This 10th year of Daily Tech News show is made possible by you the listener. We cannot do this without you Thanks to every single one of you including Ali Sanjabi, Andrew Bradley, and Dale Mulcahy Coming up on DTNS, tech needs data centers and data centers use energy Is there a way out of that expanding spiral? Mollywood tells us plus haptics for VR that don't get in the way of your hands and our phones Finally just the commodity like a camera or laptop Yes This is the Daily Tech News for Thursday April 27th, 2023 in Los Angeles. I'm Tom Merritt and from studio red But I'm Sarah Lane deep in the heart of Texas. I'm Justin Robert. Yeah, and from Oakland, California I'm mollywood and I'm the show's producer Roger check my friends We have assembled the most wonderful panel you will get in technology probably all month certainly today And we're here to celebrate the fact that Microsoft announced its mice keyboards and webcams will no longer be Microsoft branded But surface branded instead Or I will never stop crying. No, no, I know we'll try to get through the rest of the quick hits Amazon has killed again One of its product lines the company has stopped selling its three health tracker halo products That's the view the band and the rise and that's it for the halo division as well Support for halo devices including cloud services will end on July 31st and all remaining data will be deleted Anybody who bought a halo device in the last 12 months can get a full refund and unused prepaid subscription fees will be refunded as well Some good news out of meta's quarterly earnings if you're meta Facebook averaged 2.04 billion daily active users in March and that is up from 2 billion last quarter And when you throw an Instagram and what's that they reached 3.02 billion daily active users up 5% Tick-tock imitator reels is starting to have an effect on time spent on Instagram that grew 24% That's enough for the good news revenue for meta's reality labs fell 51% on the year But CEO Mark Zuckerberg says that's expected they plan to lose money on it for a long time In other meta news the US Court of Appeals for the District Court of Columbia ruled in meta's favor letting stand a lower Court decision that meta did not violate antitrust law with its acquisition of Instagram in 2012 or what's up in 2014 well Samsung is having a little bit of a rough go its profit fell to its lowest point since 2009 that's down 95% on the year revenue fell 18% on the year and so Samsung said it will reduce memory Production however like TSMC it still is Expects a limited recovery in chip demand in the second half of the year on the bright side the galaxy s23 led a resurgent mobile division Which reported business rose 22% Remind us to check in on that second half chip recovery in autumn sometimes if you would folks. Thanks Monday Google launched cloud syncing for Google authenticator. This is similar to what athi provides You can you can store them securely in the cloud Well, mostly securely Tuesday security researchers at misc concluded that the sync was encrypted in transit and at rest But not end-to-end meaning that potentially somebody at Google's endpoint could see your two FA codes Now if you trust Google to safeguard its end and not misuse its own access fine but many security conscious people don't trust anybody so Offering end-to-end encryption would mean that they wouldn't be having to worry about that on the other hand Average users might lock themselves out of their authenticator In fact sophisticated users might lock themselves out of their authenticator And not be able to get their codes back because they're the only ones with the key Google says it will offer end-to-end encryption pretty much when it figures that part out down the line in compliance with the European Digital Services Act Apple disclosed that the iOS app store has 101 million users in Europe and iPad OS has 23 million the Mac app store has six million and the TV OS app store has One million the watch OS app store has somewhere under one million hat-tip to i-generation Which spotted the disclosure first the numbers were based on an average taken over six months ending in January and show that Apple books and Podcasts paid subscriptions are being used by less than one million people in Europe per month. All right Who's are the quick hits? Let's talk phones. Let's do it So IDC reports that smartphone sales fell 1.6 percent on the year not a ton But it also is the seventh straight quarter that smartphone sales have fallen year over year IDC's research director said The industry is going through a period of inventory clearing and adjustment adding that IDC thinks that the sector will recover by the end Of this year, but will it people are using phones for a lot longer than they may be used to Phone designs are less variable less important to customers than they used to be Might sound familiar sounds like what we've been saying about laptops and tablets in the past So Molly let's start with you. Do we feel like the smartphone is becoming more of a commodity? I Hope so I sincerely do like simply from a sustainability perspective It makes no sense for people to discard perfectly good phones year over year And I understand that there are plenty of recycling options But still these are great devices that you can hold on for two for a long time And yes, it is not very exciting to get a new phone anymore. You might have like us another little camera Blob on the back and you don't really know why or what that has and then you transfer over your Stuff from the last phone and then all of a sudden the new phone looks exactly like the old one I also would not discount the ability to have Apple replace your battery now and some of the new repair ability Things that have come into play that actually make these devices last longer and that's a win across the board. I think Well, I think that part of it is we've seen such incremental change in not only the hardware But also the software and a lot of the top tier phones that normally would drive this kind of replacement Factor in also that we had this gigantic pandemic Crunch in terms of chips and so there were just less phones available or people were not buying them at the same kind of Pace that they were buying other things that they would use for a home office At the same speed the one thing that I would say that I can see being a killer feature in the way that we thought of killer features Through the tens really driving phone sales would be something that would be specifically chipset powered that would allow you to do AI Stuff on the phone. I think that that is a huge revolution that will probably come for this But until then yeah, I do think that these are commodities. Yeah, and that's fine I used to replace my laptop every 18 months. Don't thank goodness. I don't need to do that anymore laptops last a long time and yeah every once in a while you get an Apple Silicon you get an M series Chip that makes you go Hmm I might want to swap my laptop out a little earlier because that seems pretty amazing and when we can definitely have that with phones Like you're talking about Justin and I think we will But it is something where this story was up near the top of tech meme today And I'm like I don't know that this is really a story other than we've arrived We've arrived at that point where like yes, smartphone sales are not going to like go crazy The bigger story to me would be if you saw a significant change It's still Samsung at the top then Apple then Xiaomi Oppo and Vivo what you know that starts to significantly change Then there's something interesting the way it would be interesting if suddenly a brand new laptop maker was dominating laptop sales It'd be marginally interesting Also, I would be very I'm sorry Sarah. Go ahead. No, please I was just gonna say I would be very curious to see who would be willing to give up the data in order to Allow on device AI processing nobody Well, there's a lot of device AI processing happening I mean, yeah, I mean there is but like in terms of needing a chipset big enough to be doing like AI level or chat GPT level I would think that they want the two-way data share there not to derail us. No, no, no I do agree with you I think that I don't think that on device fully on device AI is something that we are going to see in the near-term future especially as we have become hooked on The AI that we have seen now which it requires a lot of computing power But something that makes the process more streamlined and easier to ping a server somewhere I could see it I and I certainly said whether or not the technology is ready. We are going to be sold phones with AI Being a marketing ploy starting five. We already are that it's just been on cameras for now It's gonna it's gonna expand off of the camera stuff It's also gonna expand on to the commercials It's going to be a thing that you will be so what's on the commercials now, but they don't use AI which that's it are going to do Yeah, they say The photos are better. They don't say AI AI something GPT large language. That's going to be a thing I mean, we've joked about the coming CES for which every toaster Yeah, for sure I do think that there will always be things that the larger machines can do in the cloud better than you can do on Device, but I have noticed that a lot of new features make a point of marketing themselves as on device By the way, this is on device. We're not sending things to the cloud So I don't know Molly I think there is a little pressure that's causing them to want to do things on device More often than they used to I think also and you know, I mean I used to do an iOS Specific show so I was getting a new iPhone because that's that's my My mobile phone of choice every year, but that was basically a business expense I wouldn't have done it otherwise if it was just coming out of my own pocket, but even then until the last I'd say three years. It was you know, there's a new size You know or the camera significantly different or the OS itself is doing stuff that you know It apples really really you know pushing the envelope here I don't feel that way and again Maybe it's just because now we have so many choices with I'm not just talking about iOS But just using iPhones as an example There is no like the iPhone comes in lots of sizes now and it has for a while And if you have the one that you like and you haven't cracked the screen and maybe you got Apple care and your batteries doing okay Why would you upgrade? I mean you can upgrade to new software, but until yeah, it's like this foldable phone can fly I'm gonna keep my iPhone 13 for the foreseeable future. I don't want that to fly. I wanted to stay with me Like it's a what if it's a jet pack Okay foldable jet pack iPhone 27 I'm in yeah until then I'm not buying it. I'm not not now when Well, let's look towards the future VR has been the future of technology for at least 30 years And we have another advancement for it haptic feedback is important for VR applications You want to be able to feel the virtual objects? But that usually means you have to hold something or maybe you can strap something around your hand But that gets in the way right? You can't actually grab things with your hands if you got a big strap around them Scientists at the University of Chicago's human computer integration lab have demonstrated a way to give you haptic feedback in VR Without needing anything on the front of your hand So your hand can be free to do whatever you need to do in the virtual world You know sometimes you might have an actual prop like a golf club if you're playing mini golf or something like that Their devices attach electrodes to the wrist and the back of the hand and the back of the fingers And then sends a modulated electric signal through the hand from the back to the front That ends up giving the feeling of a tactile sensation at 11 points on the front of your hand Even though the signals begin on the back because the front of your hand has around 60 times as many receptors as the back And they were able to calibrate this to come from not only the right spots But at the right intensity that your brain doesn't notice the stuff in the back But localizes the sensation to the front and in fact when they tested this about 90% of the touch Sensations were felt in the front as intended it can let you feel things like the touch of a button the shape of an object and One demo showed a user molding actual clay so the haptics weren't getting in the way of the clay and They were wrapping it around a virtual teddy bear In virtual reality Justin is this just cool science? Which it is or is there a significant change this could make for VR? Significant it would probably be the word that I would debate I Would say it's an important step forward for not only VR But also any kind of immersive element of technology. I would say that haptic technology is something that is probably a very very invisible but impressive technological march forward, and I'm thinking specifically about AirPods and Apple watch and and iPhones There's a lot of stuff that's done that makes things seem like they are physical or tactile buttons when in reality It's just very very clever haptic feedback in terms of VR Obviously, I think the biggest Impediment there is just processing and getting the field of vision that you were seeing through to be something that you feel to be immersive without making you throw up but Having applications that don't require you kind of pointing and clicking like a mouse Would would certainly help for things to be more immersive Yeah, and let you grab they should one where they had an actual rope and they were doing a virtual rock climb Because you could actually grab the rope it didn't you didn't have the haptics getting in the way And then you could have virtual handholds and do a virtual rock Depends on what you're doing What your brain is telling you that you are in a place that you are not right that you are buying into things that are That are functionally not your reality. This does make things go faster But I would see this in the same way to be very very beneficial in AR to be very beneficial in Just wearing them as gloves so you yeah and interact with other Elements right right now.  So it's not exactly convenient But though, you know, it's in the also doesn't answer the sort of fundamental question. Does it make you want to wear this on your face? Like we just keep coming back to that all the technology related to it Gets cooler and cooler. But do you want to wear it on your face yet? Because I'm still kind of in that That really depends on the this right if the this is is the glasses that you're wearing right now You're already there right if the this is a gigantic box that hurts your neck I mean, I and I feel like I'm sort of in the opposite end of the camp like Tom said I I'm very into VR because I like exercise games and I don't know how I would play those Well, I could play a version of the game, you know with my controllers in a TV, of course But it wouldn't be the same. I'm used to it. So I'm like, it's fine now in 10 years I'm gonna laugh at this I'm gonna laugh at exactly this moment and be like remember when I used to wear that thing on my face and say it's fine Because that's the only thing I knew how to do. Yeah, you know The idea of playing golf without kind of something in my hand that feels club like even if it's just a controller I'm like, do I want that even if it maybe sort of feels like a club? Like I I like the idea of touching things that go beep and boop Even playing Tetris, you know, it's like I don't know that I want to do that with my hands But once I am able to I might change my tune as if you could grab the block and just pull it down Okay, that'd be fun. I could be fun. Hey folks quick reminder tomorrow We are closing our 2023 survey so we can start compiling the results So if you haven't done it already and it's not past Friday, April 28th Please fill out our latest survey. Just visit daily tech news show comm slash survey A lot of people note that data centers use a lot of energy they do but then does it all industry use a lot Of energy banks use a lot of energy factories use a lot of energy So I've always felt that it's probably more complicated than just pointing at the energy and saying bad But it's also true that as we build more technology and tech gets more pervasive in more people's hands used by more people Tech is using more energy than tech used to is it contributing to more energy use overall? Well, Molly just wrote a column on this at mollywood.co and you brought up the Jevons paradox is that how you say that? Jevons, okay, I was Exactly the Jevons paradox But that that kind of sums up the idea here. Well, what what what is the Jevons paradox? Yeah, I mean first I do want to say that globally Data centers specifically account for anywhere from one to one and a half percent of all energy demand on the planet and it's closer to three percent of the EU's energy use so That specifically there are other industries that do a lot of emitting and whatever but data centers alone just as a class Do in fact consume a lot of it or not consume. I guess energy can't be Created or destroyed and there are literally people Will correct you but they use a bunch the Jevons paradox is very interesting It is the idea and it's been a big sort of pillar of environmental economists and environmental Economics, it's the idea that the more efficient Electricity gets the more efficient or resources the more you consume so a really good example of this actually is LED lights Like everyone got super excited about LED lights because they are way way way more energy efficient than fluorescent light bulbs and Then that led to us putting up strings of LED lights everywhere and getting a whole bunch more for outside And then putting like a light bulb over here and 50 million more like putting way more lighting Installations in our houses and so that you could argue that we basically made up for all of the energy efficiency by Adding a bergillian LED lights everywhere. I've got a personal example on this I got a heat pump right suddenly the same air conditioning cost me less. I Had to really fight to resist the urge to be like well, I could let the air conditioner run a little more I'm using less energy, right because right that's what you do Exactly. It's more efficient. Yeah, and so it comes up a lot in the column I talked about how I was watching a guy on CNBC Justifying not even justify just saying like yeah, I'm buying a ton of oil and natural gas stocks because We're moving so much more to the cloud and more and more technology whether we all get a new iPhone every year or not We've all got one or you know six per person And and the more technology we use the more energy we consume meaning we're not going to be able to keep up with renewable energy Resources, yeah, so that was going to be my question is do we get to a place where we Generate enough energy from sources that are less polluting or even non polluting as some companies promise will happen in the foreseeable future Or do we increase efficiency of cloud services hardware or is it a combination of both? It's pretty much all of that. Yeah, it's more and more deployment of renewable energy, which you're starting to see be a bigger deal the inflation reduction act that just came out actually all of the major pieces of legislation that have been passed the Not including although there's even a little bit in the COVID relief bill but the chips act the infrastructure bill and the inflation reduction act all Collectively include something like two trillion dollars of incentives for clean energy rollout and for climate-related R&D, so The big challenge is deploying it in a way that keeps up with energy demand And there are lots and lots of startups actually working on I mean certainly like Google and Microsoft have a very vested interest in Making their data and Amazon anybody who has a bunch of data centers and making them more efficient I would argue those companies actually have done a pretty good job And then we're starting to see all kinds of new technologies come out to try to you know improve the efficiency of air cooling and So that it uses less water and less energy But yes, it's a both. It's a solid everything Yeah, because it seems to me that the problem isn't the energy usage If we make the data centers more efficient, we'll just build more data We just talked about that with the Javits paradox What you want is sustainable energy that that is not going to make things worse in other ways And that you've got plenty of Which is why the heat pump situation for me to go back to that was interesting because I have solar panels So I was trying to keep the extra use of of my efficient heat pump under the amount of energy My solar panels generate because then it didn't raise my cost and that that feels like a very small analog to what we're trying to figure out But it's it's sort of exactly the right analog and then I think the question becomes I think fundamentally It sort of becomes it needs to be part of the conversation every time So I wrote about it in the context of AI which is massively energy energy intensive, right? It takes a lot of energy to train a large language model specifically, right? There are lots of kinds of AI and then when we're talking about large language models specifically they need a lot more training and they Consume energy every time they generate a response like somebody Effectively did the math and determine that every time I asked chat GPT some dumb question It is the equivalent of like charging my iPhone six times over and then happen to know somebody who works at our goal who said that Those numbers are probably way worse than internally. They know it and so it so I tried to sort of point out that We did this with cryptocurrency and Bitcoin Which is massively energy consuming to produce and then you saw the aetherium network switch to a much less energy intensive technology But we just ran headlong into it and now we're running sort of headlong into AI in the same way And we need to have that conversation at the same time like are we okay? With propagating a technology that's only going to get more energy hungry And especially is there any stopping it because if we stop AI there'll be another use Maybe it's technology. Maybe it's not but but that's where I go back to the Jeven's thing is like Humans are hard to keep from using stuff So it's like we it feels to me like we really need to focus on coming up with those sustainable sources Yeah, absolutely. It's all about it's all about energy transition. I would just like to point everybody to Mali series how we survive because I do think that the key to all of this is Understanding that innovation tends to run wild looking at innovation and saying stop it Will often be a very very futile thing and I think we're seeing that right now with AI the solution is to figure out how to innovate alongside of these things and and Create solutions that that actually integrate into it as opposed to just pointing at it saying shame now Yeah, yeah, there's a lot of possibilities, right? There's there's way generation Sea cooling not saying any of those are a silver bullet, but we can try the better chance We have a hitting on one that really works You can have rules, right? Like you can have rules without saying stop So you can say if you are a data center training in large language model You are required to have a mix of energy use that is primarily mobile energy, right? You have to have a plan you can't just like do it and then try to fix it later So I do think there's a I like that. This is like the Texas Oakland Conversation, you don't have to stop it No, you can have rules for your rollout before the rollout has gotten away And that's a thing and understanding and being aware of the actual tools that you have to do it is is a key part of it before you know As we understand that the world around us being realistic is I think an incredibly important part Especially if you are focused on issues like green energy Well speaking of energy and power NASA's Voyager 2 If you haven't thought about it in a while, maybe it's because it's 12 billion miles away from Earth It also takes 22 hours for signals to reach the probe that comes from NASA It's been doing this a while Voyager 1 and Voyager 2 launched in 1977 and Voyager 2's power has been gradually fading over time So mission planners had planned to shut down one of its pretty key five scientific instruments next year until now NASA's Jet Propulsion Lab announced in a press release that the probe got a little adjustment That redirects a tiny amount of power meant for an onboard safety system to keep all five Scientific instruments aboard the probe active until 2026 No, there's some risk to doing this because the system was originally protecting the Voyager 2 from voltage Irregularities so that could be an issue, but NASA says we're gonna give it a try Yeah, it kind of feels like the time for that of like well Let's not protect it from voltage irregularities when it's about to just run out of power Anyway, might as well use that see if we can squeeze a couple more years out. I love it Yeah, I just really want to say voltage irregularities a lot of times Can I throw that into the title ring because that's amazing. I feel like I have I have them right exactly Hold on guys. I'm having a voltage irregularities. I have like senior moment voltage irregularities. Sorry regularities. I did not say that, right? It sounds like a forgotten hair metal band Yeah, it might actually be I'm not gonna bet against that So many levels. All right, let's check out the mailbag Let's do it Martin wrote in and said I wanted a voice that in the ad study which was discussed We talked about it two days ago Tom mentioned that people who had pre-existing knowledge about say coffee We're able to use that to make a more informed decision when buying something that was being served as an ad Martin says I think I speak for most of the DAT Nest crew that we have family and friends ask us about technology all the time I always get asked if the new Mac or PC or gadget is worth purchasing or replacing for existing tech because they don't want to make their decision only on what that company is marketing to them ads work Especially if people are tired and don't get help when they don't know otherwise just my five cents Ah, thanks for the extra three cents Martin. Appreciate that. No kidding. No, it's true though I I I I can't tell you how many times I know we've all been there somebody says well, this looks pretty great But what do you think Sarah expert that I know? Hey, can you look at my DNS records and make sure that they're accurate because I'm trying to get That's what Molly sent me earlier today Yeah, that's just double-checking It's a short list of people you can get send that screenshot to so the next time you get like I don't know some Instagram ad for like DNS brownies Back in stock you can be like nah Tom said there wasn't a thing worth that money Were these made at a hundred seven twenty seven dot zero dot zero dot one Anonymous who works in tech also wrote in reaction to our discussion of people over fifty who game to say I'm happy to say I'm fifty nine and my favorite games at the moment are God of War Ragnarok Which are three and dishonored so one of the twelve percent who are not doing the puzzle games. Thank you anonymous Also, thank you to you Molly wood for being with us today Excited for all that new stuff. You've got cook and let folks know where they can keep up Thank you. You can find it all at mollywood.co. That's where you can subscribe to my newsletter and keep tabs on the forthcoming Podcast it's coming. There's a podcast coming soon. Yeah Also, thanks to you Justin Robert young also a busy bee these days let folks know where to keep up with you Buzzing around the internet Sarah world's greatest con is The all four of our scripted episodes are out right now So if you want the full story of project alpha two teenagers in the late 70s pose as psychics and in turn bring down The vast majority of all parapsychology research Please go ahead and listen to that on all podcast platforms We have two more episodes coming out an interview with the two boys now men and then a Q&A episode after that But we're very very proud of it So please go ahead and listen to it as part of the dog and pony show family as well as know a little more Oh, yeah merit. I got we had a we're not wrong live show on Monday many people many people are saying It is the number one show that you should be listening to Please go ahead and check that out know a little more as well Well, we're glad to have you both on the show today Many many things also a special thanks to D laser D laser is one of our top lifetime supporters for D TNS And we see you. Thank you for all the years of support D laser a big virtual hugs for D laser You're the best D laser is a patron and if you are a patron stick around for the extended show good day internet We're going to talk about a sperm injecting robot that can be controlled using a PlayStation controller Now if you can resist hearing the rest of that story good on you. 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Mediation analysis is useful because it allows us to study mechanisms. In this video I'll talk about the modern approach to mediation analysis called causal medias. If you come from regression analysis or structural mechanism model in background, the literature and causal mediation analysis might be a bit difficult to understand because the terminology is a bit different. Instead of building on any particular statistical model, this literature builds on the counterfactual model for causality. This little glossary from this guidelines article for medical researchers is useful to have at hand when you start reading about causal mediation the first time. Let's go to the axon mediation model. The first approach to mediation that we're usually taught on research methods course is this product of coefficients or Marian and kidney approach. The idea is that we have two models, we have model for Y as a function of X and M and then we have model for M as a function of X. We can have some controls too, but this is just the simplest possible case. And then we learn that the mediation effect is the product of two coefficients. So it's this path beta M1 multiplied by this path beta Y2 and that gives you the mediation effect. Another thing that we learn is that there are two kinds of mediation. There is full mediation and there's partial mediation. If this direct effect from X to Y is zero after controlling for M, we have full mediation. If it's non zero we have partial mediation. Of course this linear model can be extended by for example adding a correlation between these two error terms which would make it an instrumental variable model for mediation. This approach and the linear models have a couple of important limitations. The problems are first that this approach is applicable to only a few special cases of non linear models. So for example if this model for mediator is logistic recursion model, the product of coefficients wouldn't really apply. The product would not make any sense in that case and in some cases the product might make sense but the result that it gives would still be incorrect. The second problem is that this model assumes no interaction between beta M1 and beta Y2. The idea here is that there is causal heterogeneity. The effect of X to M is not the same for all people. The effect of M to Y from M to Y is not the same for all people. And if these variations in these two effects correlate, then this model no longer holds. The third problem is that this is not really a definition for mediation. So mediation is a causal concept and defining mediation in terms of a particular statistical model would be problematic because we might want to think about mediation in broader terms as well. Let's talk about each of these three problems in turn. The non linear mediation model, one example could be something like that. So we have an exponential function for Y and this might be for example Poisson recursion analysis. Let's see how it works. So we take the equation for the mediator and we plug it in in place of M and that's what we get. So we have exponential function for Y and then the equation for M is there inside the exponential. We play around the equation a bit and we get that kind of war. So we simply multiply out and remove the parenthesis and we can see that this is still a pretty nice exponential model. We can actually interpret the product of coefficients in terms of exponential model coefficient. So we multiply them together and that is interpreted as a relative change in outcome. Why does it work? It works because the effects are interchangeable. So we multiply two coefficients together and the product, they are interchangeable in the way that they both contribute to the product the same way. They are also interchangeable in a way that if we multiply one by two, we can divide the other by two and the outcome will be the same. So because these coefficients work the same way in the equation, we can multiply them together and that gives us a sensible interface. Let's take another example. So this is an only one again, but we have an exponential model for mediator like Poisson-Ricoson analysis for mediator and let's try to do the same. So we have the equation for Y, we take the equation for M, we plug it in place of M in the equation for Y, we get that kind of equation, we try to multiply to remove the parenthesis and we get that kind of monstrosity here. In this case, the product of coefficients does not work. The reason is that these coefficients don't work the same way, they're not interchangeable anymore. So beta M1 and beta Y2 work differently because beta M1 is exponentiated, beta Y2 is not. The model also is some kind of weird combination of additive model, so we add beta 0 and beta Y1 together and then we multiply these coefficients together. So it will be very difficult to interpret that model. So this is the nonlinear problem. Then we have the second problem, no interaction assumption. And let's take a look at what that means. Ima and his co-authors use this table to demonstrate the no interaction assumption. They show that there is a positive causal effect of the treatment of the mediator and there is positive causal effect of the mediator on the outcome but still it's possible that the mediator effect is negative. How can that be? Let's take a look at this table piece by piece. So we have first two potential outcomes. So this builds on the counterfactional model for causality. And we have potential outcomes means that we could assign an individual into treatment or control but not both. So there are two potential outcomes out of which only one is realized. The causal effect is the difference between these two outcomes. So we have the outcome for these individuals. If there is the treatment for some, mediator is positive for some, it's zero. And then we have the outcome for the control cases and for some it's positive, for some it's zero. Then the causal effect is the difference between these two potential outcomes and we can see that we have causal heterogeneity here. So for the first part of the population the effect is positive. For this part it is negative. And then for these two other parts there is no causal effect. So we normally can't estimate these individual causal effects. The best thing that we can do is to estimate the average treatment effect which is shown here. So it is simply the average of the individual effects weighted by the population fraction.  That's the average treatment effect. Then we have these two other columns and these show the scenario where the mediator is manipulated. So if the mediator is 1 versus the mediator is 0. So this is the outcome for mediator treatment. So what is the value of y when mediator is set to 1 and then we have the mediator control when mediator is set to 0. What is the value of y for the different fractions of the population. And again we can see that we have a causal heterogeneity in these mediator effects but the average treatment effect is 0.2 calculated the same way minus 1 times 0.3 plus 1 times 0.3. That's 0 minus 1 times 0.1 plus 1 times 0.3. That is 0.2. So we have 0.2 is the causal effect if we manipulate the treatment and if we manipulate the mediator the causal effects are 0.2 in both cases. So how is it possible that the mediator effect is 0.2? Let's take a look at this table. So we have here positive average treatment effects for mediator and for treatment and then we have negative average treatment effect. How can that be? The reason is that if we calculate the mediator effect we are not looking at these averages but instead we are looking at the individuals. And for this part of the population and this part of the population the treatment has no effect on the mediator. So there is no mediation effect we can just ignore those.  Let's take another look at this example to really understand what is going on. And this is a simulated population of 10 subjects which corresponds to the table shown on the previous slide. And this is the mediation model. So we have T2M, M2Y and then product. We can see that the first three subjects are the mediation effect the product of these two coefficients is 1 then we have 3 0s, 1 or minus 1s, 3 0s, 1, 3 0s and the average is minus 0.2. How is that possible? So let's do a bit of math. So we have beta M1, beta Y2 and then the product of coefficients. And the product of coefficients approach works when the expected product of coefficients is the product of the expectations. So normally when we calculate the product of coefficients we calculate this beta M1 which is an estimate of the average treatment effect it's not individual treatment effect then we have beta Y2 which is an estimate of the average treatment effect again and we multiply them together. So we do this kind of right this multiplication here we multiply two average treatment effects together but we should really be looking at the average or the expectation of the individual treatment effect instead. So when does this equation hold? If we Google product of expected value of product of the random variables we learn that this holds when these two effects beta M1 and beta Y2 are independent. A bit more Googling tells us that the expectation of product is the product of expectations plus the covariance of these two X and Y. So this X and Y are these two betas here. And if we calculate the covariance between beta M1 and beta Y2 the individual causal effects we can do that in R. And that's the covariance we pluck the covariance here it is minus 24 plus 0.2 times 0.2 gives us minus 2. So we can apply math to come to the same conclusion and here we need to multiply by 9 and divide by 10 because we are working with the population covariance instead of our sample covariance which we normally calculate. So the no interaction assumption means that these two causal effects should be uncorrelated. So this is the second problem and what's the third problem? The third problem is that causality or mediation is really a causal concept and not a statistical concept tied to a particular model. So what will happen if we define mediation as a product of two coefficients? So let's define that mediation effect is product of two coefficients where beta M1 and beta Y2 come from linear model. If we define mediation this way then these two examples that we just went through wouldn't be mediation but this is something that we would consider as mediation. So most researchers would say that yes this is a mediation model because M is affected by X and then M affects Y. So there's a chain of causality same here. So if we define mediation in terms of linear model it's incompatible of how researchers actually think about medias. So this is the mediation as a product of coefficients. And then the next question is how should we actually define mediation? So if the product of coefficients does not really work as a definition what should be the definition of medias? Let's take a look at the causal mediation literature. This article by Nyen in Psychological Methods talks about the definition of mediation effect and how we can actually define the mediation effect using counterfactuals in a few different ways. And they start with an important distinction. So we have three things. We need to first define what is a mediation effect. This is the first problem. The second problem is identification. So what kind of assumptions are needed for us or what kind of research designs, what kind of data are needed, are required to make a causal claim about mediation. So this is the causal identification problem. And then we have estimation problem. And these are three distinct things. So we have the definition, then we have resources and assumptions. And this is just the mechanics.  And I'll talk about the definition of mediation from now on. I'll talk about estimation and identification in other videos. So how do we define a causal mediation effect? IMAI has written a really nice paper. It's a bit technical, but it's a classic paper in 2010 in Psychological Methods on how do we define mediator and mediation. And they consider four cases that we have. So we have four combinations of treatment and mediator. So we have these four cases. We have treatment, an individual received a treatment, and their mediator was observed after the treatment. Then we have individuals who did not receive the treatment, and their mediation was observed under the condition of no treatment. So we mark this as y1, m1, y0, m0 to indicate no treatment, and mediator was not affected by treatment. Then we also have two counterfactual conditions that we can think of. So we have this counterfactual, where this individual received the treatment, but their mediator is as if they would not have received the treatment. And then we have this fourth case, individuals who did not receive the treatment, but mediator is as if they had received the treatment. We have, of course, no way of ever observing these two outcomes, and that is a statistical problem, an estimation problem, but it's not really a problem for definition of mediation. So let's regroup these outcomes, these four cases a bit, to see what Imai's definition of mediation is. So we regroup them a bit, and we can see that the individual causal mediation effect is the difference between two outcomes. So for in Imai's paper it's defined this way. So for the treated cases, the mediation effect is the difference between the observed case and the counterfactual case, where the mediator would not have been affected by the treatment. For the controlled cases that did not receive the treatment, the mediator effect on the individual level would be calculated by setting the mediator to the treatment condition, but holding the individual still in the untreated group. And this equation shows it. So the mediation effect is the difference between whatever was observed for the treatment compared to whatever was observed in the treatment and had the mediator been observed in the opposite treatment condition. So it is the difference between the observed case and the counterfactual case, where either the mediator would have been affected by the treatment for the untreated cases, or the mediator had not affected by the treatment for the treated cases. And there are a few nuances on this. This article by Sally gives a more accessible explanation. So they write that the natural direct effect is how much the outcome would change if the treatment was exogenous set to 0 or 1 for each individual, but the mediator was kept at the level it would have been taken. So this is natural direct effect. And the natural indirect effect or the mediator effect is the same thing except that we manipulate the mediator counterfactual instead of the outcome. One important word in this is the natural. And this is something, these natural effects are contrasted to controlled effects. The controlled effects in this causal mediation literature refer to effects that you would get from studies where you manipulate the treatment and you also manipulate the mediator. But natural effects are much more common and they refer to scenarios where the treatment is allowed to naturally affect the mediator without the mediator being manipulated by the researcher. So most of the time when we talk about mediation effect, we refer to the natural mediation effect or natural indirect effect and the natural direct effect. To make things a bit more complicated, Nydang here explains that there are actually a couple of different ways that this mediator can be, these mediation effects can be thought about. So they think about three words. And one word is where the individual is assigned to the treatment and their mediator is naturally observed after the treatment, sorry the control, so the assigned to control, the mediator is observed under the control condition and then the other condition that we can observe is the individual would be assigned to the treatment and the mediator is observed under the treatment. And then we have this in between world where individual is assigned to treatment but their mediator is not affected by the treatment. And they show that this contrast, the difference between these two outcomes is the natural direct effect. So this is the natural direct effect if we manipulate the treatment but we fix the mediator to be the non-treated value. And this is the natural indirect effect where we have the fixed treatment at one and then we manipulate, allow the mediator to get its natural value instead of being fixed to the untreated case. But this is not the only way. We could also have this contrast here. So we could have this contrast where we start by not manipulating the treat but we manipulate the mediator. And this is a non-trivial issue. How do we choose the comparison point? So let's take a look at the numerical example then. So we have five subjects here. We have the effect mediator under treatment, mediator under control, T0, mediator under treatment. We have the natural, untreated, non-mediation, treated, mediation. And then we have these counterfactuals that we can never observe. And these are calculated based on this simple model of exponential effect on Y and linear model of T on the mediator. The question now is which counterfactual do we use when we start to decompose the total effect? So the total effect is simply the difference between the outcomes of not having a treatment and mediator under control and having been treated and the mediator affected by the treatment. So this is the total effect, the difference between these two potential outcomes. So do we use this manipulate treatment first, mediator then, or this manipulate mediator first treatment then outcome? So which counterfactual do we apply? This is a non-trivial question because the difference is going to be quite big. So this is called the direct indirect decomposition in UN's article. So we can see that we manipulate the treatment first, the dot shows the manipulation treatment, the mediator is fixed to the untreated scenario and the average is going to be 7.2, so that's the average treatment effect. Then the average natural indirect effect through the mediator when we fix the treatment to be 1 and we manipulate the mediator, that's the dot here would be 73. So it's the difference between 85 and 11.1. If we use the other counterfactual, then we get slightly different results. So we manipulate the mediator first, we get the natural indirect effect would be 27.2 and the natural direct effect would be 53.8. And quite often we want to know compare the magnitude of these two effects. So how large share of the effect is mediated. Here when we make a comparison 73.7 is about 10 times as large as 7.3. So we would based on this first decomposition, we would say that the mediation effect is 10 times as strong as the direct effect. But in the second comparison we would show that the actually there are natural indirect effect, the effect of the mediator is 27.2, the natural direct effect is 53.8, so it's actually the mediator effect is just half of the direct effect. So is the mediator effect 10 times stronger than the direct effect or is it half of the direct effect? That's a 24 difference. So how do we really reconcile it? The new newspaper talks about how to make this choice, but my take on this is that there's actually a better way of approaching this. The idea of thinking about this as absolute difference is not ideal. The reason is that we have an exponential model here. And interpreting exponentials in terms of absolute differences is not as useful as interpreting exponentials as relative differences. If we calculate relative effects, then the NDE natural direct effect is 2.7. So the outcome increases by 2.7 and the natural indirect effect is 7.4. The outcome increases by 7.4 and now the order doesn't matter. So if we calculate the ratios of these two effects, they are going to be the same in both cases. So NUENG's article gives guidance on which counterpart to apply. My take is that if you really have a non-linear model in the outcome, which would produce different effects for the natural indirect and direct effect depending on the decomposition, it's better to interpret the model as non-linear instead of looking at absolute differences. So in this video I talked about the definition of causality. So what is the causal effect to the mediator? And I went through the counterfactual definition of causal mediation effect. Now this is a lot more complicated than Baron Kenny. And can we say that the Baron Kenny is outdated because of availability of this more rigorous definition of causality? The answer is yes and no. In the sense that the yes answer is that the Baron Kenny product of coefficients probably should not be used as a definition of what is medias. But as we'll see in my video about estimation of these effects the Baron Kenny product of coefficients is still a useful estimation technique. So how do we define an effect? How do we identify an effect? And how do we estimate an effect? Are three different things. And as an estimation technique this is still completely valid.


Welcome to Toffy TV. It is the Everton News Daily. There is a new name in the frame for the Everton job. That man is Fabio Canavaro, the ex-Italian captain, the man who lifted the Whale Cup for Italy in 2006. Currently managing in China. According to Jason Bates of the Telegraph, he was not only interviewed today, but he interviewed well, spoke good English, and maybe on the shortlist now with Wayne Rooney and Frank Lampard for the Everton job. It's a very, very strange saying of events. The report in Italy that it's between him and Wayne Rooney. This one has come from absolute left field. If we thought Roberto Martinis was a strange one, then Fabio Canavaro was even stranger. Someone who's not really been on the radar of European clubs and has not been on the radar for certainly Premier League clubs. Now it seems that Everton could be going after him. Listen in terms of a player, fantastic player, speaks good English, got good connections around the world. Very unproven as a manager, but I suppose he was Duncan Ferguson and so was Wayne Rooney and so was Frank Lampard. So we'll have to wait and see on this one. Everton are trying to get this, trying to get the job done filled very quickly as quickly as they can. They don't seem to be taking any time. Obviously we know Duncan Ferguson is in charge on Saturday and spoken today in an interview. Well, listening to him makes me feel 10 foot tall so I don't know what he does to the players, but Canavaro, can Everton fans really see that? Does this seem like more folly from the Yone again? Not really looking at it from a sensible point of view. It just seems to me a very, very strange one for the position Everton fan themselves in. An unproven manager who's got no real track record or has no track record in the Premier League either and has no real track record in one of the top five leagues either. So a very, very strange one for me this, but this story which came, you know, only came out a few hours ago is really, really gone on really fast today to the point where it seems like he's being spoken to. And he's now on the shortlist. That's according to Jason Bair from the Telegraph who seems to have the inside track on this. So a very, very strange one, but listen, it's, I think, you know, there are other managers still in the mix and Frank Lampard and the fact that Frank Lampard doesn't have a club and that he has managed in the Premier League seems to be an attractive one to go for. Wayne Rooney, doing a good job at Darby, would seem to be more of a one maybe for the summer. And there's other names being mentioned that obviously Duncan Ferguson with him being in charge at the moment, but yeah, very, very strange one. Very, very, loved them as a player. Fantastic player. Absolutely loved them as a player. We'll have to wait and see. Listen, it's not out the realms of possibility. It's not out the realms of possibility that he would end up the Everton manager with the track record we have of picking managers. There you go. We'll wait and see how that unfolds. Today, the ESSG launched to get a fan, ultimately get a fan on the board. It will have a group, like a shadow board in place by the end of the season to ultimately have a fan on the board. There is an independent steering group with different people from different backgrounds being part of it, from the many different supporters, clubs and groups and the fans forum. And ultimately they will have a group in place, a shadow board to try and get someone in place for the end of the season to get someone on to the board at Everton Football Club. I've done a video with jazz ball from the fans forum to tell you all about this. It's a little bit complicated, but ultimately it's to get a fan on the board. The video is available now to watch. You'll get a better understanding. This is the first process basically of getting a group together, which will create a shadow board. One of those members will end up on the Everton board. That's what we want. That's the process. It's a little bit convoluted. It takes a little bit of explaining, but ultimately the group is there to get a fan on the board. So if you want to find out more about that, check out our video and check them out on the socials so you can understand a little bit more. But as I say, ultimately this is a group to set out to get a fan on the board, which I think is what a lot of people want. So make sure you watch that video to find out more about that. And the only other news is that Yeri Miina has been picked by Columbia to go to their Whale Cook qualifiers against Peru and Argentina. There's two games. The good news is the second game is played on the Tuesday night going into the Wednesday. So hopefully he should be back by the Thursday ahead of the game against Brimford on the Saturday. So it's not the best news in the world that he's going, but hopefully they'll take care of him a little bit more than they did last time. So yeah, it's not good news because he's only just come back from India. He hasn't played a full game since he played last time for Columbia. So not good news at all. So there you go. So there's news coming out all the time. Make sure you stay tuned to our social media sites at Toffy TV, EFC for any breaking news. I'll be back tomorrow for the Everton Daily Extra show live. And we'll talk about all the news going on at Everton and who's in place for the manager job. Also reacting to Duncan Faggs and Press Conference ahead of the game against Aston Villa. So join me then. Make sure you give this video a like. Subscribe if you haven't already. If you want more great videos join us over on Patreon where we do daily live videos. Thank you for watching. See you later.


The statement of cash flows is one of four primary financial statements. Of the four financial statements, the income statement, statement of stockholders' equity and the statement of cash flows are prepared for a period of time, like a month or a year. For example, these financial statements would be dated for the month-ended December 31st, 2015, or for the year-ended December 31st, 2015. And that difference would let investors and creditors know if the information was for one month or one year. The balance sheet, you recall, is for a point in time, so it tells investors and creditors about the financial position of a company on a specific date. The primary purpose of the statement of cash flows are these four items shown here. Let's look at each one in a little more detail. One of the purposes of the statement of cash flows is to predict future cash flows. Past cash receipts and payments are reasonably good predictors of future cash flows. Another purpose of the statement of cash flows is to explain the change in the cash account balance from the beginning of the period to the end. Comparable balance sheets show us the change in cash, but the statement of cash flows tells us why the cash balance changed. Another purpose of the statement of cash flows is to help investors and creditors determine a company's ability to pay dividends and interest payments. And finally, another purpose of the statement of cash flows is to explain the relationship between a cruel accounting net income and cash flows. Although high net income usually equates to strong cash flows, this is not always true. The history of business is littered with companies that went bankrupt while having record sales. So having strong cash flows is a positive signal of the financial strength of a company.


When thinking about sound signals, especially when used in music, we tend to think only of frequency, or pitch, and amplitude, or how loud it is. However, there is a third property of a sine wave that can be changed, and that is its phase. To demonstrate what phase is, let's take a sine wave. We've already seen how we can change its frequency and its amplitude. We can also pause a little before playing the last note. We've delayed the last note in the scale, shifted it a little in time, or to put it another way, we've changed its phase. Now, we can obviously hear the difference when we started to play the note. But once the note is playing, it sounds exactly the same as it did when I played the scale before without the delay. This is because our ears are much less sensitive to changes in phase than they are to changes in amplitude or frequency. So why is phase important? Let's take a sine wave with a frequency of 440 Hz. That's to note A above middle C on the piano. Now I'm going to take another sine wave with a frequency of 660 Hz. That's roughly the note E above the A we had before. But instead of playing the A and the E together, I'm going to play the E a little after the A, shifted in time slightly. Now I'm going to add them together. This is the way that I get. You can hear the two frequencies playing. However, if I start to change the phase of the second wave, look what happens to the shape of the wave when we add them together. They still sound the same, but the shape of the signal has changed. Therefore, if we are to accurately represent this signal as a series of sine waves like a Fourier series does, then the phase information of each wave is important too as it has an effect on the overall shape of the signal. So how do we present this shift in phase mathematically? Let's take two sine waves. We'll draw our first wave in blue and it has a phase of zero. The other will draw in red, but shift it by 30 degrees. Now hang on a second. We've just been talking about changing the phase of a signal by shifting it in time. How comes we're suddenly talking about angles? Well, a memo of Fourier said about signals in general. He said any function of a variable can be expanded in a series of sines of multiples of the variable. Our variable, or in other words, the thing that goes on the x-axis, is time, as we are talking about sound signals. However, when Fourier came up with his theory, he was measuring heat flow, so his variable may well have been distance. Therefore, we need some common variable that can apply to all types of signals. When talking about sine waves, angles are the common variable. This variable can then be scaled to apply to whatever signal we are dealing with. So in our example, if we have a sound wave with a frequency of 660 hertz, it means that the air around our ears is being compressed and expanded again at a rate of 660 times per second. This means that the time it takes for one compression expansion cycle is one 660th of a second. It takes 360 degrees to complete one cycle of a sine wave. That's one complete rotation of the line within the circle. Therefore, we can map the time it takes for one cycle of our sound signal onto the 360 degrees of a circle. So if we want to phase shift our signal by 30 degrees, 30 degrees is a 12th of 360 degrees, one cycle of the sine wave. So for our 660 hertz signal, which takes one 660th of a second to complete one cycle, a 12th of one 660th of a second is 0.00126 seconds. So to convert from the angular variable of a sine wave to the time variable of our signal, we divide the angle by the 360 degrees in a circle and multiply by the period of our signal. In this case, one 660th of a second. But remember that multiplying by the period of a signal is the same as dividing by its frequency. After all, what is frequency? It's the number of signal cycles per second. 660 hertz means 660 complete sine wave cycles per second. What if we wanted to go the other way and convert from the time variable of our signal to the angular variable of a sine wave? In this case, we divide by the period of our signal and multiply by 360 degrees. Alternatively, because this time we divided by the period, we could just simply multiply by the frequency instead. So to convert from time to angle, we multiply by the frequency and then by 360 degrees. So back to our question. How do we represent a phase shift of 30 degrees mathematically? Well, the key to answering our question is to notice that the second sine wave is lagging the first by 30 degrees. If at an angle of 30 degrees, the amplitude of the blue sine wave is 0.5. The red sine wave won't reach 0.5 for another 30 degrees when its angle is 60 degrees. Therefore, the equation for the red sine wave is sine of the angle, let's call it x, minus 30 degrees. Or to put it another way, the amplitude of the red sine wave's current angle is the same as what the amplitude of the blue sine wave's angle was 30 degrees ago. What about if we shift the red wave the other way so that the red wave now leads the blue by 30 degrees? Well, not surprisingly, the red wave's equation now becomes sine x plus 30 degrees. Now it just so happens that if we shift the sine wave by 90 degrees, we get a wave that can be described by another trigonometric function, the cosine function. So sine x plus 90 degrees is equal to cosine of x. The sine and cosine functions come in very useful when dealing with right angle triangles. If we take the sine of this angle and multiply it by the length of the hypotenuse, we can calculate the height of the triangle. If we take the cosine of this angle and multiply it by the length of the hypotenuse, we can calculate the width of the triangle. But we've just seen how a cosine function is simply a sine function shifted by 90 degrees. And that the sine of the angle allows us to calculate the height of the triangle. Look what happens if we rotate the triangle through 90 degrees. What used to be the width of the triangle has now become its height. So the sine of any angle, let's call it x plus 90 degrees gives us the cosine of that angle. So now we have two ways of looking at a sine and cosine function. Either as a wave whose phase we can change or as a triangle whose angle we can change. But why is this important? Why bother with the cosine function at all if all it is is a sine function shifted along the x-axis by 90 degrees? To answer this, we need a map. I'm standing at point A on my map and I want to get to point B which is behind me over there. Now there are two possible routes I could take. I could take the shortest route and go straight there or I could go the scenic route and take two different roads to get to the same point. Now if we look at our map in a more schematic form we can see that the roads form a right angle triangle. I could describe the direct route by the distance I walked along the hypotenuse and the heading or angle I set off in to get there. Alternatively, we could get to the same point on our triangle via the scenic route by first walking along the side adjacent to the angle and then walking up the triangle on the side opposite the angle. So even if we don't know the heading or angle we need to set off in so long as we know how far across and how far up the triangle to go we can still reach our destination. When we looked at the rotating triangle before we saw that this angle corresponded to the amount by which we had shifted the phase of our sine wave. It may not surprise you to learn therefore that just as we can describe any heading by combination of a cosine and sine function we can also describe any phase shift by adding together two different waves a cosine wave and a sine wave at the same frequency simply by altering their amplitudes in a certain way. Let's see this actually happen. I'm going to start with a cosine wave with an amplitude of 32. You can see that this cosine wave is just a normal cosine wave with no phase shift. Now I'm going to take a sine wave with an amplitude of 29. Again the sine wave is not phase shifted at all. I'm now going to add them together. Look what happens to the resultant wave. It's a cosine wave that has been shifted by about 42 degrees. But what's its amplitude? To find out let's go back again to looking at this idea modeled as a triangle. Here is the amplitude of the cosine wave 32 represented by the length of the base of the triangle. And here is the amplitude of the sine wave 29 represented by the length of the height of the triangle. What is the length of the hypotenuse? Well Pythagoras showed us that the square on the hypotenuse is equal to the sum of the squares on the other two sides. Let's look at this actually happening with a little help from a really simple demonstration I found on a visit to the Bloomfield Science Museum in Jerusalem with my 4 year old son. The base of the triangle has an length of 32. So the area of the square on the base of the triangle is 32 squared which equals 1024. The height of the triangle is 29. So the area of the square on the height of the triangle is 29 squared which equals 841. Now let's turn the triangle round. The coloured water in each of the squares on the sides of the triangle is pouring into the square on the hypotenuse. We can see that Pythagoras was right. The square on the hypotenuse has been completely filled by the water flowing from the sum of the squares on the other two sides 1024 841 equals 1865. Now how do we find the length of the hypotenuse from the area? Simple. We just take the square root of 1865 which gives us 43.18. This is equal to the amplitude of my phase shifted wave. How do we work out the angle of the phase shift based on the amplitude of the cosine and sine waves? Well again, we look at it as a triangle. If I increase the width of the triangle to keep the height the same, the angle decreases. If I increase the height of the triangle to keep the width the same, the angle increases. If I increase the width of the triangle then to keep the angle the same I have to increase its height too. This means that there must be some relationship between the angle, the height and the width of the triangle. Ah, so there's a relationship. A relationship suggests maybe a division. Keeping the width of the triangle the same and increasing the height makes the angle grow. As the numerator of a division operation grows so does the result of the division just like the angle of my triangle. So the height must form the numerator of the division. Keeping the height of the triangle the same and increasing the width makes the angle shrink. As the denominator of a division operation grows the result of the division shrinks just like the angle of my triangle. So the width must form the denominator of the division. So now I'm going to plot on the x-axis of a graph the result of dividing the height of my triangle by its width and I'm going to measure the angle of the triangle and plot it on the y-axis of the graph. When I join up the dots of the graph we discover something. There is a relationship between the width, the height and the angle of a triangle but it isn't a direct or even a linear relationship. That is to say that dividing the height by the width isn't enough to give us the angle. There must be some other operation we need to do before we can recover the angle of the triangle if we know only its width and its height. How can I calculate the actual angle from this relationship? In order to calculate the height of the triangle we multiply the hypotenuse by the sign of the angle. In order to calculate the width of the triangle we multiply the hypotenuse by the cosign of the angle therefore maybe we could recover the angle by dividing these two expressions the hypotenuse times the sign of the angle divided by the hypotenuse times the cosign of the angle. Well if we do that To do that, the first thing we notice, that it doesn't matter what the length of the hypotenuse is, as the hypotenuse is just divided by itself, which equals 1, and we are left with sine of the angle divided by cosine of the angle. But this is equal to yet another trigonometric function, called the tangent function. So to recover the angle, we use the inverse tangent function, and that is what we have drawn on the graph. So to calculate the phase shift of the wave we made before, we divide the amplitude of the sine wave by the amplitude of the cosine wave, and then take the inverse tangent function. So from the previous example, if my sine wave has an amplitude of 29, and my cosine wave has an amplitude of 32, then to work out the angle, I take the inverse tangent of 29 divided by 32, and that's how I arrived at my result of 42 degrees. So by adding together a sine wave and a cosine wave of the same frequency but different amplitudes, we can change the phase of the resultant wave. At school we all learned that there were 360 degrees in a circle. However, there is another way of measuring angles, and that is in radians. The definition of one radian is that angle for which these three lengths are all equal. So for example, if the radius of my circle is one, then at an angle of one radian, the length of this arc will also be one. If I now increase the angle to two radians, what will the length of the arc be? Well that's easy. The length of the arc is always equal to the radius times the radian angle. So on the unit circle, that's a circle with the radius of one, the length of the arc will be two, just like the radian angle. Now you might recall that the ratio of the circumference of a circle to its diameter is 3.14159265358979 or, as it's otherwise known, pi. The diameter of a circle is simply twice the length of the radius. So the circumference of the circle can be calculated by multiplying pi by two times the radius. On the unit circle, the radius is equal to one. So if the radian angle is equal to the length of the arc, there must be two pi radians in a circle. But why if we have a perfectly good way of measuring angles in degrees, do we now have to get involved in radians and complicated numbers like pi? Well the answer is to do with the way that the cosine and sine functions are actually calculated, as we'll find out in the next lecture. So now we know the three properties of a sine wave that we can modify. We need some mathematical system that combines all the things we have learned so far. Sine waves, cosine waves, amplitudes, frequencies and phases. This was the point which I finally lost the plot back in my days at university. As we are now about to enter a world where numbers are both real and imaginary, and where the square root of minus one actually exists, we're about to enter the realm of complex numbers.


ನочьর ರೀ್ಗ್ ಗಾರಾಕಽ್ಬೀದನ ಟೇಟಕೆನೇ. ಷೊರವ಼್ಲಾವ normalmente.ಮಮುಕೆ ಆನಾ BTJ magnificent ಕುಕೋಕ Responsable ᇚುವ್಴ges ಆನಡಡಹ್reg обяз mushroom ಔಲ್ಲೋಸ್ರೀಸಾ ಬಲೋ jogosಮರಗಳ made ಖಕರಯ ಮ಻ ತಾರಾಗಿಕ, న్ర్ప్ిఎసిం ల౜ికుమువ్చాందిందివ్న్చివ్పిదాత్ర్చిల్ప్కుమాసందిగాతపివర్చికుమాట్పకులికులిస్టిట్చాత్చా. צ Denis bullen the time to chat with Jedhip and I this, this evening. So, I would like to begin with just your personal association with East Bengal both as it was, as a player, as it developed. But before that, as someone who was following football as a youngster growing up, what was the impression that East Bengal left on you? And how did it fit in with your idea of football in India at the time. there is no doubt about it, and it was in 1969, the year was 1961, sorry 1961, and that year we had a bunch of footballers who were really of a very high standard, apart from Balram, Oruly Hosh, they were all there, but there were at least 5-6 new insults to Espegel Club that year in 1961, and our coach was under the guidance of Mr. Shushil Bhattacharji, he was a wonderful coach and a fine gentleman too, he built up the size of Espegel team in such a manner that we had a tremendous team spirit which was built by all of us with the efforts of all the players and also the coach Shushil Bhattacharji. So the very first match, from the very first match we started, you know winning, the first match was against the police, the second was Vienna, Vienna incidentally I tell you, that was my second match with Espegel Club, and I scored a goal, it was something of a, what should I say, magnificent goal as people say, because after having eluded past 7 people, 7 opposition defenders, I didn't know, I didn't, at least I could not, while I was playing, I could not see the numbers, I had dodged past, but I was told later on that it was 7 people I dodged past and then shot into the goal, it was just outside our penalty box, so I got the ball from Ramadhu, I started running, running and dodging past, about 7 people as I told you, I was told later on by the people, the supporters and the members, and after having eluded so many defenders, I could see the Vienna goal, just from the top of the box of Vienna club, and I took the shot, and by the grace of God it was a correct shot and I, thereafter I don't know what happened, you know, but then whenever I meet anybody, any Calcutta, not only anybody, any football lover, people of Calcutta, whenever they beat me at this age of mind, they refer to that goal that we can never forget that goal, against Vienna, you know, second match it was, and one after another we started winning matches, that is how we met Mr. Mohan Vagan in the first leg of league, and Balorau was in great form in that year, you know, Balram, Arun Ghosh, as I told you, and if you really forgive me, it may amount to saying something about myself, I was also in a good form, very good form, so as I told you, the team was wonderfully built by Shushil Bhattacharji, so when we met in the first match against Mohan Vagan, it was evenly played, it was an evenly played match, but Balram scored a wonderful goal by covering journal six top around Mohan Vagan's love, so wonderfully he covered and he left journal on his right, in his back, and he took a left footed right, it just entered the quarter of the day, through the quarter of the day of Mohan Vagan and that goal filled their fate, so which won the match, but the return league was something of a different tale, when we met in the return league we were on a path, on a path in respect of points, we had to win the match to steer us out, and our defender Arun Ghosh, he actually throughout the year played so well, what happened, you know, in any of the matches, just before the match we used to take a bath, we take a bath and then without talking with anybody, we used to dress up, that Arun showed up at the tent a bit late, and he was unlike his normal self, he was doing something which was not to the liking of other footballers, we couldn't follow why he was doing like that, but we could later on after the match we could follow why it was doing, he was doing like that, that match in particulars between Thurigoswabi and Arun Ghosh, 2-3 moves by Thurigoswabi after in eluding past about say 4-5 defenders of our club, he was confronted with Arun Ghosh, and Arun had a wonderful, you say, as a defender, he had certain distinctive points in his play, what he did in the very first move that Thurigoswabi was confronting him, just to deceive Thurigoswabi, he stretched his left foot, so that Thurigoswabi will try to elude past through his life, and it works so wonderfully, Thurigoswabi did that and he was pretty prepared for that, Arun Ghosh prepared for that and he just stretched the ball from Thurigoswabi, I mean Thurigoswabi, it was the identical move again in the same second half itself, identical move after about say 5-6 minutes, then this time Arun gave another thing which complicated matters for Thurigoswabi, he stretched his right foot, you know, and Thurigoswabi wanted to dust past him through his left, again he got stuck by Arun Ghosh, so it was a tremendous performance by Arun Ghosh, we won that match and on that day itself, we became the champions of this, champions of Calcutta Valley, and it was after long, long 8 years, the last time we played on where champions was in 1953, so that is how 1961 started. Yeah, Sugumadha, Sugumadha, I will ask you, I wanted to ask you one question which I am looking for. That is, that will be comfortable for me. See, you have played in East Wingall in a club at a time when East Wingall was not today's East Wingall, East Wingall were known as the club of the have-nots, if MohanBagan was a club of the have, who had all the things in the corridors of power, whether it is writers building or at the ruling party's office, I don't want to get you to explain, but East Wingall was known as a club, which is for the club, for the deprived club of the have-nots, clubs who have, people who have come from across the, because of the partition have come to this side of the country, so since you have played in both the clubs, I would like to ask you how was your impression about the general feeling of the fans in the East Wingall club, those days? Very good question, I was about to say that. In fact, as you said, after the partition, there was a tremendous extraders from East Wingall, I mean eastern part of India and influx of all the refugees to West Wingall and most of them lost their heart and homes and most of them got killed by Pakistani goods, in a number of cases, you know, so they were nothing, no life before them to look before, you know, that was, they were all suffering from a tremendous sense of frustration, at that time East Wingall were the beacon of light before them, you know, and East Wingall team were tremendous at that time, the forward line was, and backs were, Bhibhosh, Monkesh Bosh and Taj Mahal, Taj Mahal, S.Rai, Pulturoi, so many others, so that was the gleam of light for the refugees, you know, although it was very difficult for them to save a family, So, they were finding that some light was there before. And that is how they started you know absor guest manufactures to make themselves know that was the greatest blog, analogues to those people, and contribution of those people నినేరంప౅రాంతాంటినిషింధరంసంథమారిపనిసంపాంత౮ాడియకి సిర్మిసటిక్వడిక్టిసిసా. నినివాంచిదిఎరఇరిసా. పారంనినికురాంది. apart is why brotherism has been called a club up to Hussein bodies which are Cosmic�밀 has been called heads and so I would say వంభానультат మట౿నిని కిని. మన్నాకిను పక్ కు మాన్పిను పరన్త్రస్త్ని లకితు మ్ప్న్ పిమ్రడండి మాన్ౚరికు మి నాన్మనికికి. సంింనిని. � వరలాయె ఈవరినెటో కింట్చ్చక్చానెనాారినెనెట్. క్ట్చ్చాన్చామరిన్చ్చా. కింట్చాటికోచాంఎ. ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ' ڈ , rivaya  Budget র. র র র র র র র র র রidences in the last 40s or 50s, the position was the different. র র র র and that is why..... র র র র But I'll tell you one thing. I have continued saying this on any forum, on any occasion, that the kind of love that players receive from East Bengal fans and members and supporters టరకింద్చినినింద చౕట్ద్చికెట్పినిన్నినె. ఉన౩లెతార్చిసందామానెళ్కెన్టపెసందిటందిక్చింట్. but just before the appointed death, he came to Ishwagal Tech, Amit Khan, and asked for a blank check of the club's account from Jyotish Dha. Jyotish Dha was a little startled, but he didn't answer any question to Amit Khan because he knew that Amit is very cunning. He had something back in his mind, you know, so he got it. And the very next day, it was the appointment with Jyotish Dha and Manada. So accordingly, Amit Khan went there to Borbagan office in Dalhousi Square. So in the beginning, Jyotish Dha was very delighted that he was very happy that you have, after all, at the request of Manada, you have agreed to come to Borbagan club. But before that, he said, but before the deal is achieved, I would say one thing. He took out the checks from his pocket and put it on the table. He said that, I will ask Fahilal Manna to put area about here. And this would be a quick roco, you know. I will be signing for Mohan Baghan and Manna will be signing for Ishwagal. Is refreshing for us to hear over time when conversations around material gain were not the only focus. Now if you look at not just in India but around the world football, how it's going and how players go from one club to another. It's all about money essentially. But there are also the real consideration. How did first division footballers manage to then survive and continue their passion for the game?  No, you know, that time, money was not really that big a factor. At that time, although, you know, the players had one definitely advantage. Those who played well, they used to be provided by different offices, you know, banks and offices. Like, I got it which came back to India. And before that, Churi Goswami joined as probationary officer, so did I. I joined in 64. Churi Goswami joined in 1961. So the money that used to be paid, you know, from players like us who hail from very low middle class families. The money that we got, say, 4,000 or 5,000 or 6,000. And that had given the value at that time. That was utilised in a very wonderful manner. Like, when I got from 1961 from East Bengal Club, 3,500 rupees zero to start with East Bengal. I gave it, whatever I got, I used to give it to my mother. And my mother in return used to give a part of it, say 200 or 300 rupees to be paid, you know. So from that amount, you know, my mother, my father was definitely a sage-like person. He did not have anything in mind to make, you know, houses or something like that. But my mother was very clever in this. So she purchased a plot of land in Behala. With the money that I got from East Bengal Club in the very first year with that. That is how we players, coming from all middle class families, you know, got our, what should I say, our families stabilised in life, you know. Sir, what I wanted to ask you, what was the difference between Mohanmagal fans and East Bengal fans? Was the East Bengal fans more aggressive? Definitely. More impulsive, I would say. More impulsive, East Bengal supporters and members are more impulsive, don't doubt about it. And whenever they love anybody and anything, they go all out, you know. Mohanmagal also, but Mohanmagal, because of the tremendous, what should I say, glory behind them, which started from 1911, by which Yorkshire is efficient. They had a place of pride in every member and every supporter of the club, you know. So they used to take themselves as something superior to those of East Bengal Club, which is not a fact actually, you know. It should not be the fact. So, it is like that, you know. But once a player plays for East Bengal, he would love to continue with East Bengal only, I can say. Such is the atmosphere, such is the wonderful atmosphere, reverence between the officials and the players and that between the supporters and the members and the players, you know.  But there is a degree of difference between what they do and what the supporters and members of East Bengal Club do, you know.  Not really, not really. I frankly should tell you about the foundation day of East Bengal Club. While we played for East Bengal, we were not in the know of the foundation day of East Bengal Club, you know. But we all loved because it's a tremendously glorious organization, both Mohanmagal and East Bengal, and they used to be called arts rivals always. So, the thing which paid me very much, Mohanmagal Club will be joining ISL along with ATK and East Bengal, what to speak of getting a new, you know, financier, whatever the financier was there, you know. I mean, what is it they might forget? They lost it and they are still in search of an organization like that. And this really pays me and this is certain because I went through the paper and I have seen that that the joining ISL this year is almost or not almost disclosed. That will not happen in this year and that pays me tremendously because and not only me, it pays everybody, whoever is a football lover, a person in Calcutta, it pays everybody because they will not see their clubs, Mohanmagal and East Bengal, their choice of clubs and they will not meet in this tournament, in this ISL tournament. That is one very sorry part of it. Nobody is happy about it. No, my only last question to you was that what will be your message to the new age East Bengal Club and East Bengal fans? What will be your message as someone who has watched the East Bengal Club for the last 60 years? You know, as I said, it is very unfortunate that East Bengal Club has got only a place in ISL this year but I would only look forward to getting some financial at least to come forward to help East Bengal Club and I don't think the manner in which the club is being run now is to the liking of East Bengal supporters. You know, that has to be, there has to be with the financial.  So I have to have respect for them. Likewise, they have to have respect for the club officials and the club members and supporters. You know, if that thing can be achieved, I suppose although this year is very out of question to join ISL from the very next year, I suppose that that would be possible and my only wish and to the empty supporters of East Bengal Club to hold themselves with better breath, to hold themselves and to look forward to something very good coming from the next year onwards. On that optimistic note, Mr. Subhuma Samajpati, thank you so much for taking us to places which we have not even imagined. You know, when you were saying you close your eyes and it takes you back to those moments through your career and your time with East Bengal Even for us, I think listening to you, it took us back to at least, you know, because also for a new generation, whatever images we have of that time are largely in black and white.  So thanks for bringing that to life for us somehow. Likewise, I thank you very much for having given me this opportunity to tell something about East Bengal Club in the club's sensory ear. So it is all grateful, I am grateful to you and it is a, you know, mutual respect between you and me and I am really thankful to you. I mean, I am indebted to you that you have allowed me to say something about East Bengal Club. It's fast, particularly it's fast and about the time I played at East Bengal Club. Thank you, thank you so much sir. Definitely and I think Jayaditha will agree if I say that the pleasure has definitely been all ours. All ours, absolutely. Absolutely. The pleasure was mine, you know, the pleasure was mine, really, pleasure was mine.


Um, the him and Russell Wilson thing just doesn't seem to be vibing anyway. No, it doesn't seem to be vibing at all. I don't think Russell Wilson is his guy. I'm not really sure how it sets up with his contract and everything sitting him the next two games. Obviously, if they can get out of his contract and get away, uh, from paying him next year, I'm not really sure how it works or the year after they're gonna do that. The Denver Broncos, they're gonna move on and they're gonna get strategic about this situation in order to move on where it doesn't hurt them financially. So they can they can come in and bring another quarterback in or draft the quarterback in the future this year or next year. But yes, it's not gelling with the Denver Broncos. Russell Wilson isn't the leader that they were looking for. And I can possibly see Russell Wilson on the new team next year as early as next year. Now, I know that they are that that Jared Stidham has a lot of respect in that locker room. I know you. I don't know how well you know him or if you know him at all. Obviously former Patriots. Maybe you've heard some things or or whatever like Stidham Stidham having a big shot here. And a lot of these quarterbacks like Tyrod Taylor, Jacobi Brissette, former team made of yours, of course, of course, and former Colton, fortunately for you. Um, getting a shot here. What do you make out of Stidham sort of potentially having a nice little opportunity here these last two weeks? Yeah, I'm not you know, I don't know that much about Jared Stidham. I know he was on the New York Patriots, but it was after I laughed and then he was with the Oakland, the Las Vegas Raiders with Coach McDaniels, I think, and then he signed with the Denver Broncos this year. But I know this for one thing. I watched a preseason game with the Denver Broncos and it was versus the Los Angeles Chargers and Jared Stidham was a quarterback for the preseason game that year. And he absolutely lit up the Los Angeles Chargers defense from the first quarter all the way to the fourth quarter. And let me tell you he was getting the team motivated. He was getting the team going. That's what Sean Payton likes to see out of a quarterback is what Jared Stidham has in him.