, I will have lambda square e to the power of lambda t plus p and lambda, the first derivative, and e to the power of lambda t plus q. Oh, I forgot. Sorry. It's not just q. I'm sorry. It's supposed to be x of t plus q to the power of e to the power of lambda t. I know that e to the power of lambda t should cancel out, should factor out and cancel disappear, right? So that's how I noticed that I forgot to put the x of t. So this is the type of linear equation of the second order with constant coefficients. And we are looking for a solution in this form where lambda is some complex number. Question is, will I be successful to find the solution? Well, quite frankly, yes. I have already been successful because right now I will just cancel out this and now I have just a quadratic equation for lambda. And any quadratic equation, as we know, has two roots in the area of complex numbers. Well, sometimes the roots can coincide, double root. But in any case, it's still considered to be two. So we have two different lambdas which will make this a solution. Okay, fine. So we found, let's say we found lambda one and lambda two. Two solutions to this quadratic equation, which by the way is called a characteristic equation. So for this differential equation where p and q are constants and x is a function of real argument, this is characteristic equation, which again within the realm of complex numbers always have solutions. So solutions are lambda one and lambda two, which means e to the power of lambda one t and e to the power of lambda two t my two different solutions particular solutions. So I'm not saying this is the general solution. This is particular solutions, two of them. Now, since these are two different solutions, it means this solution makes this identity equal to zero, identically equal to zero. And this one makes this thing identically equal to zero, right? Well, it means that obviously any linear combination of them also will make this. So this represents a general solution. So can I assure you that there are no other solutions but this type where c1 and c2 are any complex, by the way, numbers? No, I cannot. However, I'm just asking you to take it for granted that this is the case. So this describes basically all solutions to this particular equation. Okay, that's very good, actually, because we have found a very important expression for a general solution. Now, this is a general solution, where do I get particular solution, which corresponds to my physical experiment? Well, obviously, c1 and c2 must be somehow defined. Right now they're undefined, and how can I make them defined? Well, I have to basically use the initial conditions. You know, what's the value of the function? Let's say it's t equal to zero, and what's the value of the first derivative? You remember, for acceleration for the second Newton's law, we were using the initial position and the speed, because our differential equation was about acceleration, which is the second derivative. If I'm talking about the second derivative as part of the equation, I have to have initial conditions on the first derivative and the function itself. So it's always like one order below that should be defined somehow. And that's what actually makes the complete solution. Now, we know how to solve equations of this type. All right, so let's return back to what we have. Oh, yes, one more thing. Well, this is a solution in the realm of complex numbers. Now, if we are talking about physics, we don't have complex numbers. Like distance, for instance, cannot be complex, right? So out of this, I should really extract only the part, which is the real part. And basically, get rid of the imaginary part of the complex numbers. Because otherwise, because any function of this type can be represented as the real part and the imaginary part. And obviously, imaginary part should not get involved. So this is a very interesting moment, actually. Because you see, we have started with physics, which is completely real world, right? Then we have added trigonometry, exponents, complex numbers with all these Euler's formula, which relate them together, added differential equation. And now we have to get back to the real world to extract from whatever solutions we have, only the ones which we are interested in, which are real solutions. So let's go back to our spring. Now, our equation was x of t plus k over m x of t equals to 0, where k is a spring constant and m is a mass. Well, traditionally, we are using omega as square root of k over m. That's easier, right? So now, what we do, we do exactly what I could just prescribe using a generalized second order equation with constant coefficients. So our equation is x of t plus omega square x of t equals to 0, right? Where omega is square root of k over m. So let me wipe out this and let's solve exactly the way how I was just prescribing. So first, we are looking at the solution in the form. Now, if we will substitute, we will have lambda square e to the power of lambda t plus omega square e to the power of lambda t equals to 0. We cancel e to the power of lambda t and we get lambda square is equal to minus omega square, which means lambda is equal to plus minus omega i, right? Which makes these are two solutions, 1 comma 2, which makes my general solution to this equation equal to c1 e to the power of omega t i plus c2 e to the power minus omega t i. Well, obviously we don't like this. To express our solution in the real world, this i is definitely not needed here. So we have to go back using the Euler's formula and represent it with cosine and sine. So it's c1 cosine omega t plus i sine omega t, right? Plus c2 cosine minus omega t plus i sine minus omega t, okay? Now what we can do? Well, first of all, we can get rid of these minus sign is here, right? Cosine of minus something is the same as cosine of the something. Cosine is an even function. Now sine is odd function, so this cosine of minus is minus sine. And now we can get together all these parts. Now, by the way, where c1 and c2 are any complex numbers, right? You understand that? So there are any complex numbers. So what it actually gives us? Well, if I will represent c1 as a complex number again, and c2 as well, so this will be a1 plus b1i. And this would be a2 plus b2i, okay? So what will be if I will do the multiplication? Well, I will have certain real parts and certain imaginary parts where I participate. So the real part will contain cosine of omega t with some coefficient here. And it will contain a sine as well, because you see this is minus i and bii. So if I will multiply them, i times i would be minus one. So it will be again the real value. So I will have certain real values with the cosine and the sine. So basically, I can say that I have this equal to some kind of constant with a cosine omega t plus another constant sine omega t plus everything else would be imaginary. I just don't want to to do whatever it is. So I can say that at the cosine, what I will have with the cosine? Well, a1 would be a cosine, a2 would be cosine, all right?  So it's b2 minus b1. That will be equal to d2. So I can always find exactly what are these coefficients. But it doesn't really make much sense to find out exactly what these are, because c1 and c2 or a1 and b1 and a2 and b2 can be any constant, right? We're talking in the very beginning that I can use any undefined, unknown constants, and the solution will still be the same. So here is exactly the same. Since a and b's are any constants, I can basically say that d1 and d2 are any real constants right now. And whatever is imaginary part we are not interested in. So I can concentrate basically on this. The real part of my solution is represented as two unknown constants with cosine and sine and omega is given, because spring is given, that's the k, the spring constant and mass is given at the end of the spring as a point mass. So we have a solution, a general solution, real solution of our equation. So this is it. Now let's just think about how can we find a solution which corresponds to our problem exactly. So let me just get rid of the imaginary part. This is my solution. By the way, it would be nice if we can check it out, right? So what would be in this particular case? The first derivative of this would be minus g1 omega sine omega t, right? That's the derivative of this, g1 is remaining, cosine will go to minus sine and omega will go the same, plus d2 omega cosine of omega t. So that would be my first derivative. This is x, this is x of t. Okay, now the second derivative is derivative of this guy, so it doesn't really work well. I use this one. So the second derivative of this would be minus d1 omega square cosine omega t. Now this would be minus d2 omega square sine of omega t. Now, if I will multiply my x of t, which is this one, by omega square and add to this one, I will get exactly zero, right? Because this is exactly omega square greater than this, and this is also omega square. So my solution is correct. I just don't know what d1 and d2 are, right? Now, I can determine these d1 and d2 based on certain initial conditions. So what did I have as an initial condition? Remember, this is my spring, mass m. This is my table, frictionless. So this is my x is equal to zero and I have stretched by d. And then let it go. What does it mean? It means that x of zero is equal to d, because that's the position and I have stretched. That's my initial position of my mass according to this system of coordinate. And then I let it go, which means I did not really have any initial speed. So x of zero first derivative is equal to zero. That's my two initial conditions. And they must be sufficient to determine my coefficients, d1 and d2. Okay. So if I will substitute zero into this, this would be sine of zero is zero cosine of zero would be one. So I will have d1, which means my d1 is equal to d. Okay, I've got that. Now how about d2? Now we have a second condition. So first let's just have a derivative, which is minus d sine of omega t plus d2 omega, n times omega, sorry, d2 times omega times cosine of omega t. So with t is equal to zero, my first derivative must be zero. Well sine is equal to zero anyway, cosine is equal to one. So if this is equal to zero, my d2 must be equal to zero, right? So that's my function, d2 is equal to zero. So this is a solution which not only is a solution to my differential equation, but also satisfies my both initial conditions. So if we will stretch our spring by the distance g and our spring has characteristics k and the mass attached is m, then this is the equation of the motion. Now what does it mean actually? Let's just think about it. When t is equal to zero, my function is equal to d, right? So that's my initial position. From neutral position we stretched it. Now as time goes by, what happens with cosine? Well, this particular function, you know, the cosine, it goes like this, right? This is zero. Now this is, if omega would be equal to one, then that would be my pi over two, right? But if omega is not one, then that should be what? t should be equal to, omega should be here, right? Then if t is equal to pi over two omega times omega would be pi over two, cosine would be equal to zero. Okay. Now what does it mean zero? So it means that at t equals to pi over two omega, my position, my x of t would be equal to cosine of pi over two, which is zero. So it means at this particular point it will return back to a neutral position. What happens next? Well, then t is increasing and this is pi over two omega. What happens in this particular case? You see, my cosine is negative, which means that after going through this point, my spring will start compressing because my x of t would be negative, from the neutral position to the left. So it will compress. And at some point, it will reach the minimum, which is cosine would be minus one, so it would be minus d somewhere here. So it will compress to minus g. So from pros d, it will go through the zero point to the minus g. And then again back to the neutral point, and it will oscillate back and forth, back and forth infinitely because there is no friction. And the spring is assumed to be ideal spring, so it doesn't have internal frictions. The table is not, it's frictionless, etc. So basically it will oscillate infinitely using this particular law of motion. Well, okay, that's basically all I wanted to talk about today. Again, don't forget what I said in the very beginning that the whole physics is actually filled with differential equations. My previous lecture where I was talking about acceleration and this one about Hooke's law, these are just two examples.  And after I finish this course of mathematics for teens, I'm planning to start physics for teens, and I will use all these mathematical apparatus to present the physical concepts. All right, that's it. Thank you very much and good luck.


Jackass couple other people asked like what happened to the snatch like that's ideal we kind of talked about that the other day when I use this low single here I get to this angle like I want to just make contact I don't want my head that angle back from here that's ideal that's my ideal low single there's no scramble there's no roll there's no fight there's no circle he just drops to his butt that's that's perfect for me that's ideal that's gonna happen very rare that's when we kind of catch the guy in an exchange that catch him off his whistle roll and start we're talking about we're kind of hand fight maybe in an exchange and I get to this position right here now I really want to focus on keeping this position is way different than this position give this guy a lot like a live match but I want him to try to sit down on top be out here trying to get some of this stuff so I want him to keep this leg and this head position tight so I can't get back to him I gotta be this head remember we gotta jam the shoulder or we can cover the head or jam the shoulder I'm feeling trying to squat down try to drink right back into my finished position don't reach too high don't reach too low okay so just play in that position a little bit and then this guy's 25% and then back out get your shot and this partner's trying to squat on me a little bit okay so so I'm circling get into my low well attack here I'm kind of keeping him and getting to this track down they're pretty good positions just got to put him on his hip okay don't just shoot through the hole all right because your momentum is going use your post hand to stop keep your head in there start circling try to find your angle so I get a look perfect every time like we're drilling it right now okay still get two points I don't get extra style points if I hit a drill rep in a match good hey but talk to your partner like kind of fell to the side you probably gonna do that in a match or let him know hey I felt fell a different direction I would have done that in a match maybe follow direction we need to talk about good


This is why in the morning Hashtag Fasting Vibes where we get to give you good music, great conversations and we get to tell you what is happening around you know its entertainment, politics, business, everything you know every other thing that is happening and you know today's on Thursday how we do this we get to do music and lifestyle we're just from from having a comprehensive talk on software development, chat, gpt, you know yeah now we've gotten to the part where we get to do the interview on music and lifestyle in this week's music and lifestyle you're just from watching her video she is called Dorika but she is in studio so I want to allow her to introduce herself. Thank you so much, I'm Dorika Kaye, I'm Dorika Kaye that's the name that I use in the music industry and I'm saved and I'm married and I have three children by the grace of God and I really thank God for that and I really love Jesus to be my saviour amazing amazing you know it's not like it's not nowadays what's happening it's a mom a lot of times so it's it's really interesting it's really nice that you're able to say it out there that you know but just starting right into it who is Dorika what defines Dorika in terms of music now how yes I'm a gospel artist I also write music by the grace of God and I really thank God for that when did you why music how did you end up into yes doing music when I was young I was in class seven that's when I got saved and then God gave me a song I composed my first song when I was in class seven so that's when I got to know that God has given me that talent and I had to use it even when I was a young I was a choir mistress in my choir at home I used to compose songs I used to train the choir and then we go to the competitions you understand that at Shads we used to go to competitions and then I grew I grew in that way then later in 2018 that's when I did my first album called Nenomoja yes yeah um what what does Nenomoja talk about it's your first song right yes it's my first album um Nenomoja I called this album Nenomoja because uh the only thing that I want to to to to have in my life it's only called because in the book of Psalms 27 uh and verse four uh the Psalmist David say that the only one thing that I ask of the Lord and this is the only that I seek that I may dwell in the house of the gaze upon his beauty all the days of my life and that is my desire all my life to be in the presence of God and to gaze in his beauty all the days of my life yeah nice and one person who appreciates stories you know I believe before someone is made before you're able to sit here and we talk about your music do you have a story you don't want to share of your success story of course you want to share with us yes okay thank you I would love to maybe I can encourage someone true um when I started my music in 2018 actually my music um it did not come out clear in the first studio that I uh I recorded my music and I was so disappointed that I did not give up because I have a goal that I must achieve in uh in this music industry so um I recorded again in another studio and then the studio was closed so I had to go and repeat it at third time yes so I was so determined wow yes so uh up to where I am I can say that it is by the grace of God not by my power or might but it is because of God that I'm here today yeah so what what inspires your message in terms of um how you write your music because I think you said you write your own music right yes I write music and uh I can say when I write a music it is the message that I always hear from God it can be different messages from God when I hear the message maybe through a dream or someone has talked a certain message and I feel that that message I'm supposed to put it in writing a song I do it yes amazing amazing um minus the songs you have written minus the songs you have done you have a favorite I love all the songs uh because I'm the one who has done them and uh they have uh different messages and I love them all but there is uh I can say two songs that if I'm not sung them I'm not feel okay the first one is Nenomoja because that's the only thing that I desire in my life and I would love uh even to tell someone outside there that the only thing even when we are in this music industry if you'd not ground yourself in court then you are going and you're not going anywhere uh another song uh in everything that you do I'd love to encourage someone that lean on Jesus Christ because it's their founder and the perfecter of our faith yes because in him we are perfected we are weak but we are perfected in Christ Jesus yeah wow you want to sing Nenomoja uh portion of it yes it's okay um so so What are some of the challenges you have experienced as an musician, writing music and doing music? Especially in the gospel industry. In writing music, I can say that most of the common challenges you must find the contents. And coming up with the content that people can listen to, sometimes it may be a challenge because you can come out. I think you have listened to so many new musicians who have sung. And sometimes someone can come up with a content and you listen to it. You feel like this is not the real message that I want to listen to. So you have to go into prayer and seek God to help you. So that any message that you bring out, it may help because my work, it is to preach to people. So that people, when they listen to this music that I have done, they will be saved. They will be encouraged. So that is my reason of doing this music. And another challenge, maybe in recording, sometimes you may lack fans. Sometimes you may find that you do not have even the time to go and record your music because like right now I am a married woman. So sometimes it's a challenge balancing here and there, but the grace of God is sufficient in everything because when God has put a message in you, he always finds a way out that you can put it outside there so that people can listen to what is given you in your heart. There is a discussion that I think I feel has not been exhausted about worship ministers. I prefer to call them that, about worship ministers being appreciated in the churches they serve. What's your opinion on that? Okay. Appreciated or paid? One of the two. Okay. To me, appreciation, it's okay, but maybe I can go to this direction. You may not be appreciated, maybe at the church that you are serving or in another church that you are going to minister. That's what I tell myself when I go to minister outside there. I may not get to be appreciated. So long as I'm doing what God has sent me, the message that God has put in me, so long as I'm giving it to people, it doesn't worry me. If it is appreciated, it will just come later, at it is on time. That's what I tell myself because if I focus to that direction, then I will not be able to minister to God. I will not be able to minister. I will be discouraged each and every time and I will not be able to do the work of God the way it is supposed to be here. Should worship ministers have a rate card?  So should worship ministers have a rate card? When you invite them, should they come and tell you for you to have me come into your show, you need to give me 100,000 or 50,000? Well, I think most of us, we have forgot what's called the purpose to which God called us to. If you know the purpose to which God called you, then you will not do that. To me, if you call me, if you love to appreciate me, yes. I will accept. But if you would not want to appreciate me, then I just leave it. So to me, no. To me as a gospel artist, and a gospel artist who is saved, this is the message God has given you for free. Just spread it for free. But if that money comes, someone calls you and tells you we are going to give you this and this. Just come and grace our event. Then it's okay. But you have invested money into your video and into your work? Of course. But if you put regressions in this ministry, let me tell you, you will not be able to minister. That's all I know. You will not be able to minister.  I've gone to so many churches and I've not been given even a single seat. Because maybe this church, they need your ministry. There are some people there you're going to encourage. There are some people there who get saved because of your music. And then you are telling them you must pay me 50,000 so that you can get saved. No, even the city sometimes, I give them for free. I was telling another pastor that I missed in his church, like two months ago, one to two months ago, I was telling him, I feel like I can give out this seat for free so that people can listen to this message. Because what if I tell you that I'm selling this seat and you'd not have money? Have I preached the gospel? Have I accomplished the mission that God has sent me? Because in Matthew 28, verse 19 and 20, the Bible says that you go, I command you to go and make disciples. So to me, this is the gift that God has given me. And I'm preaching through my music. It's like a pastor who is standing on the pulpit and preaching to people. So to me, I'm preaching through my gospel. The gospel that God has given me, by grace. As we approach a close of this conversation, what would you say is the greatest need of the music industry right now? In terms, especially now that you're in the gospel industry? Sorry? What is the greatest need of the music industry, the gospel music industry as of now? In your opinion? Okay. I can say that the need that is in the music industry, the gospel, is that we need to rise. We need to rise and preach the gospel. Because I can tell you, people are lost outside there. We always say that the laborers are few. The harvest is plenty. But the harvest is plenty. So it is me, as the wrecker, to go outside there, being appreciated or not, to preach the gospel of God. So that we can... Our goal is to populate heaven and to populate hell. Yeah. Nice, nice, nice, nice. Any other thing you want to share? Maybe I'll have to encourage someone outside there. Maybe someone needs to upcoming minister and they have challenges. They want to put their music into recording and maybe they are not able... I'll just encourage someone outside there that when you are in God, you have everything. Just write your music and the appointment of God will reach.  Because he is the one who has given you that gift. You have not given it to yourself. So get encouraged. Be hardworking. Be determined. And above it all, be consistent. Because without all those, and put God ahead in everything that you are doing, God will make it a success. Yeah. Nice. Thank you so much. Thank you for coming. Thank you for sharing. I want to ask you to give us a parting shot using that camera. Salimi and my fans, tell us where we can find them on social media. Okay. Thank you for watching me in this channel Y254. We God bless you. I love to greet my husband who is watching me. I love you so much. And thank you for making this day a success. Because if you have not allowed me to come to this place to preach through gospel, I would not have been in this place. So I appreciate you so much. And I love you so much. Even my children in absentia, they are in school. But I love you so much. My fans who are watching me, continue watching me, continue subscribing to my channel. And I would love to appreciate even more say who made it that I come to this place today. And also, I would love to greet my sit-up members. I felt like sit-up gone. I love you so much. I know you are watching me. May God bless you and some of you for being mentors to me. That's why I'm here today so that I can propagate this gospel of God to many people so that we can populate heaven and the populate hell. So may God bless you. You can find me on YouTube, Dorica K. Dorica K is D-O-R-C-A-H. And then K. And in YouTube, you'll find me as Dorica K. That's where you can find me. May God bless you all as we get blessed with the music. Thank you. I love how you appreciated your husband. It's amazing. It's amazing in this age and era. Thank you so much. Do not touch that dial.


The best sports fellowship in the world happens to be in Vail. The Stenman Clinic has been amazing, patient care is number one. We have multiple experts in every procedure and joint you can possibly imagine. It's about becoming your own physician. I have not only acquired some professional colleagues, but also a great group of friends living here. The hands-on learning, the labs, the ORs, the clinics, the research, it just goes on and on and on. The research opportunities here really are endless. This year definitely feels like the cherry on top. Amazing facilities, amazing resources, amazing faculty. This is a great group and we will share this bond forever. I look forward to continuing our relationship as we grow our careers. It really is a special place and a special year.


to the clue about a safe artifact on a moon and the droidless system. Go investigate, and be careful. The dark side is very powerful in these places.


100 meters under 20 champion, Camarillo Bygrave. Camarillo, when we spoke earlier, just before, about a week ago, before you came here, you did tell me that you were gunning for that gold medal. You were gunning to achieve the win. Are you satisfied with the performance that you have after the disappointment that you suffered last year in the Bahamas? Well, first of all, thank God, you know, that this year I've finally finished in my season, helped it and last year, you know, seeing the disappointment that I had last year after and, you know, all that was playing back in my mind was that, you know, this year, gotta change, gotta make things different, gotta come back to vengeance and to prove that I am indeed a champion. Yeah, it was certainly, certainly proved that congratulations to you, Camarillo. And we were looking forward to seeing what else you can do this season. Yeah, back up to you, Ricardo and Terry. Yeah, thanks very much, Brendan. Vanderpool in the pole vault.