Welcome back to our lecture series, Math 3120, Transition to Advanced Mathematics for Students at Southern Utah University. As usual, I'll be your professor today, Dr. Andrew Seldine. And so in this, the first lecture video for lesson 26, we're going to introduce the notion of an equivalence relation. Now, just as a reminder, in our previous lesson, we learned about a partial order, which is one way of trying to quantify comparison. Relations are all about comparison. The relations are the mathematical ways of comparing different types of quantities. Partial orders give us a way of measuring when one object is larger than another, at least some of the times. Equivalence relations, which is probably the most popular relation other than functions themselves, that we would study in this lecture series. An equivalence relation is trying to measure when something is the same. Equivalence relations, as the name suggests, tries to measure sameness, when something is the same. And so let's be explicit in this definition. All right, so an equivalence relation, first and foremost, it is a relation.  So if it's, first of all, a relation, so it'll be a subset of the Cartesian product x cross x. And much like a partial order, it satisfies three axioms. The first axiom is the reflexive property, so that with an equivalence relation, every element is related to itself. So for all x and x, we have x is related to x. We also will have the symmetric property. This is where we disagree with the partial order. Partial orders, we said were reflexive, anti-symmetric, and transitive for a equivalence relation. Instead, we take it to be reflexive, symmetric, and transitive. So in particular, the second axiom, we replace the anti-symmetry with symmetry, and that gives us an equivalence relation. So symmetry, remember, says that if x is related to y, then y is related to x. The direction of the relation is always reversible. And then the transitive axiom, as I remember there, the transitive property says that if x is related to y and y is related to z, then you're going to get that x is related to z. And this gives us an equivalence relation. Now, when it comes to an equivalence relation, we typically take a symbol that in some way or manner resembles an equal sign. So equal sign, I should mention, is the golden standard for an equivalence relation. If two things are equal to each other, they should be the same in all important aspects. Equivalence relations are really the generalization of equality. So this will include things like, you could talk about congruence inside of a geometry. So we could say that two triangles are congruent to each other. That doesn't mean they're equal as triangles. They're not the same triangle, but something about them is the same. Because they're the same in that they have the same angle measures. They have the side measures the same, but they're not the same triangle. They're different places in the plane potentially. And so lots of symbols you could use would be things like the following. Again, these are all examples of symbols that kind of look like equivalence relations, some modification of the equal sign. And so for us, our generic equivalence symbol will be this one. Just so you're wearing latex, this is backslash sim. It's short for similar. And so it's like a symbol. It's like the two objects are similar in some manner, because that's when equivalence relation measures, as opposed to like a partial order, which measures what things are bigger than another. Equivalence is measuring similarity. Now with regard to any equivalence relation, which to show that something that equivalence relation, you check these three properties, it's reflexive, symmetric, and transitive. We'll do some examples of that as well. Let me also introduce another important vocabulary term with regard to equivalence relations. If we have an element X inside of the set X for which this equivalence relation is established, then for that element X, we can define the set, which is typically for us can be denoted bracket X bracket. This set right here is going to be the set of all elements in X that are related to X. So we're gathering everything that's related to X inside of this equivalence relation. This set right here X bracket here, this is called the equivalence class of X. And it represents everything that is equivalent to X inside of the set there. Some things to notice, of course, is that this set is non-empty. X itself belongs to the set because it's a reflexive property. So we get that X is related to X. And so there's always something in these equivalence classes. And we also will see in the future that you can potentially have different elements representing the same equivalence class. This happens if and only if X is related to Y. Again, we'll talk about this another time, a little bit more details here. And so this element is often referred to as the representative of the equivalence class. Because it turns out there's more than one way to represent the equivalence class, but I get a little ahead of myself here. Let's look at some examples of equivalence classes. So we have a better grasp of what's going on here. So one very simple equivalence class is the parity relation. So take the integers Z. So this includes positive, negative, and zero integers. And we could define a relation similar on N and M, which would mean that N is related to M if they have the same parity. This forms an equivalence relation. Now let's see why this parity relation is, in fact, an equivalence relation. We have the first show it's reflexive. So why is it the case that N is related to N? Well, you have two cases. If N is even, so it equals 2k, then that also means that N is even. So if N is even, so is N, so they have the same parity. Conversely, if N is odd, then N is odd. And so in either case, N has the same parity as N. So it's a reflexive relation. What if we take something like N is related to M? So if that happens, well, again, there's two cases. If N has the same parity as M, and if M is even, then that means that N is even because it has the same parity. And that would imply that M is related to N since M has the same parity as N. And in the other case, of course, if M is odd, since N has the same parity as M, that means that N is likewise odd. And therefore, that would imply that since M and N are both odd, that M has the same parity as N. There we go. So you get the symmetric property. Let's now suppose that N is related to M, and we have M is related to, say, k. In that situation, again, we have a couple possibilities. If k is even, then since M has the same parity, that means M is even. Now, since N has the same parity as M, that means N is even. All right? In which case that would imply that N has the same parity as k because they're both even numbers. And you can see where this is going for the second case. If k was an odd number, I guess I can't call it 2k anymore. I just realized I used k over here. Whoops, should have called it something different. But you can see where we're going to call it l this time. I'll fix it. If you have like 2k equals 2l, it's an odd number. Well, then M will likewise be an odd number. And then N will be an odd number. And so we see that k and N have the same parity in the same way. So this is a very trivial argument here. But it's important to establish that this parity relation is an equivalence relation. There's something the same about these numbers. Now, with regard to this relation, there's only going to be two equivalence classes. There's the equivalence class involving odd numbers. So you can represent the odd numbers using the number one here. This would be the collection of all numbers of the form 2k plus one, where k is an arbitrary integer. That's the first equivalence class. The second equivalence class you could represent using the number two. In which case this would be the set of all numbers of the form 2k as k is allowed to range over any integer like so. This is in the collection of even numbers. For the parity relation, there's just these two equivalence classes. But in terms of representatives, you could represent the even numbers with any even number you want. Because if you have the same parity as 2, then you also have the same parity as 4, which you also have the same parity as 6. Any one of the even numbers could represent the class of even numbers and any of the odd numbers could represent the class of odd numbers as well. All right, let's look at the second example that's here on the page. This one's a little bit more involved, but it's really not much more difficult. I will introduce a new symbol here. We know that this right here is the set of real numbers. So we're going to take r bracket x to denote the set of all polynomials with real coefficients. This is terminology, this notation I should say that's borrowed from abstract algebra. So just so you're aware, what this thing looks like is that you're taking the collection of things that look like a0 plus a1x plus a2x squared all the way up to anx to the n, for which all of these, the number n itself is a natural number, including 0. And all of these a's is considered real numbers. So we're taking the collection of all polynomials where n is allowed to vary and the coefficients are allowed to vary as well. So this would include things like, oh, we could say that x squared plus 1 belongs to our set. That would be acceptable. We could take 7x cubed minus 3x squared plus pi x minus the square root of 2. This would also be a polynomial in there. I mean, don't get me wrong, this last one would be like a math 1050 students nightmare. Oh, those poor college algebra students. But nonetheless, this is an example of a polynomial with real coefficients. So that's the set we're describing right here, this r sub x. On the set r sub x, we can define a relation where we say that two polynomials are related to each other if f has the same degree as g. Now remember, the degree of a polynomial is the largest power of the variable x with a non-zero coefficient. So x squared plus 1, this is a polynomial of degree 2. x cubed plus x squared plus 7x minus 5, whatever that would be, degree 3 polynomial. Again, we're just looking for the largest exponent which has a non-zero coefficient. It's the power of the leading term, as you probably remember from previous algebra classes there. I claim that the relation of degrees on the set of polynomials is an equivalence relation. So we have to first convince ourselves that f is related to f. So if a polynomial has a degree called n, then f will have the degree n and so they have the same degree. So this is a reflexive relation here. Now if f is related to g, then we could say that, okay, f has the same degree as g. If the degree of g is n, that means f has degree g, which then means a degree n, excuse me. And then that means that g whose degree is n will be the same as f. So it's a symmetric relation. What about transitivity? So if f of x is related to g of x and if g of x is related to h of x, this means that f has the same degree as g and g has the same degree as h. Well, if the degree of h is n, that means the degree of g will likewise be n. And the degree of f will likewise be n. f and h then have the same degree because it's n. So then we can conclude that f of x is related to h of x, and this then proves the transitivity property, the transitive property. So we then have established, of course, that this is, in fact, an equivalence relation. Whenever we have an equivalence relation, we're often concerned with what are the equivalence classes. Now, it turns out the equivalence classes of this relation, you can take as representatives the monomials x to the n, where n can range over all natural numbers. This does include zero, of course, because you take x to the zero, this will give you the constant polynomials. So this right here would be the set of all polynomials of the form a0 plus a1x, all the way up to anx to the n, where the ai's belong to the r. Now, so that you don't confuse this with the set we were talking about beforehand, this is not rx here, this set, because in rx, the degree n is allowed to vary over any possible natural number. But in the case of this equivalence class, n is a fixed number, and you're just allowing your polynomials coefficients to change, but the power is always the same in each and every one of these. So there's going to be a class for the constant polynomials, there's a class for the linear polynomials, a degree one, there's a class for the quadratic polynomials, degree two, there's a class for the cubic polynomials, degree three, as well as quartic polynomials, and quintic polynomials, and all of the other ones we can keep on going. So for each natural number, that gives you a class of polynomials, and that polynomial degree will then be exactly the n that gives us the equivalence class right there, that's the representative. xn is sort of a very nice, simple representative for the entire class, because it has that information about the degree right there. All right, let's look at two more examples of equivalence relations with their classes. These ones are going to be a little bit more involved, and unlike the previous two, we're going to be a little bit more detailed in our proofs that these, in fact, are equivalence relations. Okay, so let's consider the set x, which is the set of ordered pairs, a comma b, where a and b are integers such that b is not zero. So be aware, this is a subset of z cross z, like so, but we allow for every possible pairing, except for that the second coordinate here cannot be zero. So it's not equal to z cross z, but it's most of z cross z in that situation. So x, that's our set, our set is itself ordered pairs of integers, and we're going to define a relation on this set x, such that the ordered pair, a comma b, is related to c comma d, such that, well, this happens if and only if the product a times d is equal to b times c. So notice that a is the first number of the first pair, and d is the last number of the last pair, while b is the last number of the first pair, and c is the first number of the last pair there. So you look at the product a times d versus b times c. If those two products are equal, then we say that these ordered pairs are equivalent. Now let's go through the details here. We have to check the reflexive property. We want to show that an ordered pair is related to itself. Now note by this formula, if they were the case, like if we were working this thing backwards, we're like, okay, if a comma b was related to a comma b, then that would mean that a times b, this one right here, is equal to b times a, this one right here, which of course, this is the case, because that's just the commutative property of multiplication. So note, so this is our scratch work over here, right? We don't show this to anyone. It's a secret, keep it secret, keep it safe. No, what we do is we actually turn the argument around. It's like, note that ab equals ba, and since ab equals ba, that means the pair ab is similar to the pair ab. So this relation does satisfy the reflexive property. We have a reflexive relation. Now we're going to check for symmetry. In my experience, these arguments kind of go on the difficulty they're listed for equivalence relations. Reflexive is usually pretty simple. Transitive is one of the hardest ones. Symmetry is usually about the middle. This was opposite when it came to the partial order, anti-symmetry was generally the hardest one to prove there. Symmetry is usually not so bad. Let's see what it would look like.  So you assume if ab is related to cd. So you make that assumption. Then let's unravel the definition. If ab is related to cd, that means that the product ad is equal to the product bc. Now you want to finish with cd is related to ab.  You throw this napkin away when you're done. If cd were related to ab, what would I be looking for? I would want it then to be that cb is equal to da. Now if you of course relate that to the equation we have before, it's like, okay, well equality is a symmetric relation. So cb is equal to da. That means da equals cb. And we also have that multiplication is commutative. So I can flip these things around ad is equal to bc. So by properties of multiplication and equality, we actually get exactly what we want. So we're turning to the original proof here. If ab is related to cd, that means that ad equals bc. This implies that cb equals da. I didn't justify the steps there because I feel like the audience probably knows those properties. And therefore, since cb equals da, that means that cd is related to ab. This then shows that this is a symmetric relation. So next we have to check the transitive property. All right, so with transitive, this is also a conditional statement, an if then statement. The only difference now is that for the transitive property, your premise is double. There's two statements. It's an and statement. You assume that ab is related to cd and you assume that cd is related to ef. This just gives us extra assumptions. So if ab is related to cd, that means that ad equals bc. That's the definition of this relation. Now if cd is related to ef, then that means that cf is equal to de. That's again how this relation works. Now our goal is we want to show that ab is related to ef. If you unravel the definition there, we need to show that af equals be. So I need to get af on one side of an equation. I needed be to get one side of the equation. I have an equation involves a and b. I have an equation involves c and f. I don't care about c. I'm sorry. The equation involves f and e. cd basically, I don't care about those. But that actually helps us with the connection. D is involved in both equations. C is involved in both equations. So that's how we're going to try to connect these things together. I'm going to take this equation right here and I'm going to multiply both sides of the equation by f. So on the left hand side, we're going to get adf. On the right hand side, we're going to get bcf. But here's how the second equation comes into play here. Cf is the same thing as de. So we make that substitution and so then we have that adf is equal to bdf. And so that's how c plays its role. c is now out of the equation because of that substitution. Now we have this d. But notice how both sides of the equations are d. And there's also a hypothesis we haven't used yet. Remember in describing the set x, we're taking the set of all ordered pairs a, b such that a, b are integers. But what was the other condition? Ah, yeah. We want to b to be nonzero. We haven't yet used the fact that the second coordinate is nonzero. This is exactly where we can use it. D, which was a second coordinate, we can divide both sides by d because it's nonzero. So this is not nonsense. The d's would cancel and then we get the equation that af equals be. And that shows exactly that ab is related to ef, exactly what we were looking for. So this is a relation on this set x. Well, why do I care about this set x so much? Well, let's look at the equivalence relations. Okay. If I were to take a typical equivalence relation, let's take an example like 1, 2. For example, 2 is nonzero. That is a perfectly good relation. I'm looking for all of the ordered pairs a, b such that when I multiply these things together, 1 times b, which is equal to b, is going to equal 2 times a. I'm looking for integers that satisfy this condition. And there's a lot that I can do. Of course, there's 1, 2 itself. There's 2, 4. We'll do it. There's 3, 6. We can also throw in some negative numbers, of course. You can take negative 1, negative 2. That would also work. And this keeps on going and going here. And when you look at these things right here, these ordered pairs, I feel like I've seen these numbers somewhere before. Could I not also say that 1 half is equal to 2 fourths, which is equal to 3 sixth, which is equal to negative 1 over negative 2? All of these ordered pairs are related to each other by this equivalence relation, much in the same way that these fractions are equal to each other. And in fact, this equivalence relation that we just described gives rise to the rational numbers. We can actually define the rational numbers to be the set of equivalence relations, excuse me, the set of equivalence classes where x comes from the set x right here. So this is actually the definition of the rational numbers. The rational numbers is the set of ordered pairs of integers where the second, where the second coordinate is non-zero with the equivalence that two pairs are considered the same with regard to this equation right here. Because after all, when you look at a fraction like 3 sevenths, is this not really just an ordered pair? You have the number on top, you have the number on bottom. There is a specific order to them. That's what a fraction is. A fraction is just an ordered pair. Now a rational number is a fraction whose denominator is not zero and satisfies this equivalent relation. One half and two fourths are different fractions, but they're considered the same rational number. It's the same quantity. And in fact, one half versus two fourths are just two different representations of the same rational number. So this gives us a good example of why equivalence relations are so important to us. We use them all the time, even if we didn't know it. We've talked about the rational numbers many times in this lecture series and you've probably talked about it in many previous mathematics courses. The rational numbers is a set of equivalence classes and we define the rational numbers using these and we often work with the rational numbers using specific representations, but you can switch from one representation to the other because they're equivalent to each other. Let's look at one more example here. This one comes from linear algebra. Let A and B be two N by N matrices. So these are matrices with N rows and N columns. We say that two matrices are similar to each other. A is similar to B and we'll denote it using our usual symbol here. A is similar to B. If there exists a non-singular N by N matrix P such that A equals P, B, P inverse. Now, again, as a reminder, a non-singular matrix means it's a matrix with a matrix inverse. So the reason that we want P to be non-singular is because if P is non-singular, it means P inverse exists. In general, an N by N matrix doesn't have a inverse. It could be a singular matrix. So we're saying, okay, we can connect A and B together using this non-singular matrix. A might be singular, B might be singular, but this matrix that connects them together is a non-singular matrix. I claim that similarity is an equivalence relation. So we have to first show that A is related to itself, that A is similar to itself. Now, notice that A is equal to the identity matrix times A times the identity matrix inverse, which, of course, the inverse of the identity matrix is itself the identity matrix, and the identity matrix has the property that if you times it by any matrix, you get back A. This is why it's called the identity matrix. It acts like a multiplicative identity. So when you look at the right-hand side here, that would simplify.  So this shows that A is similar to A. We get the reflexive property. All right. Why is similarity a symmetric property? So suppose that A is similar to B. That means there exists a non-singular matrix P such that A is equal to P, B, P inverse. Okay. Now, to show that B is related to A, I'm looking for some non-singular matrix, let's call it Q, such that B equals Q A Q inverse. That's what we're looking for. So who is my candidate for Q? Now, to find Q, I'm actually going to take this equation and we rework it. So notice, these are P is a non-singular matrix. If you times both sides by P, you're going to get that A, P is equal to P, B. Give me a little bit more space there. P, B. Because the next thing I'm going to do is I'm going to multiply on the left by P inverse. Remember, with matrix multiplication, multiplication is non-commutative. So multiply on the left is not the same thing as multiply on the right. We have to be mindful of these things. Okay. Of course, on the, on the right hand side, it simplifies just to be B. And so we can't write a factorization here, B equals, and that's exactly what we have here, B equals P inverse A, P. What we want to do is then take Q to B, P inverse. Now, if Q is P inverse, then Q inverse will equal P inverse, inverse, but the double inverse is just the original matrix P there. So that's exactly what we have here.  Now, since P is a non-singular matrix, P inverse will also be non-singular. So this shows in fact that if A implies, if A is similar to B, then B is similar to A. And this is symmetric relation. Now the last one we want to do here, transitivity. If A, suppose A is similar to B and B is similar to C. Well, since A is similar to B, then there exists an invertible matrix such that A is equal to P, B, P inverse. And likewise, since B is similar to C, there exists a N by N non-singular matrix Q such that B is equal to Q, C, Q inverse. Now in order to show that this is transitive, we have to show that A is related to C, A is similar to C. That means we need to have some matrix we'll call it U, such that A equals U, C, U inverse. That's what we're looking for. Now in this situation, the way we're going to combine these together is actually using multiplication, because properties from linear algebra, the product of non-singular matrices, is likewise non-singular because at one point we're going to have a matrix PQ, which is non-singular. It's invertible because its inverse is actually Q inverse, this is the show called shoe sock principle.  The inverse process reverses the directions of things. All right, so let's put this together. Let's start off with our equation for A, A equals P, B, P inverse. Now I'm going to replace the B with this right here. We're going to substitute it in so that we get that A equals PQ, C, Q inverse, P inverse. Rewriting things, you can redo parentheses because matrix multiplication is in fact associative. Redoing the parentheses here, we get the PQ. And then for the second one, like we mentioned a moment ago, Q inverse, P inverse is the same thing as PQ inverse. You can flip the order around so we get exactly this. Since PQ is a non-singular matrix, we now show that A times a non-singular matrix times C, sorry, A is equal to a non-singular matrix times C times the inverse of the non-singular matrix. So this shows that A is similar to C in this situation. This then proves that similarity is in fact an equivalence relation on matrices. Now describing the equivalent classes of similar matrices gets a little bit harder, at least at this point of our educations. Now I should mention that similar matrices deserve the name similar because they're similar because they share certain algebraic properties. For example, similar matrices have the same determinant. They have the same trace. They have the same eigenvalues just to name a few things that they have the same. There's more than of course than that. And every non, every n by n matrix, singular or non-singular, belongs to a similarity class. So it sort of begs the question, well, who should be the representative of that similarity class? In more advanced linear algebra courses, which I'm assuming, if you're watching this video, you probably haven't participated in such a thing yet, the canonical choice of representative is what's often referred to as the Jordan canonical form, which of course I won't say much more about this right now, but the Jordan canonical form is sort of like the best representative of a similarity class because it's a matrix that is almost diagonal. In linear algebra, you might have talked about diagonalizable matrices. Diagonalizable matrices, what that is is basically you're saying that a matrix is diagonalizable if it's similar to a diagonal matrix. And if you're diagonalizable, then your Jordan canonical form will then be a diagonal matrix. And that's sort of like the best matrix in that family, in that similarity class. But of course, not all matrices are diagonalizable. So if you're not diagonalizable, who's the simplest version inside the similarity class? Well, again, this is where this Jordan canonical form goes in. You can be almost diagonal, and this study of topics helps you understand that. But that goes beyond the scope of this lecture series, but just let you be aware that in lots of branches of mathematics, including linear algebra, these equivalence relations are all over the place. And we just need to learn how to discover them and how to prove them. And the proof is just like we saw here. To prove that something is an equivalence relation, you always check three things. You prove that it's reflexive, you prove that it's symmetric, you prove that it's transitive. And that's how you prove that something is an equivalence relation.


So I'm filming this during the middle of the coronavirus pandemic in the UK. We're all in lockdown and people are feeling pretty stressed So a lot of people have requested can I put together some calming and relaxation Strategies that can be used if you're worried or if your children are worried So in this video, I'm going to explain what a body scan is to you And then I'm actually going to read a body scan script so that you can give it a go I hope you find it helpful if you'd like me to put together other kind of guided calming strategies like this Let me know. I'll be really happy to So body scanning essentially involves paying close attention to every single part of our body We start with our feet and we work our way up through to our head We're really focusing in on bodily sensations noticing every ache and pain and focusing right in on our body rather than out there on the world Some people find working through a body scan with the aid of a body scan script to be helpful So for the next couple of minutes, I will put some calming imagery on the screen And I will read you through a body scan script so that you can try it There were lots of them out there So if you don't like the sound of my voice or you'd like a different script go Google it body scan is what you're looking for Equally once you got the idea of how it works. You can do it without a script if you prefer Begin by making yourself comfortable Sit in a chair and allow your back to be straight, but not stiff with your feet on the ground Allow your eyes to close or to remain open with a soft gaze Take several long slow deep breaths Breathing in fully and exhaling slowly Breathe in through your nose and out through your nose or mouth Feel your stomach expand on an inhale and Relax and let go as you exhale begin to let go of noises around you Begin to shift your attention from outside to inside yourself If you are distracted by sounds in the room simply notice this and bring your focus back to your breathing now Slowly bring your attention down to your feet Begin observing sensations in your feet You might want to wriggle your toes a little Feeling your toes against your socks or shoes. Just notice without judgment You might imagine sending your breath down to your feet as if the breath is traveling through the nose to the lungs and through the abdomen all the way down to your feet and then back up again and out through your nose and lungs Perhaps you don't feel anything at all. That's fine, too Just allow yourself to feel the sensation of not feeling anything when you're ready Allow your feet to dissolve in your mind's eye and move your attention up to your ankles calves knees and thighs Observe the sensations you are experiencing throughout your legs Breathe into and breathe out of the legs If your mind begins to wander during this exercise gently notice this without judgment and bring your mind back to noticing the sensations in your legs If you notice any discomfort Pain or stiffness don't judge this simply notice it Observe how all sensations rise and fall shift and change moment to moment Notice how no sensation is permanent just observe Allow the sensations to be in the moment just as they are Breathe into and out from the legs Then on the next breath allow the legs to dissolve in your mind and move the sensations in your lower back and pelvis Softening and releasing as you breathe in and breathe out Slowly move your attention up to your mid-back and upper back become curious about the sensations here You may become aware of sensations in the muscle Temperature or points of contact with furniture or the bed With each out-breath you may let go of tension you were carrying and then very gently Shift your focus to your stomach and all the internal organs here Perhaps you notice the feeling of clothing the process of digestion or the belly rising or falling with each breath If you notice opinions arising about these areas gently let them go and return to noticing sensations As you continue to breathe bring your awareness to the chest and heart region and just notice your heartbeat Observe how the chest rises during the inhale and how the chest falls during the exhale Let go of any judgments that may arise On the next out-breath shift the focus to your hands and fingertips See if you can channel your breathing into and out of this area as if you are breathing into and out from your hands If your mind wanders gently bring it back to the sensations in your hands and then on the next out-breath Shift the focus and bring your awareness up into your arms Observe the sensations or lack of sensations that may be occurring there You might notice some difference between the left arm and the right arm. No need to judge this As you exhale you may experience the arms soften and release tensions Continue to breathe and shift focus to the neck shoulder and throat region This is an area where we often have tension Be with the sensations here It could be tightness rigidity or holding you may notice the shoulders moving along with a breath Let go of any thoughts or stories. You are telling about this area As you breathe you may feel tension rolling off your shoulders On the next out-breath shift your focus and direct your attention to the scalp head and face Observe all the sensations occurring there Notice the movement of the air as you breathe into or out of the nostrils of your mouth As you exhale you might notice the softening of any tension you may be holding And now Let your intention expand out to include the entire body as a whole Bring into your awareness the top of your head down to the bottom of your toes Feel the gentle rhythm of the breath as it moves through the body As you come to the end of this practice Take a full deep breath Taking in all the energy of this practice Exhale fully When you are ready Open your eyes and return your attention to the present moment As you become fully alert and awake Consider setting the intention that this practice of building awareness will benefit everyone you come in contact Actually or virtually today


Live from Barcelona, Spain, it's theCUBE! Covering Cisco Live 2020. Brought to you by Cisco and its ecosystem partners. Hello everyone, welcome to theCUBE 2020. It's the first CUBE segment and session for 2020, next 10 years. This is the 10th year theCUBE has been in operation. We're here in Barcelona for Cisco Live, but we're going to spend the next few minutes talking about the enterprise tech trends for 2020 and beyond. Really looking back at the past 10 years and then looking forward 10 years. I'm John Furrier, host of theCUBE with Dave Vellante and Stu Miniman. The CUBE team, the analysts, we're going to analyze enterprise tech. You know, we'd love to do that Dave, but I think more notable is, this is our first interview in 2020. For the year we're kicking off our 10th year as we close down theCUBE for 10 year anniversary in May. Quite an evolution. A lot of things we got right with Wikibon research and theCUBE insights. A lot of things we saw early and that's the benefit of theCUBE. Now more than ever, it's more complex. It's a lot of noise. A lot of people talking about value propositions here, there, a lot of cloud. I think the reality is set in, cloud is here. It's not a question of why and when it's now. And the impact is just hitting mainstream tech. And enterprises is now leading the category in investments, venture capital, private equity, M&A, over consumer companies. You're seeing a much more focused emphasis on what's going on in the enterprise, which is business. Incredible opportunity ahead. So 2020, what's in store? Well, you know the last decade we obviously saw the consumerization of IT. There was all that social media hype and I think you're right John, the enterprises now, well the action is, but the last 10 years have been all about cloud. And what got us here to 2020 is not what's going to power us through the next 10 years. I think it's not only cloud, it's cloud plus data, which we definitely bet on and got right. But now the injection of machine intelligence on that data, which of course is running in the cloud for scale. So the real big question now is, what's going to happen to the cloud guys? Amazon and Azure clearly have momentum, Google actually beginning to pick it up a little bit. But particularly the case of Amazon who dominated the last decade, it's going to be not as easy for them going forward. Everybody now realizes, wow, they got it right. You've said many times they were misunderstood. Well, I think now people are beginning to realize how powerful they are and the enterprise players have really begun to respond. And they don't like to give up their position. So it'd be really interesting to see how that goes. And of course, we're going to talk more about Cisco, but Stu, what are your thoughts? Yeah, so John, I think some of the things that we looked at as bleeding edge over the last 10 years are becoming a bit more mainstream. The role of the developer, we know the developer's a new king maker. You look where we are in the DevNet zone. DevNet zone a couple of years ago was small and there was, you know, people were kind of excited and everything. You look at it today, it looks much more like the regular show. It has really become mainstream. Dave said cloud, you know, cloud is mainstream. Developers mainstream, that connection between the business, enterprise tech that we talk about and these other pieces really are coming together. That's where the data really is the next flywheel for what's happening. And obviously machine learning, the application developer, and still it's about moving faster that companies are looking to do. And that is what all of the last 10 years has been building for. And now it's the new normal. Great, and I want to get into some of the ways. I think when you look at this, we can always rattle onto any kind of technology, but you know, one of the things that we'd love to do is look at the waves. What waves are going to come? We're going to get into your thoughts on that. But I think just let's reflect on what's going on around us right now. The Q business 10th year, finishing up his 10th year. We're in the media business. I had a comment from someone here, a distinguished engineer at Cisco said, I can't believe you guys are a technology company. I had tweeted out yesterday on Barcelona about our Q alumni list. It's turning into an expert network. If you look at what's going on with Facebook and with Trump and the impeachment, you're seeing a changing of the guard in the media business. So we as media with theCUBE and SiliconANGLE has become interesting. And I think I bring this up because not only to kind of tout our new model that we've been doing for 10 years, but if you look at how people share information, misinformation, quality information, you start to see a paradigm where you don't know what to trust. Vendor A says they can do this. Vendor B says they can do that. Amazon says this. Azure says that. So I'll think that the practitioners and the consumers of IT and enterprise tech, the buyers, where's the truth Dave? I mean, the models are completely changing. I've heard comments that the analysts firms are struggling to get modern. Press outlets are being dwindled down to a handful in the enterprise. New networks are being formed. These new expert apps are out there. So this is a tell sign that the world's more complex and different than ever before. Well, the authentic community doesn't lie, right? And your peers, at the end of the day, when you're having private conversations, that's where the truth comes out and to the extent that you can, we'd like to bring that to theCUBE in sessions like this. That's really where you would say, extract the signal from the noise. And I think that, you know, we try to do that. We've tried to do it for 10 years and I think that's part of the reason why we've been so successful. I mean, at the same time, look, we know we're funded by sponsors, which is great. We really appreciate their support. But at the end of the day, we've always got to put forth what we think is actually happening out there. So let's get into some of the ways because this sets the context. So as you have these networks forming, you have cloud technology, you know, OSI model, I look back at the 90s and I think this is apropos to the Cisco show. At that time, Dave, during the mini computer wave that set the stage for what became the PC revolution and then ultimately, inter networking category, you had proprietary network operating systems. IBM had SNA, digital equipment corporates had Decknet, et cetera, et cetera. And in comes the open systems interconnect. Seven layer stack that changed the industry. In today's world, we have open source, but people are chirping about open core. There seems to be a trend towards proprietary now. Amazon is the big proprietary cloud. I don't mean proprietary in the sense of you can't work with it, but scale is the new proprietary. So you almost have this revert back to old tactics of differentiation. And I think that's not good for customers. I think you look at the customer situation, it creates more complexity. So I think that's why we're seeing multi-cloud, really be a trend because whoever can connect all the clouds and do that seamlessly is going to win big. And I think that's TCP IP like dynamic. Yeah, John, it's a really interesting point because open source in general is more important than ever before. Enterprise companies are contributing. The big vendor community is spending more time on open source than they are on standards anymore. Over, if you look at the big projects out there, Linux, Kubernetes and the like, more than half of the contributors have full-time jobs. They work for big companies. But as you said, how am I consuming that? GitHub is a company at the core of open source, but the GitHub platform itself is a proprietary. It's that open core model that you talked about. And of course, Microsoft built them for a big number. And some people have a little bit of concern as to when Microsoft built them. And GitLab is there. And GitLab, right, of course, if similar, they deliver their application itself is that open core model. So open source is there, open core is the model that they're doing. Absolutely, it is interesting, because as you said, open source is more pervasive than ever, but I'm consuming it more as a service from Amazon or from these providers. Do you see the bitching and moaning that's going on in the open source community? Because there is kind of a lot of a chirping going on around. Well, you know, if I build this in the open, is it truly open being co-opted by, say, the big clouds? And you've got Microsoft. I mean, look at Microsoft, Office 365. That's not going to go away for the next 10 years. They've satisfied their core offering, almost like a lock-in. I mean, so it seems to be, it smells like that old NOS days. Yeah, but so the other thing too is we're entering this decade with four trillionaires. I mean, Amazon hit trillionaire club in 2018 that sort of dropped down, lost a comma, as Russ Henneman would say, but Apple, Google, Microsoft, and Amazon, they look invulnerable, don't they, in the trillionaires club. But I mean, I would point out, you're saying, John, there will be a backlash. Open source, open distributed computing, peer networks. I don't think, I mean, history would suggest that these big whales, they're not invulnerable. They can be taken down, and open source is one way out. Well, it's interesting. One of the things you look, one of the big threats for Cisco for a long time was like, oh, SDN's going to take over what Cisco's was doing. Well, Cisco's still doing just fine with software-defined networking, and what that's having. The open compute model for networking is also a threat.  The big hyperscalers aren't necessarily coming to Cisco for gear, so there's that shifting as to where Cisco will be involved when we talk about cloud models. They're spending much more time up the stack, John, in the layer four through seven, than they are down in their traditional zero to three. The pressure on these monopolies historically to continue to perform as public companies has been enormous, and they get more proprietary to your point, John, and eventually, the open market says, hold on, you know, that opens up new opportunities. It takes a while, but it's always happened. I don't think, I think your point about the big incumbent players are not going to yield to just being rolled over by the incumbent growing cloud companies, but you cannot deny the fact that, say, Amazon, Dave, I want to get your thoughts on this because what Amazon did to compute changed the game in my mind. They completely changed the capabilities, the consumption models, the cost structures. All the economics were changed with compute. You look at outposts, wavelengths, some of the things they're getting in, they have their own networking. So the question is, if you have the cloudification of the whole eternity of infrastructure, which is storage, compute, networking, okay? You can see almost the cloud guys are almost changing radically, all three of them. Compute's already done, storage is already done. Stu, networking's left, so you have networking. The battle ground, because you've got to move the packets around. You don't need MPLS routes because you just go through the cloud. How things are stored, data backup and recovery. The list goes on and on. Ultimately, that's the infrastructure as code ethos. That's going to change the application environment. So, if we'll Amazon, we'll Google, we'll Azure commoditize or change networking. Yeah, I mean, John, we already see that happening. When we came two years ago, one of the challenges for most network engineers is what I need to manage. A large part of it, I can't actually touch. I have to rely on third party, it's outside. I don't control it, but if something goes wrong, I'm on the hook for it. And if you look forward a little bit, if I'm deploying serverless architectures, is there networking involved? Yes, do I know what it is? Nope, my platform underneath it is going to take care of it. Sitting here talking about that transformation of the workforce, Dave, you wrote about it in your piece. That future of work is if you're really putting together, I'm a CCIE, my job is being a Cisco certified engineer and my role will be racking, stacking, configuring and changing and managing those boxes. Today, it's, well, I better get involved in the security side or the application side because that's where I'm actually connected to the business and the data of things because if I'm just concerned about the moving of packets around, yeah, there's going to be either automation or a cloudification or a combination of those things, they're going to take that away from me. A couple of thoughts on this. John, you were the very first to report the trillion dollar opportunity for Andy Jassy and Amazon and they're what, 35 billion? So they got a long way to go. So I think a big theme for Amazon is going to be TAM expansion. And one of those areas is, of course, networking.  I reported this in my Wikibon post from the ETR data, the cloud slowly eating away over the last 10 years into the networking share. And then one practitioner said, as we put our data into the cloud, we're going to spend less on traditional networking. So it's clearly a threat. So Cisco, obviously diversifying its portfolio, we're going to talk about that this week. But more focused, as we've said, to under the leadership of Chuck Robbins than it was 10 years ago. Well, Dave, here's a question for you, because if you look at enterprise spend, they're increasing their spend on public cloud, but their data center stuff, it has stayed relatively solid. We haven't yet seen the erosion there. So are you saying networking's going to erode before the rest of it? Because the storage, I have data gravity, what's your expectation? I think you're seeing it. I think you're seeing the networking erode, not necessarily in terms of shrinking Cisco, although they're guiding to a flat to down quarter, but you've certainly seen their growth slow down, and especially in their core networking space. I mean, they've tried to double down on their switching and core routing, and they've just made new announcements in that space that John, you know well. But unquestionably, the cloud has had an impact on Cisco's business. Well, 2020, let's look ahead. So the next 10 years, we've got a lot going on. So I think we can see the big wave. So to me, the big wave, I'll start, Dave, on the waves. I think the big wave is value proposition is the business model evolution. I think that's going to be a way that will constantly be the North Star for transformation. If whatever people are buying or operating, whether it's their infrastructure or their operating model, has to have direct contribution to the business model of the company. So I think that's one. Two, I think AI and data will continue to power a lot of the value, and I think networking is going to be cloudified. And the impact of that is going to be that as cloud and hybrid computing becomes a technical solution that changes the operation model of companies, you're going to start to see multi-cloud emerge as a solution of that, meaning multi-cloud isn't a technology. It's an outcome of hybrid combination of cloud. I think that's going to change how packets are routed, how packets are networked. I think data AI and a complete transformation of the engine of business will is going to happen in the next 10 years. More than we've ever seen before. I call this DevOps 2, 3, 4.0 to do. This is a complete new engine of innovation technically with storage compute and networking where the application focus is going to be business-driven, almost dynamic, almost real-time. I think that will be a 10-year horizon. I wrote a Twitter post on this just a few minutes ago and the lead architect for Azure tweeted back, I mean, said latency, latency never changes. John, the innovation cocktail, as you said, is what's the driver going forward, right? Yep, exactly. Well, to your point though, the speed of light, you're not going to solve that problem without putting points of presence all over it. But the network architecture is what defines us too. And I've been talking about network automation. We've talked about DevOps. But if you think of hybrid as a technical solution, how you work with public and private premises, edge, it's just now a new network configuration. That is going to be, to me, a very instrumental engineering task, which will actually impact how the software engineers will deploy code. And to your point though, latency, that's physics and that's the plumbing and the plumbing's got to be there. But I do feel like we're exiting the cloud era into a new era of this innovation cocktail that you talk about or the sandwich, which is cloud data plus AI plus digital services. And that's really what we're going to be talking about eight to 10 years from now, is how organizations are applying those digital services and which companies, whether they're cloud native companies or guys like Cisco and IBM and HPE and Dell EMC, how they're leveraging those waves and applying them to their business. And I'd be curious to see how the standards evolve around, whether it's de facto standards around interoperability around data. And look at what's happening, Stu, data privacy. You're starting to see the tell signs that data is going to be starting to be managed, just like packets are managed. So this is like a whole interesting dynamic. But really, this is the payoff for what companies have been working on to be able to move faster. It was before, it was okay, it used to take me 18 months and now I can do it in a few months, but now I can react to that business between the automation, the machine learning, putting together cloud and you're going to be able to refocus your workforce to be able to respond to the business and drive new value. All right, guys, we got a wrap, we got the guests coming up. Appreciate the commentary. I'll just say that Dave Tesla, he mentioned in one of your breaking analysis, what Tesla did to the automobile company, I think there's going to be someone in the enterprise that comes out of the woodwork that changes the game on everybody. I think there's an opportunity for that kind of new entrant. In the same way Amazon did, you think? I think Amazon is now an incumbent. I mean, if you look at the size and the scale of it, there's always an opportunity for that bold startup, this bold company. So again, it takes a kind of new dynamic, electricity with cars, so we'll see. Okay, that's a wrap up. This is theCUBE conversation here in Barcelona, in the Cisco Live. I'm John Furrier, Stu Miniman, Dave Vellante, breaking down the enterprise for the next 10 years. Thanks for watching.


Yog Yogeshwara Bhutabhseva Shanno Itir Dayachuchadavo Inavamshotam Natrama Bhavasagrami Dhanon Nalina Dhaleksana Sri Raghunan Sitaram Stritjan Poshakara Bhaktvarada Kannadika Vasavanuta Ramadasa Poshakara Vandhanam Ayodhya Rathasarchita Makhabayamu Sanghave Dasherati Raghurama Dasherati Say this after me. Ram Ram Ram Ram Ram Ram Ram Ram Ram Ram Ram Ram Namaskaram to everyone. Today is Ramanaami, a very important celebration in this country, but everybody is staying home. Well, celebration is not about doing a particular thing. You can only celebrate something if you know how to be playful. Where there is no playfulness, there cannot be celebration. There can be grand yoke of situations, but no celebration because without playfulness, celebration cannot happen. Well, why is it that we remember somebody, celebrate somebody, after a few thousand years, six to seven thousand years, why are we still remembering these people? What is their significance? Well, over a period of time, with people's investment of their emotions, slowly a great human being becomes a god, which is an unfortunate weakness that people have. Any wonderful human being comes, we want to make them god, our sons of god or messengers of god, so that we can nail them on the wall and we can go about our business the way we want. If you see them as human beings who lived extraordinary lives, most human beings will have to put their heads down in shame because if another human being could live like this, why am I like this? This question will naturally come up. So we make them gods so that we can go about our business just the way as usual. One week of staying home, just one week of little bit of seclusion, Rama went for fourteen years of Vanavas, social distancing. There was no epidemic for political reasons. Everywhere in the popular WhatsApp culture right now, once again the Lakshman Rekha that was drawn for Sita not to cross and she crossed and what a disaster unfolded is going around, it's very appropriate. Right now the social distancing is a kind of a Rekha. Rekha means a lion, that you should not cross. Those whether you cross is inadvertently out of ignorance or by intent, results are same. This is the nature of the existence, whether you do it with evil intent or out of ignorance. If you do a particular act, the results are same when it comes to the physical world. The inner world is different. So in the material world, the results are same. Whether you fell off the coconut tree by accident or by intent, same number of broken bones will break unless a coconut also decides to fall after you and breaks your head. So Rama's life is so celebrated today, but during his lifetime, his life was a serial disaster. As a young prince, an accomplished young man, a brave warrior, marries a very beautiful young woman, but due to political reasons, he has to take this princess. She's not a tribal woman, she's a princess. He has to take her and go into the jungle. Well, I think once again they're playing Ramana and Sagar's Ramayan in the television, I believe there's a lot of controversy about that also. In that television serial, you will see it is made to look like Rama and Sitar and a honeymoon in the jungle. Well, that's not how tropical jungles are. I've lived there. Well, if you spend two-three weeks in the jungle and come back, people in the town won't recognize you. You will become like that. Head to toe, there will be insect bites and there are lots of challenges. Today the amount of wildlife has come down, otherwise this is tiger country, this is elephant country.  You must be extraordinarily careful and conscious, otherwise either you will get crushed or you will become a wonderful breakfast for... to somebody. So in these conditions, he takes this young wife and goes and lives there. This is not a honeymoon or a picnic, this is a punishment. As if that was not enough, this Sri Lankan people, nothing against you, they came and kidnapped his wife, whatever the reasons. Everybody has justifications but it happened. Well, he's a king. He's not that kind of a man, but he's a king. A king means in India or anywhere for that matter, they were allowed unlimited number of spouses. Men are looking depressed. What, Sadhguru? One? Unlimited how? But kings were like that. So he's not somebody, okay, this one is gone, find somebody, he's not that kind. He loves his wife, he values her, so he pursues her. You must understand, from Uttar Pradesh to southern tip of India, not a easy journey. He was Ram in Ayodhya. When he entered Andhra Pradesh, he became Andhra Pradesh Karnataka, he became Rama. He came to Tamil Nadu, they made him Raman. But just two of them, him and his brother, looking for his wife, not a easy journey. No Google Maps to guide, just by people's guidance you have to go totally unbroken terrain everywhere. He reached here and then he saw the man who's kidnapped, his wife has a formidable army and fully organized. But they're just two of them. So they sought the help of Tamil people. I must say something about Tamil people here, because this is a land of very exuberant, enthusiastic, devoted people. They did not look up even now in this culture, at that time not at all. There was no god up there, there god was here in the earth. So they're very earthy people, full of involvement, vigor, but no fancy ideas. I wish we had lived like that, but now lot of fancy ideas have come. People have made you feel like there is a place, another place somewhere which is better than this. That's why we are making a mess out of this. So Tamil people were like that, then they're still like that. In many ways. I'm not saying this to insult other volunteers and others, but this is my observation in the last 40 years of working with volunteers. Everywhere, in every country we have fantastic volunteers, but you will see always Tamil people are little extra vigour. You want to do the most difficult things that nobody wants to do, you will see it was always Tamil people who will take it up and do it. There is a certain sense of innate commitment and devotion, which is probably culturally cultured over a period of time for thousands of years. And even when Rama came, he found that, that they became so dedicated to this new man who came from somewhere. And they put themselves to it, they built a small causeway to cross to Sri Lanka. And they fought the battles, they won the battle, he got his wife back and went back. Then he went for one year of repentance. So his brother Lakshmana asked, what are you repenting about?  He said, yes, there were many negative qualities about him, his ego, his arrogance, his whatever all those things, but he is a devotee. I killed a devotee also, a great devotee of Shiva. I killed a devotee on one level, but that one year he went off into penance into Himalayas. Can you believe it? Being already out in the jungle for fourteen years, not fourteen days like corona, corona isolation is fourteen days that people are fighting and creating a nuisance in the country. Fourteen years of isolation for a king.  That's the kind of man he is. As if that was not enough, political situations evolved, when the wife is pregnant, he has once again sent her into the jungle once again without him. Teperation. For a king, the queen is pregnant is a very significant thing because having a hair to the kingdom is a very big thing. Don't know whether she has a boy or a girl or what, no sonogram. He sent her to the jungle. There she delivers twins unknowingly. He almost kills them, gets into a fight with them.  He almost did it. And his beloved wife for whom he traveled over 3,000 kilometers, fought a battle and took her back. He never again saw her. She died without seeing him. This is a serial disaster life. For most human beings, if any one of those events that happen to him happens, they will get freaked out. They will become full of anger, hatred, angst, fear, all kinds of negativities. But he maintained absolute balance. He is even today celebrated as one of the best administrators among the kings of this land.  You have caused hurt to me, so I will cause hurt to you. This is not the way. Whatever happens to me, I remain peaceful in absolute balance and do the best that I can do. People who are questioning me during youth and truth, is he fair to his wife? Is this the way to treat the family? Well, if you are just another man, that's a good question. But if you have a king or a leader for the nation, a leader who puts his nation above his family is the leader that we want. That's a leader that we want, not someone who puts his family above the nation. So this is the leadership he showed. He could have easily discarded or not taken into account what comments and commentaries that were happening about him and his wife and has kept his wife with him because she matters to him. No, he sacrificed his family, his unborn children for the sake of the nation. This is a kind of leader that you need for any nation. And it is because of this balance, because of this sense of purpose and duty in his life, that we still celebrate him and worship him today is his birthday. But the South Indian people who served him, one of them went with him. Today he's become a superhero all over the country, Anuman. But after Rama's time, some people, little crooked in their head, projected South Indian people who lived here six, seven thousand years ago as monkeys. So South Indian people still little disturbed by that. They have love for Rama, but they're angry little bit with the way they have been depicted. But also they enjoy that no matter what they say, they anyway worship a South Indian man as the ultimate hero. Even if they want to win an election today, they will sing praises of Anuman even today. So South Indian superhero is still worshipped all over the country, literally all over the world. Even a president of United States was carrying a small figurine of Anuman in his pocket at one time. Yes. So today is Ramanaami, it's wonderful. You are just not even an one of us, just homestay.  Let me show you what happened in Pedder Road in Mumbai yesterday morning. See the video. That's in a... Aren't they happy that you are not there? So you can see in Isha Yoga Center, they're always happy because we are keeping social distancing, not just today, all the time from all the creatures, peacocks, snakes, everything else are very happy here because we've kept certain distance with them, allowed them to live their life, we've learned to live with them, all kinds of creatures. But not the case with cities. So on a busy street in Mumbai at 8.39 in the morning, if a peacock can dance, well you can't complain, the world is going bad. Well, well, well, a lot of people are going to get very upset with this. Do you know what is happening in the stock market? I know there is loss and pain there. Yes, a lot of people have lost their wealth, a lot of people could lose their livelihoods. If you don't manage well, it could lead to starvations. All these situations are there. But this is what life is about. Today is Ramanaumi. Let us take this one quality. When challenging times come, you're not facing the kind of challenges Rama faced in his life, simple. Maybe fourteen days, maybe twenty-one days, maybe forty-two days, you just have to stay in your own home. Hello? You can't complain about this. We're not asking you to go and fight a battle. We're not asking you to go and live in the jungle without any protection in your own home. Your problem is not about the situation. Your problem is your mind is in such a state that going to work you are complaining, sitting at home you're complaining. Let's change this. Now that this is confronting you, let us change this. Don't wait for that day. April 14th, April 15th, I'm going to be out. Maybe you will be, maybe you will be not. We don't know yet. We thought we will be but in the last two days, certain people have changed the whole dynamics of the virus in the country. So we do not know whether we will be out on 15th April or not. We will be partially out or fully out or not at all out. We do not know. But first thing is, this is one thing you must do, this is one thing you deserve that your experience of yourself is a wonderful experience. This must happen not because of what you do, not because of what you have, simply because of what you are. This one thing you must do to yourself. If you don't do this to yourself, you may have many things but you will never be at ease. You don't know what it means to be at ease means you're in a disease. You may not have virus but you're not in ease means you're in dis-ease. If you're in dis-ease, you may be medically healthy but you're sick as a life. Let us use this time that we have. When there are no external demands on you, let us use this time to transform this one person. I am not asking you to transform the world. I took up this crazy job of trying to transform the world.  Well today people say that we have touched over a billion people. But my intent was to transform the entire humanity. A billion people, a billion people is just still sixteen, seventeen percent. Maybe just about that or even less than that of the entire population.  For sure.  That's for sure. This happened for those of you who do not know. Some thirty-eight, thirty-nine years ago, I was just sitting in one place and I just burst into ecstasy for no reason. Every cell in my body dripping ecstasy. So I kind of thought, what is this? After some time I realized, if I don't just mess with my mind, I am ecstatic. Messing with my mind means just this. See, you have two significant faculties with you, which are unique to a human being. No other creature has this faculty. This is a very vivid sense of memory and a fantastic sense of imagination. Now sitting at home, these are the two faculties that you are suffering, your memory and your imagination. You've suffered things which happened ten years ago.  You're suffering things that may happen day after tomorrow, already.  So you're suffering significant faculties that you have, which makes you into a unique life on this planet. A very vivid sense of memory and a fantastic sense of imagination. This is what you're suffering. When you suffer your blessings, not curses upon you. When you suffer the highest values invested in you, then what is left? What is left? This is what is the significance of Rama. Life can be a serial disaster outwardly, inwardly. You use your intelligence, your memory and your imagination and above all, this privilege that we are the most evolved creatures on this planet, it's not a small privilege. Number one spot, being a human being on this planet earth is, nature has delivered you to number one spot, that's what it means. Peacocks are dancing on the street of Mumbai. At least within your home, you can do something. Social distancing because I'm not asking you to do ball dance or tango.   If you knew how to be, you would definitely keep yourself blissful, that's what you should do because this is something that you owe to yourself. This is one thing that must happen. This is your fundamental birthright that your experience of life on this planet is pleasant. This is what Rama represents and signifies.   With all of them, we don't know what kind of game the virus will play with us. But what kind of game we play within ourselves, let's fix this today. It's very important. Satguru, this question is from Anoop. I have done my inner engineering and I wanted to recommend it to my family as well. However, due to the lockdown, we are considering the inner engineering online option instead. Can you please shed some light about inner engineering online and its benefits? Oh, why did you wait till lockdown? If you were immensely benefited by inner engineering, why did you wait so long to give it to your family? Now that you're locked up with your family, now you want them transformed. I appreciate the intent. But really, if you have gotten, if you have really imbibed inner engineering, in its essence, your family need not go through it. You go through it. By your very presence, you can transform. Obviously, such a thing has not happened. So they must go through it. Fortunately, the preparatory part of inner engineering is online, available online also. So let them do it. What are the benefits? Well, these... you can't call this Vanavas. What is the traditional word for a lockdown? Maybe there's no word. Anyway, you're homebound. This homebound experience for the next few weeks will become pleasant for you if all of them go through inner engineering online. Because inner engineering online is that part. Inner engineering process by itself involves the body, the mind, emotion and energy. What we need to do with the body and energy, we will have to do direct because that's a kind of a transmission that is not a teaching. But what we do with mind and emotion is a kind of a teaching that you can experience online. For most human beings, if the way they think and feel changes, you will see there is a tremendous change in their life. If right now, if you can think of what you want, not compulsively about something else, you would naturally be blissful. If right now, you can keep your emotions very pleasant. Oh, your home would be so pleasant. So all the psychological and emotional benefits which naturally translates into social behavior, these benefits are there. The energetic dimension and the physical aspect, well, that needs to be done as direct transmission that will not be taught online because there are many implications to that. The Shambhavi Mahamudra, you have to learn separately, but inner engineering online will transform the way you think and feel. Most human beings think this itself is ultimate transformation. If somebody can think differently and feel differently and they become pleasant human beings, people normally start saying he's a spiritual person, he's so wonderful. No, no, no, he's just a regular human being. Others are still evolving. If a human being is conscious, thinks what he wants, not compulsively, and holds his emotion the way he wants, this is just a human being. This is not something, he attained to something. No, he's just a human being. Others who cannot even think the way they want, feel the way they want, there's an evolutionary issue. So this evolutionary issue can be handled within the family with the inner engineering online program and in the country and in the world.


Born in Europe, the public law of Europe established by the peace of Westphalia spread around the world to become the fundamental paradigm of international law. In 1776, 13 American colonies of the British Crown seceded from it to become independent states. They created between them constitutional bounds within the American Republic, but they did not intend to change the fundamental paradigm of international relations and law based on equal sovereignty. Latin American colonies of Spain and Portugal followed suit a few decades later and again the basic social structure remained the same equal sovereignty of states. In 1815, at the Congress of Vienna, the turmoil resulting from the French Revolution and the Napoleonic Wars was put to rest by an exercise of restoration at the domestic level and by the re-establishment of a balance of powers. Balance of powers whereby one state alone was not sufficiently powerful to put in danger the peace of the continent. In 1885, at the Congress of Berlin, European states shared an apportioned between them the African continent extending to their colonial domination the logic of balance of power between them and then in 1914 the balance of powers proved its limits, failed to keep peace and Europe collectively committed suicide. The Great War raged for four long years only to leave the continent on its knees both materially and spiritually. These of progress, science and industrial development were turned into a terrible war machine. It was total war and the first international war in which citizens of all social classes not only professional soldiers were called to fight and to die. The war ended because of the late involvement of the United States of America in the war which tilted the standoff in favor of the Allied and associated powers. Germany was finally defeated together with the Austrian, Hungarian Empire and the Ottoman Empire and after the war the peace was largely based on the famous 14 points made public by the United States President Wilson in January 1918. It resulted in the peace treaty of Versailles and the other peace treaties concluded with the central powers in 1919. Germany became a republic, Germany had to pay war reparations, Germany lost all of its colonies, Alsace-Lorraine was restituted to France, the Austrian, Hungarian Empire and the Ottoman Empire were dismantled. On the ruins of the Austrian, Hungarian Empire new states were created on the basis of the principle of nationalities and Poland which had disappeared as a state for 123 years, Poland was re-established. Furthermore and for the first time in human history an international organization was set up for the purpose of maintaining international peace and security. That organization was called the League of Nations and its covenant was the first part of the peace treaty of Versailles. Versailles was a defining moment in history and that is why I chose a painting representing the ceremony of the signature of the peace treaty as the banner for this course. The painting is by William Orpen and it is to be seen at the Imperial War Museum in London. However when you think of it, Versailles was a very ambivalent moment for international law. It was a peace treaty and it embodied the hope that international law, notably through the establishment of the League of Nations, that international law could bring peace to the world and as we know that hope, that promise of international law, dramatically failed only 20 years later. After the rejection of the peace treaty by the US Congress and the isolation in which Western powers had kept the young Soviet Union since the revolution of 1917, the League of Nations was born as a very weak organization and it proved incapable of reacting to the challenges posed by fascist Italy, Imperial Japan and Nazi Germany in the 1930s. Furthermore and despite presenting itself as an instrument of peace and justice between nations and the beginning of a new era, the Treaty of Versailles was also an instrument of continued domination, therefore pointing to the deep ambivalence of international law. It was of course an instrument of domination over Germany but look around the table, you only see faces of white males except for an Indian Maharaja as obedient servant of the British Empire. True, if you look at the whole painting through the link that you will find after this video, you'll also see the representative of Japan represented on the painting but that's it. That was the world and the world order in 1919. And of course today the face and the concerns of the international community have dramatically changed but the ambivalence of international law, both as a promise of peace and justice and an instrument of domination, that ambivalence remains and that is why Versailles is so appropriate to illustrate this course.


Are we? No! We're live! Hello! We are alive! Day two, day two of root stack and we're here. It's Mags, it's Aowyn. Murph mousse is here. Murph the mousse, look at her. The genie of mascot. The genie of mascot. Yeah, there we go. Oh and we have, we have many of our regulars. We have Mary, Sleppy, let's scroll to the top here. Lisa, hey Ottawa! There we go. I saw store-bornings for you guys. Oh no. I had to park at the very top level. Yeah, in Toronto. In Toronto. He's going to have to dig his car out again. Yeah, it's going to be. Yeah. Well, Hamlin, uh, Susan and Judy. Hey Judy! There we go. Appalachian project. Send me a biscuit. Oh and there's Chris Ferriolo. Hey Chris Ferriolo. Um, there we go. Azure, hey there, Azure! Hi! Nancy, Nancy Wilson. John Tiner's first. John Tiner all the way from Ireland. Ireland, the Emerald Isle. The Emerald Isle. Shelly is here. Janine. Hey Pat. Patricia, oh cousin Patricia Rye. Stephanie. Stephanie O. Nancy Wilson. Oh, this is hard, holding it up with one hand. Oh, Karen Stewart. I said Mary already. Just go. Who's Jaleigh LaFont? Who's Tall? Tall and Z Rider. Shirley. Hey Shirley. And Shelly. Okay, now you can hold my two hands. Oh my goodness. So, so I've had an exciting day. So I started off with a class, a session on X chromosome. And then I was here with these lovely people and helping out some people with tech at the booth. Then at noon, I went over and I got part of the organ recital at the Tabernacle. Oh, you got to do that. I did. Well, I didn't get the whole one, but I got half of it. It was great. Amazing. The man was so excited when he came back. Yes. I thought the whole place was gonna be great. That's right. And the organ he was playing, I think it had six manuals, like six keyboards. Really? Five organ. Yeah. Did it have too many rows of foot pedals too? I couldn't tell because from the angle he was very, very far away. But then the other thing is, on the way back, there's the family search library, you know, the humongous one. And he went and he found more relatives. I did. I found a great grandmother who I didn't even realize was in this set of records. And it was great because anyway, I never knew who her parents were because she married someone with the same last name. So it was a Suzanne Fountain, Marietta Joseph Fountain. And there are two different versions of the family tree. But this one was the baptism of Suzanne Fountain. So I know definitively who her parents are. So I know which family tree is right and which one is not. So I was very excited. So here we are. We're here. We're here. How was your morning? My morning was good. I think I've talked to this many people and I've taken this many pictures with people who've come and all of them get to have the picture taken with me with the Wicked Tree banner. Right. Oh, you mean this banner right here? Yeah. Wicked Tree banner. There we go. That banner. That banner there. Yes. And Avin, how was your day been? You know, Murph has an earring. No way. Do you see his earring? Well, he's cool. He's got a Wicked Tree earring.  Don't look at his eyes because he's, oh no. He'll just draw you in. No. He's getting hypnotized. There's a guy walking around in costumes. Oh, there we go.  We don't know. There's a guy and I killed it here, Pip. Yes. Pip, if you're around. And what clan was he from? I don't remember. I saw two people in kilts. Okay. Yeah. He was from a clan and it's set on it, but I can't remember now. He was from a Scottish clan. A Scottish clan. There we go. I want to clarify that. Oh yeah. Oh, I didn't even. Okay. Good. A Scottish clan. Yes. So what have you been doing? Have you been Wicked Treeing? Have you guys been, yeah, people in costumes? That never happens. Yeah, it does. It happens all the time. Yes, Murph is Canadian. He is. He has Canadian ribbons and stuff. No, we don't know Murph's parents, but he looks like he's 100% moose. Oh yeah, I think so. So there's so many people wandering around and looking. So there's that guy. Oh, there's my friend Bruce. Hey, Bruce. He's a Matthew. He's another Matthew. Okay. Yeah, he says it's not snowing here yet, so that's good. Yeah. Well, I saw some storm warnings, so you guys, yeah. For those of us not at Roots Techs, we played Mingo. Okay, good. Yeah, yeah. So we're in between classes right now, so there aren't a lot of people walking around. But here comes, here comes Daniel Horowitz. Daniel, come here. Hello, everybody. How are you? Daniel Horowitz is my heritage. He's here. He's here. He's here. Wow. And if somebody else comes by, we'll grab him. And call house has been here. Johnny, Johnny was here yesterday. Oh, I missed Johnny. Diane Southerg has been by. If you check my Facebook page, you'll see some of the pictures. That's right. Jen Baldwin, Jen Chad, Jen Baldwin was here. Robert Estes has been here. Yeah. So many people have been here. It's been so much fun. Yeah. Devin Welle. Devin's been here. Devin's been here a couple of times. She came out and got her suitcase. She left her suitcase here. She did. Oh, okay. And she told me not to look. Oh, yeah. You didn't, I hope. There were gold bricks in it, I believe. Oh, wow. She said it was very heavy. She was very heavy. Oh, yeah, Johnny Perl. He was here yesterday. He actually jumped in the live cast. Right. And look who is walking up right now. Hey. Do you see that man? That's Peter Roberts. That's Peter Roberts. DNA hard hat. DNA hard hat. Who has been missing in action for hours. Where have you been, Peter? I've been happy. I got a person in the wiki tree. I got them into various databases all associated with the wiki tree. Yeah. He's very happy now. So you have been working the booth away from the booth. I've been sitting, yeah. Wow. Saving my knees and legs. We are experiencing great feet pain. All of us. Oh, oh, we're being taped. We're being taped right now. This is a wiki tree live cast and this guy is taping us. So you never know. You look too good. You never know what's going to happen when you're at Roots Tech. So that's happening. That's happening. Wow. I asked somebody today what the numbers were for people being here. And there's less people here. But being an exhibitor, we have had so many people at the booth. We've had so many people talking about wiki tree. Lee and Kruger mentioned us. Johnny Perl mentioned us. Diane Southerd mentioned us in their talks. And we've been inundated with people. Thanks, man. We've been inundated with people coming by the booth to ask questions about wiki tree, like DNA projects, name studies, one place studies as I've got people that are just going to be calling you. Yeah. Are you doing something? We're just having, no, we're not doing anything. We're working on the good news. We're introducing people to wiki tree. That's what we're doing. That's what we're doing. So when somebody walks by and they look like somebody we want to talk to, we grab them. So like there's a celeb. Okay. Let's watch. Watch Meg's in action. Hey, you don't know him. But you should. You should. This is Brian Casey. Hi, whoever this is. This is the wiki tree live cast. He's watching us. He is the guy that does all he's not all. He does a lot of the programming behind. He's been with Chris from the beginning. He is developer extraordinaire and right behind him. Oh, there's Jamie. Jamie. Oh, where'd you go? Yeah. Sorry. Sorry about that. So that's what we're doing. We're we may be having fun. Thanks. Sure. Yeah. That's Brian. You don't know him, but he is a huge wiki tree. Yes. Very nice. That's beautiful. Yes. Yeah. He was instrumental in the Hacktoberfest. Yeah. He's a big developer along with Jamie and lots of others. So there we go. I don't see anybody. We could walk around if we wanted to, but nobody wants to walk. Chances are we might drop something. Yeah. Okay. I'm feeling a little seasick. Yeah. No, maybe not. Sorry. Okay. Oh, Julie.  What did she say? I'll miss you. I went away. She said, Oh, okay. I'll put it back. There we go. Having fun. Having bless. I'm missing Greg. You don't know who this is. This is Julie Clark. This is Greg's wife. Yes. That's so great. Yeah. So we're hanging out having fun. What are you doing at wiki tree this weekend? Have you noticed a lot of people coming into wiki tree because they've been by the booth? I have a question. Yeah. What is it? Friday? This is Friday. I don't know what day it is. I'm pretty sure it's Friday. Yes, it says Friday on my watch. Is there something going on this afternoon to bingo? There was a, look at Chris. Who's Chris who? No, Chris is not. Hi, Mrs. Clark. Watch out, Julie. Watch out for him. He's one of our students. Show A.O.N. right now. Oh, there's A.O.N. Oh, he's riding on the, very nice, very stylish. He's a little buddy. Yeah. I had to leave my dog at home, so I kidnapped Max. Oh, you're without your dog, okay. But your dog's being well taken care of, right? Gosh, spoiled. This dog will not want to be one of us. My mom keeps setting pictures. She's like, here she's in the sun. Here she's in the spot we made her. Oh, in the spa? She's happy with her dad. In the spa? She, they made her a little spot. They needed a little spot with pillows and stuff. Not a spa, though. Not as far as I know, but, you know, we have another wiki tree. Oh, another wiki tree. Okay. Oh, oh, we lost, oh. Sorry. I just, I just banged Max in the face. Oh, sorry. Okay. Now, Max is just randomly calling people out in the crowd. You want to say hi to the wiki tree crowd? This is Dick Eastman. Who am I saying hi to? These are wiki treers. All right. Yeah.  I'm not sure about that. I think so. Yeah. So, what you were saying? Yeah. So, Dick is here and we've broke him in. Do you have anything to say? What is your genealogy, Jim, for today? Jim, I don't know. Have you met anybody here today that is incredibly interesting, like Chris Whitten? We've never met. You've never met Dick? Never. They're pulling my leg. I think probably at the first root stack I was at. Wow. Yeah. And he's kind of hard to miss. He's still wearing the same hat. He's not taken it off since. He's washed it, though. He's got it all the way between, but other than that, I don't know.  No, not having that here this year. I wasn't sure how many people were going to be here. Actually, the crowd turned out to be somewhat bigger than I was. So, you're excited about the size of the crowd with him? Absolutely. Yeah, I think so, too. And you're excited to ask about anybody that I ever met that that was interesting. The answer is there's too many people. Yeah, there's so many people here. You're not going to be running for the next three hours, so I can talk about the interesting people I met. No, for three hours. Have you been in any of the classes? Yes, several. I just came for a while, a commercial presentation by one of the vendors. Okay. Yeah, which was fascinating. Fascinating. Ooh. To give a plug. This is the company that sponsors my newsletter, so I'm going to let you know what I'm going to do. Go ahead. My heritage. Okay. Gellat Jeffits, the CEO just gave a presentation and he ended it with a whole new beat that the employees made. Oh, how nice. If you ever get a chance to see back to the future with my heritage. Oh, watch it. If it shows up on the video channel, you can watch that. It will show up today. This is the first time he's ever shown it to the public. He only showed it once. He said last week through his employees. Nice. And today he has shown to non-employees for the first time. That is cool. I'm hoping it circulates around in the following weeks. So that's fun. So you're going to laugh at your posterior. He almost said bomb. I almost said something worse. Thanks for dropping by. I appreciate you jumping in. Yeah. It's kind of like, you know, putting out the hook. Chief programmer and database specialist all the way from Slovenia? No, I actually moved. Oh, you moved to New York. So let's see what it's people. I am Mrs. Tricknick. Oh, you see Mira here. Mrs. Tricknick's here. That's so funny. So all of the spouses are walking in to check up on these guys. Now, make sure where we're supposed to be. Yeah. Yeah, there she is. That is so cute. Greg's wife's in here checking up on you. Yeah. Yeah. So, yeah. Thank you for everything you do. Oh, nice. There's Lynn Kruger. She's a Canadian. She's had like 18 sessions here at Roots. She's been very busy. And she drove so much traffic to the site this morning because she talked about wiki tree. What did you talk about? Cername studies and how to load and put your information about your study on wiki tree. Yes. That's good. So that's Lynn Kruger. She's Canadian, eh? Yeah. From Red Deer. Yeah. From Red Deer. Oh, that's so fun. We've just been grabbing for a while. You're live live. Yeah. So do you have anything you've done this weekend that was extraordinary? No. Okay, no. No. I talked. I spoke. It's been fun. She's been running around. That's a nice shirt. This is a nice shirt. I'm going to go down a little bit. Oh, there we go. Yeah. Very nice. Yeah. All right. Cool. So, bye. I love how Mira and Julie showed up to check up on you. Yeah. Yeah. I said, well, you know, it's going to be hard work and stuff because she didn't buy it for a second. She didn't buy it for a second. Are feet hurt? Are feet hurt? Yes. That's true. Let's see what the new comments are. Oh, is it touchscreen? No, it's not. So why am I trying to touch the screen? Yeah, I don't know. We don't have Starbucks here. No. Yeah. And when you, Smarties means something very different. Yes. The rockets. The rockets. And Julie is watching. Julie is watching. She's having lunch over there. Oh, right. She's supposed to be at this booth. She's having lunch. That's hilarious too. Oh, man. Yeah. That's right. We can't because we don't have a stabilizer. We don't want to make all of our people. Well, I've already made them seasick. Yeah, we already made them seasick. Sorry about that. We shouldn't do this. I did that with a bit. Yeah. We wish you were all here. We took the wiki tree picture this morning. So check things out. Oh, look, Merf Moose is here again. Oh, and there's Ray Owen.  So we did took the wiki tree booth picture. What else have we done fun today? We talked to people and she's really excited about it. Can you tell? She loves it. That's right. So that's probably it. And so we're back at 10 o'clock mountain time tomorrow. Mountain time tomorrow. So 12 o'clock your time. Yes. So show up at 12. Not for John Tyner. It's not 12 o'clock for John Tyner. No, John, can you stay up for us? Oh, yeah, because it's two hours later for him. Yes, Mira. Julie is here. Is there? Yes, she's here. She's here. Yeah, so I miss you too. Alya was very sad. We're very sad. Alya, Alya's daughter is our favorite t-shirt salesperson. There is no t-shirt salesperson. But there's no t-shirt salesperson left. Everyone just exited left. Let's see. Thanks for making a great Saturday morning. You're welcome. Yeah, it's so tall. Surely is somewhere far away. Okay. Yeah, so, yay. Yeah. You want to sign off? Sure. Yeah, we're probably good. Yeah, we'll see you tomorrow morning. We'll see you tomorrow morning, afternoon. Yes. Ciao. Bye.