From Hollywood. It's time now for Johnny dollar Barney Wilson, mr. Dollar special deputy with the DA is office Understand you talk to Danny Haines. You've got a good grave mine. Mr. Wilson. Oh tolerable Well, what do you think? Well, I'll go about six to five. He hasn't murdered anybody. Oh, well, that's close to even money So you're not too sure. No, I'm not too sure But then I'm not even sure yet that mark. He is dead. Remember Well, maybe we can settle that question this evening. What do you mean?  All right, you meet me at Harbor police headquarters at 730. I'll be there good I'll introduce you to the late William Markey Somehow I started doubt that mr. Wilson Tonight and every weekday night Bob Bailey in the transcribed adventures of the man with the action-packed expense account America's fabulous freelance insurance investigator yours truly Johnny dollar From special investigator Johnny dollar to the home office Delta liability Hartford, Connecticut Assignment the Phantom five matter location Miami, Florida expense account continued Item six three dollars and eighty-five cents taxi fare to the Markey beach house Occupied for the past three days now by his wife since William Markey's accidental death According to all reports a very beautiful woman the reports were correct Won't you come in mr. Dollar? Thank you Come this way I've been practically living in here in the study since I Just haven't had the heart to even look at the rest of the house. Yes. I I imagine it's been quite a shock for you Mrs. Markey. Yes, terrible.  Thank you. I I Really don't know very much about these matters if there are papers to sign. Maybe I should have a lawyer or something No, that won't be necessary for the present. There's nothing to sign But aren't you with the insurance company? I'm working for them at the moment as a special investigator I'm to supply them with a full report of your husband's accident They have to have that before they can do anything about paying off the policy Or couldn't the police give you all that and there's a mr. Wilson. I think his name is who's it with the district? I have talked to mr. Wilson. He's cooperating in every way possible But some of the details I have to get from you Have you talked with Danny Hane? Yes, what didn't he tell you what happened? He gave me a statement. Yes But only covering the details he actually knew about Well, I'm sure there's nothing I can add mr. Dollar. I wasn't even there as you know, of course I know Mrs. Markey I'll get all of those details elsewhere But then I don't see why you I'd like to know a few things about your husband Things you know better than anybody else His actions and behavior during the last few weeks his mental attitude I See you think maybe he committed suicide. Is that it? I don't think anything I'm just trying to find out but that's what you're driving at suicide. It's a possibility, of course And of course your company isn't liable I suppose if it's so it's still be liable But only to the extent of twenty five thousand dollars under the particular terms of the policy not seventy five thousand I see is that all mr. Dollar?  I have no reason to think it was But these questions are going to be raised by the claims board when they meet to consider settlement And they're not going to pay out any money until they have the answers So that's why I'm here Mrs. Markey to get those answers ahead of time Now you can help or you can hinder But I think you ought to realize that you'll be mainly hindering yourself. It was not suicide Bill wasn't that kind you didn't know him I resent your implications to dollar. He'd never do a thing like that. I said I have no reason to believe that he did Please forgive me I Guess I'm sort of living in a state of shock. I'm not like this really Suspicious belligerent sure I understand and I'm sorry to have to bother you this way, but there are certain questions I know these things have to be done. It's all right Would you like a drink mr. Dollar? Not unless you're having one Yes, I think I would like something in that case. I'll have a scotch on the rocks, please. Oh here. Let me fix it Thank you. Make mine the same. I guess it was the mention of suicide that set me off Bill and I were married for three years. We were completely happy every minute of it Nobody in the world had less reason than Bill to do a thing like that. What about financial problems? None that I knew about Did you work before your marriage mrs. Markey? I? Was an entertainer chorus Yes, I suppose that gives you the usual impression Well, do I seem like a visiting fireman? No, I just thought you might have been a dancer because you carry yourself so well Live and graceful Well, I I've been away from it for quite some time. It doesn't show Here's your drink. Thank you Maybe it'll help me relax a little. I think it might tell me mrs. Markey How did your husband and young Haynes get along? Well, that should be obvious We brought him down here with us had him living here in the house for a month, but I uh, I understood that was primarily your idea Who said that did you suggest bringing Haynes along or was it your husband? Hi, I might have I don't remember how it came up now, but bill was all for it Otherwise he'd have put his foot down any possibility that he resented Haynes presence, but kept it to himself Of course not. Why should he I don't know? Well, if you're trying to imply something, I'm just asking I Understood your husband had spells of brooding during the last few weeks and I was trying to find out the reason for it If he did I'm sure I didn't notice it What are Danny Haynes feelings towards you? I think you're pretty insulting I wasn't intending to be well, what would you call it just another routine question I wasn't meaning to imply that you encourage him in any way. I certainly didn't but he's young and petuous.  He thought of me as a friend That's all no attitudes on his part that your husband might have misinterpreted. I Don't believe I care to answer any more questions like these mr. Dollar Look, I'm not just asking them for my own pleasure mrs. Markey I'd a lot rather not ask them but but I've got a job to do well I failed to see why it's necessary to probe into our private lives. I'll tell you why Your husband supposedly died out there beyond the surf when a cruiser burned and sank What do you mean supposedly his body hasn't been recovered so at present the evidence of his death is purely Circumstantial in fact there isn't much evidence one way or another who could possibly doubt it the insurance company will doubt it Mrs. Markey and they'll hold up processing any claim for payment until one of two things happens Until I turn up sufficient proof of death to convince them or until a court declares Your husband legally dead Barney Wilson from the DA's office for reasons of his own is going to file for an immediate court decision I'm pretty sure of that is but as things stand now my company will fight it and with no more evidence than Wilson has They'll be able to find it successfully What was the point? What were you driving at your husband's death had to result from one of three possible causes one an accident two suicide? three murder But that there was there was no one with him except Do you mean Danny? That's one possibility one out of three. No, I have no reason at the moment to give it any more weight than the other two But there is one thing certain Mrs. Markey And view of the circumstances not one set of insurance is going to be paid until one of those causes is proved But what can I do? I don't know anything about it. Maybe you don't or maybe there's something you've forgotten Don't think is important or something you haven't wanted to talk about I don't know of course But it might be worth thinking about It was nearly dark when I left the house And I wouldn't have noticed the man standing under a palm tree by the driveway if he hadn't made a sudden move to get out of Sight then when I walked toward him he scurried out of the drive and slipped into a car parked at the street I could see it was an old model, but I couldn't identify the make I Caught the last three numbers on the license plate before it disappeared around a bend. I couldn't quite figure it Might have been Haynes or some ghoulish swindler who was scared off when he saw the widow wasn't alone The numbers were 642 Expense account item seven three dollars and seventy-five cents taxi back to my hotel Item eight six dollars and a quarter dinner and incidentals there an item nine a dollar and forty cents taxi again to the waterfront headquarters of the Harbor police Thirty minutes later I was in a police launch with deputy agent Barney Wilson several miles down the coast Skimming across the water toward a bright cluster of spotlights where a salvage barge was working into the night to raise the burned hulk of the charter cruiser fathom five You still got your mind set the same way mr. Dollar. What way was that that there hasn't been any death there any murder? Oh, come now mr. Wilson. You're mistaking an honest scientific skepticism for a set of mine. Well, that's very pretty mr. Dollar What does it mean? Well, I haven't taken any definite position yet But I've got to see more evidence before I'll consider proof of death to be established without a question That means you'll file a demurrer against the declaration by the court It's not up to me. It's up to the company, but I can tell you right now that if you petition They'll move to block it. You have no real evidence mr. Wilson I'm getting it though piece by piece the sea is starting to give up its prey mr. Dollar What do you mean the boys found a shoe late this afternoon washed up in the surf just about where you'd expect to find it If it had been carried in by the current identifiable from the same New York shop that Markey's other shoes came from same size same style Well, it's something all right, but it's still not conclusive who would he ask that Markey walks up and tells you he's dead No, I guess I'd settle for just seeing him that way. Oh By the way, I wonder if you could have an auto license check for me a partial license on a used car Florida plates The last three numbers are 642. Well, it might take a while with no more than that to go on I've got an idea the car may have been purchased within the last three weeks or so. Maybe that'll narrow it down You got an idea it may mean something look. I have no idea at all. I'm just playing the hunches But it's about time something in this case started meaning something We edged the launch up the side of the barge tied up to a stanchion and climbed on deck The power winches on the Derrick's were still grinding away in the sunken hull of the burn cruise It was nearing the surface a Crew of men waited with salvage pontoons ready to float the supporting cradle into place as soon as the waterlogged hulk was raised Wilson and I stood by the rail watching not talking Wondering I suppose what answers the wreck might supply us with The taught steel cables inched their way slowly up from the depths and finally the boat itself broke the surface of the water Then the men moved in with the pontoons and other crew members dropped a suction hose into the water filled hull and started a pump to empty Finally the whole thing was high enough so we could see that the cabin in the deck were badly burned almost destroyed But strangely enough the hull itself seemed to be undamaged Then Wilson and I both noticed something at the same time a solid column of water spotting from a round hole near the keel of the boat And we both realized what it meant Look dollar look there somebody opened the seacocks Somebody left them wide open so one thing is certain. It wasn't an accident. She was sunk deliberately That's exactly what I've been trying to tell you right from the start William Markey was murdered Here's our star to tell you about tomorrow's intriguing episode of this week's story tomorrow a Photograph a silver cup a herried widow and the dead begin to stir with life Join us once you yours truly Johnny dollar truly Johnny dollar starring Bob Bailey is transcribed in Hollywood Written by Les Crutchfield. It is produced and directed by Jack Johnstone Be sure to join us tomorrow night same time and station for the next exciting episode of yours truly Johnny dollar This is Roy Rowan speaking


It's been a pretty long day. What is going on everyone? Welcome to my channel. My name is Josie Linge. That was awkward. The last couple of days have been pretty hectic and the reason being is because the company I work at put on a hackathon. They call it a co-jam but I just call it a hackathon because that's what people are familiar with and it was in partnership with IBM and we had to use IBM cloud technology and integrate it into an app that we created and instead of it being 48 hours or 24 hours like a typical hackathon is it was only the work day for two days so about 16 hours maybe a little bit less considering the fact that we had presentations around 2 p.m. today and we started around 8 or 9 a.m. but I digress. Been a pretty busy pretty busy person the last few days but that's not what this video is about. This video is about unboxing this new 16 inch micro pro that I got and let me tell you it's been long overdue for me to get a computer that has the specs that this laptop has. The reason being is because my last year at college I had a MacBook Air.  A MacBook Air is a great reliable computer but it's not great for power users like myself and then I got a refurbished 13 I got a 13 inch MacBook Pro that I was refurbished and the reason being is because I don't want to spend a ton of money and I just wasn't impressed with the laptops at that time and that was you know probably like six months before the new 16 inch came out but let's talk about the 16 inch. So I'm trying to figure out where I want to unbox this thing at. It's monitors kind of in the way but I guess this mount helps I think we could do it right here. Now we're situated I know it's really late for an unboxing but how could you not do an unboxing if you get a new MacBook? Right? One thing that never gets old is the Apple unboxing experience. I love that Apple doesn't overlook the importance of product delivery and the unpackaging or unboxing experience. I had to throw in a cardigan because I'm just getting a little nippy in here. It's officially time to take the laptop out of the box. This thing is huge. For the 16 inch you actually get this 96 watt charging base opposed to I don't know what the 15 inch one is I can't remember. I know that the 13 inch that I had was like 61 watts and obviously this thing needs a lot more power and of course the two meter and length USB type c charger. The 16 inch laptop that I decided to get is the 2.3 gigahertz 8 core processor with one terabyte storage in the AMD Radeon Pro 5500m. We'll say that since I've been using the 15 inch I think 2018 model I'm not sure which model it is but it's definitely the 2016 or yeah 2016 to early 2019 15 inch MacBook Pro with the touch bar. I've been using that the last couple months because of work and I will say if I was doing this unboxing about four months ago before I started my new job I'd have been a lot more excited because it was it's funny I hadn't ever really used a 15 inch MacBook Pro before I started my new job. Needless to say I'm very excited to use this laptop it's a lot more powerful than my work laptop but I thought I'd just say that I don't know why but I'm definitely very blessed to be able to afford a device like this. Now one thing I've noticed is that typing on this thing is so nice this typing experience is great the keys feel so responsive they're not as flat Apple went back to that scissor style keyboard and ditched that butterfly keyboard I'm hoping they do the same thing for the 13 inch this feels great. See it's the little things that Apple does that keeps customers purchasing their laptops even though they could spend 25% less on laptops that are great it's just that you just trust Apple and I think the the new keyboard they listen to their customers thank you the new keyboard the huge trackpad the unboxing experience the customer service the Apple store makes you feel comfortable you feel like you're investing in a product that is going to last you a long time I didn't get the 32 gigabytes of RAM and I have 15 days to return this if I decide that I want to but I just didn't think it was worth spending that much money for 32 gigabytes of RAM but I did get one terabyte of storage as I mentioned earlier which will help me a lot especially when it comes to the 4k editing so I won't really need my external hard drive unless I want to use it to backup videos and backup footage which is what I would like to use it for but the i9 I think will help me when it comes to that processing power with 4k video editing and programming with Xcode and doing things in node with Node.js and MPM angular apps react apps progressive web applications I just feel confident that this device will not what am I trying to say this device won't be a hurdle I have to jump to create and um we won best presentation at the hackathon so we got this JBL clip 3 I guess I could like clip this to my book bag which I think that's that's a nice feature because I like to I like to I like to play basketball a lot and um I never want to lug around my bluetooth speaker but I love love love when music is playing in the background while I'm hooping it just allows me to get a rhythm but this is really really cool this is not sponsored by JBL but JBL if you all are watching hit me up but let's collab yeah this thing is literally literally like a little a little bit smaller than my palm it's like the size of my palm look at this thing this is great I could put in my book bag I could always I could always carry it around with me sometimes in an office we play music especially on Fridays built feeling feeling funky why do I why do I say that I never say that in person gotta be more authentic this is this is actually really nice I'd never buy this if I'm being honest I'd never buy this unless I went on hikes more which I plan on doing during the summer so this came right on time but it's actually really nice build quality like this doesn't feel cheap at all okay back to the MacBook an interesting thing my friend said to me was didn't you just get a new laptop and I thought that was funny because I did but the thing is that 13 inch just wasn't powerful enough like when I would run Xcode and try to do other things maybe do a little bit of Xcode and video editing some people would say why would you do both at the same time I would say why not but also if I'm spending money on a laptop especially north of a thousand dollars you would think that you could do both of those things especially if your laptop isn't a 15 or 16 inch hey Siri hey Siri open the documents folder all right I'm about to set up this dark theme okay look at that it's like an appearance auto so I guess auto changes it to dark mode when it's light outside and like I don't know I'm gonna just go with the dark theme laptop is all set up now and as you can tell this isn't a very technical video I'll drop a more technical review of this 16 inch MacBook Pro one terabyte i9 processor I'll drop something like that later on maybe after a couple weeks or a week or maybe a month of usage I don't think it'll take me too long to release a video about the technicalities of this device just considering the fact that I've already used MacBook MacBooks in the past and Apple products in the past so I kind of know how they work but I'm going to focus more so on how this will make my day to day life and running my youtube business a lot easier and working on passion projects a lot easier but I'm already really excited about this 16 inch display all right so the next thing that I need to do is I need to hook this up to my Dell U27 17D monitor so I can edit this video and get it up in the morning on Saturday guys I never do that never but I'm motivated and I'm actually I'm so pumped to see how fast I can edit this video and I can actually scrub footage I could scrub 4k footage without having to render it and I can export a 4k video that's 10 minutes long in less than in two hours this laptop's big so I mean they're going to have to get a longer desk which I definitely need but I think I'm going to get a laptop stand or like dock that I could put maybe over here just because I don't want to block the view of this monitor I don't know if I can yeah I can't lift this up vertically I got this all set up it's time to video edit so I can get this video out in the morning because during the weekends early bird gets the worm thank you Jesus for this laptop and all seriousness you all like I'm so grateful I don't take big purchases like this lightly and I'm gonna keep reminding myself this is a business investment keep telling myself that business investment but with that being said that concludes this video if you're still here give this video a thumbs up if you liked it at all give this video a thumbs up and comment down below some of your thoughts if you have the macbook pro 16 inch like myself comment down below some of the specs that you all have and if you all want to see more videos like this share with someone who you think might benefit from it and as always stay blessed I will see you all next week peace


Okay, so what we were doing in the last class, we were looking at multigrid methods, right, we were looking at series of mechanisms by which we could accelerate convergence of our schemes, numerical schemes. So these are in a sense modifications to a fundamental scheme, you have a fundamental scheme and now you are asking the question is there a way by which I can make this scheme faster, meaning from the point that I start the computation to the time that it takes, wall clock time, I look at the clock and say it takes so much time that it takes for me to get the solution, okay, I want to reduce that, making sense I am not really interested in other details, I mean there are situations where you can look at, right, you can say that the hole is equal to the sum of the parts, if I minimize, if I optimize the individual parts then the hole will also get shrink down, but you will see sometimes that does not quite work out when you try to shrink one the other expands and so on. So we have to keep our eye on the fact that the metric, the measure that we are using to see whether we have made an improvement is we start and we look at the clock, it stops and we look at the clock and we say yes it is taken less time, okay, never lose sight of that because it is easy to get caught up in all the numbers, CPU times, all of this kind of stuff and lose sight of the fact that the overall time is not either reducing so you are putting in effort but you are not getting anything out of it, fine. In the last class we looked at a particular scheme, right, the last sort of half of that class we looked at a particular scheme which was essentially a multigrid method and the idea was that we are going to use multiple grids just to recollect multiple grids in order to accelerate convergence, fine. And that, where did that come from, that came from the fact that we said that high frequencies when we say a signal, say now I will, today I will use a little signal processing kind of terminology, we say high frequency, right, when we say high frequency we have already noted from a previous demo that when we say high frequency we mean high frequency with reference to a grid, high and lower comparative term, the terms that you use to compare two things. So you need two things and you have to have another, right, so the other is the grid, the underlying grid, what is the structure of your underlying grid. So on an equally spaced grid, a high frequency and low frequency with reference to that grid are defined and there were schemes that we saw where high frequency is decayed faster than low frequencies. See now I am careful, there were schemes that we have seen where high frequencies decay faster than low frequencies, that means that there are schemes for which that may not necessarily be true, right, in which case we need to do something for that. Today I will tell you something about that, okay. Then so what we basically said was well if the high frequency is decayed faster than low frequencies and then we have this low frequency error with which we are trying to contend essentially the grid that we have at hand is struggling to decrease that error, why not transfer the problem to a coarser grid so that this low frequency error on the fine grid turns out appears to be a high frequency error on the coarser grid, okay and therefore we will decay faster on that coarser grid, that is the idea, that is the basic idea of multigrid method, okay. Now today what we will try to do is we will try to write out the whole scheme, so first I will recollect where we left it, try to write out the whole scheme and then we will see what are the steps that we need to take in order to how should I say make sure that everything is fine, little patch work that we need to do, right. There are schemes which may not be inherently you know high frequencies decaying faster than low frequency, we have to do something for that, that is one thing, we still want to transfer the problem from a fine grid to a coarse grid but we may have to do something for that, okay, that is one thing that we have to do and the other thing is all I have said so far is, all I have said so far is it is going to run faster, it is going to decay faster, will it, what is the effort involved in doing this, how much work are we actually doing, right, so before you write the program and look at the wall clock time and so on, we are going to ask ourselves the question, how much work is it actually going to take in order to do this, okay, work in the sense that computational work, there is also implementation related work and I will sort of say something about that as we go, is that fine, okay. So first just recollect where we were, we started off remember that the grid size we talked about was H, so this is a typical grid size, what that means is that if I have, that is supposed to be equally spaced, it does not quite look equally spaced, if I have equally spaced grids, right, a typical grid size is H and if I have a linear problem and I will tell you what to do when you have a nonlinear or quasi-linear problem, linear problem, I chose Laplace equation to, I chose Laplace equation as an example but it could be any system of equations that we talked about, AH, PH equals FH, we are trying to solve this and what I indicated was that we iterate, we iterate this a few times or if it is a time marching scheme, we march in time, right, a few time steps, so we do this, what was the symbol that I used for the number of iterations, was it alpha, n times, n times, n times, n times, I am going to regret that but anyway n times, we are going to iterate it n times, okay. So then what, what we do from here, remember the algorithm, we get the residue, we get the residue, so we get RH which equals FH-ph where this phi is that intermediate solution, capital phi is the intermediate solution, we get the RH, then what we transfer RH to F2H, F2H, right, if you want to write it as a equal, an equation in books that you may look at, they may write something like F2H, this is a typical notation, right, so if you can actually write a matrix form, matrix form of this, I will recollect for you what each of these things, right, we will go through that, so you transfer from RH to F2H, on the grid with whose size is 2H, you then solve, you then either solve or you iterate a few times or take time steps appropriately, okay and do this, if this was n1 times, this could be n2 times, they could be the same, they could be different, you have some magical reason for making them different, it is up to you, okay. Then we said look, right, if you start with a very fine grid, it is possible that the 2H grid is also reasonably fine, so you can then compute after iterating a few times and then you say oh it is not converging fast enough, I am not happy with this, you can actually compute a residue there, which you transfer to F4H, am I making sense, okay and then consequently we will solve and repeat this process, at this point actually you know the phi is not actually phi, it is a correction, if you think back to the algorithm, phi is actually a correction, so how the reverse mechanism, how does the reverse mechanism work? You take the phi 4H that you have got from your iterations, that is your iterate, you could go on but I will tell you what happens from phi 4H and you transfer that to E2H, that is the correction at, okay and the new phi 2H equals the old phi 2H, okay now you have lots of options, see this is the thing about the algorithm, developing the algorithm you can see there are lots of options, if you want and I would do this, you can also sort of iterate a few times there, m times if you want, okay, so you iterate at that level and then you get a phi at that level, right, the F does not change if you want, right, then you can transfer, okay, this transfer by the way you could write, if you wanted to write it as an equality just so that if you would look at books I want you to make sure that you have the notation, you would write this V2H equals along the same lines, I4H to 2H, phi 4H, right and you can actually write it as a, if these are vectors you can actually, you can actually cook up, you can find out what this matrix is depending on what kind of interpolation or whatever it is that you are doing, right, we will look at, I will give you the appropriate terminology, we will go over this blackboard again one more time, right, is that fine everyone and then you would say phi H equals, right, that is the correction at the H level, maybe m times and at the finest grid you always ask the question, you compute RH, say I am repeating now, I am repeating the first line now, we are back to the first line but you can ask the question, have we converged, right, you always iterate on the finest grid a few times and ask the question have we converged, does that make sense, you want, I mean the reason why we are making this effort is I want a grid on that, I want a solution on that fine grid because that is the resolution that I want, that is what I am looking for, right, I have decided I have looked at the problem, I have looked at, I have an idea, I have a sense as to what the flow features are like and I have said okay I need a grid that is 1 millimeter in size, let us take actual physical dimension, I need a grid that is 1 millimeter in size, I want a solution on a grid that is 1 millimeter in size, so having decided that I pick an H which is 1 millimeter and I go through this process, right, so I want to make sure that when I finally decide, yes I have the solution, I am making the decision on the 1 millimeter grid, not at the other grid, okay, the question always arises at this point, okay, I do not care about the other residues that we have calculated, is that fine, is that okay, are there any questions? Now we will go over this with a little detail, we will check out, fine, we will just check out little of the few of the things, how do we decide, what is the point here, how many times do we treat, is there a mechanism by which we can decide how many times we treat, is that just an arbitrary parameter, should we have a method by which we should decide how often we treat, think back to our demo, see I said there is a highest frequency that we can represent on a given grid, okay, so if I am going to go from a grid, okay, maybe we should say something about grids first, okay, so if I am going to go from this grid to a really coarse grid, it has only one unknown, right, I am going to go with 3 interior points to 1 interior point, then I have to make sure that I have iterated enough on this, that there is no component of what I am going to transfer, the residue that I am going to transfer, which has a frequency higher than what this can represent, okay, if you go back, think back to the demo, otherwise what will happen is you will get what the signal or signal processing friends in electrical engineering call aliasing, basically that high frequency error will fold back into a low frequency end, am I making sense, and we will start getting a residue here which is spurious, which is not the right residue, okay, so if you talk to your friends who have done signal processing in electrical engineering and so on, they would call this process either decimation or down sampling, so if you are going to do decimation or down sampling, the first thing that you have to do is you have to remove the frequency content that you cannot represent on the coarse grid, if you cannot represent it, it will only show up as an error, it will only contaminate the residue that you have in the coarse grid, okay. So one possibility is you iterate enough number of times, so that all that high frequency error, that is right, right now that is what we have, all that high frequency error is eliminated on possibility, okay, we clearly have to come up with some other way to do this because remember I said there may be schemes that do not decay high frequencies, there may be schemes that do not decay high frequencies fast enough, right there are all sorts of issues, so but we have to decide, so you iterate enough number of times, you have to make sure that you have done it enough number of times, that you have only the frequency content in the residue that you are going to represent on the coarse grid, is that fine, otherwise anything that you transfer from the fine grid to coarse grid will show up in the wrong place, okay, right, okay, you show up in the wrong place in our frequency domain, that is if you look at it in terms of frequency, okay, right, so that is bad, that is not good, that is not what we want, fine. The second thing is, so this is, this we have to see is there something else that we can do here, right, what else do we have? You transfer from here, maybe we will stick with this, maybe I will finish with this first and then let me see, where can I write that, I have this, I am already at Rh, I will write it here, so just say you have a scheme, so before I get back to that, so let us just say, right, we will take an aside and look at this, let us just say you have a scheme that is not dissipating fast enough or, right, or you decide that you are going to iterate a fixed number of times or take time steps a fixed number of times, 5 times steps, 10 times steps, right, simply because you remember something I told you earlier when we are doing SOR, I basically said look, do not look, wait for it to converge to certain extent because you do not know how long it is going to take, you are committing unknown amount of CPU time, right, unknown number of iteration, always bound the amount of computation that you are willing to do, so you say 5 times, I am willing to iterate 5 times, but that why not eliminate all the high frequencies, but we know one operation that eliminates high frequency, we have seen it, when we did our, when we did our looking at high frequency, when we first encountered high frequencies decays faster than low frequency, that is what, that is either the heat operator or the Laplace operator, we have seen it, that is guaranteed, that really kills it, right, so if you have in two dimensions, if you have four grid points, you take the middle fellow and take the average as the average of the four, right, we have seen that, it is a solution to Laplace's equation, right, that sort of decays and it decays quite fast, I do not want, I mean I actually have a value here, right, so I do not want to just throw away what I have at that point, so instead what I will do is I will take the average of these two, average of these four, right, that gives me a central value, I already have a central value, I will take the average of those two, what do I mean by that, I have values a, b, c, d and at the center I have e, okay, this is what we would call Laplacian smoothing, what I would do is I would say a plus, right, that is the Laplace operator, we recognize that for an even grid, okay, that is like taking omega equals half in SWR, right, omega equals, does that work out half, omega equals what, 1.5, 0.5, we are not sure, 0.5, okay, I just throw with that, I am just throwing that out there to see, okay, fine, I am just painting you, okay, so what do we have, so this of course turns out, so the way this would, the way this would work out if you were to, so you can see the Laplace operator here, the way this would work out if you are going to actually apply it to R, so what are we going to apply it to, we are going to apply it to R, I have iterated a few times, I have decided say five times, I have iterated, I have iterated this equation five times, I have had enough doing iterations at that level, I compute the residual, I have no clue what is the, what is the spectrum, I have no clue what frequency is Rhs, all I want to do is I want to eliminate those high frequencies, okay, so what I am going to do is, I know this will do it, I know the Laplace operator will do it for me, so I am going, I am proposing to smooth R before I do the transfer, am I making sense, I am proposing to smooth R, this is called Laplace in smoothing, so you would write R at any grid point as, is that okay, if you work out that fraction that I had earlier, you will see it will be four times, so the R smoothed, the R smoothed would be basically that, okay, so you can do one sweep, you do not feel comfortable, do two sweeps, I guarantee those high frequencies will be gone, now transfer the smoothed R, okay, so now we are going to add a new, we will add a new step, now we have a new improved step that we have, so which is why I strategically left myself a gap here, okay, so smooth Rh, fine and then do a transfer, then do a transfer, is that fine, so at each level you can do that, at each level you can smooth Rh and then do a transfer, so this F2H now, this F2H is not going to have any content that it cannot write, that grid cannot represent and then as a consequence you can iterate this and again I would iterate it a few times, smooth, again so we will have smooth and do the transfer, okay, fine, so at every point when you are doing a transfer you smooth, you calculate, compute the residue, find R, that is how it goes, that is how it goes, okay, is that fine, everyone, okay, so this is as far as making sure that there is no contamination, there is no contamination when going from the fine grid to coarse grid, okay, so we need to do one more thing, we will look at, is that fine, okay, everyone, you can do smoothing, of course you can do, you can do a similar kind of smoothing on the way back, we will get to that, the next thing that we do is we want to look at this, what is this operation, what is this operation that we have, okay, so how are we going to do this average, I mean how are we going to do this transfer Rh to F2H, how do we do the actual transfer, I think I can remove this, I need it, I will come back, right, okay, but in order to see the transfer we are going to actually look at what are the kinds of, what kind of grids, what are these multiple grids that we are going to generate, we look at the, we look at how it would, there is an underlying structure, we look at that, okay, and then look at what is the transfer, how, what is the business of transfer, what are the ways by which you can transfer, so we will start at the courses level because that seems to be the, and see if we get a pattern, that seems to be the easiest, so the courses level is 1 grid point, interior grid point, 3 grid points on the whole, the next level is 5 grid points, is that right, what is the next finer level, 9, where do you think this is going, so it is going to be basically going as 2 power n plus 1, now you know why I did not want n iterations, 2 power, 2 power I have also used them, k plus 1, okay, is that fine, right, 2 power k plus 1, so k equals 1, k equals 2, k equals 3 and so on, fine, okay, so you could for instance, you could for instance if you wanted a fine grid, so you would not start with, I would not start with 1001 by 1001, right, because that is thinking decimal, I would start with 1,025, you know I would start with 1,025 grids, if I had a 2 dimensional problem it would be 1,025 by 1,025, whether I start with 1,025 grid and the next level of grids would be 513, you understand, and 257, now you understand why you need to go to multiple levels, this is 257 grid, this is still pretty fine, it is just that we want the answer on, 1 meter length, we want the answer on something that is at the order of 1 millimeter, okay, 1025 is close enough, okay, so then you would go to 129 and so on, and you can go all the way down to 3, right, if you want, so this is the number of levels that you can transfer, so this is h, that is 2h, 4h, 8h, we have tried, I mean I think we have gone up to like 7 levels or something like that, right, okay, so you look at this process, so now we know we can pick up grids like this, this is in 1d, what about 2d, we take the Cartesian product of it obviously, right, so that could be 3 by 3 grid, am I making sense, to that you can add maybe I will use a different colored chalk, oops, that is a 5 by 5 grid, am I making sense and we can go on, you can make it a 7 by 7 grid and so on, right, you can make it a 7 by 7 grid, maybe I will choose that, is that okay, get a 7 by 7, right, 9 by 9 grid, okay, I am back, 9 by 9 grid, sorry, thank you, 9 by 9 grid, doing suddenly 2n-1 instead of 2n-1, 9 by 9 grid, that is one way to do it, right, so I am constructing it up, the other thing is if you had a 9 by 9 grid, you can throw things away in what we call the checkerboard pattern or the chessboard pattern, okay. So you do not have to, you can for instance, you can start, you know, you can retain this grid point, retain that grid point, retain that grid point, retain that grid point, okay, then you can retain this one, retain this one, retain this one, am I making sense, oops, am I making sense, It is like the black and white squares of a chess board, is that okay. So there are obviously once you go to 3 dimensions, 2 dimensions they are in different ways. So this is called coarsening, there are different ways of doing of coarsening, okay, is that fine. So now what we want is, so we want, if you want to go from a coarse grid, if you want to go from a fine grid to a coarse grid, in the multi-grid, right, as I said signal processing, they would call, say you go through a down sampling or whatever, the multi-grid terminology that is called a restriction, you restrict, right, you restrict. So what you would basically do is, you would now, this is what I was talking about, how do I find that, I will write that here. So what are the ways by which we can do it, right. So one thing is, just pure simple injection as they call it. What you do is, you just throw away the points that you do not want, right. So if you have, okay, let us look at this, you have 5 grids and you want to go to 3 grids, you just throw this away, that is one way to do it, right. Another way to do it of course, a better way to do it, another way to do it, a little more expensive, we have looked at it in the last class, you take the average, okay, and a familiar average. The average would be, if this is p, p-1, p-1, the average would be, so we are going from, this is residue, remember, so rp-1-2rp-rp-1 divided by 4, would give you the value at that point. It looks very suspiciously like Laplacian, right, very suspiciously like Laplacian. These are all at h, this will be rp-at, rp-at, 2h, the value here would be twice this, plus each of those divided by 4, okay. What if you are doing in 2D, how would you do it in 2D, I am not going to do 3D because it is, I mean, you can work it out but it is a pain to draw the picture but I will do it in 2D, okay. So this would be a full, the best transfer and the most expensive transfer, most operations, you want to get that, you want to transfer the value at that point. So you have 1, 2, 3, 4, 5, 6, 7, 8, 8 of those, so what are we going to do now? 8 of those plus 8 of these, right, divided by 16, am I making sense? 1, 2, 3, 4, 5, 6, 7, 8, add up all of those plus 8 times the central fallout divided by 16, am I making sense? So the logic is now, you can see the where it is coming from. So that would be, that would be a, of course I mean you could in theory add more points to it, right, you could increase the support so to speak, you could add more points to it but this is itself, there is a certain expense but you are taking all the points that you are planning to throw away, you are taking data from all the points that you are planning to throw away, let us say idea here, right, if you are going to take this point, its neighbours are not going to be used, right. So in this case, if you are going to take this point, unless you are doing the checkerboard pattern, unless you are doing this pattern, if you are just doing the standard, right, the standard coarsening, this is called the standard coarsening, so if you are going to do only the standard coarsening, then you are going to throw away all the a neighboring point right. So this should be determined really by all the neighboring points. Am I making sense? So you would say summation what should I say? So L in the surrounding set L not equal to P simultaneously or L P not equal to I should write that a little more carefully, Lm so except for that, except for that 1 plus 8 times okay, is that fine? So this is how we do the, this is how we do the transfer, this is how we are going to do the transfer. So this will allow you, if you work it out for a grid for a, I would suggest that you start off with a one dimensional grid. You are not and you are never really going, this is only for the sake of our explaining the algorithm to ourselves. You are not going to really you know write this matrix but you can just for the fun of it to see what the structure looks right, try to write it out and see what it looks like okay. So you do the transfer okay, you do the transfer this way. Am I making sense? Is that fine? You do the transfer there are different ways by which you can do it, you can do the averaging depending on 1D, 2D or 3D right and you transfer it to the coarser grid. Maybe we will come back to this, I will leave that portion. What else do we have? So we have done the, we have done, we are now going through this whole process. How do we get back? How do we do this transfer? How does the reverse transfer take place? So I want to go from a coarse grid to a fine grid. So I have to interpolate. So now see there will be cases. So you have to look at the various cases. One case is the point is actually in this set okay. So typically the notation that you would write is, this is the grid, well this is the grid at 2H and that is the grid at H and 2H but it is okay. What you would basically, so if this belongs to the finer grid, just transfer the data directly. If it does not belong from the coarse grid, there is no candidate, take the average. 1D it is obvious. So go to 2D. In 2 dimensions, if this grid belongs to the fine grid, transfer it directly. If it does not belong but it happens to be, so in this case this is a funny mesh. Let me draw another mesh. Where can I draw it? I will draw it here. I need to erase something. I will erase this. I no longer need this. There we go okay. So what you have done is, this is the coarse grid. That is the coarse grid. I am doing standard coarsening. That is the coarse grid. So if it belongs to the same grid line, it is on the same grid line but does not belong to that mesh, take the average, same thing okay. So you can take, in order to find this, you can take the average of these 2. If it does not belong to the same grid line, so this works even here right. Even in the vertical direction it works. If it does not belong to the same grid, that is like this. It is a little more complicated. You take the average of the 4 okay. Is that fine? Right? So on this side, take the average this way. On that side, take the average that way. And in the center one, take the average of the 4. Have I missed anything? I think that covers all possibilities. Is that okay? That covers all possibilities. Right? So that is how you transfer from a coarse grid back to a fine grid. So the correction. That is how the correction would be transferred from a coarse grid back to a fine grid. Is that okay? So if you say that I want phi 2h to go to EH, this is what you would use. Fine? So now we come to the critical question. So we have got an algorithm. What we are able to do is we are, we have the solution presumably. We iterate a few times on the fine grid. Right? And we can transfer down residues to coarser and coarser grids. Transfer back corrections to finer and finer grids. We have these nuances, residual smoothing and so on. Do all of those kinds of things. Right? All that needs to be done. We have an algorithm. What does it cost us? Okay? What does it cost? On what grid do we want the solution? So back here, on what grid do we want the solution? We will pick a big problem. 1025. So maybe I would say 1025 by 1025 or 1025 by 1025. Okay? This is the grid on which we want the solution. Fine? So if you were to take either whatever equation you are solving, Laplace's equation for example is a good place and you are iterating, it would take a certain number of iterations to get a solution on the grid of size 1025. A solution that is to your satisfaction. Right? 5000 iterations. 5000 iterations, 1025 grid point. Am I making sense? Okay? So if you were to in between transfer the problem to a 513 grid point, grid, a mesh that has 513 points, then 2 iterations here is the same as 1 iteration there. Right? Remember when we are talking about one of the things that I said when you find out how fast is my computer program running, what was the, what did I ask you to do? I told you to find CPO time per grid point, per iteration or per time step. Okay? CPO time per grid point or per iteration or per time step. That gives you a measure of your program, what it is up to. So if you, right, I do not, why should averaging be more expensive just because I am on a course of grid? That does not make sense. Right? So I do not expect, right? Unless you do something really bad in your programming, I do not expect that the 513 by 513 CPO time per grid point per iteration will be more than this. So the work per grid point is the same. Okay? Work per grid point is the same. So now I want to get a measure, right? So I will say wait a minute, if you did not do multi-grid, you would be doing so much work, so much work on 1025 grids. So I will call one sweep or one time step or whatever scheme that you are using through this 1025, your finest grid, I will call that one work unit. Right? We will start off by defining what do I mean by this work. We will call that one work unit. Am I making sense? Sweeping through this, your finest grid, making one iteration or one time step, I will call that one work unit. So if I have one work unit here, two iterations here will correspond to one work unit or basically one iteration here would be one half work unit. One iteration here would be one fourth work unit. Right? And so on. One eighth work unit. Am I making sense? So it is better for me to be doing 8 iterations here in comparison to one iteration there. Okay? So I will show this process of going from course grid to fine grid in a graphical fashion. And this is a standard graphical fashion that people use in order to demonstrate multigrid method and because the picture evokes an image, I mean there is a letter. It gives it a name. So what you do is, this is at the level h. I go from h to 2h, 2h to 4h, 4h to 8h. It will go 4 level. Back to 4h, back to 2h, back to h. Okay? So this represents one cycle because of the way it looks. It is called a V cycle. And of course, you know it is called a V cycle because there is going to be another cycle. Right? A different cycle. What is a different cycle? I basically look at this and say wait a minute. You mean this takes one work unit and this takes only one eighth work unit? I want to spend a lot of time here. After all, I am always going to end there. So I want to spend more time here. So what you do is you go h, 2h, 4h, 8h, 4h. Now you have a choice. And go back to 8h, 4h. Yeah, I like that. I like that. Right? Fine. This is called a W cycle. And obviously, W cycles come in lots of flavors. Right? The minute you see, the minute you create the renovation, lots of things that you could go 8h, 4h, 2h, come down. Or you could go 8h, 4h, 2h, 4h, 2h, 4h, 8h. You know, you can see. I want to spend a lot of time down here. Right? Because it does not cost me anything. Right? As long as I come back and iterate a few times at 8h, because then I say, hey, residue has gone to 0 at 8h, I have got the solution. Am I making sense? Right? Okay. Are there any questions? The work units in one dimension go as 1, 1, 1, 1, 1, 1, 4, 1, 8. How about in 2d? It goes down faster. Right? So in 2d, so in one dimension, this is work units per sweeper, time step or iteration or whatever. 1 by 2 power k kind of a thing. Okay? Like 1 by 2d, 64. That is great. Now we know 3d is where we want to do this. Though I have not shown anything. 3d, so the savings are enormous. 1d you may not, you know, you do a toy problem just to learn how to do this. But you have to do at least 2d. Right? In order to say that wow, I have got something really great. So this is going to be 1 and that is going to be 8. Right? Am I making sense? 32, what is that going to be? 128, 64, 2 power, this is 2 power 2, 2 power 4, 2 power 6, 64. So this is going to give me 2 power 8, 256. The powers of 2 are worth 3k, 512. But you have to pick the right power of 2. They are not only worth knowing but you have to make sure you pick the right power of 2. No use knowing the powers of 2 if you pick the wrong power of 2. Okay, fine. Fine. I mean just look at this. You just go down, right? You just go down a few levels. This is nothing. I mean, so you do, you take 10 time steps on this. 512 time steps on that. That is like taking one time step on the finest grid or one iteration on the finest grid. Why would you not want to hang around there? Right? So if you are doing in 3D, if you are doing 1,025 by 1,025 by 1,025, it is a lot of effort. 1 billion, more than a billion. Right?  It is not that bad. It is really not that bad. Okay. As long as you make sure that you are always checking for your convergence at the, do not forget that. Okay. There is one last thing. You know, there is always a little wrinkle that we can throw in. So why start at a fine grid? Right? This is remember when we talked about initialization, we said, hey, one way to do it is start at a coarse grid and transfer. Yes, we can do it here. Right? So why start at a, so you basically say, why should it start there? Start here. Right? Start at 8H, transfer it to 4H. That is the way to do it. You understand what I am saying? You already have it. You already have it. So the critical thing is what is the, so this multigrid methods, okay, lot of people just do not get into multigrid. You do not see multigrid methods used as often as they should be. Okay. This is what, this is my observation. There are lot of research being done, lot of enthusiasts. If you want to go on the net, you can search for, you can just search for MG net. Enormous amount of resources, huge amount of resources. Right? The critical thing that you have to do to make sure that all of this works is something that you have to do anyway. So you have to make sure, you have to make sure first that you implement this. Right? If you do this, you are set. What are the things that we have here that are different from your standard solution? The standard solution is given a grid, take time steps. Right? Given a grid, take time steps or do iteration. So first of all, your program that you have, the program that you have has to be somehow changed. Right? So if you are talking about Laplace equation, if you have phi and you have a Laplace equation solver, right, that you are using right now, you just have a solver. Right? That says, so give me the boundary conditions whatever in some fashion and solve Laplace's equation. Right? What you need to do is you need to convert that into a function that can be called. So you convert it to a function get phi which takes the grid. It takes the grid or the grid level or whatever it is, which takes the grid level. Am I making sense? Right? Possibly an initial guess and all of that kind of stuff. I do not put everything else. It takes the grid. Right? And it should return to you, it should return for you the residue. Should do an iteration, come back and return a residue or do any iterations and come back and return a residue. Am I making sense? So your program that you have right now that solves Laplace's equation or whatever it is, it has to be changed. It has to become a function because you are now planning to put something piggyback on top of it to make it run faster. Right? So you are going to say do this on a 1025 by 1025 grid and it should come back one iteration and give you a residue or you should be able to say take 10 iterations. This is a little better. Take 10 iterations with this initial guess. Okay? So maybe I will make it a little more. With this initial guess at the level k, take 10 iterations. I am just making it up. Take 10 iterations. Okay? So now you have got this, you can just pass it. Right? And it takes 10 iterations and what it returns is the residue. You can then do, you need to have, what is the next thing that you need to have? You have to be able to do Laplace's smoothing to it. You have to smooth it. Right? So you have to have some smooth which takes a residue. Right? And returns a smooth residue. Am I making sense? Right? As to whether you actually implement it in this fraction, whether you actually have these functions, you will have to figure it out. But what I am saying is these are operations. They are atomic operations. You implement each one of these tests then make them make sure that they work. If you have got this then the rest of it is relatively easy. Then what is the other critical thing that you need? Transferring. You understand what I am saying? So you have to have something ih2 or 2 if you want whichever, I do not know what you call it. You know capital H. Let us make, let us say otherwise we will have too many 2 Hs. Okay. Right? Fine grid course grid. Or it takes R and gives back F, whichever way you want to do it. So this gives me R. This gives me R. This also gives me, this gives me an F. In fact if this is a generic function it will take 2 arguments. It will take the K because you need to know not K. It will take the K. Right? You need to know what level you are. As I said the actual implementation will vary. So you will need to know what level you are. You get the F. Then what? What else you need? You need the other way around. Fine to course. You need correction equals which will take you from fine to course to back to fine. Am I making sense? If you do this, this is the critical part. If you do this you are set. Right? But the idea is to implement this. Make sure that for any grid it works. Do not worry about where you are solving Euler equation, Navier-Stokes equation, Laplace equation. It does not matter. The minute you start worrying about water then that gets to be a problem. Okay. Is that fine? Okay. Right? So I guess that is what we have for multi-grid method. You can get a tremendous amount of speed up. We will see where it goes. Okay. Let us try it out.


My name is Kaylee, I am a 2017 graduate of AMBS and my heart is on fire for the future of the Church.


Here in Boston, security is increased at the airport and train stations, and the concern about college students studying abroad in Europe is way up. Boston University sponsors a number of study abroad programs, and BUTV reporter Natalie Robson has this live report about the reaction. Thanks, Elizabeth. We are live at Boston University near the study abroad office. Today, we spoke to official Colin Riley, who is our media relations official that said that all programs scheduled this summer for study abroad will resume as scheduled. Currently, there are no changes to the study abroad program going out of BU. Today, students spoke out. Boston University has study abroad programs in 30 cities across six continents. Almost half of these programs taking place in Europe. I actually had thought about studying in Belgium because I actually have a family from there, but now I think that it doesn't determine completely from studying abroad more the location is something I'm going to be more aware of choosing. Despite the violent terrorist outbreaks in Belgium, as well as in Paris last November, students are not letting this deter them from furthering their education overseas. It's more important to go to these countries and say that we're not going to let this stop us from learning and keeping our lives going. Three Quinnipiac students survived the attack on the Brussels airport. The girls were on spring break in Belgium during their study abroad program in Ireland. Although students don't plan on changing their decision to study abroad, they might consider changing the country they study in. Really have to be sure that where I go somewhere that's going to be safe and also not just for me but for my family to be totally okay with me being there and not have to be on their toes wondering if everything's going to be okay. BU students say the only thing you can do is be cautious. Be aware of your surroundings and be smart about where you go and just, you know, always be cognizant of where you are and who you're around and those kind of things. And if you ever feel unsafe, just go back to where you're staying and anything like that. U.S. travelers are being advised that there are now potential risks while traveling in Europe. Oftentimes these are areas where a lot of students study abroad. Live from Boston University, I'm Natalie Robson. Elizabeth, back to you.


From London, England, it's theCUBE! Covering KUPA Inspire 19, EMEA, brought to you by KUPA. Hey, welcome to theCUBE. Lisa Martin on the ground in London at KUPA Inspire 19. Can you hear all the buzz around me? You probably can hear it. It's electric. The keynote just ended and I'm very pleased to welcome, fresh from the keynote stage, we have Rachel Bossman, author and trust expert from Oxford University. Rachel, welcome to theCUBE. Thank you for having me. Your talk this morning about the intersection of trust and technology is so, to say it's interesting as an understatement, you had some great examples where you showed some technology brands that we all know. Yes. And have different relationships with Uber, Facebook and Amazon. And the way that you measure the audience is great. You know, clap the brand that you trust the most and it was so interesting because we expect these technology brands to, they should be preserving our information, but we've also seen recent history, some big examples of that trust being broken. Yeah, yeah. Talk to us about your perspectives. Well, so what I thought was interesting, what kind of unexpected for me was no one trust, no one clap for Facebook, no one person in the room. And this is really interesting to me because the point I was making is that trust is really, really contextual, right? So if I had said to people, do you trust on Facebook that you can find your friends from college? They probably would have clapped, but do I trust them with my data? No. And this distinction is so important because if you lose trust in one area as a company in a brand and it can take time, you lose that ability to interact with people. So our relationship and our trust relationship with brands is incredibly complicated, but I think particularly tech brands, what they're realizing is that how badly things go wrong when they're in a trust crisis. Talk to me about trust as a currency. You gave some great examples this morning where money is the currency for transactions, where trust is the currency of interactions. Yeah, well, I was trying to frame things, not because they sound nice, but how do you create a lens where people can really understand what is the value of this thing and what is the role that it plays? And I'm never gonna say money's not important, money is very important, but people can understand money, people value money, and I think that's because it has a physical, you can touch it, and it has an agreed value, right? Trust, I actually don't believe, can be measured. Trust is, what is it? Like it's something there, there's a connection between people. So you know when you have trust because you can interact with people. You know when you have trust because you can place their faith in them. You can share things about yourself and they'll share things back. So it's kind of this idea that think of it as a currency, think of it as something that you should really value, but that is incredibly fragile in any situation in any organization. How does a company like Koopa or an Amazon or a Facebook, how do they leverage trust and turn it into a valuable asset? Yeah, I mean, I don't like the idea that you sort of unlock trust. I think companies that really get it right are companies that think day in and day out around behaviors and culture. If you get behaviors and culture right, like the way people behave, whether they have empathy, whether they have integrity, whether you feel like you can depend on them, trust naturally flows from that. But the other thing that often you find with brands is they think of trust as like this reservoir, right? So like it's different from awareness and loyalty.  We've seen this with like Mattel, the toy brand. They launched a smart assistant for children called Aristotle. And within six months they had to pull it because people didn't trust what it was recording and watching in people's bedrooms. We were talking about Facebook and the cryptocurrency Libra or their new smart assistants. Like I wouldn't trust that. Amazon have introduced smart locks. I don't know if you've seen these. Well, you know, if you're not home, it's inconvenient for a very annoying package slip.  I trust Amazon to live my parcels. I don't trust them to give access to my home. So what we do with the trust and how we tap into that, it really depends on the risks that we're asking people to take. That's a great point that you bring about Amazon because you look at how they are infiltrating our lives in so many different ways. There's a lot of benefits to it, right, in terms of convenience. You said, I trust Amazon because I know when I order something it's going to arrive when they say it will. But when you said about trust being contextual, I said, do you trust that Amazon pays their taxes? I went, wow, I hadn't thought of it in that way. Would I want to trust them to come into my home to drop off a package? No. Yeah. But the, I don't know if I want to say infiltration into our lives is it's happening whether we like it or not. Yeah, well, I think Amazon is really interesting. First of all, because so often as consumers, and I'm guilty, we let convenience trump trust. So we talk about trust, but you know what, like, I don't really trust that Uber driver, but I really want to get somewhere, I'll get in the car, right? I don't really trust the ethics of Amazon as a company or like what they're doing in the world, but I like the convenience. I predict that Amazon is actually going to go through a major trust crisis. Really? Yeah. The reason why is because their trust is largely, I talked about capability and character. Yes. Amazon's trust is really built around capability. The capability of their performance centres, like how efficient they are. Character wobbles, right? Like does Bezos have integrity?  And when you have a brand and the trust is purely built around capability and the character piece is missing, it's quite a precarious place to be. I saw a tweet that you tweeted recently. The difference between capability and character and it was fascinating because you mentioned some big examples of Boeing. Yes. The two big air disasters in the last year, Facebook obviously, the security breach. We work this overly aggressive business model and you said these companies are placing, maybe the blame is not sure if that's the right word, on product or service capabilities and you say it really is character. Can you talk to our audience about the difference and why character is so important? It's so interesting. So you know sometimes you post things. I actually, I post more on LinkedIn, I have more of it. But, and suddenly you hit a nerve, right? Because it's, I don't know, it's something you're summarizing that many people are feeling. And so the point of that was like, if you look at Boeing, Theranos was another example. Yes. We work hundreds of banks. When something goes wrong, they say it was a flaw in the product. It was a flaw in the system. It's a capability problem. And I don't think that's the case because the root cause of capability problems come from character and culture. And so capability is really about the competence and reliability of someone or a product or service. Character's how someone behaves. Character gets to their intentions and motives. Character gets to, did they know about it and not tell us? Even BW is another example. Yes. It's not the product that is the issue. And I think we as consumers and citizens and customers where many companies get it wrong in a trust crisis is they talk about the product fix. We won't forgive them or we won't stop giving them our trust again until we really believe something's changed about their character. I'm not sure anything has changed with Facebook's culture and character which is why they're struggling with every move that they take. Even though their intentions might be good, that's not how people in the world are viewing them. Do you think for taking Boeing as an example?  And when the accidents happen, I'm sure everybody including myself was checking what plane is this. Because when you know, especially once data starts being revealed, that demonstrated pilots, test pilots were clearly saying something isn't right here. Why do you think a company like Boeing isn't coming out and addressing that head on from a integrity perspective? Do you think that could go a long way in helping their brand reputation? I never, I mean, I do get it. I'm married to a lawyer. So I understand legal gets involved, governance gets involved. So it's like, you know, let's not disclose that. Like it's, they're so worried about the implications but it's this belief they can keep things hidden. It's a continual pattern, right? And that they try to show empathy but really it comes across as some weird kind of sympathy. They don't really show humility. And so when the CEO sits there, I have to believe he feels the pain of the human consequence of what happened. But more importantly, I have to believe it will never happen again. And again, it's not necessarily, do I trust the products Boeing creates? It's, do I trust the people? Like, do I trust the decisions that they're making? And so it's really interesting to watch companies, Samsung, right? You can recover from a product crisis with the phones. Yes. And they kind of go away. But it's much harder to recover from what Boeing is a perfect example is become a cultural crisis. Right, right. Talk to us about the evolution of trust. You talked about these three waves. Yes. Tell our audience about that and what the third wave is and why we're in it, benefits and also things to be aware of. Yes. I didn't really talk about this today because, you know, it's all about inspiration. But so just to give you a sense, the three, the way I think about trust is three chapters of human history. So the first one is called local trust. We're running around villages and communities. I knew you. I knew your sister.  And it was largely based on reputation. So I borrowed money from someone I knew. I went to the baker. Now, this type of trust, it was, it was actually phenomenally effective, but we couldn't scale it. So when we started to want to trade globally the industrial revolution, moving to cities, we invented what I call institutional trust. And that's everything from financial systems to insurance products, all these mechanisms that allow trust to flow on a different level. Now, what's happening today is not those two things are going away and they're not important. They are. It's that what technology inherently does, particularly networks, marketplace and platforms, is it takes this trust that used to be very hierarchical and linear. We used to look up to the CEO. We used to look up to the expert and it distributes it around networks and platforms. So you can see that at Cooper, right? And this is amazing because it can unlock value. It can create marketplaces. It can change the way we share, connect, collaborate. But I think what's happened is that sort of the idealism around this and the empowerment is slightly tinged in a healthy way, realizing a lot can go wrong. So distributed trust doesn't necessarily mean distributed responsibility. My biggest insight from observing many of these communities is that we like the idea of empowerment. We like the idea of collaboration and we like the idea of control. But when things go wrong, they need a center. Does that make sense? Absolutely, yes. A lot of the mess that we're seeing in the world today is actually caused by distributed trust. So when I read a piece of information that isn't from a trusted source and I make a decision to vote for someone, just an example. And so we're trying to figure out what is the role of the institution in this distributed world? And that's why I think things have got incredibly messy. Certainly it has the potential for that, right? Looking at one of the things that I also saw that you were talking about, I think it was in one of your TED talks was reputation capital. You said, you believe that will be more powerful than credit history in the 21st century. How can people like you and I get, I want to say control over our reputation when we're doing so many transactions digitally. I know. I think you were saying in one of your talks, moving from one country to another and your credit history doesn't follow you. How can somebody really control their trust capital and create positive power from it? They can't. They can't. Oh, no. I mean, I don't want to disappoint you, but there's always like something in a TED speech that you wish you could take out like 10 years later and be like, not that you got it wrong, but that there's a naivety, right? So it is working in some senses. So what is really hard is like, if I have a reputation on Airbnb, I have a reputation on Amazon, on either side of the marketplace, I feel like I own that, right? That's my value. And I should be able to aggregate that and use that to get a loan or get a better insurance, because it's a predictor of how I behave in the future. So I don't believe credit scores are a good predictor of behavior. That is very hard to do because the marketplaces, they believe they own the data and they have no incentive to share the reputation. So believe me, like so many companies after, actually it was wonderful after that TED talk, like many tried to figure out how to aggregate reputation. Where I have seen it play out as an idea, and this is really very rewarding, is many entrepreneurs have taken the idea and gone to emerging markets or situations where people have no credit history. So, Tullar is a really good example, which is a lending company. Insurance companies are starting to look at this.  Everyone has a reputation somewhere so they can tap into these networks and use that to have access to things that were previously inaccessible. So that's the application. I'm more excited about versus having a trust score. A trust score that we would be able to then use for our own advantages, whether it's getting a job, getting a loan. Yeah, and then unfortunately what also happened was China, and God forbid that I in any way inspired this decision, decided they would have a national trust score. So they would take what you were buying online and what you were saying online, all these thousands of interactions and that the government would create a trust score that would really impact your life, the schools that your children could go to and there's a blacklist and, you know, if you jaywalk, your face is projected and your score goes down. This is like an episode of Black Mirror, so. It's terrifying. Yeah. There's a fine line there. Rachel, I wish we had more time because we could keep going on and on and on, but I want to thank you for coming right from the keynote stage to our side. And that dog was not due. And that dog was not due. Yes. Yes. For Rachel Botsman, I'm Lisa Martin. You're watching theCUBE from Coupa Inspire London 19. Thanks for watching.


Can everybody see it? I'm Paul. I'm going to talk about polymorphism 101. We promise to have a 101 session for every talk. And I just used Sunkist style to use terminal presentation. So first, that's polymorphism is that we have kind of interface so that we could reuse the copyright. Saying that we want to replicate something with just integer, then we just replicate a number three times. It's in dot pass. And so replicating all of them will give us three elements, right? But if I want to reuse this function, then it would be better to pass in anything and replace the same thing for three times. So how to make it into polymorphic? Like saying that we want to pass in anything beside integer, we could just specify a type variable for any character you use. And with that, I could define a replica of polymorphism and for that, then I want to replicate true for three times, replicate poly for three times, or replicate 1.0 for three times. That could be anything you want to pass in by still integer will work, right? So specifying a parameter as a type variable, that will make the function polymorphic directly. So because with type variable, that means it will serve as a placeholder for type information. So that means without any constraint, we don't know about what you are going to put in. So for the implementation itself, it also assumes nothing about it because it's pretty straightforward, just calling itself and pre-pending the element to the head of the list. So with this information, we don't need the object, any information about the object itself, right? Because we just put something we don't know yet to the head of the list, OK? And the AC both could be anything. You could want to make an emoticon like that. That would also work, as you want to add some constraint for the object you pass it in. And with this, I'm going to introduce a concept called type class. But I'm going to just introduce how to use it without presenting how to define it. That would be next one-on-one session. So with print function, that means we want the thing passing in to be printable on the screen. That means the object could be encoded into a string. And the string itself could be put into the console. So we show which is defined in the prelude. So that means we construct the A passing with this parameter to be showable. That show would have its building definition of how to convert an object into a string. And with that string, we could print it out to the screen like passing with 3.14159 as double. Then with double, that is building inside the previews. So we could know that is printable in the print. So besides show, there are a few of type class that means constraint here to use. If I want to implement a function that's checking if the element exists in a list, like I'm passing an element, which is here, the E element, and passing another list, I want to return true for the element exists in the list and false without the element in the list. So it's pretty straightforward to define a recursive definition without any element and just return false. And with pattern matching, add just the head of the list and comparing the head with the element passing. If it's equal, then return true. Otherwise, return false. But with that, there's a presumption here is that the A have to be comparable to be equal or not. So we add an EQ, means equation for A. That means the A element passing, we have to work on an equal operator on that. Without that, we can't just assume there's an equal operator in them here. So with that, we return true because one is in the list right, otherwise, then it's false. So with these two examples, you could also constraint the element passing by type parameter. So this is for the function implementation, especially for pure function. But with the data structure, you define that you could also use type parameter. Here's A that in the previous one line session, we know how to define a recursive data algebraic type right. With this, it's either a now or the rest of this element. So this is our user defined list. It's not built inside the compiler. The A could be anything. So this is a polymorphic list. Then with the left implementation, then I'm just adding one for each of the elements using type parameter. One side bounding to accounts, then adding one and calculate the rest of the list. This is implementation also not related to the element itself, because I'm just calculating how many elements inside. I have no information about the element itself, but I have information about the list. So this define. And I could change it to other stuff like flow double or then evolve into anything about the element in the patient. So A could be anything. And we didn't add any constraint on that. So yeah. So here, basically, it's the definition. And so beside specifying type parameter in the signature, the one thing special to Haskell is that we have higher order thing. That's sort of you can specify the information on the underlying structure that, say, we have a higher order function called map. That's just changing the underlying structure's elements. So with given list, which is structure, then I could transfer it into another list. But without any information about the A, and later on in the later of the talk, I would also say that the list could also be changed with the higher order structure defined. So map means that just given a function, then it could work on the element type A. And with that fx applied, then the output of the function will be type B. Reconstruct the list again to be the transformed list of type B. So with this define, and I could just say I want to check if the list is odd, then it will transform the list into the result of whether it's an odd number or not. It's true and false and true. With the A, it's defined as 1, 2, 3. Any questions so far? A bit harder for that is phone. That's something just mentioned about the phone on one side. That phone is reduced in list or Ruby. That given a list of that binary operator, that you like, squash it into the result. That with 1, 2, 3, and plus, then we just sign up the list. And there's two versions. One is make the operator map associative. That means just apply the function first. If you draw into the abstracting texture, that means apply the parenthesis to the left side first, then to the next one. So with this recursive define, then we could just fold everything with that. So fold the associated. And start an initial value with 0, then I could get the sum of 6. And another version is make the phone right associative. Because the false is a higher order concept that we could use it for redefine the end of the function we previously defined. The right is basically the same as left associated. If you draw into an abstracting texture, it's just you have a parenthesis for the right-hand side first, then keep going until the left end. So you could see that you could just use, you recursive apply to the function itself, then call the function passing at the outer most. So with that structure, that means we skew to the end of the list, then getting forward, then finally get our result. And with these two functions define that higher order concept, we could use that function to redefine any. So with fold out, it's the building definition for a phone left associated. And with that, with any, then we just passing a function, which is the result so far and the current element. We want to order it's a shortcut override. So with the current result, and comparing it to the current element, whether they are equal. If they are equal, then means the element exists in the list. And start with the false. So any one of them comparing equal, then the whole list will be true. Otherwise, keep going, then it will be false. So it's the same implementation. But I could reuse the concept, the folding concept, that it could, in my opinion, is also kind of polymorphism. Because I could use it with type class to foldable. It's built in the premium library. That means the container with a folding defined. I can't strength. It's a metaphor, not exact metaphor, but it's easier for comprehension. It's no longer a list here, right? It's the, comparing to the, here is an list, right? But here I specify a T. And the T, I also kind of strain, adding a constraint to let it to be foldable. And with the T defined, as well as the structure or the container dosing passing, define the fold function, then you could reuse this function. With this defined, I could still reuse any fold one. Because the list is half a fold, already defining the standard library. So that's somehow generalized any to another level. And I didn't define here, I promise, for animated. For map, you could also use map specifying it's a spunker T with the same definition, so far. Funker means that you could, sorry, Funker means the structure is have a map defined on it. Then with this, it's also defined, with the existing list, it's already defined the standard library. But this, I didn't define it. But with that specifying that, you could also make the map we use for any container have a map defined. So that's all. It's not too complicated for, especially for foldable. Is it OK? Like foldable means you specify a constraint that you could squash the structure into a binary operator into one final value. Yeah, but because they involve the type class, I would rather to leave it for the next session. Yeah, it's a trade-off that if I involve too much, it's too much that puts, like, involve too much to involve type class. So I only teach how to use it without defining. Because with that, you have to define either a folder or a folder map or folder on the underlying container. It's right. It depends on the strictness of the emulation, that there are a few versions of fold, that there are a strict version of fold l, and which would apply this function first before expanding the structure. And for this version, it's like, without evaluating this function and expanding the whole list to the end. It had to be called pyramid. Yeah. I could just derive the folder before our customers. Like, full managed, we don't have it. But could we just derive it? Not pretty sure. Is there an answer to that? Could we define foldable for a user because they define an algebraic? I think yes, yeah. They could just try. There's an extension for that. Should I add something? I would just do it. I would just do that. Derive foldable. Yeah, yeah. Derive. Set, but you load the source file, or you copy and paste a bit. You didn't load the source file. Because it's just CI, it's another session. OK, you could say that. .task, or whatever. What you can do is call on set minus x, derive foldable, that would work in general. Call on set, set, set. And then you can skip arbitrary, derive, fold. Just be socializing. I don't know beyond having anything that maybe we could move to the hawker center if we wanted to take this place down. Yeah, this is just someone out there with the tables. But we do need to go around a lot. Yeah. I've got a plan. Put your tables back in and go to the box. I'll be right back. I'll see you in a couple of minutes. OK. OK. I'll be right back. Put yourself in my pocket. I'll be right back. Do you still have to look at that? What would be your priority? What would be your editor? Because eventually, I'll have some time to talk about the behind the sign. Yeah. Yeah. Right? No. It's working. Let's see if you can figure out how to turn that on. It's nice to be loud. Yeah.


When the narcissist realizes life isn't good without you Narcissists are very arrogant and entitled They feel entitled to your time energy money and resources But then when they've used up everything you have to offer Or when they think they can do better They ghost you They discard you And the cycle starts again with a new victim, but narcissists have poor judgment And they often make bad decisions So sometimes the narcissist will realize that life isn't good without you It depends on how good of a supply you were for the narcissist And it also depends on what type of narcissist you were dealing with If you were their primary or secondary source Their life will not be good without you, but it's not because they love you It's not because they care about you They saw you as an object that existed solely to meet their needs They didn't see you as someone who has an independent existence from them So when you leave, they feel like they have lost something They feel like something has been taken away from them Something that was useful and beneficial So they're not going to let you go so easily They will hoove you They will love bomb you Or they will become threatening and intimidating towards you But if they were the ones to discard you They won't see it as though life isn't good without you They only discard something if it's garbage If something is wrong with it If it's useless to them If they think you're against them They don't want you So they get rid of you But they might just be a threat But they might just place you on the shelf of future use They might have a purpose for you in the future But when they do that They don't think life isn't good without you If they did think that they wouldn't have placed you on the shelf But if you are the one that got away There is a possibility that their life isn't good without you The power is in the person who discards the narcissist But that's only if the narcissist notices If you were already on the shelf when you escaped They may not have noticed It may take them some time to realize that you're gone, but when they do notice Their life will not be good Especially if they try to hover you and you reject them Narcissists hate rejection It's a blow to their ego It makes them feel unimportant Does the narcissist ever realize that life isn't good without you? It really depends on the type of narcissist that you're dealing with Narcissists that have low intelligence and self-awareness Will not think life isn't good without you They will just get very angry Especially if you reject the Hoover attempts, but they're not thinking life isn't good without you They will just see you as someone who is very offensive Someone who has betrayed them Someone who is deceptive They will believe that you deserve to be punished They may make threats They may become violent But some narcissists will just see it as though you've made a mistake You're missing out and then they will find someone else very quickly Because in their minds They are the best thing since likes bread and They have plenty of other options They won't think life isn't good without you They won't think they did anything wrong They won't regret their decision They will either move on to new supply Or if they don't have any suitable replacements They will just be really mad at you They will see it as though you have betrayed them But narcissists who have a lot of options May be surprised to see you leave Because for them it's very unusual But they're not going to see it as though life isn't good without you They will just move on to one of their many other options They won't feel like they have lost anything Because they have plenty of other options to choose from So they will find someone else to replace you But narcissists who do have some level of intelligence and self-awareness Will feel like life isn't good without you Especially if you resist their Hoover attempts They will feel sorry for themselves They will play the victim They will feel like it's unfair They will feel like you abandoned them And then they will get very angry But after some time They will reflect on their exaggerated sense of their own abilities and importance And then they will find someone else So while they may initially feel like life isn't good without you It won't last for a very long time Unless they're a self-righteous narcissist Because they think they're good people They may even think they're empaths And they will be surprised that you have left them They will be surprised that you don't want to be with them Because in their minds they did a lot for you They expect you to see it as a privilege to be around them So their life will be miserable without you And they will feel sorry for themselves They will play the victim So that they can gain attention from other people And still get narcissistic supply But they will really believe that life isn't good without you They will feel like the world is against them They will feel like nothing ever goes right for them And they will be very upset But it's not about you They don't really care about you It's just how it pertains to them It's about how it makes them feel Narcissists only care about themselves They're self-absorbed that they lack empathy Even when it may seem like they're upset and they miss you It's still all about them Thank you for watching I hope this video wears in it with you Please like, comment, share and subscribe If you would like to donate My PayPal link is in a video description Coaching inquiries You can email me at coach.narcisfiver.uk Thank you for watching and I'll talk to you soon


In my new book, The Great Spiritual Migration, I suggest that many people in my religion are driving down the highway with a gun in their glove compartment and a license to kill. That license is the Bible, interpreted and applied uncritically. Something similarly scary is going on in many other religions. That's why we need a new generation of interpreters who will disarm our sacred texts and interpret them with a bias or peace.