In our last lecture, we had started with giving some equations which were equivalent of kinematic equations in the normal traditional classical mechanics in which we assumed that force is constant. We assumed that the motion is along a straight line. So, that force and acceleration are in the same direction even in relativity and then these equations could determine the velocity after a given time and the distance travelled by the particle in a given time. After that, we evolved the concept of force 4 vector. We had already defined what is a force. We defined in last lecture what is a force 4 vector and then eventually came to the transformation of forces. We realized that once we change the frames, the force on the body also changes in relativity. The force is also relative depending upon the frame from which you are looking, the force on the particle would also appear to be different. So, this is what we have mentioned here. To recapitulate, we found out some equations relating to the motion of a particle under constant force and we discussed the force 4 vector and then derived the transformation of forces. Now, from today onwards, we will come to essentially the last topic of this particular series of lectures on special theory of relativity, which is about the electric field and magnetic field transformation. If you recall, right in our first lecture, when we are trying to discuss the issues or the problems with the classical mechanics, at that time, we had mentioned about the Lorentz force. So, this is what I have written. While beginning our lectures, we pointed out an issue with the magnetic field in classical physics. We had mentioned that in classical physics, what this is to even relativistically, the force on a particle is given by if it is a charge q, if the particle is charged with a charge q, the force is given by qE plus V cross B, where V is the speed of the particle in a given frame of reference. Now, we had earlier discussed in the classical mechanics, in the traditional classical non-relativistic mechanics that acceleration is frame independent quantity. It means if you go to different frames, the acceleration in the traditional classical mechanics, non-relativistic classical mechanics will turn out to be same, but the velocity of the particle may differ and in general, they will be different. So, we had said that if this force is a velocity dependent force, velocity being dependent on different frames, the force would also appear to be different in different frames. Take for example, a frame of reference in which V is 0, it means the particle is at rest. In that particular frame of reference, the force on this particular particle because of the magnetic field would be 0. Let us assume that E is 0. So, it means there is no force, but on the other hand, in any other frame of reference, when V is non-zero in principle, the particle will experience a force which is V cross P or the charge particle won't experience a force which is V cross P. So, it looks funny. Of course, we know that force is a frame dependent quantity, but we do not expect that relationship to be obeyed when force is 0 in one frame of reference and in another frame of reference, it is a finite thing. Of course, at that time, we also mentioned that some people can always raise the question, having our traditional classical mechanics knowledge that after all V is also due to a motion of charge carriers. And if I change the frame of reference, I also expect that probably magnetic field will change. And that time, we had mentioned that actually the correct representation or correct transformation of magnetic field and for that matter, electric field comes when we discuss special theory of relativity. So, that is what we are going to discuss today. In fact, what we will be essentially telling is that once we change the frame of reference, both magnetic field and electric field will change. So, in principle, as far as relativity is concerned, there is no difference between electric field and magnetic field. Depending upon the frame of reference, the field may appear to be an electric field or may appear to be a magnetic field or a combination of the two. So, let us start our discussion on this particular aspect today and then we will give eventually probably some of the later lectures, some examples where we can discuss this particular aspect little bit in more detail. So, this is what we had had written. We realize that the magnetic force is a velocity dependent force and velocity is frame dependent quantities. I have just now discussed that this is the Lorentz force which is F is equal to E multiplied by E which is E is the electric field plus V cross B, where V is the velocity of the particle and B is the magnetic field. So, this is the force which will be experienced by a particle which has a charge Q or in this particular case I have written E. So, a charge E. So, now let us look for the transformation and for this particular transformation, we would essentially need the force transformation that we had earlier discussed in our last lecture and we will see that how the electric field and magnetic field should transform so that this particular force transformation is obeyed. So, we will take some specific examples and using those examples, we will derive the electric field and magnetic field transformations which appear to be somewhat more general. So, this is what I have written. We discussed at that time that the electric and magnetic field transformations are actually found out from relativity theory. So, that is what we are going to do today. So, this is what I say, electromagnetic field transformation. So, E m essentially represents electric field as well as magnetic field. So, as we said that in relativity, we do not differentiate strictly between electric field and magnetic field because what may appear to one frame of an observer in a frame electric field may appear to be mixture of electric field and magnetic field to some other observer. So, we shall obtain it by taking a specific case. The results obtained are general. Now, let us consider the case. Let us consider that there is a charge q which is instantaneously at rest in frame s. We can always assume that that though this particular charge could be moving or could be accelerating or whatever it is, but there is a frame of reference in which this particular particle or this particular charge is instantaneously at rest. If you remember in our last lecture, when we discussed in force transformation, also we considered this particular case. So, of course these frames are inertial frames. So, if actually the particle is accelerating, then if it is instantaneously at rest in this particular frame of reference, at a later time it may not be because the frames are actually inertial frames and all I am requiring that at instant of time when I am described in the situation, this particular particle is at rest in this particular frame, at a later time it may not be. Now, in this particular frame, I assume that there is a particle is experiencing in electric field which I am writing as E prime and it is also experiencing a magnetic field which I am writing as B prime. So, the particle is instantaneously at rest in this particular frame and it is experiencing electric field and magnetic field which are given by E prime and B prime. Let us read this again. We consider a charge Q which is instantaneously at rest in a frame S prime. However, it is experiencing in electric field E prime and magnetic field B prime. Once I know this particular aspect, I can always write what will be the force on the particle which will be given by the Lorentz force and now let me use the relativistic notation because this is the particle which is experiencing a force in this particular direction. So, in fact, the speed which will be given will be U prime because this is S prime frame of reference. Remember the symbol V we have reserved for the relative velocity between the frames and U and U primes are the speeds or the velocities of the particle in respective frames. So, let us write the force on this charge as the speed of the particle or the velocity of the particle is 0 at that instant in this particular frame. So, at that instant U cross B is 0. This was my force V cross B. Of course, here we have written U cross B. F is equal to Q E cross B prime. I am in frame S prime. So, everything is being primed. This is the force which is being experienced by the particle in S prime frame of reference. This is the electric field E prime and this is the magnetic field B prime. All I am insisting that this U prime is 0 at this particular instant of time. So, this force is 0. Therefore, the particle is experiencing only the force is due to only electric field. The magnetic field would not cause a force on this particular particle because the instantaneous velocity happens to be 0. So, the only force is due to the electric field. So, that is what I have written. F prime is equal to Q E prime. I can write this as component wise because this will help me. So, all I have to do is to write three components because electric field I can always write as E x prime i plus E y prime j plus E prime E z prime k. I will just take the component. So, I am writing F x prime which is the x component of the force which will be given by Q times x component of the electric field, y component of the force is Q times the y component of the electric field and the z component of the force is Q times the z component of the electric field because I am going to use this particular equation. So, what I have done?  So, this is the equation which I have written here on this particular piece of paper. F x prime is equal to Q x prime, F y prime is equal to Q E y prime, F z prime is equal to Q E z prime. We will look at other equations later. Now, let us assume that there is another observer S in another inertial frame S and this is viewing this particular charge. So, there is another observer S which is viewing this chart which is I am writing here. Let this chart be viewed by another observer in frame S and let me assume that this S and S prime obey exactly the same conditions which we have been using right from beginning from Lorentz transformation. It means x axis is I mean the y axis is parallel to y prime axis, z axis is parallel to z prime axis. The relative motion is along the x direction and it is along the x axis and x and x prime axis are always coinciding. This is the standard thing which I have written here. As usual we shall assume that the axis of the frames are parallel and the origin of S prime moves on the x axis of S with speed v. The relative speed between the frames we have always reserved a symbol v. So, this is still I am using the same symbol. Now, when this particular observer looks at this particular particle at the same instant of time, it will assume that it will find out that the velocity of this particular particle is not 0. But because this particle is at rest at that instant of time in S frame. So, therefore, this particular particle velocity will turn out to be v which is the relative velocity between the frames. This also one can use the velocity transformation. We have done some examples earlier. This is very straightforward. We will always get if a particle is at rest in S prime, its velocity will turn out to be equal to v which is the relative velocity between the frames in S frame of reference. So, the velocity of the particle is v in S frame of reference. So, that is what I have said. According to S, the charge moves with a speed v along the x axis and of course, this is along the x axis. Now, we have said that in general I expect that the force on the particle, the electric field sorry, electric field on the particle will turn out to be different. And let us assume that the field that will be seen by this particular charge in this particular frame S will be E and B, electric field being E and the magnetic field being B. So, these fields in general will be different from the fields which have been seen by S prime observer using the arguments which we have just now given in the beginning of the lecture. So, what I can do, what is our methodology is that I can always calculate what will be the force on this particular particle in S frame if I assume what will be the value if I take the electric field to be E and magnetic field to be B. Then I know how the forces will transform from S to S because we have already derived the force transformation equation use these but the same equations and using those equations I will be able to find out the relationship between the electric field and magnetic field as seen in S and as seen in S prime. So, this is my logic, this is the way I am going to proceed. So, what I am going to do now is to calculate what will be the force assuming the electric field to be E and magnetic field to be B in this particular frame and then I know how the forces should transform using that I will calculate how the magnetic fields and the electric fields should transform. So, let us go to the next transparency. So, as I say according to S the charged particle is not at rest. Therefore, it would experience a magnetic force also not just the electric field, not just force because of the electric field, but it will also experience the force because of the magnetic field and that particular force will be given by f is equal to Q E plus V cross B because and this V of course is along the x direction and its magnitude is equal to the relative velocity between the frames. That is what I have written according to S the force on the charge shall be given by f is equal to Q E plus V cross B, here V is along the x direction. So, let us write this particular equation in a proper vector form and try to extract what will be fx, what will be fy, what will be fz. That is what I am doing in the next transparency. Here I want to be little more careful so therefore, because there is a magnetic field term also. So, therefore, I am writing in explicit form f is equal to Q times E xi plus E yj plus E zk. Then a term due to magnetic field plus Q V is having component only in x direction. Therefore, I am writing as Vi cross. This is the magnetic field which in general can be in any direction. So, I write B xi plus B yj plus B zk. Now, as far as this first term is concerned, it remains unchanged. I have just copied it here. This is exactly identical to this. But now, I can write this cross product and simplify the second term. I know that I cross i is 0. So, when I take Vi cross B xi, this will give me 0. So, that term will not contribute. Then I take cross product with the second term which is i cross j. i cross j would give me k. Therefore, Vi cross B yj would give me V multiplied by By in k. So, this is what I have written, V multiplied by By in k direction. Now, i cross k is minus j. If you remember, you have to go to ijk, ijk, i. So, if I go i to j, then I will get k. If I go to jk, I will get i. But here, I am getting k to i. Then I must get j. But here, I am going from i to k. So, it will be minus j. So, this is what I have written here. V multiplied by Bz, i cross k is minus j, which brings this minus sign and this is j. So, this is what I have written here. Now, like before, I will pick up the x component of the force, y component of the force and z component of the force. So, these will be the force which will be experienced by the particle in S frame of reference if the electric field was E and the magnetic field was B. Note, at this moment of time, I do not know what is E and B. I am only writing the force component and only thing which I know is the transformation of the forces. Same equation which I have written in the last transparency, I have copied it here and I am picking up the different components. So, I am writing the x component of the force, which will be the only i part. See, i is appearing only in this term, nowhere else i is appearing. So, I just have picked up one term which is q E xi. I am not writing because I am just writing the x component of the force. So, x component of the force is given by q E x. Let us write the y component of the force. For that, I have to pick up the terms containing j. This term contains j. This term contains j. So, they are both contributing to a force in the y direction. So, this will be E y minus V V B z will be the y component of force multiplied by q. So, F y will be q E y minus V B z. Now, let us pick up the z component of the force. So, I have to look only at the k terms. There is a k here. So, this is E z k. There is a k here. There is a plus sign here. So, the F z will be E z plus V B y force multiplied by q. So, F z will be q E z plus V B y. This is what I have written again here because I am going to use immediately after that in this particular piece of paper. F x is equal to q E x, F y is equal to q E y minus V B z and F z is equal to q E z plus V B y. Now, I know that what are the transformation equations? Remember, the particle is at rest in s frame of reference and in that particular case, our force transformation equations were somewhat simpler. So, those equations I can write now because the particle was at rest in s frame of reference. So, force F x of course does not change, will be F x prime. Force in y direction F y will become F y prime divided by gamma and force along the z direction F z will be F z prime by gamma. This is a special case of the force equations which we have written. Force transformation which I have used last time in which I have said that if the particles happens to be at rest instantaneously in a given frame, then the transformation equations become somewhat simpler and this precisely the case in this particular situation where the particle is at rest in s frame of reference. So, I can write these equations in rather simpler form and this is what I have written here and this also I have written in this particular piece of paper here where I have written F x is equal to F x prime, F y is equal to F y prime by gamma and F z is equal to F z prime by gamma. Now, let us look at this particular paper carefully. I know that my force transformation equation must obey these because this is the way we have derived the force. If we have to be consistent, these equations have to be obeyed. I do not know what is the relationship as yet between E x and E x prime and E y and E y prime and other fields, other components of the fields. But I can always use in this particular thing that F x must be equal to F x prime, F y must be equal to F y prime by gamma, F z must be equal to F z prime by gamma because they have to obey these force transformation equations. So, if I use this particular thing, I can quickly find out the relationships between the electric fields and the magnetic fields as we will be seeing in the next transparency. So, this is what I have written. This is the first equation which is Q E x must be equal to Q x prime which is because F x was equal to F x prime. The second equation was F y is equal to F y prime by gamma. This was my F y, F y prime was just Q E y prime divided by gamma. This is F z must be equal to F z prime which is Q E z prime divided by gamma. So, these are the three equations. First equations is straightforward, Q will cancel gives you E x is equal to E x prime. Let us look at the two equations and see what do they give us. This is just writing these equations in simpler form as I said E x prime is equal to E x. If you look at back equation, the Q will cancel out here. E y prime this gamma will come here on this particular equation and this will give me E y prime is equal to gamma E y minus V V z. Similarly, if you look at this particular equation, Q will cancel. This gamma I can take on this side. So, E z prime will be equal to gamma times E z plus V V y. So, these are precisely the equations that I have written in the next transparency. E x prime is equal to E x, E y prime is equal to gamma E y minus V B z and E z prime is equal to gamma E z plus V B z, V B y I am sorry. So, what do these equations give us? These equations tell us that if my force transformation equation has to be obeyed, then the x component of the electric field must remain identical between S and S prime framework for us. As far as the y component of the force is concerned, if electric field is concerned, y component of the electric field will change. It will become, I mean in the y, in the S prime component it will be given by E y prime. If E y and B z happen to be the y component of the electric field and z component of the magnetic field in S frame of reference, then the electric field in the y, the y component of the electric field in S frame of reference will be given by this particular equation. Similarly, the z component of the electric field will be given by this equation where E z is the z component of electric field in S frame and B y is the y component of the magnetic field in S frame. So, it means if I know what is E x, E y, E z and if I know what is B x, B y, B z, I will find out, I will find that these will be the electric field. So, I get these equations which will tell me electric field in a given frame. If I know the electric field and magnetic field in a different frame, what is interested to realize that this electric field does depend on the magnetic field in the other frame. Similarly, this electric field also depends not only in the electric field, but also on the magnetic field in the other frame. That is what we had meant by saying that relativity electric field and magnetic fields have, they do not have a really in that sense a separate context, because what this particular magnetic field is contributing so to say to electric field in a different frame of reference. So, electric field does depend on the magnetic field in a different frame. So, this is what I have written, the above equations give the electric field in frame S, when electric and magnetic fields are known in frame S. Of course, I can always do a inverse transformation. If I know what is the electric field, what are the electric field and magnetic field in S frame of reference, I can always find out the electric and I mean at the moment electric field in S frame and for that particular matter, all I have to do is to change prime to unprime quantities, change the sign of V in the standard prescription of going from a direct transformation to inverse transformation. This is what I have written, inverse transformation, it is given by usual prescription. So, I have written E x is equal to x prime, because that does not change. Here I have changed the sign, here E y is equal to gamma E y prime plus V V z prime. Here also I have changed the sign, E z is equal to gamma E z prime minus V V V V y prime. So, if I know electric and magnetic field in S frame of reference, I can calculate what will be the electric field in S frame. Of course, there is a missing component you might have realized in these equations. All I have done in this equation is to evaluate the electric field, but I have not given the transformation, I have not given the equations, what will happen to the magnetic field. We also realize that magnetic field will also change, this is what we have been saying. So, these equations only give me the values or the components of the electric field in a frame, if I know electric field and magnetic field in a different frame. I must also, I ought to calculate the components of the magnetic fields also in this particular frame, if I happen to know electric field and magnetic field in a different frame. So, for that I have to do little more exercise, which is not that simple as the way we have done it, but let us do it, because that is also equally important, because in principle I must be able to calculate both electric field and magnetic field in a given frame, if I know electric field and magnetic field in a different frame. That is what actually the electromagnetic field transformation would mean. So, this is what I have written magnetic field, I have to find out now the magnetic field components. To find magnetic field in S, when we know the electric and magnetic field in S, we need another set of equations that we have not yet found out. This is what I will do now to find out what are the components of the magnetic field, if I know electric and magnetic field in a different frame. Now, I look again to any special case and the results happen to be general enough. Now, I alter the situation little bit, which makes things little more difficult mathematically, little more difficult. In the earlier case, I had assumed that the particle was at rest in S frame of reference. Now, I will assume that this particular particle is actually moving along the plus y prime direction of S frame of reference. It is not at rest in S frame of reference, but it is moving with a velocity, but that velocity is directed along the y prime direction of S frame of reference. So, we now consider a charge q, which is moving with a speed u dot prime along y prime axis in a frame S. Of course, like before, I will assume that this is experiencing a electric field E prime and a magnetic field B prime in this particular frame, exactly the simple situation. The only thing is, which is different now that I am assuming that the particle is not at rest and therefore, the Lorentz force will also have a term because of the magnetic field. So, let us write that particular term. Again, we do exercise. The methodology is exactly identical. I take this particular force, write the components of the force, then I go to S frame of reference, then I evaluate what will be the velocity of the particle, which will now be little more complex. Assume what will be the electric field and magnetic field in S frame as E and B, then again write the forces, then I know what are the transformation of forces in the two frames and of course, in this case in neither of the frames, in general you will find the particle to be at rest. So, I have to use generic, most general force transformation and using that I will be able to find out magnetic field equations. So, let us do that. So, this is the force on this charge, which has been given as F prime is equal to Q E prime plus U not cross B prime. This is S frame of reference. In my earlier situation, this term was not there, but now it is there because I am assuming because that the particle is moving around the J direction. This first electric field term I have written just as a, in the component form E x prime i plus E y prime j plus E z prime k. U not prime I realize is purely in the y direction. So, I have written U not prime j cross this B prime. Again I have written in the component form B x i plus B y, I mean B x prime i plus B y prime j plus B z prime k. Then I will expand this particular thing. I will take this particular cross product. I will write all these terms just like before then take out x component of F prime, y component of F prime and the z component of F prime just like before. This first term is exactly identical of what I have written. This first equation is exactly identical of what I have written in my last transparency. Now let us try to evaluate this. If I take J cross i, this will be minus k because i cross j is k, J cross i will be minus k. So, you will have U not prime B x prime minus k. So, this is what I have written here. There is a negative sign U not prime B x prime. J cross j will give me 0. Then J cross k will be i. So, U not prime multiplied by B z prime i and there is a plus sign here because J cross k is plus i. So, plus U not prime B z prime i. Now using this equation I can resolve, I can take out the x components, y component, x component, y component and z component of the force in S frame of reference. Same equation which has been written here without any change. Let us pick up the x component. It means F x prime. So, let us look at those terms which contain i. There is E x prime which contains i. There is a U not prime plus B z prime which contains i. So, this becomes Q E x prime plus U not prime B z prime which forms the x component of the force. As far as the y component of the force is concerned, there is only one term which contains J. There is no other term which contains J. So, F y prime is just equal to Q E y prime. Pick up the z component, z component. This term contains k. This term contains k. So, z component is Q E z prime minus U not prime B x prime. So, these are the x, y and z component of the forces as seen by an observer in S frame of reference. Now I have just copied like before these equations in this particular paper because I am going to use these things. F x prime is equal to Q E x prime plus U not prime B z prime. F y prime is equal to Q E y prime. F z prime is equal to Q E z prime minus U not prime B x prime. These equations will be seen later. So, like before, this charge is being viewed by an observer in frame S satisfying the normal Lorentz transformation condition. And of course, I will assume that in this particular frame S, the field seen by the particle or seen by the charge is E, electric field is E and the magnetic field is B. And then again write the force and do the force transformation equations. According to S, the charge moves with a velocity U which now have to be obtained by inverse velocity transformation because I know the velocity in S prime frame of reference. I want to find velocity in S frame of reference. So, I must use an inverse transformation and if I use the inverse transformation equation, I can find out what will be the value of U in the vector form or other x and y, x, y and z components of U. Once I know what are the components in S frame of reference. So, let us do that first. These are the inverse transformation equations. X component U x prime plus V divided by 1 plus V U x prime by C square because the charge is moving only along the y direction in S frame of reference. Therefore, U x prime is 0 because it has only a non-zero component along the y direction. Therefore, U x prime is 0. So, denominator gives you only 1. This component is 0. So, U x is equal to V. It just picks up. The x component is the same as the rate of velocity between the frames. As far as the y component is concerned, of course like before because this term is 0. So, there is only 1 here. U y prime is non-zero and there is a gamma. So, this will be given by U naught prime divided by gamma because we have written the speed along the y direction to be U naught prime. So, U naught prime divided by gamma is what is the velocity along the y direction. U z is equal to U z prime divided by all these things and I know that U z prime is 0 because the particle is moving along only the y direction. So, this gives me 0. So, I have velocity 2 components. The x component is equal to the V. E is equal to V and the y component is U naught prime by gamma. So, my U has two terms as I have said. Now, using these two terms, I can again write the force. So, as I said according to S, the force on the charge shall be given by Q E where E is the field seen in this frame plus U which we have just now evaluated by inverse transformation cross B where B is the magnetic field as will be seen by an observer in this particular frame of the set where the velocity components have just been given, have just been obtained. So, I will now write this particular equation vector form and then eventually take x, y and z components of the forces then compare with what I have obtained as f x prime, f y prime and f z prime and I know that they must obey the force transformation equation.  So, I have written that as V i, y component was U naught prime divided by gamma. So, this I have written plus U naught prime divided by gamma j cross again B like before B x i plus B y j plus B z k. First term we just write like that exactly in the same way here. Second term let us take the cross product and write it open it up. So, let us first take V i cross B x i this will give me 0 because i cross i is 0. Then I take the second term i cross j will give me k. So, first term will be V by k. So, this is what I have written V by k. Then I take i cross k, i cross k will be equal to minus j. Therefore, I write this as V B z with a negative sign here j. So, it is minus V B z j. Now, I try to take cross product of the second term j cross i will be giving minus k. So, this is minus, there is a minus sign here U naught prime gamma B x k. j cross j will give me 0, j cross k will give me i plus i. Therefore, plus U naught prime divided by gamma multiplied by B z. I pick up the x, y and z component of this particular equation like before. Let us look at the x component. x component will have a ex term and you will have a term U naught prime divided by gamma B z which I have written here. y component will have a term Ey here. It will have a term V B z here. There is no other term which contains j term. So, we will have Ey minus V B z. So, what I have written here Ey minus V B z. Let us look at the z component. z component, there are three terms which contain k, this term, this term as well as this term. So, this will be Ez plus V By minus U naught prime gamma B x. This is what I have written here. So, the three components have been written here, which I am writing again here for the convenience here. fx is equal to q Ex plus U naught prime by gamma B z. fy is equal to q Ey minus V B z. fz is equal to q Ez plus V By minus U naught prime by gamma B x. Let us just look at this particular equation here and here. Now, when I am writing the relationship between fx and fx prime, I cannot use those simple relationship which I could use in the earlier case, because the particle happened to be dressed in one of the frame of references. I will use the generic relationship. So, let us write that. We have to use the general inverse force transformation to relate the forces in the two frames. See, if you remember this was the x component transformation of the force. The force term of the four vector was work, which was related to f dot U. So, fx was equal to fx prime plus V divided by c square f prime dot U prime. If I take the dot product, I am sorry, this will be given by fx.   And of course, denominator because U x prime is 0. So, this denominator, there is only one. So, I can straight away write only the numerator, which gives me fx prime plus V divided by c square f y prime U naught prime. So, this is the relationship between x and x prime. Relationship between f y and f y prime can also be formed from the general relationship. This term happens to be 1 because U x prime is 0.  Because U x prime happens to be 0. These are the equations, which I have written here.   All we have to do is to substitute in these equations. Let us first take only the x component of this equation. Substitute this value of f x here, which is q E x plus U naught prime by gamma V z here, f y prime is equal to q E x prime plus U naught prime V z here. Then there is f y prime, f y prime we put q E y prime. So, I substitute these things in this particular equation and let us see what we get.  This what is f x prime plus V by c square, this is what was f y prime. Using this particular equation, you can see that q gets cancelled out and I can write this particular equation with E x prime is equal to E x because E x prime is equal to E x has already been evaluated, has already been found out when we did transformation obtaining the E x E y and E z components. So, E x prime we know is equal to E x. So, what I will do is cancel this q, substitute E x prime is equal to E x. So, using the following transformation that is E x prime is equal to E x, we can write the equation as follows, which I am writing here. q has been cancelled out. Instead of E x prime I have written E x, as you can see that this E x would cancel out. Here we have U naught prime divided by gamma B z.  So, here I will only get B z by gamma. This gamma I can take on the right hand side and multiply it. So, B z will become equal to gamma, which is this gamma which gets multiplied here. This term has already cancelled out with this particular term. U naught prime has already cancelled out B z prime, which is B z prime plus V by c square, which I have written here. U naught prime has already cancelled out and this is E y prime, which I have written here. So, as you can see I get a equation B z is equal to gamma B z prime plus V by c square E y prime, which tells me the z component of magnetic field in S frame of reference. If I know the z component of the magnetic field in S frame of reference and electric field, y component of electric field in S frame of reference. So, this is one of the equations which we have obtained using these force equations, which is part of the velocity, magnetic field transformation giving me the magnetic field. So, as I have written, this gives the inverse transformation of the z component of the magnetic field. Now, when I look back at this particular paper, this particular equation F y is equal to F y prime by gamma, you can try it yourself, does not lead immediately to a new equation. I will use this third equation F z is equal to F z prime by gamma. So, for this F z, you know that there are three terms U E z plus V B y minus U naught prime by gamma B x and for F z prime, you have two terms U E z prime minus U naught prime B x prime. So, in this equation, I will substitute this value of F z. Here, I will substitute this value of F z prime. This is what I am writing in the next transparency. So, let us use the equation corresponding to the z component of the force. So, this is this gamma I have multiplied because on both the sides. So, I get gamma times Q E z plus V B y minus U naught prime by gamma B x. This quantity was equal to F z and this was F z prime, which was actually divided by gamma, gamma I have taken on this side. So, this becomes Q E z prime minus U naught prime B x prime. This E z prime, I know how to convert in terms of E z by using the transformation of electric field, which we have just now obtained. So, this is what I will be substituting in the next thing. Using the following transformation, E z prime is equal to gamma E z plus V B y, which we have just now derived. I will substitute in this equation and I will get this equation. Left hand side remains exactly identical. Q has been cancelled out. For E z prime, I have written gamma E z plus V B y and this term remains as it is. Now, if you can see very clearly, this gamma E z will cancel out with this gamma E z. There is a gamma V B y which cancels out with this gamma V B y here. If you look at this term, this gamma will cancel with this gamma. You have minus U naught prime B x. On the right hand side, you will have minus U naught prime B x prime.  For these minus signs, you can always cancel. This gives me B x is equal to B x prime. So, like behind E x is equal to x prime, I get B x is equal to B x prime. So, this gives us the transformation of the x component of the magnetic field. So, now I know how to find out B z and how I know how to find out B x. I have still not been able to find any equation corresponding to y, which requires a little bit more effort. For obtaining the transformation of y component of the field, we have to assume that the charge is moving in the plus z direction, z prime direction like we have assumed in plus y prime direction in s prime frame of reference. So, we do exactly the same calculation again, but now we assume that the charge is moving in plus z prime direction in s prime frame of reference. Otherwise, we do all the calculations exactly identically. We can carry out exactly similar analysis as we have done just now. The first equation would give the transformation of y component of the magnetic field. Just like in this particular case, it had given me the transformation of the z component of the field. If I would have assumed that the charge is moving in plus z prime direction in s prime frame of reference, the first equation will give me the transformation corresponding to the y component, which we will not work out here. One can try to do it yourself and the result that we will obtain will be equal to B y is equal to gamma B y prime minus V by c square E z prime. So, now I have found out all the three inverse transformation corresponding to the magnetic field. I can always find out the direct transformation by doing the same prescription replace V by minus V prime by unprime, unprime by prime. So, these are all my equations which are relating to the magnetic field. This is what we call as the direct transformation. I know electric field and magnetic field in s frame of reference. I will find out the magnetic field in y, s prime frame of reference. Here I know the electric and magnetic field in s prime frame of reference. I can find out the magnetic field components in s frame of reference. We have already found out the relationship, which gives me E x, E y, E z, E x prime, E y prime, E z prime. Essentially means that for example, if I know what are the magnetic field and electric field in s prime frame of reference, I can always find out what will be the electric field and magnetic field in s frame of reference or vice versa using these equations. So, essentially we have three sets of equations corresponding to the electric field components and three equations set of equations corresponding to the magnetic field components. So, if I know electric field and magnetic field, I can find out electric field and magnetic field components in any other frame of reference. And as you can see very easily from these equations, they are all interdependent. For evaluation of electric field, I also need to know the magnetic field. For evaluation of magnetic field in general, I also need to know the electric field. So, here I come to the end of this particular lecture. I just summarize. In this particular lecture, we have done lot of special calculations to find out the transformation related to electric and magnetic field. Thank you.


News and analysis from Big Data SV 2014 is brought to you by headline sponsors, Actian, accelerating Big Data 2.0 and WAN Disco. We make a dupe invincible. Welcome back everyone to day two wrap up. This is Big Data SV, Big Data Silicon Valley, the hashtag Big Data SV. Go to crowdchat.net slash Big Data SV, where all the action is. This is Silicon Angle and Wikibon's the Cube, our flagship program. We go out to the events and extract the signal from the noise. We're live in Santa Clara, California to Hilton, right across the street from the Santa Clara Convention Center where Stratoconference is taking place. We are eyes and ears all over Stratoconference, like a blanket. Our live coverage here at the Big Data event here at the Hilton. Amazon's here, the Big Data party tonight. A lot of events map are big action happening at the Hilton, Big Data SV. I'm John Furrier, the founder of Silicon Angle. I'm John Michoos. Dave Vellante, co-founder of Wikibon.org and Jeff Kelly, senior analyst at Wikibon on Big Data. Guys, wrap up here just to summarize day two. We got one more day tomorrow is more of the same, Vistrada. I mean, we're seeing a sell out. We're seeing every slot filled keynotes. They went from, I think, 10 minutes to five minutes to get more keynotes in. So rapid fire of speakers. Their format's changing a little bit, but still, they're selling out the tickets. All the sponsors are sold. New startups and packed house for Stratoconference here in Silicon Valley. We're covering the innovation. Going the extra mile covering the startups. Got the analysis. But it's all about Hadoop meets Big Data analytics, big announcements, and you start to see, Dave, the vendors finding their groove. The ground settling, you're seeing the different Hadoop players, Cloudera, Hortonworks, MapR finding their swim lanes. Peace. The three families are having peace among themselves, right? Different approaches. So what's your take? So first of all, yes, Stratoconference is sold out. We were over there last night and everything is sold. I mean, we're talking about the spaces on the carpet are being sold as advertisements. So it's a very good BD event. You talk to people here. They said that they're sort of getting lost in, I mean, the customers are getting lost in the business development that's going on, but it's good BD event. Whereas in the early days of Stratoconference, it was a big data science event. So that's sort of evolved. I think the other thing is, as you said, John, you're seeing real traction, especially from sort of the big three distro vendors. They're not only evolving their business model like Cloudera, continue to tune it, fine tune it, and so forth, but MapR, Cloudera, and Hortonworks, all three of them are doing business. This is a big beach and they each got their corner of the beach or they strip a sand on the beach. It's a sunny day and they're doing business and you're going to see some IPOs come out of this. You certainly already have with guys like Splunk and Tableau, I think I would put them into a big data adjacent category, but some of the core Hadoop vendors are going to be going public soon, which is great because then we'll start to get some real visibility on Jeff Kelly's numbers. I look forward to the IPOs to validate my numbers. We're also talking about some people dropping out and maybe tapping out, but all growing or consolidating in an ecosystem. So Jeff, I want to ask you the question, two things. One, the $50 billion market number, you're targeting that number. One, and the other question is, how does the market look from a formation standpoint? Are things settling? Is it still dynamic? What's your take? Well, certainly things are still dynamic, but they are starting to take shape. So as I mentioned earlier today, I think what we're going to see a lot more this year, and we've seen it this week here is Strata and Big Data SV is we're going to see a lot more partnership news and integration related news and reseller arrangements between these different ecosystem partners because it's very much as an ecosystem. Big Data has got a lot of different parts. It's not one thing. It's not just Hadoop. It's not just analytics. There's data integration. There's security. There's all different components to this. And really, with the exception of a couple of the, I guess, mega vendors, there's no one company that's got the complete platform. So you're going to continue to see partnerships. And I think that's an important evolution of this market because it's clearly showing that the technology now is solid enough where these companies are ready to start integrating, getting out into the field and actually deploying this stuff in production. And also starting to see the partnerships. So guys, big news to me, the big game-changing sentiment that I'm feeling and also through the announcements and the news is, Juan Hortonworks' announcement with Red Hat. They were relationship with Microsoft. The Red Hat News is an expanded partnership that's significant, that validates and puts an exclamation point on their strategy. You're seeing Cloudera with the Enterprise Hub go in that direction. And then recently, we had on theCUBE today, we had two entrepreneurs turned CEOs, if you will, oh, in this case, Collins and more of a general manager, HP and the MapR deal, Dave. I mean, that's very interesting. And that could be the big dark horse in this entire show is that the MapR, John Schroeder, he's no dummy. He knows this business. He's an entrepreneur. He can see that relationship. HP needs a dance partner, not a bad fit, Dave. So let's talk about the big three. So when you're talking about MapR and HP, I think you're right on, John. And you were asking John Schroeder really good questions. Like, are you afraid you're going to get lost inside of the HP machine? And you know that, speaking from experience. But I think he had- Getting lost? Yeah, you had to get lost. But you know what I'm saying? It's sometimes hard to navigate, but he was very confident. Now, in the case of Hortonworks, you're right. The Red Hat deal is a big deal because the significance of that is, Hortonworks has now knocked down the two big operating systems, Microsoft with Windows and Red Hat with Linux. So they've locked in, as partners, those two companies. For Cloudera's point of view, what I learned here this week is that Cloudera is getting traction with some of the big SIs, like Accenture, Deloitte, Ernie Young, and Capgemini. And that's how companies like Cloudera are going to be able to compete with the likes of IBM, who has deep domain expertise and can compete with those companies that I mentioned like Accenture. And so Cloudera, I think, has an advantage there in terms of they were the first to market and they're leading a lot of the trends. So a lot of the SIs know who they are and are willing to work with them. That's a good point. I think from Hortonworks point of view, I mean, give them a lot of credit. Their strategy has not changed one Iota. It's remained open and use that openness to leverage partnerships and reseller arrangements to get mass adoption in the enterprise. From Cloudera's perspective, I would just echo what you just said. If they're going to try to compete with IBM, which is their stated goal, they need the services partners. And the services partners, the extensions of the world, they're competing with IBM as well. They need a partner. They need a dance partner. And this kind of relates to what I said earlier about, this is an ecosystem play. There's not one technology or one service that kind of covers it all. It's many moving parts. So again, we're going to continue to see those kind of partnerships. But I think on the one hand, we're going to see all three of those companies can succeed and do well. The market's big enough for that. But I still think, look, there's still going to be some, they're still going to fight it out. This is not, I don't think they're playing nice. Maybe I think we might disagree a little bit on that, John. I think it's still, I think it's still a pretty heated competition. There's room for them all to succeed. But don't get it.  There's still, obviously, skirmishes in the open source community. There always will be. That's just the way it is. But I think from a fundamental business model standpoint, I think, you know, it's a nice position here. I think it's all kind of, there's a balance of power there. They're all got their, no, there may be some cognitive dissonance around their decisions. I mean, some may like the other guys position, but the other, that's just the race. Certainly that doesn't appear to be the case right now. I think right now they're all kind of in enough separation in terms of competitiveness where I think they're fine. I think it's comfortably numb for them right now with respect to kind of where they're going. I mean, Cloud Air clearly going after the enterprise. I mean, they basically changed their pricing, Dave, to accelerate the sales inhibitor or calls saying, are you in bucket A, B or C? And then if you're flag-shared, we go right to outcome discussions, which is essentially a long sales cycle, but lucrative if they can penetrate. So to me, that's a risk on Cloud Air. If they can penetrate those sales cycles, they're gonna win. So I don't know the distribution of their sales, but you know, my guess is mostly mid-range, but we'll see. Well, I think the two, the Cloud Air repricing was all about, I mean, first of all, it was too complicated. The transaction model was too expensive for them because I'm sure they're going back and forth with people. That was one of those deals that, at some point early on in the cycle, somebody said, hey, we can optimize revenues if we sell each of these little piece parts as little bites. And then over time they realized, well, it just got too complicated and why don't we just bundle them all together and then focus on adoption and not worrying about, okay, negotiating each little piece part. I also want to add, talk about Pivotal. So Pivotal all of a sudden took the misfit toy, EMC, VMware took the misfit toys, threw them in the Pivotal bucket and all of a sudden, boom, we got a $300 million company, a leader in big data overnight with the data lake marketing, that's Pivotal's deal, EMC, VMware, good marketing, Pivotal has now joined that fray. And so they're out pushing their messaging and they're doing business. They're doing business because they got relationships, they got partnerships and it's kind of the EMC Federation, the EMC mafia, they know how to do business. And so they're sort of just almost forcing themselves on the world and they're gonna get some production out of that. The other one is IBM. IBM's a leader in this space, they went from nowhere, not even in the discussion to number one and you've quantified that. And number one in a substantive way, there's a lot of action in services, we heard a lot of discussion about that, 40% of the business in your revenue report comes from services, IBM's the number one services company out there and they are just again doing a lot of business in this space and people can criticize IBM and say, oh, they're sort of old school and modern architecture, blah, blah, blah, blah, IBM's about doing business. So those are two other companies that at different ends of the spectrum, but they're players. Guys, what do you guys expect now? What's the game-changing take here, day two and the summer rise? And tomorrow's gonna be kind of a heavy day for us but mostly friends of the queue will track some more signal but I think right now we got a good feeling in the show, Dave. Day two is really kind of where you get the meat and the bone in terms of the vibe. What's your take? Let's go out on a limb and saying, what is the game-changing moment right here? This moment for big data. Well, the missing moment is apps. Where are all the big data apps? We've been talking about that for a long time. Jeff, a couple of years ago, you predicted this is gonna be the year of the apps. My goals and predicted that never happened. Why is that? Because the infrastructure and the ecosystem has to mature, that's happening, but it's happening very slowly. I can't wait to hear what Abhy Mehta has to say because there's a company that's actually developing the big data apps. So I'm excited about that to hear what he has to say. So I'm still squinting for that game-changing moment, John, but I'll bet you you have a sense of what that might be. What do you think? Well, I mean, I look at the startups in Silicon Valley as a good barometer of how I call the patch of innovation where the mushrooms grow, the manure of innovations, money, ideas, and just seeding and fertilizing all the innovation. That to me, that's a bellwether. Then you look at the financing market, Dave, and you look at what the rounds are going for, AB, financing, series A, series B, then it'll be what the M&A market looks like, and then the IPO, it's the latter of how I benchmark it. And right now, valuations are very high. The startups, I'm not impressed with the startup situation. I'm really not, I gotta say. It's like looking at the startups, not as much advanced thinking and big data as I would expect some folks to have. A lot of gimmicky apps out there on the consumer side, but I haven't yet seen the game-changing enterprise. What about ClearStory? I like ClearStory. I think the idea of what Charmille is working on is great. See, this is a great example. You look at Charmille at ClearStory. That's a hard problem, and it's not easy to simplify the knowledge worker, and they're doing a great job to make visualization and analytics work. But again, I wanna see more startups solving real computer science problem. That's why I like what Spark's doing. I like some of the computer science engineering stuff happening at Stanford and also at Berkeley. To me, I think a whole other crop of innovation is gonna come out of that wave. I have yet to see the startups on the other side. There's some good stuff being funded. We know platform, continuity, guys we know. Those are real guys with jobs, but I just don't see a lot more guys. And when I walked through the show over there at Strada, it's not a lot of names. I'm not shaking my head going, wow, that's kickass. I'm not blown away at all. I don't fall out of my chair. So to me, that's a real indicator. Yeah, I think when it comes to apps, look, I think we were a little premature in predicting the year of big data applications, and part of that is related to the underlying infrastructure, and there's still room for improvement in terms of making Hadoop rock solid for the enterprise. Made a lot of progress, but, and this is a very fast moving market, but it's still gonna take time. These things don't happen overnight. These are hard problems people are trying to solve. The analytics, the complexity of these analytic problems that people are trying to solve is challenging. To deliver that into an actual end user polished application takes time. Let me finish my thought too on that, because the startups is one area, but we look at the other ones, the established valuations of the companies, like Cloudera, like these big analytics ventures, the valuations Dave are very high. Jeff, when you look at the numbers, they're almost, you know, they're betting on the ranch. You got the big VCs betting against it. So if the M&A market doesn't develop between two to 700 million in terms of acquisition, then that's gonna be an opportunity for the ecosystem. So what I'm watching is startups, the valuations of these well-funded Series C, Series D financings, growth firms, quote, growth firms, they have to produce revenue. The value on that is, are they gonna produce the cash to support the valuations that get them on an IPO track or a big acquisition number? Right, I think, well, this is the year companies like Cloudera, they need to turn out the revenue machine. It needs to happen this year. Impressive what Alan has laid out in terms of messaging. I gotta give Cloudera major props on that. Very tight, very clean positioning and the messaging's great. Yeah, but again, when we're back here this time next year, those revenue numbers need to be, Cloudera's gotta hit 100 million this year. That's the goal. Okay, final word day, final sound by bumper sticker here, day two. My bumper sticker, it's all about the wallets. We've gone from geek to wallet. That's what happened in the big data world. Jeff? I'd say bumper sticker is open for business. To me, show me the money, justify the valuations and let's see the startups. I think it's gonna be still innovation, ton of growth, a lot of opportunity. That's a wrap from day two here at theCUBE. Big Data SV, that's our hashtag, hashtag Big Data SV. That's our event, Big Data NYC was a few months ago. We'll be back in New York in a few more short months. Big Data NYC, Big Data SV, innovation and silicon value. We'll be right back for day three tomorrow. Stay tuned and keep watching.


This little thing is the reason I wake up every single day with an attitude of gratitude to tell as many people as I possibly can. Thank you. This little thing is the reason I am personally relentless about returning emails, voicemails, and text messages. Because I believe if one of the winningest, most successful, and most decorated coaches in the history of all of team sports can make the time to hand write me a note back, you better believe I can return your email. You better believe I can call or text you back. Just remember that little things make a huge difference.


Okay, we're kicking things off with Rob Emsley, who directs product marketing for Dell's data protection products. Rob, I'm really excited about the collaboration that we're doing the series and great to have you back in the studio. Oh, it's great to be back, Dave. I mean, it's been only a few months since we did the future of multi-cloud data protection event with you.  Yeah, now, as our audience knows, we've covered many data protection topics on theCUBE over the years, but this topic, it seems to continue to dominate the headlines, Rob. Why is that? Yeah, I mean, I think you're aware that every year we run a global data protection survey of rough and tough about 1,200 customers around the globe. And one of the things that we've really started to inquire about a lot more in our surveys is the question around cybersecurity and cyber resiliency. One of the things that we found is that two thirds of the organization surveyed last year are really concerned that they don't believe that their existing data protection measures in infrastructure is sufficient to cope with malware and cyber threats. Also, the same amount, two thirds also believe that in the reality of work from anywhere, learn from anywhere, that's actually increased their exposure to cyber attacks. So certainly, there's just a lot of concern as far as do I really have what I need in order to protect the business? So it's interesting, basically you're saying that people are aware of it. So some of these numbers might surprise you a bit when you think about just the sheer number of vendors that are offering solutions in this space. And as folks know, cloud really doesn't solve the problem. So why do you think we continue to struggle so much? I think a lot of it is because we have a very fragmented security market. I think we've sort of seen research that says there's somewhere north of 4,000 incumbent vendors, startups, adjacent players, addressing various points of the security landscape. So we really believe that the challenges are that there's just a lot of inconsistency because there's so many solutions that are out there. And that's one of the things that we're really looking at here at Dell to try and address by bringing our perspective about how you actually navigate through this complexity. Well, and we saw this during the pandemic, Robert. There was so much funding that went in and a lot of that went to cybersecurity. And so people naturally say, okay, here's a tool that's gonna solve this narrow problem. Let's try it because we have a, maybe we just got snake bit and got hacked and now we've got this new little shiny toy. And so 4,000, I mean, that is just incredible number. Yeah, I mean, I think it's the old adage that in order to solve cybersecurity challenges, you need technology, people and process. And you really need to be wary of vendors that come to you and say, buy this solution and it will solve your problem. I think the reality is that it's a multi-faceted challenge. And that's where you really need to look at the entirety of the problem and break it down into piecemeal chunks that you can address and build a holistic solution. Okay, so let me set up this sort of next part of our discussion. We have a lot of noise in the market, as we just talked about. You got more sophisticated attacks. You got too many organizations that don't have adequate preparedness. CISOs tell us they still have lack of skills inside their organizations. So what we want to do with Rob is we want to go and understand like where do we go from here? And more relevant to our series is what's the relationship between data protection and cyber resiliency? So Rob, how does Dell think about cyber security in general? Yeah, well, we really frame the conversation into three specific areas. The first is protection. So it's really the goal is to stay secure against evolving threats. So that is certainly an area where all of the work that many customers have done to protect their perimeter, protect their infrastructure. Certainly if you think about some of the techniques within infrastructure itself, things like hardware, router, trust, certainly work that we do with our partners like Intel within our data protection appliances, even down to the components that we use. So if you think about things like our Broadcom components, Silicon Root of Trust becomes really so important. Also, the fact that the infrastructure that you deploy comes through a secure supply chain, that we guarantee hasn't, has got to you in a very secure way. So protection still remains a key element of the conversation. The second one though, is really where I think this series is going to really focus on, which is resiliency. How do you withstand and recover from attacks? And I think that's where the data protection and the backup and recovery market becomes such a close adjacency to the overall cybersecurity space. Backup has been around for a long time, but I think that you and I have discussed how the entire industry is really spending so much more time now, talking about how your data protection and your backup and recovery infrastructure helps you become more resilient and allow you to recover from cyber attacks. So those are two very key pieces. And the last one, I think is a real key element to Dell's message around security, is you need confidence. So yes, protection and resilience are great. A lot of that is around technology and process, but confidence really comes from the people that you work with. And one of the great things that Dell's able to provide is a global set of resources that are able to not only help you implement techniques and processes and tools, but also is there for you to respond when you need it. And nobody knows when you're gonna need it, but the pure scale of global services from Dell, you know, we have many situations where we have been able to work with customers immediately when they need it. You know, and I think that's such a key important piece. So protection, resilience and confidence. You know, this idea, I'll share, our audience knows that we've talked about this a lot during the pandemic. So many CIOs told us that their resiliency, their business resiliency was way too focused on disaster recovery. So we talk about cyber resiliency. We're talking about being able to survive an attack and specifically being able to recover and resume your critical business operations. Now Dell's been in the market for a long, long time with cyber recovery solutions. So my question is, does your solution have staying power in the market? And what can you say that gives customers confidence that it's going to get them, you know, through the future, this uncertain future that we face? Yeah. So certainly if we go back to our global data protection research, you know, last year, you know, one of the, you know, the really upsetting facts is that, is that 48% of the organizations that we surveyed had actually suffered a cyber attack in the last 12 months that prevented access to their data. So this is something which, you know, is deeply concerning. I think one of the realities is that bad actors are not only going after production systems, but invariably they're going after backup infrastructure. So as you mentioned, they're literally half a decade ago and it was really after, you know, the infamous attack on Sony that we really introduced the concept of isolation into our backup and recovery solution as a additional layer of security that we could provide to our customers to make them more secure and make their backup infrastructure more secure. So really our cyber recovery solutions is really focused on three distinct areas. First is immutability. You know, and certainly whether or not you're implementing a cyber recovery vault, immutability nowadays is effectively something that you should be implementing across all of your backup infrastructure. Certainly our backup appliances that have been in our portfolio, as you know, for many, many years, have inbuilt security and inbuilt immutability and they have done for a very long time. But we continue to make those systems more highly protected with things like multifactor authentication, things like very specific role-based access control. So that's on the protection side. And certainly you would like to think that being able to recover from your primary backup copy would be your first line of defense and your first line of recoverability. But over the last six years, we've been supplementing that with this concept of isolation. So immutability first, isolation, and then intelligence being the second two elements of our solution. And that's really where the whole concept of delivering a backup copy, maybe not of all of your data, but certainly of your critical rebuild, applications, systems, and the data that they need in order to get you back up and running and make that copy of that environment completely isolated from the rest of production, from the rest of your backup infrastructure. You know, I like about what you're saying, Rob, is, I mean, Dell Technologies is a product company, but you're talking about much more than product. It's a wider scope. The supply chain security, you know, not just a single point product. You're talking to services or a key piece of it. You kind of alluded to that earlier. I really appreciate you helping us set up this series and episode one, really appreciate it. You're great, thanks, Dave. Okay, you're very welcome. Okay, keep it right there. We're coming back with Daniel Newman who has voted the number one independent market analyst. You're watching Navigating the Road to Cyber Resiliency.


How are you feeling? I feel good. Yeah? I'm ready to up the intensity. Right, S-Fan? Oh, absolutely. S-Fan was just talking shit, and he said this is too easy, that's what he was telling me. By the way, I'm not trying to say, S-Fan, is this not actually... No, I like it. It's literally this not actually... I like it. For once, somebody appreciates my body for what it is. No, S-Fan is good. I think it's good. I like it. I like it.  And that's the thing, there's a lot of things you have to think about. The first thing you have to think about is your grip placement. A lot of guys, beginners, they just go to the par, and they just grip it and pull it up. That's the wrong way.  We'll just go at it and keep training, and I've been a bit, I want to see how a S-Fan does first. Look who asked, man. Look who asked, man. You have some back issues, so let me know if there's any issues, if you're feeling pain, let me just stop that access today. Come on, S-Fan. Look who asked. Look who asked.  That's why I asked.  Dude, he literally came across the world to help us out.  Go crazy. We're trying to do it again. I need to be more active on tweets, and I want to be. I want to be. I just need to be more consistent with it, you know. That's the thing. I haven't been consistent. But I love the problem. I'd love to see you working out.  I'd love to see it. Okay. Okay. Spend a minute. Deadlift. Feel good? Yes, it's okay. I've got some herniated discs. A little bit of bleeding. I'm working with these guys. They're working out too hard in the other group, but I'm getting tired. I'm stuck over here. I'll work it with you guys. Give me 12. Okay. All right. Actually... Squeeze. Squeeze. Squeeze.  Control the weight. I think I need more weight. Oh, yeah. You like it? Yeah, I hit myself in the face.  Really? How's this weight? It's real. I think maybe more, I don't know. Maybe more? Yeah. Cheap weight. Yeah. Okay. I'll do it. Okay. Yes. Let's go, dude. Did you do pull-ups at all whenever you were at your biggest? When you're competing? I don't know about biggest. We were all so strong. I was able to do pull-ups. But now, because I haven't been training a lot, I honestly have no clue of a can to pull-ups. I haven't done this for a long time. There you go. There it is.  Keep doing that. Keep doing it for sure. I don't know. That was good. What's your weight right now? My body weight right now is like 155 kg. Oh, wow. So that's like 320? I use kilograms, guys. Sorry. Is there another space in this gym? Yeah. It's the home of the side. Should we check the result? Hey, E-Rob. One of us three has the most potential. In what? Life. In life? His dad owns a gas station. It's very famous. Okay, he wins. It's called 7-Eleven. He wins. Seriously? No. Yeah, yeah. Good. His dad owns a famous gas station. It's not his own. He wins. He wins. Seriously? No. Yeah, yeah. Good. His dad owns a famous gas station. So, hey, can we just tap? Tap? Other side? We'll have your next steps. Yeah. Thor, how many kids do you think you would take to beat you up? It's a weird question. It is a weird question. Like, let's say like 30 kids between the pounds of 100 to like 130 pounds attacked you all at once. Could you fend yourself? No.  You know, I can't fight back, so I just have to run away.  I told the six of you.  Mom, what do you want? It's for me. Mom? Yeah. Yeah, it's Matthew.  Okay? I'm tired of you complaining about dad to me. Okay? And yes. No, I know. No, mom. I broke my night. At the end of this gym session, we're actually all going to fight that group. But we're going to beat them all up. For sure. Come on.  Come over here, then.  Now we're running. Jesus Christ. Yeah. Six. So. I want to do something different, something fun, huh? I'll add some conditioning right in the end. I'll do a soft pike. You do 30 seconds all out. 30 seconds slow. 30 seconds all out. 30 seconds slow. 30 seconds all out. Do you like being called coach store? Sure. You asked me if I wanted to be called Matthew. 30? Half store? Yeah, 30, you know what I'm talking about. Coach half store. All out, all out, all out. You got it, you got it, you got it, you got it.  Wait, is this that hard? This is hard, yeah. All out, all out, all out. Come on. Come on. Finish strong, finish strong. Finish strong. Nice. One minute left, one minute left. Come on, one minute. That's easy. Anyone that's saying it's easy to do it, that's easy. That's your 4K and 12K. Bro, it's not, it's just hell.  No, it's not that.   Really? You got this, you got this. You got this. Can't take it slow, can't take it slow. Can't take it slow. Don't stop. All the way, don't stop. All the way. Good job. Oh, it's a 77. Minus 77. So, 50. Yeah, he won. He won. 11. To be fair, he's also double our weight. It doesn't matter, actually it's more. Divide by 2. Because it's not calculating your weight. That is? No. That's been these comparison. No, I got more juice, that's what it is. Bitch. How has this been on sale? Dude, S-Men, all he does is he walks and paces all day. He was made for this. Hey, Thor. Do you know not an extra mat for me? I'm going to, I'm going to join in. I want to do abs. You only come in at the park, you know you're going to be in a set. No, I wanted to do the other stuff.  I was doing the other. I wanted to join in, but... No, no, it's cool, you can take my spot.  You guys ready? Yeah, yeah, yeah. I'm kidding. Go. What?  Thor, am I right?  Me, over here. Yeah, you were probably the best on the wall.  Honestly, I'm not very good. It's not my exercise. I always appreciate a coach that does the workouts, you know. Canute always just makes us do everything. The thing is, I can't even tell if Thor's doing the set up or not. Why? Because your shirt is so big.  What's your good idea? I'm doing that next time. But I'm not going to tell you you're not doing it, so... I want you to be completely transparent with me. If your back is still feeling good, if the plank is too hard, then I'll never just call it a day. Okay. Dude, my quads, after the thing, I was, like, not sore anymore from legs, but I was kind of tired. Doing the bike, shot my quads. Walk, go. Come on. Let's go, guys. Come on. Come on.  Come on. Please don't come my way. You got this, guys.  No, no, no. Come on. The good boy is here always. Squeeze that. Squeeze that. Hold, hold, hold, hold. Ah, how much time? There you go. So close, so close. Okay, guys.  How long? How long? Give it up. One, two, three, four, five, six, seven, eight, nine, ten, ten, ten. Dude, if you did boxing, training on stream, that'd be sick. You did it before, right? I think it's done some streaming, but the thing is, guys, like, when I train, I am boring for the viewers because I don't think I'm a fun guide for the viewers. I don't talk. I train. And I think that's boring for the viewers. For us, we're just training for ourselves. And when you're training to compete, you don't have time to worry about content as much. That's the thing. When I train, I find this year is distracting. But you guys are amazing, though. Don't get me wrong. You guys are amazing. Like, I have a program, I have something to do, and I have to do it. Yeah, so it's different. It's different. Our workouts now on stream are like two and a half hours. But in reality, we don't know... An hour is enough. That's exactly what we were saying the other day.  You were so big. That's such an agility-based sport, and you were quick.  Thank you, man. I appreciate that. That's why I believe that anyone, literally anyone, can, if they have the mindset and willpower to be great at something, like the moment that you start to not believe in yourself and tell yourself that you can't do something, that's the moment that you're lost. You have to believe and you have to put in the work. I have things that I'm insecure about, and that's, for example, being around camera. My whole career, my whole career, believe this or not, guys, always being in the camera has always been something that I've never felt comfortable with and always been trying, I've tried to be better and I've done it to try to improve myself. Is it cooler to be at the top or to labor towards becoming that person who can be at the top? That's a good question.  If you're always in that bubble, then you'll never grow. Get yourself out of that comfort zone and grow, and you'll do some great things. Are you gonna come with bossing? Yeah, I'm down.


What's next? 5k subscriber channel update. When I started my YouTube channel, the goal was simply to share bioinformatics lectures and key concepts and tools. I did not expect to ever reach 5k subscribers. I also didn't expect the Novonautics Foundation Centre for Approaching Research to be shut down. That resulted in a recent series of YouTube shorts that I received a lot of positive feedback on, including from industry. So thank you very much everyone. This also means that I've had a very busy time and as a result of that there have been no longer videos recently. But worry not, I'm working on new material, covering topics such as deep learning and new aspects of network biology. I'm also considering making new content types. This includes working on actual research problems and answering questions from viewers possibly in the form of live streams. I'd love to hear your thoughts on this in the comments.


Hi this is Jack and I'm here to talk about firing the ham, our newest pilot batch that we just brewed on our brand new system utilizing our cool ship. So a really cool beer utilizing all smoke malt, decoction brewed, naturally carbonated, horizontally watered. The same recipe we've been brewing for close to 10 years now. Really excited to get this beer out to you all.


In this video, we're going to be going over how to convert from rectangular form, which is when we break it down to an x and a y coordinate, when we take a vector and we work out what its x is and its y, we're going to take the rectangular form and convert it to polar. So what we're going to do here is we're going to start out with this vector right here. We've got an x of 25 and a j of 50, which means that we've got an x of 25 and a j of 50. Here means we're going to be in quadrant number one.  So I've got 25 on my x and I've got 50 on my y. So let's just draw the vector in. So I've got 25 here and 50 here. So now what we need to do is figure out what our hypotenuse is going to be and this is our resultant, which is the first part. This is the magnitude that we're looking for when we're talking about the polar form as we learned in our last video. So we're going to go 25 squared plus 50 squared gives me the square root of. We end up with a resultant of 60. So that is the magnitude. Now we need to figure out what direction it's heading in and that would be our angle. So what I'm going to do is use cos. I'm going to go 25 divided by 60 and then I'm going to inverse cos that. And if you wanted to know why I'm doing that, you just need to watch the videos on trigonometry, but I'm taking my adjacent side and my hypotenuse and adjacent over hypotenuse is the ratio of cosine. So I do that, the cos of 25 divided by 60 inverse cos that I get 65 degrees. So now I've done it. I've figured out that my magnitude is 60. That's my resultant, the hypotenuse. The angle here is 65 degrees because I'm in quadrant one, which is this quadrant here. Again, watch the video in quadrants. It's anywhere between 0 and 90 degrees. I can just easily say that it is 60 at 65 degrees. So there you go. 60 at 65 degrees is the polar form of 25J50. That's in quadrant number one. Let's move around the four quadrants like we've done in the previous videos and let's see what happens. So in this example now, we've got negative 45, which is negative 45s on my x, so it means it's heading this way. 60 means it's heading up. So that puts me in quadrant number two. So let's get that started to be drawn up. So I've got negative 45 right here and I've got 60 here. Then through the power of Pythagoras, 45 squared plus 60 squared gives me the square root of 75. 75, again, is my resultant. Now what we're going to do is we're going to figure out what the angle is in here. And this part's really important. So let's take 45 divided by 75 and inverse coset that. And that gives me 53.1 degrees. So now I've got all the sides and the angle here. Now, if I was going with polar form, I could say 75, but I cannot say at 53.1 degrees because we need to look at which quadrant we are in. We're in quadrant number two, which means that our angle has to be anywhere between 90 and 180 degrees. Well, we know that this guy here is 53.1 degrees and we're looking at the angle as in reference to zero. So we want this angle. So what we're going to do is just take this guy here, 180, minus the 53.1 degrees here to get my actual angle in this quadrant. And I get 129.6 degrees. So now I can easily say that this guy here, this negative 45j 160, it's got a polar form of 75 at an angle of 126.9 degrees. And there you go. That 126.9 tells me we are in quadrant two as well. Let's move it around. Let's go on to quadrant three. So now I have negative 120, negative j 40. So negative 120, negative j 40. We know for sure that we are in quadrant number three. Let's start playing around with this. Get it drawn up here, 120, so that's the negative 120 puts me on this side of the point of origin. 40 is down here. So now I need to figure out what my resultant is or my hypotenuse. And that works out to be a hypotenuse of 126.5, which is my resultant. So again, we're getting there. Now we just need to figure out what this angle is. I'm using cos, I'll go 120 divided by 126.5 and inverse cos, that guy, and I get an angle of 18.5 degrees. Now again, we are in the third quadrant. I can't go ahead and say it's 126.5 at 18.5 degrees, because then you think I'm talking with the first quadrant. So before, in the last one, we went 180 minus that angle that we worked out to get the angle. Now we're going to go 180 plus the 18.5, and that will give me my angle, which is 198.5. So now we can say that our rectangular form, which is negative 120, negative J40, has got a polar form of 126.5 at an angle of 198.5 degrees. There we go. So we've done the first quadrant. We've done the second quadrant. We've done the third quadrant. Let's move on to the fourth quadrant. Triangle 30. So we're moving this side of the point of origin, negative J75 going below there. Again, we are in quadrant number four. So as we've done before in every single quadrant, all we have to do is draw that in there, get your triangle drawn in, 30, 75. Using Pythagoras, we figure out what my resultant is, 80.7. Now we're going to work out what our angle is here, 68.2 degrees. So now we can say that we've got a resultant of 80.7, and we know that this little angle in here is 68.2 degrees. Now we said that this angle on this side was 180 minus, the angle on this side is 180 plus. We could say that the angle over here is 360 minus, and that would give us an angle of 291.8 degrees. So we could say that this guy, 30, and negative J75 rectangular is the same as saying 80.7 at 291.8 degrees. But what we can also say when we're dealing with the fourth quadrant is we can work our way backwards. Now, I won't go too much into why we can do this. You can do this with every quadrant, but we'll do this with the fourth quadrant because it's somewhere between 0 and 90 backwards, so it'd be 0 and negative 90 this way. We can look at it and say, okay, we've got 80.7 at an angle of negative 68.2 degrees. It's the same thing as long as you work backwards. Now we generally only do this in the fourth quadrant. So you can work out what this degree, this angle is, and throw a negative in front of it using this resultant, and you can work out what that is. Now it's very important that we understand how to do these conversions because in our next video we're going to start talking about how to add vectors. See you there.


Tom here from Lauren systems and I shared my thoughts on the firewall in a previous video You'll find link down below But I wanted to share my thoughts and why I was so critical and why I still am and going forward don't plan to change my mind About these cloud focused or cloud only type of firewalls And it's because it's been done and failed and burned many people before now I'm just not gonna dive completely into every IoT device that was purchased has a cloud lock-in and that IoT company went out of business or decided to stop servicing their cloud controller and then the devices all go defunct We're gonna narrow it down to just a couple of them because I've had interaction with these companies Specifically Winston which I was emailing back and forth with back in 2019 with Winston privacy and their tall claims of privacy That kind of didn't make sense to me They seemed a very overstated and there was so much excitement in news articles that I just felt like it was all hype and it turns out Well, they burned everybody and kind of went defunct and so did the Kujo firewall who also burned people But let's go down memory lane and talk about those because I figured hey Why not discuss this a little bit of context of history of what happened to those cloud firewalls before? I was not ever and you won't find any Videos in my channel because I never did sign up for sponsorship with either one of these companies I just felt they weren't at all a good quality product and it turns out I was right I just didn't have to look anything beyond the terrible marketing to get that impression now The first one we're gonna talk about is Kujo the smart way to fight hacking Kujo smart firewall Protects your home and business from hackers and ships the next business day good marketing here and really cute branding They got these little eyes that light up on it to tell you things about it Some of the images are broke But I think we have a couple of me probably means different things when the eyes are half open or fully open You know letting you know whether that it's got an eye on those hackers maybe 329 thousand six hundred eighty six dollars by four thousand five hundred ninety four backers and Hey, that's nice and there's all kinds of nice tech articles And there's good reviews of these you know Kujo a smite firewall for today's connected devices and nice articles about it But much less nice is when security researchers and actual cyber security people take a look at it The cute branding didn't get by the team over at Talos and they had a whole summary of all the flaws in this device It just was not built. Well, it wasn't a great device and Not only that we'll scroll right here to the important part in 2021 Kujo AI decided to discontinue their home security firewall named Kujo despite selling a lifetime License because the clouds free forever folks We want to avoid subscription fees and I always look at are these business models by these companies? Sustainable on the product and I looked at this when they had reached out to me and I said, this is junk I don't understand this very well They make a lot of claims but you know once the bad articles started coming out in real security people took a look at it And of course they go. Well, we're in trouble. Let's discontinue it And of course everyone's firewall went belly up and that was the end of Kujo Well Kujo firewall Kujo AI is an American network intelligence software company So I think they took that money and set up putting a product and just built something else and pivoted into other Areas the next one and I had some back and forth because I didn't believe their claims either Winston take back control of your online privacy plug-and-play hardware That reclaims your use of the internet on all connected devices a home stop tracking spying and hacking And I'm like you're gonna stop hacking by plugging in a magic box We're gonna eliminate my problem with advertisers big tech and data brokers and ISPs and it's a lot of claims with a very little technical details I tried emailing them and only got replies back that were also pretty vague I a lot of people back when this was popular asking me about it because once again He had lots of good articles and it raised quite a bit of funding over half a million dollars so five hundred fourteen thousand six hundred sixty nine dollars and smaller number of hackers so people are you know willing to pay a little more we Have their website that I have to pull off of the archive because it's dead and Yeah, that's it the websites got all these claims on it But none of it matters because if you go to their actual website the websites gone and once again There was the next web had popular articles about it a fast company had popular articles about it But they went belly up and then all those turned into bricks and didn't do any of the things that they claimed Now leave links down below to those devices the kujo in a Winston So you can go through the history if you're curious yourself about them But my bigger point is these are the things you should be looking for Companies that make overstated claims that seem too good to be true offer you a free cloud forever with no subscription fees And all the things we like to hear but you have to consider what's gonna happen If those companies can't sustain or run out of that large investment of capital that started will they sell enough product? Will they sell enough? Subscriptions if they have any or will they switch it from non-subscription to subscription to try to sustain the cloud and if the Cloud goes away What's your risk? You bought a device that costs x and you hoped it would work for at least a few years But when the cloud goes away, it's more than just the subscription with these that go away and the threat intelligence feeds Some of them will probably completely stop working all together Winston had some type of mesh network They were trying to build and without the cloud controller to coordinate all that it kind of quits working all together And that whole site is gone and it all just kind of fell apart and everyone that had it is been left with a little Brick-sit in there that I don't know maybe if you're an enter pricing hacker You can do something else with but that isn't why you bought it and that's my point is just to be suspicious and raise awareness As always love hearing from you leave your thoughts and comments down below Let me know if there's an IOT company that burns you that you got a little bit too Well clued close to you said I want this cool IOT device and app and then it went defunct I know there's plenty of them out there So hey at least in comments and some of the ones that you know are memorable in your mind These are memorable to me because I had actually interacted and had people ask me years ago on YouTube Hey, what do you think of these and the company had actually reached out to me with their affiliate program? And I just had no interest in it So the that's why I brought these ones up and I do cover a lot of firewalls But leave your comments and your thoughts down below if you want to see more content from this channel like and subscribe And if you want to engage with me on this or other topics I've talked about head over to forums. Lawrence systems calm or just learn systems calm and hit me up on whatever socials I'm connected to at the time you're watching this video. All right and thanks you


I've got places to go and people more important than you to see, because I happen to be a scientist, and we scientists have a tendency to be very busy and important people. If you're out there in the folding chairs, that means that you're the new guys. Bottom of the totem pole. But it also means that you passed the entrance exams. Welcome to the SAP. From this moment onwards, your job is very, very simple. You are going to punch sharks in the face. When not punching sharks, you will be planning on punching sharks. You will be developing new ways to punch sharks. You will read about punching sharks. You will write about punching sharks. You will study punching sharks. You will dream about punching sharks. You will jump the shark. Punching sharks is your life.


This is JSATV the newsroom for tech and telecom professionals. I'm Dean Perine and welcome to JSATV. We are coming at you live from the show floor of hosting con 2016 in the big easy of New Orleans, Louisiana. And I'm here with my old my old friend Phil Koblenz, but you're not old. I mean, you know, I've known him for this, the CEO of NYI New York internet and Mr. John Brenchella. He is the CEO of server hub. Pardon me for not getting that right. And the reason why we have these guys here is because there's a partnership happening between the two companies. But before we get into that, gentlemen, how's the show going for you? So far so good, Dean. Who could possibly complain about getting to hang out in New Orleans with me in New Orleans? John, how's the show going for you? It's been great so far. Good networking, good vibe. New Orleans is a great city. Upstanding. Yes, I've never been called honey and love and dear and sugar so much in my entire life is when I've been in New Orleans. And that was just in the pre-interview. And sugar baby, they call me a lot of things here in the big easy. But anyway, guys, partnerships. Before we get into that, Phil, why don't you tell our viewers quickly about NYI and then John, you'll talk a little bit about server hub and then we'll talk a little bit about the partnership. NYI. Sure, as all of the JSA TV viewers know, NYI is a managed data center provider located in New York City with facilities in the New York City area and in Bridgewater and Jersey about 40 miles outside the city. Our specialty is data center infrastructure solutions for companies that can take advantage of additional management support and things of that nature. Very good. And John? So, with server hub, we're infrastructure as a service provider. Right now we're currently in five, soon to be six data centers. With New York is our latest launch. We do dedicated servers, cloud hosting, managed services, virtualization. We really like to make IT really simplified for our users and just give them an easy experience with the server environment. Very good. So, soon to be New York City, I can only assume that you're doing that because of the partnership with NYI. Is that true? Absolutely true, Dean. Awesome. John, so why NYI? Why did you choose Phil's company? Well, we've been working with them and discussing things over the past several months and it's just a natural fit. We really love the data center, the culture. Phil's been great. Everyone who's been on the team has been just really awesome. They're really in line with the vision that we're looking for in a data center. We very carefully pick our strategic partners and it just made sense. Very good. And so what is that vision? So, we have a lot of specific criteria and there's certain things that we do that are in line with our goals to kind of simplify the process. And just when we initially went to Chris, we kind of gave him a 15-page poobla of all the stuff that we need and they're very accommodating because it's very interesting. You can go to a lot of providers and you can say, this is what I need. I'm like, yeah, I can give it to you. But then when you actually start going through that process, it doesn't really happen. And with NYI, they've been true to their word on everything and that was a very huge driver for us. It's very important because there's a lot of moving parts in this business and especially for us where we're going through different markets, different continents. We need to have a company that we can trust who can actually really help us with our vision and as well as get them in line with obviously their visions that they have. And I think that's why it became a really natural fit. Very good. And Phil, I assume that you concur. It's going to be a good partnership, yes? Of course. I mean, this is exactly the type of customer we go for. I mean, the idea is when you're trying to deploy particularly a managed services company in different markets, it's important that you find a fit within each of those markets that allow you to have the logistical flexibilities that you have in the market that you call your home market. So, you know, with our services and the way our team becomes an extension of our customer's teams, Server Hub is kind of the perfect example of the type of customer we go after. Outstanding. Phil, thank you as always. Do you guys hear that thunder? It's real out there, isn't it? John, thank you for being here. We really appreciate it. Thank you for having me. You got it. And you got it. Thanks, guys. And thank you viewers for watching JSA-TV. We'll see you soon.