For the very first time ever we have been warned that we are only allowed to broadcast for eight hours. Oh, really? Yeah. So no, no nine hour marathons for us. Damn. That eight hour five minute show we've been planning for three years. Yeah, month killed it. Damn it. I really like the conversation just before.  It was illuminating. So he brings bacon things we should test that time limit. Maybe that should be a goal, a milestone goal for us. We could do like Jerry's kids kind of telethon-y thing. Eight hours of pot people talking. I think no, I think we should we should do like to make time pass a little bit more easily. We could do a DTNS overwatch marathon where we all play together and we make fun of the people who don't know how to play very well. So you make fun of me? Well, I wasn't going to say. No, but I mean, that is pretty much what you're saying. Well, I wouldn't commit to because I think you pretty clearly know that I'm not very good at that. I mean, I can't confirm. I plead the fifth. How do you know what amendment that is? Actually, was it in Luke Cage, which I haven't seen in its entire piece in the summer? It was, I plead the eighth. Yeah, I plead the fifth. That one of those. That one. That one works. I plead the second. I think you mean the fifth. No, I plead the second. I'm going to carry an arm. Exactly. I plead the first. I get to say whatever I want. Now, I wonder if that would work if you were in the middle of a conversation saying something offensive and people are like. That's not okay to say. I plead the first. That's interesting. Yeah. Yeah. What's the third? I don't know the third. Or the fourth. Is it an assembly? I should. It's really bad. That's a good question. We know third never gets any attention, does it? It's, I think, I feel bad. Oh, it's the no quartering of soldiers in private homes. That's why. I plead the third, soldier. You will not be quartered in my home. I think if you get into that situation, you'll probably have bigger problems than pleading. I think you start a third amendment's right movement. The framers intended. Okay. What's the fourth? Oh, fourth is unreasonable search and seizure. Okay. That, okay. That does get some play. Interesting that that's number four on the list when they came up with lists. Blisticles in the time of our founding fathers. You're saying the Constitution just turned into a BuzzFeed article at some point. It's actually perfect. BuzzFeed has these long form like deep articles and then listicles. Like they just took their template from the US Constitution. They even, you know, if it was delivered back then, it would have been on a very scrolly paper. Top 10 things we forgot to include in the main text. Yeah. You won't believe the fourth or no, the second. You won't believe the third. Yeah. And then people were debating at the time, like, really? Do you think, like, the third one, what did it really need to be in there? And they were like, don't you remember the top 10 rights you didn't know you had? All right. Yes. Sorry. Let's go. It's time. Here we go. The Daily Tech News Show is powered by you, the audience, not outside organizations. To find out more, head to dailytechnewshow.com slash support. This is the Daily Tech News for Tuesday, October 4th, 2016. I'm Tom Marin joining me, Patrick Beja, all the way from France. How's it going, Patrick? It's going very well. You know, that pre-show conversation really energized me. It had non-threatening baby animals, pontificating Stephen Hawking, and the Constitution, the Bill of Rights, in the form of a BuzzFeed listicle. It was amazing. I'm going to start fighting for my third amendment rights now as soon as the show is over. You won't believe the third. We have a lot to talk about. Google, of course, had its big announcement today. Well, we'll go into what they announced. But I think Patrick and I are more interested in what these announcements mean about Google's strategy. This is definitely a shift in strategy. And we're having good conversations in the slack about that earlier today. But Yahoo, I think unintentionally, sort of upstaged Google in the middle of those announcements. And we'll get to that in our top story. Reuters reports that two former Yahoo employees and a third source familiar with the matter say that Yahoo built custom software to search incoming email in compliance with a classified directive from either the US NSA or the FBI in 2015. Now, the reason they don't know if it was the NSA or the FBI is often the NSA will have the FBI issue its directives in these sorts of cases. It sounds like the directive came from the FBI, but they don't know if it was on behalf of the NSA. What they did was scan email for a set of characters. Now, that could mean a phrase. It could also mean an attachment file name. It could mean data within an attachment. There was a selector is what they call it in the biz. They were looking for a certain bit of characters. As the messages arrived, they were searched for this string. If the string was matched, it would have been stored for remote retrieval. Now, Reuters could not determine what information was handed over if any was. Yahoo's chief information security officer, Alex Stamos, discovered the program after it was begun under Marissa Meyer's orders in May 2015. He initially and in his team believed the company had been hacked. Now, that is unrelated to the actual hacks that have been discovered around Yahoo. Stamos left Yahoo in June and now works at Facebook, and it looks like we know why. The sources are telling Reuters he was very upset about this, and that is why he left. He has not commented on this. Yahoo has not commented on this either. Yahoo unsuccessfully challenged searches on specific email accounts in 2007, so they tried to defend that. These were more targeted searches saying, we want you to show us what's in an account. Yahoo challenged it. They lost. This time, they chose not to challenge the directive. Apparently, according to the Reuters article again, because they thought they would lose. Upstream data collection based on content has been found legal when it applies to phone carriers, and that's what this is, upstream collection. So you're not going into an account to find an email. You're just asking essentially for a wiretap to say, look for anything that has this phrase in it. If it matches, store it. We'd like to see it. This is a surprising and somewhat confusing story, because it's very easy to fall on both sides of the ideological debate that we've had a million times. I'm not sure this is the place to have it again. But the one thing that is really surprising to me is that in 2015, they decided to just comply. And yes, they thought maybe they would lose, but it seems to me that it's at least unusual for a tech company a year ago to just go ahead and agree with such a wide-ranging search. Because yes, it's upstream and it's the equivalent of a wiretap, but it's a wiretap on the entirety of the messages that come into their servers, which are many. And I mean, I'm not a lawyer, but it seems like that's a very wide net to cast. So I don't know how that affects the comparison to a wiretap. But the fact that Yahoo wouldn't even fight it seems very strange to me. It doesn't, it doesn't. In some ways it doesn't seem strange, because they fought a more egregious attempt, which was we want to look at an account. That is a more intrusive attempt rather than a filter. Basically what happened was Yahoo put in HTTPS. And so the NSA couldn't just look at the email traffic coming into Yahoo servers as they could before, because it was encrypted. So they had to get Yahoo to do this. It was the only way. But up until then, up until 2014, when Yahoo encrypted their account, the NSA could have just done this on their own. So they went in with a less targeted situation and said, we just want to have that same upstream tap. I think what does shock me though is not that they wouldn't say, well, you know what, we've lost these legal challenges in the past. We don't think we're going to win this one. Is that they would then say, but, and so we're going to save the money and just give in. You still fight it. I mean, Apple fought against what they thought was an unfair request. Yahoo is being asked to create software here. And so they could have appealed and said, hey, we think this is an undue burden. On the other hand, I guess, if you're really sure you're going to lose, you don't spend the money to appeal. And yet you don't tell your security officer? I mean, that tells you something right there. Yeah. I mean, even if they, the thing is, it's even more on the philosophical standpoint. Maybe they agree. You know, maybe at the top of Yahoo, are people, you know, Marius and I or others who think this is something that should happen. And maybe that explains it. But it's just an oddity in what has become the world of tech in the past few years where they seem to be shifting more towards trying to protect their users' privacy. Because they feel, I mean, it seems like the tech world feels there's been a shift in another extreme, which is not enough privacy and too much surveillance. And at the same time, they shifted to HTTPS for a number of reasons. Maybe it could be argued it's just security and not, you know, when it comes to this. Just good practice, yeah. Right. But doing that and then allowing for the government agency to just cast such a wide net. I mean, again, it could be defended as saying they're just filtering and looking. Once they have a certain piece of content that matches the filter, then they send it. So it's not like the NSA or the FBI is having a look at all of the user's data. So yeah. They're only looking at all of the user's data. They're not keeping it. They're not even reading it and understanding it. They just have a filter on all of your emails. Every single email sent to your Yahoo account. Like, yeah, man, no, I get it. I get it. It's less than reading. It's less than storing. But a lot of people are not going to be okay with that. And I think Alex Stamos would not have been okay with that. And that's why this Reuters article says they didn't tell it. They left him out of it and kind of just hoped he would never discover it. The problem is that Alex Stamos and his team were very good at their job. And so they did find it. Or at least they were good at their job in this case. Yeah. I mean, we only have half of the story, too. The certain set of characters also could cast another light on this. You know, maybe it's just imagination running wild at this point, which maybe we shouldn't be doing. But let's say it was a certain passcode that criminals were using in specific communications to detail some terrorist attack, for example. And it was a specific set of characters that was like a password or something. I don't know. But it was a piece of malware as an attachment that would have been very damaging, right? I mean, we don't think that was it, but we don't know. It's a very good point. I think the most telling piece of this for me is the fact that Alex Stamos quit after this happened and went to Facebook. It tells me something about Facebook. They met Mr. Stamos's measure as far as like, will you not do these kinds of things? Not to say that they'll never do them, but at least he was convinced by them like, no, we hold a standard this high. And it shows a lot about the disarray of Yahoo, desperate to figure things out and keep things from getting out of control in the middle of a sale. We saw that with the 500 million accounts that were accessed, which I think was overblown in that case, because while it was vast, Yahoo is vast. And in other ways, the hack was not materially different than things that have happened at Dropbox and LinkedIn and other places. That said, there are certainly questions about the fact that it happened at a certain point in the middle of an acquisition. And now this, I think this is even more damning that she would circumvent her own security organization in order to comply because she just didn't want the controversy.  Right. That also could have played a heavy role into it. So anyway, I guess the thing we all agree on is that this is raising a few eyebrows at least. Certainly I'm raising my eyebrow, at least one. Yeah. Well, it's on the eyebrow ranking level. It's one eyebrow. Okay. On the other end of the spectrum, the security spectrum. Like I said, the other eyebrow. I really did. Maybe I should have. Reuters reports that documents unsealed last week show open whisper system received a subpoena earlier this year requesting email addresses, history logs, browser cookie data, and other information associated with two phone numbers of signal messaging app users. The request was part of a grand jury probe in Virginia. The documents show signal was only able to supply the duration of a user's membership. Open Whisper Systems security expert, Moxie Marlin-Spike, said it is the first subpoena that the company has received. So an entirely different situation in comparison with Yahoo today. Now becomes a little compare and contrast. What signal does is end to end encrypts everything and doesn't hold the key. So they can't do what Yahoo did. They're like, we could scan all day long. All we're going to see is encrypted traffic. We're not going to see anything. And so all we can tell you is the user signed up on this day. And that's it. That's all the information we have. And if they close their account, we can tell you that too or we can tell you whether it's still active. That's all. They have set their system up. Open Whisper Systems has set their system up such that it's just not in their hands to hand this data over. I wonder how there's the story. Is it Brazil where they want WhatsApp to deliver some information? It's like a ping-pong game, right? There'll be one judge who doesn't quite get this and say, well, we're going to suspend you or find you. And then another judge goes, well, hold on. They physically can't give you this information. We're not going to make them do that. But yeah, it's happened like three times in Brazil. Yeah. And in this case, it seems at least that, well, Open Whisper Systems is saying we just don't have it. So I wonder if this will have a different kind of repercussions as well because I don't think we've had many cases where the request was made and a company that was using heavy encryption has actually said, well, we don't have anything. So you can ask, but we can't provide it. So the other thing here is this is a grand jury probe. This is not a surveillance secret court order national security letter. It's none of that. This is out in the open. A grand jury issued the thing. And that's why Open Whisper Systems can actually comment on this. I think it's very interesting that Moxie Marlin Spike was able to say this is the first subpoena the company has received. Now granted, subpoena is different than national security letters. So I mean, they haven't been approached in other ways, but that is important. Japan's NHK has created a 1 millimeter thick 130 inch 8k display. What they did was took 65 inch 4k OLED panels, put four of them together. They're from LG display, LG display panels to make this 8k display. They also had to mount them on a 1 millimeter thick board, doubling the thickness, Patrick, from 1 millimeter to 2 millimeters. But in the end, it does play video at 7680 by 4320. So 8k at 60 frames per second prototype was developed for research purposes. They're showing it off at SeaTac in Japan. NHK demonstrated 8k broadcast during the real Olympics this summer, if you remember. And they're hoping to have regular 8k broadcast by 2018 because they definitely want to do the Tokyo Olympics in 8k in 2020. This is so first of all, the screen. Do we not have 8k screens, even prototypes at this point? I thought 8k was almost good. We've had some 8k screens, probably just not quite this big or thin maybe. Sorry, you're silenning out for me, so I hope I'm not for you. I said we have had them before, but maybe not this big. Okay, so the thing is they have a very visible line in the middle in both axes. So it's not quite as impressive as you might think, but 8k is to me. The more I look at 4k, the more I'm wondering if 8k is really got to be a thing. Because 4k is already hard to discern when you're close enough. Do you think, I mean, that just begs the question again for me, is 8k really going to be something other than a demonstration, a technical mastery demonstration for the Olympics that no one is really going to use this? I don't know, it's like too much. I wonder what the 8k use case will end up being. What I remember was when 4k came out, a lot of people said, doesn't look that much better. I can't really see it. And there were a few people, including Sharif Sark from Engadget, who said, dude, skip 4k, let's just go right to 8k because he had seen an 8k demonstration and said the beauty of 8k is you can tell the difference when you walk up to it. You can make bigger screens at high resolution, but you can also, it's almost like looking at paper. You can walk right up to the thing and see detail that you can't see definitely in 1080 and certainly not 4k. HDR came along and made 4k viable. People say it's not the 4k itself. It's the fact that 4k makes HDR a viable difference to see like these crisp colors and true blacks and all of that sort of thing. So I wonder what 8k will make possible. I mean, obviously you can zoom in on an 8k screen and see an amazing detail, but I don't think that's enough to answer your questions. It's going to be some way they're able to put that resolution to use, not simply the resolution itself. That's interesting. I didn't really think of it that way that you actually have. I mean, people are not going to get up in their living room and go look at the screen. Not after the first day that they get the TV for sure. But maybe there are other use cases. Yeah. What is that resolution going to make possible that we weren't able to do before or maybe haven't even thought of before? Yeah, magnifying glasses. 2020 Olympics. The 2020 Olympics are not that far off, so it maybe, you know, I mean, I already have my 2020 Olympics t-shirt that I bought at the airport in Japan, so. You do? Yeah, I do. Actually, about the Paralympic t-shirt, to be honest. But does it come in 8k? It did. It came in all the k because it was a real object, so I can see every pixel. All right. Well, let's move on to Lenovo CEO, John Franco Lanci, who said, the company does not intend to release any new Windows 10 phones. Speaking at the Canalist Channel Forum, Lanci said, I am not convinced Microsoft is supporting the phone for the future. He did say, however, Windows 10 is doing well in the business world on the desktop. And let's be honest, we're only noting this because it's a milestone, right? It's a mile marker. It doesn't shock you, does it? So no, it doesn't shock me, but I think it's interesting that manufacturers are now stating the unspoken truth of the mobile phone world, which is, it seems like Microsoft is actually not even supporting the Windows 10 phone platform anymore. And if Lanci is saying this as the CEO of Lenovo, which is a huge manufacturer, it probably means that it's a kind way of saying, no, even Microsoft has told me they're not planning to support it in any way. And yes, we knew it. But the fact that they're saying it publicly now, a manufacturer is saying it like that, makes me look back at the journey of Windows Phone. And how many times has it been a, I mean, Windows 10 on the phone? Are you guys getting a little dusty in there for you when you look back at the journey of the Windows Phone? It's getting, I'm seeing all the bumps in the road. And I'm wondering, I'm wondering, you know, how much Microsoft ever really wanted it, I guess. I think they did, but it's just, I don't know, they moved on, now it's a new Microsoft. And I think they don't really look at Windows on the phone as, I'm even wondering how much they're looking at it in the context of Continuum and the use in the workplace. I think they'll come up with some kind of mobile platform, because they haven't given up on tablets. I think what Nadella might be doing is saying, let's just rip up the past. Let's let that just fade out and we'll start over with something else. I'll be curious to see what that ends up being.  Thanks to all those who participate in our subreddit. You can submit stories and vote on them at dailytechnewshow.reddit.com. All right, here is what Google announced. 5-inch Pixel and 5.5-inch Pixel XL. These are OLED phones that have Google Assistant built in, and you can access it by long pressing the home button or speaking a keyword. They played up their camera, which is the new way of differentiating a smartphone, is to talk about how great your camera is. They claim that DXO Mark has rated it the best camera ever made by anyone. Shots fired, Apple and Samsung. By the way, on that DXO Mark thing, when they were saying this, I think everyone in the world went to the DXO mobile website. For those who are wondering, yeah, the Galaxy Note 7, I believe is one point below or two points below, and I believe they haven't tested the iPhone 7 Plus yet. You can get the pixels in 32 or 128 gig versions. USPC comes on both. They made a point of mentioning that a 3.5 millimeter headphone jack comes on both. Four gigs of RAM in both. The specs are basically the same, except for the size of the screen. They're also throwing in free unlimited photo and video storage. 24-7 live customer support, a la what Amazon was trying to do with their fire phone. You can get it in quite black, very silver, really blue. Really blue is a limited color, though. It's the actual name for those who don't know. Yeah, yeah. No, I'm not just making that up. That is what they recall. In the United States, it'll be exclusive to Verizon, or you can buy it unlocked and get Google's Project Fi service for it. Here's the thing. A lot of people reacted very negatively to this price point. Patrick, $649 or $27.04 a month up to, for the top level, 5.5-inch phone with 128 gigs, $869 pre-order day in US, Australia, Canada, and the UK. So a lot of people are saying, well, yeah, okay, that's about the same as an iPhone. It's actually cheaper than a Samsung Galaxy S7 Edge, but we expect cheaper phones from Google. Well, so I think people, I think this is a momentous change in Google's strategy. In this conference, there were two main points, and the first one was this phone. I think it's a fantastic move on Google's part because they are, the problem with the cheap Google phones was that they were sort of introducing confusion in the marketplace for Android. If you wanted, you know, if you were one of the people who cares about the technology and you just want a good Android phone and you think, well, I want the pure Google experience, you would be tempted to go the Nexus route, which are excellent phones for the price, but they're not the best phones you can get, right? The best phones would be some of the Samsung or maybe even LG, these kinds of phones. And yes, people are used to having cheaper phones from Google with the Nexus brand, but that's only because that's what they've been doing until now. And nowadays, you have other manufacturers like Huawei with the Honor line and things like that, that provide excellent devices at that price range, which are, you know, almost premium phones at the price of a mid-range phone. And what's happening now is that Google is realizing and thinking in order for us to provide a premium experience with Android, we need to be in control of the software and the hardware. And they are creating a package, which I believe, and maybe that's my preference for the Apple proposition speaking there, but I believe they're creating a package that is a clear decision for people who want a great Android phone and don't want to have to deal with the issues that come with another manufacturer's, you know, UI improvements, I put that between quotes and all of that. So on the Google side, it's a change in philosophy saying, we need to design the entire package. And for the customers, it's an easy choice. Now, if you want a great Android phone, you take the brand one, the Google one and you have what you wanted. Yeah, the question, a couple of things there. One is they are very much taking a page from Apple. Who was taking a page from Alan Kay at Xerox Park on the theory of integrating hardware and software? But Google was up there echoing both Kay and Jobs saying, hardware and software, the intersection of these, this is what we do now. So that is a big shift for Google. Google is doing more than what they did with the Nexus. If you don't realize with the Nexus, Google apparently what they say is they would come in after the phone was 90% done and have some input. Now, Google is not only beginning this thing from the start saying, this is what we want, but they are managing the inventory. They are building the relationships with carriers. They are sourcing components, making supply chain deals, managing distribution. HTC is assembling the Pixel phones, but they are not manufacturing them the way they did the Nexus or the way that Huawei did the Nexus. And you don't see their name anywhere. Yeah, they are assembling them the way Foxconn assembles the Apple iPhone. Right. So I think this is a really, and the thing is for the people who wanted cheaper phones from Google, you do, that's the great advantage of the Android ecosystem. You do have that alternative. There are phones that are at that old Nexus price range that are available. But when you're talking about the true Android experience, I think Google is the one that is going to deliver it. And if you want the true real thing, I think it's good. I think it's an advantage to have a real premium phone, even if it comes with the premium price. Yeah. Now, here's the thing. The difference with an Apple situation is if you want an iPhone and you want iOS, you have to buy it from Apple. With Google, if you want a Pixel, you have to buy it from Google. If you want Android, though, okay, and Nougat 7.1 is only available on the Pixel 4 now. But you can still get Nougat 7.0 from lots of other phones. And you've got loads of other Android phones, which is, I think, part of this price-perception reaction, which is like, hey, the OnePlus is a lot cheaper. Freaking, some of the old Nexus's are a lot. The 6P is cheaper. And these specs are really close. You mentioned the Honor. Like you have a lot more to choose from that is perceived as, on the software side, pretty much equivalent. So what Google was trying to do was differentiate it on the Google Assistant, saying, we're the first phone to have Google Assistant built in. We have it integrated. It's long press from the home button. You can do all these great things with it. And we're going to introduce the Google Home, which is a device very much like the Amazon Echo that also has the Assistant built in. And if you have a Pixel phone and the Google Assistant built into Google Home, suddenly those are going to play nicely with each other and your shopping list will show up easily on your Pixel phone. Oh, by the way, we're going to introduce the Daydream View as well. That works only with the Pixel out of the gate. Yeah, it will work with other phones now. But they're trying to introduce this ecosystem that says it's not the same as buying a Samsung Galaxy S7. It's not the same as buying a Nexus 6P even. This is a phone that gives you more because we have differentiated the AI. And they talked a lot about AI and machine learning. I think this is the other huge aspect of this. It's not even this conference, but it's the trend that had been going on for a while, but that was very much accelerated by the success of the Amazon Echo, which surprised a lot of people. I think everyone thought it would be a blip somewhere in the radar. And not only has it been successful, but it has basically shown how important the AI and virtual assistants are going to be in the future. I can't remember if it was on this show that we were talking about this, but saying that paradigm shifts come from unexpected places. And the masters of technology in the 90s were basically Microsoft because they owned the main UI, the way humans interfaced with computers at that time, which was the Windows operating system. In the 2000s, that main interaction sort of shifted in a way to the web. And Google owns the web, so they have that main... If your product is how people interface with computers and technology, then you own that world. And of course, you still use computers and things like that, but it's important to have the main central hub. Again, we shifted to smartphones, and that wasn't expected. And I think a lot of people are thinking the next shift is going to be virtual assistants and AI in general. Of course, at this stage, it's goofy, it's scripted, and it doesn't work as well as the promise, but at some point it will. And at that point, it will constitute at least parts of your interaction with your devices and with computers. And that supersedes Google the homepage, because if you're talking to your phone, whoever owns that piece of the chain owns where they direct you. And the really big thing that Amazon showed with the Echo is that it's not only going to be on the phone, and they talked about this ad nosium during the conference. They showed the Google Home, the TV, the phone, everything, and basically the disembodied voice of the AI that serves as your interpreter to make computers do their thing. It's going to be everywhere in a few years. I mean, we're still at the very beginning, but this is the huge trend I think everyone agrees is going to materialize in the next few years, and whoever owns that is going to be the next Google, the next Microsoft, the next whatever. So this is why you see Google pushing it so much, Amazon pushing the Echo as well, Apple reportedly developing a kind of Amazon Echo themselves and Cortana and all of those. Yeah, by the way, bringing up Apple is silly because they have no product, but they do have Siri, so there's a possibility, and I guess they have Siri on the Apple TV.  Really, it was just Amazon who had this device in your home and they could sell dots to you in 12 packs. Google just stepped up and said, hey, our Google home is 129 bucks. That's $30 cheaper. I think it's $30 cheaper, maybe more, maybe $60 cheaper. It's cheaper than the Amazon Echo, the full version. This has a speaker built in. It's going to come with a six month free trial for YouTube Red, so you got some music in it. It's shipping November 4th, by the way, pre-order today in the US. It's going to work with SmartThings, with Nest, with Philips Hue, with Ift. So it's on par with Amazon Echo. What they tried to argue was, but because it has Google behind it, we can do things that Amazon can't. Amazon has been working with Search with A9 and certain things for a while, so they can do some fancy tricks. But Google can bring in its whole knowledge graph, all its machine learning, all its voice recognition, all its text-to-speech technology, and do things in a more conversational way. They argue, and we'll have to see once we get one of these things in our hands, but they argue that this can be a more natural conversation and a richer conversation because of being powered by Google Search on the back end. And I think you're sort of... I mean, I would disagree that the others don't have that product, because the real... They don't have this product. That's all I'm saying. Well, yeah, but that's not the product. There is no Microsoft or Apple device like the Amazon Echo or the Google Home. But that's my point. That's not the product. That almost doesn't matter, and it's interesting that they're... This is only the materialization of the real product, which is the virtual assistant, which is what they were selling. Today, I can use Amazon to be my hub. I can use Google Home to be my hub starting in November. I really can't use the others yet. No, but that's a blip. That's all I'm saying. They can do it in two months. It doesn't matter. Yeah, no, I know. And when they do, then that will be them stepping up. I'm just pointing out this is the second step up. Right. And what I'm saying, though, is that they have all been doing the work to make all of this possible, because whether or not you have one device in your living room that speaks and listens, it doesn't matter if you don't have the work, you know, the machine learning and the speech recognition and the picture recognition that you can then put anywhere. But let me say, because I get that, let me say, does Google have enough of an advantage with its knowledge graph, et cetera, being top search dog for decades now, that it will be appreciably different once we do have all the competitors in the arena? Well, that is the big question. And that, to me, matters a lot more. And to be honest, I'm not entirely sure who has the best one yet. I think we're too early in the game for it to really matter at this point, because no matter which one is the best, they're still all a little bit clumsy, right? They don't quite answer exactly what you want when you want it. I think if they're all working towards that, and it's important that they all are, because when they want to put it in your car, in your little earpiece that you have, why you're less because you don't have a phone jack on your phone, a jack on your phone anymore, or your watch, or all of this lives elsewhere, anywhere. The hardware is just a little piece of metal and silicon that beams it down from. I think you're right, eventually, that these things don't become necessary. These are sort of the Trojan horses that get everybody to experiment and try them. The other thing is to get all the things to work. So Chromecast Ultra, $69 in November, 4K HDR, Dolby Vision was announced. That's basically just them saying, hey, we're going to have a 4K version of the Chromecast if you're getting a 4K TV. You can do HDR, you can do Dolby. It's even got an ethernet port in the power adapter, because 4K takes a lot of data, a pretty clever trick. But the big point is our Google Assistant through Google Home can control those Chromecasts. So if you put a Chromecast audio on your speakers, you can just tell Google Home to play your music on that speaker. If you have Chromecast on your TV, you can say, and they showed this, because they're so conversational, play the latest Katy Perry video on my living room TV. And it will do that. So Google's trying to argue that if you play in their ecosystem, you can just have a conversation. And Google Assistant will know everything you're talking about. And I want to add on to that, Google Assistant SDK is going to come out in December for something called Actions on Google that will allow you as a developer to integrate Assistant on third-party hardware and implement either a direct action like turn on the lights or a conversation where you can say like, who is the president of the United States in 1860?  And this is, it's really interesting too, because it allows them to expand the capabilities of their Assistant. And I hope they had spent a little bit more time on this instead of some other things that you're the president of. The other, we mentioned briefly the Daydream View that's coming in November for $79. It's cloth. I think that's a really interesting competitor to the Gear VR or the cardboard, both of which are somewhat uncomfortable. It just uses NFC to connect to the phone. And it's available in slate, although they say snow and crimson colors are coming later. So it is affordable at $79 headset that is among all of these mobile headsets that are saying, hey, you don't want to spend a lot of money on a new computer in an Oculus or an HTC Vive. You can still enjoy some good VR and they showed off some games and videos and Netflix and Hulu and stuff are going to be in there. And then Google Wi-Fi, which is their mesh Wi-Fi network competitor that's $129 per unit, or you can get a three pack for $299. This works like an Eero up for pre-order in November shipping in December that will let you automatically create a mesh network in your house that adjusts to you as you walk around. Daydream View sort of tangential to some of this other stuff where it's sort of saying we're taking our toes into VR and we'll bring that into the tent once it catches on. Google Wi-Fi is saying, hey, if you're going to have Google Home and you're going to have all these Google Home things in all the rooms of your house and all these Chromecasts, you're going to have to have better Wi-Fi coverage so we'll sell you that too. Yeah, it's a little bit of a nod product to be creating for Google, but okay, why not? And because they need all of them to be on the same Wi-Fi network, maybe? Or I don't know. The one thing that was missing, though, was the very heavily rumored tablet with the Andromeda OS. And that they went, just when we were expecting them to talk about it, they were like, and we're done. Thank you very much. Goodbye. Boom. Yeah, which makes me wonder if there was a little NDA moment. After that live stream ended. Nothing has leaked out yet. Let me check my feeds. But they definitely said, now, for the people on the live stream, goodbye. Now, all it could have been was, for those of you in the hall, you'll get to put your hands on these. We've got the devices over here. That might have been all they said. I'm just stoking the conspiracy theories when I say there was something else. But yeah, I don't see anything else leaking yet. By the way, another footnote to this, Google hired David Foster Monday, not the composer, the VP of product engineering from Amazon. I'm sorry. He was a developer at Amazon. He is now the VP of product engineering at Google. He worked in the lab that developed the Kindle, the Kindle Fire. He worked on the Echo. He worked on the Zoom HD back at Microsoft. This is a guy who's worked on lots of products. So they're bringing in a little Amazon. They poached from Amazon to get somebody to work in this space. It looks like he's going to be working on the phones, no, not on Google Home. But all of them have basically a lot of the same competing products. They all have something that connects to your TV, something that on your computer, on the phone. They have very similar offerings, all of them now. All right. We're going to introduce a new segment to Daily Tech News Show today, instead of Pick of the Day. Not the Pick of the Day is going away. We'll still have it when we have good picks. But we're going to introduce Thought of the Day from Patrick. Amazon Game Studios, as we mentioned last week, announced its first titles and they announced deep integration into Twitch.  You can invite followers to play. You can set up viewer polls, allow match wagering, using the new stream plus currency, all from within the game. It's all integrated into the game. And Patrick, you've got a theory about this. So basically, I think this, along with the Twitch Prime offering, which I'm sure you discussed as well, which gives perks if you subscribe to Twitch in a premium offer, which is basically it comes in with Amazon Prime. Are the two reasons, I think, why Amazon bought Twitch?  And that might seem obvious when looking at it from here, but it was two years ago that they bought Twitch. And they're betting that eSports are going to be enormous, which we're seeing materialized now with the different sports teams buying eSports team and such. And they are trying to encourage this by making games evolve from, we had single player, multiplayer broadcasting, and now interaction in games with the audience, which makes it that more engaging. And the other thing is getting, padding, the Amazon Prime offering with the Twitch Prime makes Amazon Prime so appealing that I think it means a good portion of the Twitch audience, the engaged Twitch audience, is being converted to Amazon customers. And that makes the Amazon Prime offer incredibly, you know, it's almost, I can't remember who was saying this, but someone was saying it's almost financially irresponsible to not be an Amazon Prime subscriber. And I would say that's a joke. There's so many doorways into it, right? Like, there's the free shipping. So if you buy anything on Amazon, that could be worth it. Then there's the television and movie streaming service, if you want to watch Transparent or the tick when it finally comes out, Man in the High Castle, that makes it worth it. Then now there's Twitch and there's the Kindle Unlimited Library, like they've put so many doors on this building. But there's what? Music. And the Amazon music. Yeah, not terribly compelling. You know, you're not going to do it just for that, but it's certainly something that's like, oh, well, I have Prime. Now it might as well, maybe I'll take advantage of this music service. And none of them are incredibly compelling. I mean, video is not as compelling as Netflix, for sure, but you get all of them and they're still half the... Well, you seem to be hesitating. I think the shipping is compelling on its own. I think that the movie and TV is close to compelling on its own. In fact, that's why they now offer it on its own if you don't want to have it as part of anything else. And all of them are half the price of the Netflix subscription and you get all of them. You get goodies in the game. So it sort of completes their offering of having advantages for every part of your life is becoming better.  And the bet on eSports is just two pillars of a reason that makes buying Twitch completely reasonable when it was a little bit puzzling back then. All right. Well, thank you, Patrick Beja, for your thoughts. And we'll see, this is kind of cool, a cool way to follow up on a story and get a little more context from it. So hopefully we'll do this again. Let folks know where they can find more of what you got going on. You can go to Frenchspin.com and download or subscribe to Pixels, not to be confused with any movie or any phone from Google. It's, I was there first. So Pixels is a show about video games and we just recorded one with our good friend Garrett Winesroll and we discussed everything about this big move towards eSports in sports and in Amazon and we discussed Forza Horizon 3, which is apparently a fantastic racing game and a bunch of other things. If you like video games and want news about gaming, Pixels is the show for you. Thank you, folks, for supporting us. DailyTechnewshow.com slash support tells you all the ways you can support us. And the main one is Patreon. I just want to thank Melissa Johnson for upping her pledge. You are the best. And also a brand new pledge from Adrian Pratt. You guys are fantastic. Thank you for supporting the show. Thanks to everybody who's been supporting the show at Patreon.com slash DTNS. Our email address is feedback at DailyTechnewshow.com. We're live Monday through Friday, 4.30 p.m. Eastern. AlphaGeekRadio.com and DiamondClub.tv are the places to see us. And our website is DailyTechnewshow.com. Back tomorrow with Scott Johnson and Donald Bell talking about maker stuff. Talk to you then. This show is part of the Frog Pants Network. Get more at frogpants.com. DiamondClub hopes you have enjoyed this program. Oh, that's a new one for Frog Pants. That's hot off the press. I just got that from Scott last night. We went a little bit long. I'm sorry. Who used to do the CTR podcast? Oh. Yeah, I'm sorry. We went a little bit long. You know, I figured we were going to go along with all the Google stuff. So I don't mind at all. And I think the Amazon conversation ended up being really good, too. More than just, not that I didn't expect it to be good, but I thought it might be a quick like, Hey, here's Patrick's thought. That's really interesting. And then we engendered a little more conversation there. So I thought that was great. Excellent. Titles. Oh, titles. All the pixels. Is that what you want? Oh, it's the one I like. I don't get nitpickling. Is it a play on the word? Like nitpicking? When you're nitpicking at something. All right. I think I see you might be accusing us of nitpicking the pixels. Well, you know, it's interesting because they use DXO mark. And that's one of those things that it's not, it's not that camera, camera heads are against it, but it sometimes paints an unrealistic picture because it measures the sensitivity, but doesn't measure the entire image quality from the lens on down to the actual image product. Oh, really? Yeah. It measures the sensitivity of the sensor, which is great, which is what you want. But it's like measuring like, Hey, the engine in my car puts out 500 horsepower, but it doesn't tell you what kind of transmission it goes through.  Right, right. So all the pixels and nitpickling are both at five. Tom gives people's eyebrow. Oh, gives the people's eyebrow. I think that's a rock reference. The people's eyebrow. 8K because it does not sound like the F bomb. It's not like 4K. Okay, I get it. Third amendment. You got to fight for your rights. Oh, wait, you don't like Google. We're home. Google, we're home. Like Chewy, we're home. You know, I have a thing against, I won't go into it. All right. Google, all the things. Lenovo says Windows support is micro, soft. Pixel, I was there first. Actually, I like all the pixels. It's pretty good. I think we all like all the pixels. Should we just go with that one? Yes. Let's. It sounds like a political thriller, too. Like all you zombies. Or like a, is it Blink 182?  All the pixels. All the pixels. Episodes are available. Well, they're no longer available. Frenchman.com. All right, they are. They're still a band, but what's his name is no longer part of it. You showed a phone and I thought it was cool. By the way, we are counter-programming right now to the afternoon attack. Night attack because Justin Robert Young is in England, Mary Old England is on right now in the afternoon. So if you're watching DiamondTheClub.tv live, why are you looking at me? Go watch Night Attack. Or afternoon attack. Night attack. Day edition. Got to flash those diamonds in the chat room. It was so cool having Brian and Justin here last week. That was really fun. I'm looking forward to Patrick coming in November. Oh, are we doing the live coverage of the election? Oh, right. Well, you're not coming out here for that. No, I'll be back in Europe. Or staying out here, I guess. Yeah. As far as I know, I would like to. All the coverage of the election. Hopefully it'll be like a hanging chad situation. A what? Hanging chad. Yeah, we'll keep guy named Chad hanging outside. He's the last one to hold. When Gore and Bush, they had to recount Florida and the hanging chads were the things where they couldn't tell whether a vote was okay. Who did you vote for? We can't tell. Although someone did. Someone made a very a just joke. He was complaining about like all those voters, all those seniors, they know how to play bingo and they get it right, but they can't figure out how to vote. Usually that kind of thing isn't a problem because you have so many votes. But since we have the Electoral College, it ended up being a problem because the popular vote didn't matter. And that's when I gave up on the Electoral College ever being changed. Because even after that election, people were like, nope, we love it. Like the Imperial metric system, the Imperial system over metric. Well, it's no longer, it's not even really Imperial either. It's a offshoot of the Imperial system. Since an Imperial gallon is slightly larger. That's right. It's the American Imperial system. Well, it's the standard. We call it standard. It's standard, Tom. Just remember, we went to the moon six times on it. Yeah. Remember when we lost a thing on Mars because of it? Good thing that didn't happen more than it was. It wasn't, is it our American scientists using the Imperial system? There, yes. Sometimes. But when the way I understand it is they typically work in metric. Yes. Until they need to. But some things are provided from third parties in feet or inches. And then they, if they don't remember to convert, then you lose something on Mars. Your probe is destroyed. Oh, it's just the probe. Yeah. All right. I'm going to go. All right. Yep. We're going to go too. Thanks everybody for watching. We'll see you later.


What's up guys and gals Lane here with Layton sports cards. We're gonna do a little PSA sub review We dropped off six cards with PC sports cards during the national It was $200 per card We would get them back Sunday morning right at the end of the national and that's exactly what happened So here's how our sub went first up blue Refractor out of 150 on the first auto Jordan Lawler It did get a PSA nine, but that is still a very strong grade for that one definitely happy with a nine Of course, we would love a ten, but a nine is nothing to complain about Next up purple out of 250 George Valera PSA 10 that is a huge grade Again, there are a lot of condition issues with this set so to get a ten on a bowman first auto Especially a color auto Nothing to complain about at all Excited to watch what happens as he continues to grow and see what happens with the pop report if it stays low Or if it starts to creep up a little bit Then we have one of the hottest names of the national Jalen Hertz I think people are expecting big things from both him and the Eagles this year after they added AJ Brown So really excited to get this in a PSA 10 and that is the true rookie Genesis Not the NFL debut so again really excited to add a Jalen Hertz Genesis PSA 10 Then we have not one but two Select rookie Justin Herbert's out of 99 We got the red prism Concourse and the light blue prism select premier level So really excited both of those did ten and again both numbered out of 99 and The last card of the sub this is the monster. It was a shop walk-in customer pulled it out of a blaster box Wander Franco mother's day pink out of 50 PSA 10 Again from a blaster box at Walmart now in a PSA 10 slab. That's our six-card sub Thank you again PC sports cards. We appreciate everything that you do for us. Have a great day everyone


So, we go on with our work and I'm going to tell you about the last components of conformal filtering, which we need to know. And then after that, we use this knowledge to analyze the various estatomic models, which we come across. So, conformal filtering, I had said this before, but I will recap. So, I construct the Hilbert space by taking some state of weight H, which has the property, it's the eigenvector of the L0 operator, and it is vanished by all N positive N operators. And then the Verma module is formed by estates like this, so that from this H you take, you go down by multiplying L minus N's, and you can multiply as many of them as you like. But each combination forms a level, the level is such that, so you'd have H and your level is such that you have an N here, N here could have been produced by L minus 1 to the power N, or by a simple L minus 1 or any combination in midfield. So that all these K's, which are used to produce a state of level N, they sum up to N. Therefore, the number of ways I can do it is the partition of N. Partition of N is defined as the total number of ways. You can add up digits to sum up to, so I have a Verma module starting with H at the top, the grandfather, and then his children. All his children come below, and at any level you have here PN estates. This I call a Verma module. It's a sub-space of the Hilbert space, which has been constructed like this. And I will therefore have one for H bar, treating H bar not as the complex conjugate of H, but as an independent number from H. So H and H bar are two numbers, both of them are in this case real. And then I take a direct product, so for H and H bar I have a direct quick and then add up all of them over all H and H bar, and this will give me my Hilbert space. So in this way, a Hilbert space is constructed, and I have the operators already acting on the Hilbert space, which I had already defined as the field operators. So that almost completes my work, yes. It's not irreducible. If they were irreducible, our work would have been finished, but they are not irreducible as far as I have explained. So if these were irreducible, I would have now had a fully functional Hilbert space. The problem is that if it is not irreducible, if it is reducible, then it's possible that you have sections of it which rotate among themselves. And if I have this situation, it really means is that I have another verma module which I have not considered. So I have to extract all these things out of them, and just I'll be then just left with irreducible modules, and then I sum over all the irreducible modules to get the Hamiltonian, to get the Hilbert space, yeah? I talked about this state operator formalism that presumably this H state is related to the vacuum by some field operator, phi of H, and then they will have a correspondence between H and phi of H. So if I construct a verma module for the H, correspondingly, there will be a set of operators associated with this structure. So I have all the fields, which are all the field operators which I need also, and basically solves my fundamental problem, which is a Hilbert space and the set of operators acting on it. Then I can go on to do my calculations. First calculation which we can do relatively easy is that we take the two point function of two operators like that, and I showed you that simply by symmetry, you can derive this. I didn't show it to you completely because the last step I left out, which was the inversion, but you can do that yourselves, and you get this four. The same trick can be used to get the three point function. The three point function is fixed up to this constant C, and this constant C will not be known unless you specifically tell me which conformal filtering I'm dealing with, and then I can extract the C's for that. The next step is the four point function. The same game is played with the four point function, and you get this structure which has the right scaling properties, but the problem with four point function is that you then have this cross ratio. This cross ratio you can show is invariant on the conformal transformations, and therefore it is possible to have a function of eta multiplying this set. I don't have any way of determining f of eta unless you give me something more about the theory, so some sort of differential equation that this must satisfy, and then I can derive f. Higher point functions will be much harder because when you have five points, you have more than one cross ratio, and then you have a function of two unknown variables in the front. Yes, two independent. I cannot. I cannot. It sort of needs a presence of mind, which I don't have. Fine. We come to the point of the problem that there may be irreducible spaces of this module, and the argument goes like this. You have here n vectors which arrive out of this structure, which I call a level. The n vectors sit here, and it's not, I didn't give a proof, and it's actually not true that all of them are independent of each other. So it's possible that some vectors within this set may be related to each other. To give an example, the best thing is to look at the level two, the simplest level is level two, and here for level two, I have just two vectors, minus two. Two of h and l minus one is squared of h, and if they are not independent of each other, there may exist a linear relationship among them. Suppose such a relationship can be found. Then what have I found? I have found an operator which annihilates h. So here it looks that I have an operator which, if it hits h, h is vanished, vanishes h. Therefore, h is a null state in the sense that there is an operator that kills it. So what does this mean? It means that I don't really have two independent states. I just have one independent state at this level, and when I come down from h, I cannot create all that comes under h, but just only the ones which come out of one of the independent operator. Since existence of such a relationship gives me the ability to look for values of h which satisfies this state. So for all h, this is not satisfied, but there are special values of h for which this relationship is satisfied. This is the example for the Ising model. I will tell you in a minute that I can then, I can associate conformal filteries to statistical models, and each of these models is identified by a number of states. There is a state of weight one-half in the Ising model which satisfies this relationship. And therefore, finding values of h which satisfies the null state will also give me, will serve two purposes. One is that I will find my irreducible towers and complete my construction. And the other is that since it doesn't happen for all values of h, I will find a specific value of h for which this is satisfied, and hence identify my conformal filteries specifically. So once you do that, you find a whole series of h values which give you null states. And these are all the h values which give you null states for values of c between zero and one. And this proof was completed by Katz quite a while ago, and it's a rather involved proof. I don't really want you to know the proof. But we are looking at conformal filteries in an applicable way. So instead of going for the proofs, we want to know how we can use this knowledge. So there are states for each value of c, the central charge, then there are a number of weights which are given here which give rise to null states. And then these, in fact, identify each verma module which I have to construct. And when I construct all the verma modules for each c, I have the complete Hilbert space. And I have my conformal field theory. So instead of the proofs, let's just analyze the numbers which have come out here. I have a, I gave you a sort of half-baked argument that c has to be positive. Another argument is added to that that for this kind of construction, c has to be bigger, smaller than one. So I need to have c a smaller equal to one or bigger than equal to zero. This then tells me that c is equal to one minus six divided by m times m plus one, and m can be any number from two upwards. So at m equal to two, c is exactly zero. I gave an argument yesterday that this is an empty CFD or it's a trivial CFD. Trivial in the sense that it just has the operator one as the operator contact. Then I can take m equal to three and c comes out to be one-half. If, for that case, then I have one conformal rate of one-half and conformal rate of one-sixteen. If you work these out. Because when m is equal to three, p can take three values. And q takes values between, sorry, p can take two values and q takes values within one and p. So you have just three possible states for various values of p and q, and these three possible states are these guys. And hence, you just continue with other c values and other m's. Finally, we now try to identify what these states are. These states which we have here. So these numbers imply that for I have one state which is p equal to one, q equal to one. And that is the vacuum state. It has to be, because it has zero weight. Then the next state comes out of p equals to two, q to one. And then another state p equals to two, q equals to two. We don't know yet, but I will tell you that this is the case that these theory, this theory of c equals to one-half corresponds to the Ising model. So these two states have to correspond to the state to what you can construct in the Ising model. And it is easier to identify it with operators than states. So this, and this state are two states, one-half and one-sixteenth, which correspond to the operators of the Ising model. And we have no choice. We just have two operators in the Ising model which we can call upon. One is the spin and the other is energy density. And so on, we have to continue this game for every m. This is the simplest m. And we then find a table. The table continues for all m, I have only written the first four. So the following statistical models come out. The Ising model, the tri-critical Ising model, tri-state parts model, tri-critical tri-state parts model, and so on. What do you mean all include? All what? Not all statistical mechanical systems, no. Sorry, I can't hear you. I don't, sorry, I have to say that sentence something, somehow other, some other way. I cannot understand what your meaning is. I think the question is something like, would a three-dimensional Ising model also correspond to any question to conformal field theory? Okay, the three, that is the question. The three-dimensional Ising model, because it is three-dimensional, will not be in this table. So it is possible that there is some other conformal field theory, but a three-dimensional conformal field theory which will correspond to the three-dimensional Ising model, although it's not found yet. But another question could be that can you then, for every two-dimensional critical model, find the corresponding conformal field theory, and the answer is no. There are, and we have found for a large number of them, but not all. However, it's a matter of belief, I guess. Whether you believe that this procedure is robust enough to find everything. Central Church has a physical interpretation in that it's related to the energy density of the system, but it's a very loose interpretation. So here I can ask a very, very interesting question. Suppose I put as this top estate the vacuum. Then the question is, what are the estates which I can construct as the descendants of the vacuum estate? So I come down, the first thing that can act on the vacuum is L minus one. So level one, you only have L minus one of zero. And this has to be zero, because L minus one is just D by DZ, and what this says is that the vacuum is translationally invariant. But also it tells me that this is my knowledge state in this value, in this Verma module, because I now have a relationship like that of the knowledge state, but it's a very simple one. An operator acting on H is giving zero. Next question is, suppose the next estate level will be created by L minus two on vacuum, and note that L minus one squared gives you zero. So at this stage now I have just one estate. And the reason that this is happening is because on top of it I have a knowledge state. So the Verma module is somehow reduced. Now this estate L minus two is an interesting estate because yesterday I did a simple calculation which I showed that the central charge is related to the norm of this estate. So in fact this central charge is given by this, the norm of this estate. And worse than that, if this vanishes, see vanishes and then the entire conformal filter will be empty which will be this possibility when see vanishes. So in some sense see is telling you that there is some content in your theory. Now it's a little overstating to say it's the energy density with some content in your theory. Sometimes see is negative. Then we have a non-unitary theory. If you have a negative see, this means that the norm of this guy is negative and having a Hilbert space with negative norm of the states means that you have a non-unitary theory. But doesn't mean that it's not physical. So in this box values of see lower than one half are not written. But there are two other values which are famous and of course there are other as possible estates. This gives me the percolation model and this gives me the a billion cent part. They are both respectable models in statistical mechanics and very well studied. They come out, one comes out of a negative norm CFD and the other one comes out of a theory which should have been trivial but is not. So this is not the only possibility for see equals to zero. I can construct a see equal to zero theory but non-unitary. This emptiness is imposed if you impose unitarity as well. And there are other see equal to minus one see negative theories and these are non-unitary. In general it's a Pandora's box. Once you open the door to the possibility of having non-unitary estates, then you have removed one of your conditions views which you used for proof of things and then it is very difficult to work out the operator content and so on of these theories and therefore these theories are still, there is still a space for work to work out the operator content of these theories. I will not go into that, it's a very difficult problem. But the nice and clean result is this, that I have a number of models which connect up to CFD. Okay, the good news is that I'm not going to tell you anything more about the CFD, but I said in this lecture and a half is all we are going to need for the purpose of this lecture. So next step is to analyze a few systems which we are familiar with. So two very famous models. I'm going to analyze with all these machinery which I have introduced. And it has two purposes, this part. This is to doing these two examples. What I will get is a working knowledge of the concepts which have been given so far and also see how they are implemented in case of these two models. The good thing about these two models is that we already know a lot about them. So let's try and do this. The first point is an Ising model. The 2D Ising model is a network of spins. Spins are set on the nodes and they can be parallel or anti-parallel, parallel has a lower energy. So the tendency is to go to parallel state. I can write a Hamiltonian for it in this shape. Sigma i are spins sitting on nodes. Each i is a compound index. It refers to a specific point on the plane. And the way it is written is that two neighboring states, two neighboring spins, when they multiply each other and if they are in the same state, it will be positive. So sigma i can be plus or minus one. So if they are sitting next to each other in the same direction, two plus ones, this will be a one and lower energy. Sometimes I need to add an external magnetic field which is given in this shape. Something which, a model which I'm sure you know, so we don't need to spend a lot of time on it. At h equals to zero, the Hamiltonian is invariant under the action of the group z2s when you change the sign of all spins. The order parameter is the mean magnetization given in this form. And it's clear that this guy vanishes due to the z2 symmetry because you take z sigma to minus one, sigma m goes to minus m and the only solution for m therefore is zero. But we know that for h equals to zero at temperatures below Tc magnetization is non-zero. And this is the approximate, this is the exact form and it's approximately 2.26. So what happens? M magnetization again of the Ising model is zero above Tc and non-zero below Tc and it deviates from zero near Tc by this exponent beta. Okay, here is an example of ergodicity breaking and the thing is that at below Tc the entire phase space is not available to your calculations and you have to take him in over only half of the phase space. So if you are, for instance, in the domain that spins are directed up you just use the states which can be obtained from this state by a finite number of flips. Or in other words, I shouldn't say a finite number by a finite energy because each flip needs an energy to go to change and then a finite energy means that you can only change so many of these spins to the down and when you just add up on that magnetization will be non-zero. So think of it in this term, that we take the phi plus state as our ground state and then we assume some sort of dynamics which takes you away from this phi plus and the phase space is created by the long-time action of this dynamics. It's a sort of practical phase space which is connected to one of the vacuum. And when you just sum over this phase space magnetization will be non-zero. And this is a case of ergodicity breaking in the 2D ising model. When I talked about the 2 ergodicity breaking, here we see that below Tc the ising model phase space is broken into two parts, those which are connected to the positive ground state and a completely different section connected to the negative ground state. And hence if you add up magnetization only on this section it is non-zero and it loses its symmetry. You can no longer change all the sigmoids to negative because those fall into this part of the phase space. So this is a clear example of what I mean by ergodicity breaking. I can also calculate the critical exponents for the ising model and they are given in this table. There is an exact calculation in two dimensions. The 3D ising doesn't have an exact solution yet. So numerical simulations have produced exponents for the 3D ising model. And in four dimensions we believe that the ising model has a good approximation by the mean field theory so these are the exponents of the mean field theory approach to the ising. The other concept which I introduced was renormalization group techniques. So let's see what we can do in this case. For Rg what we can do in a spin model is follow Kadanov's block diagonalization. That is you take a number of spins, in this case four of them, you add them up and set them in the middle of the square. So in this way the number of spins which you are dealing with is reduced because four has gone to one and the size of the unit cell has also increased because in now these two spins are two A apart whereas these were only one A apart. This gives me a procedure by which I can implement the renormalization group because I'm changing the scale from one A to two A and I can see what happens to my theory as a result of that. What I have to do is then look at the interactions in the Hamiltonian and see how the interactions in the Hamiltonian change as a result of this block resummation. The problem is that it's actually very hard to do. Any of this in practice. And so there is this famous sentence by Michael Fischer which actually doesn't say anything, it just says it's difficult. It's Michael Fischer was one of the instigators of RG and what is actually saying that the actual process of explicitly doing this is non-trivial. So I'm sorry? It is non-trivial. Okay. So what I'm going to try and do is to actually do it now for a simpler model or not simpler for the Ising model sitting on the triangular lattice. And it's a process which is very interesting that one can actually see explicitly how this resummation process happens. And it's a very good, it gives you a very good understanding of RG. So let's take Ising model on a triangular lattice. So I have a triangular lattice spins are sitting here. What I then do is that I take a resummation process which means that I take these three spins, add them up and then take a sign. What is usually a difficult thing to do is that in your resummation you want to at least ensure that your dynamic variable takes on the same range of the original dynamical variable. So if I call the new spin this thing, it will have the same range. So I define a new spin which is the sign of this sum. And all the various combinations which you can take here from three ones down to three minus ones will definitely have a specific sign. Note that if I had an even number of them, a zero would have become possible which would have thrown me out of the Ising model. That would give you three values. This is why this trick is so neat that when you take just three spins, you always have either plus or minus one. And therefore what I do is that I take this rule and then set a spin in the middle. Which I will color separately and this is sigma i. So in this graph, I hope it is, or in this shape it's, I hope it is obvious that this has happened that three spins are added up and one spin sits in the middle which is on this new point and also one at this new point. So what happens is that you have a distance a prime between the new spins, which is in fact this line here as opposed to a distance between all the spins which was a and a prime is related to a. I think that's an error must be multiplied by root of three. And the other thing which happens is that the number of plaquettes that is faces which have the complete faces changes by n divided by three when you do this. It's obvious that the number of plaquettes decreases because these guys occupy bigger plaquettes. And then what happens is that as a result of this process, the Hamiltonian changes. And so I should be able to write it as interacting terms for h i's which forms the new Hamiltonian and then terms which forms the if you like the magnetic field action on the Hamiltonian which is this guy here. And then I can write the old Hamiltonian as the sum of two different types of spins. S i and s i, small s i, I have to clarify something here. You see Hamiltonian is written as the sum over, my notation from slides to here has changed minus beta h of sigma i to start with. But then I sum some of these spins and I should be able to then write it as a minus b over h s i when I do that. So let's rub this off. If I now do this summation and whenever I have three spins then something is summed up here but not everything. And you have some left over variables still here because you have summed them up with some imposed condition. So you now have a new Hamiltonian in terms of new spins. And if I now sum all of these with respect to s i, I should get the same partition function. So what now I have to do is to see what the Hamiltonian will look like after this re-summation. And this is really the non-trivial part of the statement by Michael Fisher, that to actually get out the new Hamiltonian is not an easy thing. But in this case, there is a trick which makes it easy but in some sort of an approximation. Exactly, exactly, exactly. So what you say is true. I have now two types of interaction. Interactions which are among the spins within the same triangle. Interactions of spins within the same triangle. So these spins have interactions with each other. And this is easier to deal with because I am summing up over these three spins and put a spin in the middle. Then there are interactions between neighboring triangles from here to there. So for the moment, I'm going to ignore the interactions which are inter-triangular. I will just look at the inter-triangular interactions and that's easy. So I mark these guys by i, if you like. And for each of these set, I have interactions between these three spins. Let's work that out. Now to rest your mind, this means that the Hamiltonian is divided into two parts. One Hamiltonian which comes from the intracell interactions plus a Hamiltonian which comes from inter-cell interactions. And this is the trick which makes this problem solvable. That is, you make a division which we call the main Hamiltonian and the interaction around it. The interaction around it is not necessarily a smaller interaction, but it is somehow a simplifier of the problem. So I can in fact now forget about the interaction and just do this guy and this is easy to do because we can just count the number of states and work out the Hamiltonian for it. No, at the moment before the renormalization. This Hamiltonian is the usual Ising Hamiltonian except that I have broken the interactions into inter-cell and intracell interactions. So that's the rearrangement. But now I'm going to forget about that, keep this one only and that is not the usual Ising interval. So now for one cell, I have all possible spins. So it's sigma one, sigma two, sigma three, all belonging to the cell i. You can write them down and they will have possible states. Corresponding to this, I have a sigma i which is using this rule. So these three sigmas can take various values and then sigma i can take a value which is in this case plus, plus, plus, minus, and so on. And now I have e to the power minus beta h zero because I'm keeping only this term and this gives me some values three to the power k, e to the power minus k, minus k, minus k. No, sorry, this last one is three k. k would be beta j. H zero is minus j sigma i sigma j. So h zero is the sum of spins, neighboring spins, but I am only keeping spins within the same cell. So it's not all of spins. Last line is what? You are right, this is minus k and so on. So this z zero guy now is equal to e to the minus beta h zero, somewhere all spins, but now because the spins have decoupled from each other, it actually is just somewhere all i, e to the minus beta h, but this is over only one cell. And this happens because the cells are no longer coupled to each other as in the normalizing. They are now decoupled. So I can actually calculate this simply by looking at this last column which is e to the power three k plus three e to the minus k, which is just the sum of these terms here. I should really organize this a little bit better. So if you complete the table, you will see that this is repeated. This will then be repeated for the other four. Hence, this partition function is really this guy and two sum power. So this is the value of z zero. Now what is left is what happens to the h interaction. H interaction will have terms which are a multiplication of two different cells. So this guy h interaction is equal to k times spins from different cells. You'll be exactly the same as the upper half. So we should have it distributed twice. We should have what, Salih? We should have a coefficient equal to two in the partition function. You mean we should have a two to the power n over three here? Okay, that's a possibility, but it doesn't change much because these coefficients don't matter in the calculation. All the lockspin. Yes. The weight is only two parts, k plus three to the minus k. Yes. Then there will be no factor of two. Then there will be no factor of two. So now what I want is this e to the minus beta h of sigma i, which is equal to e to the power minus beta h zero minus beta h interaction. And I can write this down in the following way. I now actually interpret this as interaction and expand it. So it gives me an e to the minus beta h zero for the first time plus or minus beta h interaction, e to the minus beta h zero, et cetera. Let us also divide by z zero. This is the z zero. So it comes out to be one plus the expectation value of h interaction. And then of course I have second order terms, et cetera. As you can guess, I'm not going to calculate these. Since this is a perturbation, I may be able to get a good enough answer by calculating just the first interaction. Of course, the inventors of this method, which are these guys, I think I should write their name, however, that and van Luywen. These two guys invented this method to actually see that is to answer Michael Fisher's dilemma that the process is non-trivial. It surely is non-trivial, but they managed to calculate h squared as well. I will only present h because it's much easier and takes less time. However, it can be taken to the next level. Right, and there is the one after the normalization. Yes? And why can you say that it is small that you can do perturbation? Okay, that's a good question. Why can I say that it is small? It's small because there are really, look, the number of interactions which are formed between cells is not many. And I am hoping that all these interactions which are formed between these two cells, somehow in this black resumption will have a smaller effect because it becomes thinned out. Not all of them will be relevant. Some of them will be simply summed up. But it's a hope. It really comes out of the smartness of these guys that they managed to show that this actually makes a small contribution. And you can only see that at the end. Here, I'm only making a hand, at this stage, I can only make a hand-waving argument that each of these terms which come out of that expansion are smaller in respect to the previous one. You kind of can see it because all the, a lot of interactions are taken into account here and then there are inter-spin interactions between here and there, here and there, which determine, so there are two interactions here between these two, which determines this cell with that cell. The interaction term before doing renormalization, because you dropped on there. No, renormalization has not happened yet. All I have done is that I have defined a block resummation. We don't know anything about renormalization yet. So the general plan of this calculation is like this. In any resummation, what you do is that you define a resummation rule, which I have defined here. In the previous slide, a different resummation rule was defined and if you have ever tried to do that, you see that this is a very difficult rule to implement. People have done it, but on a blackboard and in front of a class, this one is easier to do. So the question is, can I have a simpler resummation rule such that I can actually do the calculation? I define a resummation rule, which is this guy here and then what I have to do is to then show that the new Hamiltonian is of this form. It hasn't lost its ising personality or identity. It's almost the same shape as the previous ising. It will not be exactly the same. The interaction terms will become more complex and there will be more coefficients of coupling constants, but that is good for me because that will give me, then that will give me the renormalization group. The renormalization group equations are equations which connect the new coefficients to the old coefficients. You choose the cells because you can rotate the cells and those interactions. Yes, you are right. Most of the interactions actually are in the part you are neglecting. No, that's not true. Because when you are neglecting four out of six, isn't it? No, these spins are interacting with each other very strongly and then there is this interaction of this spin with its neighbors which will determine the interaction of this triangle and that triangle. Just counting them for one triangle appears to be less than this. So I'm taking most of the interactions in. However, you are right in the sense that this is completely arbitrary. Completely arbitrary and there is no reason to assume that this will always work. It just happens to work so that we can see the effect of it. It's an example for in practice where you can see how this resummation works and you can derive the renormalization group equations finally as you connect the coefficients of this guy to that guy. You can make the calculation more precise. That is, you include more and more effects by taking the higher-order perturbations, which people have done. And you then hope for the higher-order perturbations to be smaller than the first-order perturbation. And that hope is only justified after we do all the calculations, not before, because before your argument is correct and you can say, okay, this is not true in all statistical mechanical models which I can separate in this sense and you'll be right. Just a smart example for seeing an effect where you can actually perform all the calculations. Yeah? Go on. Now the interaction term is like that and now I want to take the mean of this thing where i and j each one belong to neighboring cells. But this mean is taken over z0, which is this guy. So I should put a z0 here as well. Now, here is the beauty of the trick and that is this guy will now, the mean, because it doesn't connect, because h0 doesn't connect the different cells, it will just be like that. The Hamiltonian doesn't connect the different cells. So the mean of operators which are in different cells will be independent of each other. So what I therefore need to calculate is sigma i averaged over 0 and this is what it comes out to be. So if sigma i is equal to 1, I go and look at the table which I rubbed off and see where does sigma i equal to 1 for which combinations and then calculate that combination. So it's e to the 3k and this time plus e to the minus k. Better write this side. In fact, in all those combinations I just had e to the 3k and e to the minus k except that now because of sigma one of them picks up a negative sign. Previously, because there was no sigma none of them would become negative. One of them becomes negative. So I will get that and of course this has to be divided by the value of z0 which is e to the 3k plus 3e to the minus k. And when sigma i is minus 1 it gives me a minus e to the power 3k plus e to the minus k minus 2e to the minus k divided by e to the 3k 3e to the minus k. So I can combine all of them and write them like this because sigma i just multiplies a minus 1 in the bottom. Probabilities or I don't understand what those factors or fractions are? It's a fraction because I have a z0 in the denominator. It's a probability but only in the sense of h0. So I'm calculating the average of an operator in the h0, in the h0 model. So one has to be negative. Yes. So let's go back here. I broke my Hamiltonian into a free Hamiltonian plus interaction. So using this Hamiltonian I will now do my calculations as though it is a statistical mechanical system. So I have a z for this and then I have averages of operators for this Hamiltonian. So if I have minus beta h interaction it means that this is equal to minus beta h interaction e to the minus beta h0 divided by z0. So in this sense you can say that each configuration is happening with a probability and I'm summing them over. When I look at b minus beta h interaction it's of this shape. This is h interaction. When I want to calculate the average value of this I notice that i and j belong to different cells and h0 does not connect the different cells. So each of them will have a separate independent or their averages can be calculated separately which is what I have written here. Now when I look at one of them which is just the average value of sigma i the problem is that what is the value of beta e to the minus beta h0 for each combination which I had a table for. I write those values but now with the difference that because sigma sometimes becomes negative and positive some of them will pick up negative and positive factors. It simplifies into that. So this term will therefore be k this ratio sigma i sigma j. However for each neighborhood of a cell there are actually two spins connecting this cell to the other cell and each connection is equally valid. So I have a 2 to add here and this is the this is now the average of this interaction. There is a square power because each sigma i has one of these factors. I still don't understand the meaning but you say that the average of sigma i is equal to something that contains sigma i I might be confused on that. No, the average of sigma i equals to this if sigma i is equal to 1. It is 1, I know that it is 1 so its average is the 1. It's the term. No, it's not the this term is not the average of sigma i itself. It has minus beta h0 in there. This is what we are calculating. In a single cell in the block we calculate every sigma of that block given that the block on the hole is plus 1. Yes, so what is happening is that I take one of these blocks and there are three spins here which can have therefore eight possibilities.  So four possibilities go into the calculation of sigma i plus 1. And therefore this factor has to be calculated for each of the four possibilities. And there are four possibilities calculated to 1, 2, 3, 4. And then when sigma i is minus 1 again these four possibilities have to be calculated. And as professor Dar pointed out four possibilities as you sum over the little zikmas. So this i is not summed over. We have just for this sigma i connected by sine of sigma 1, sigma 2, sigma 3 but all these zikmas 1, 2, 3 belonging to block i. There are four possibilities. Four possibilities has gone into this. In the denominator that factor of 2 that this guy pointed out. Yes, that factor of 2 is taking care of us. There is a factor of 2 if you want to keep everything right. Now what we do is that we get go of that factor of 2. We just work with this value of log of z0. Eventually all I want what I want to do is to take log of this and it will not be necessary. However this other guy here is important in that the interaction, each interaction actually has two terms in it because you get two spins connecting one cell to the other. But these two spins are just exactly the same and therefore the calculation doesn't affect it and it doesn't affect the calculation. I just get a factor of 2 here and so if this average is like that I can place it in this edge interaction. I just place it in there. There is a k outside. This is the k outside. This is the term which comes out of 1 sigma so a squared for the whole term. So now this is interesting because it is telling me that hi is of the same form as h0. So if I can rub this off I tell you what has happened as a whole. I have a partition function which I wrote as a sum over i and then a sum over i, a small i with the condition of sin of 3 spins bringing me sigma i. Sigma bigger. This was broken into two parts so I formed it into this shape and I have now and I then went on to calculate the value of sigma i by performing some of this calculation and expanding in the powers of h interaction and this is what I got. So I see that beta h sigma big i looks just like beta h sigma a small i which is the point of realisation group. Now I can hope to extract my RG equations because this has coupling constants this has coupling constants and I can relate them to each other. So by writing e to the power k sigma i sigma j. The other thing which we need to notice here which is implicit is that if in the big i, big j picture if they are not neighbouring there is no interaction. So this cell and that cell don't have an interaction. Only neighbouring cells have and it's a property of taking the first power. If you took the second power of the h interaction then you might have interactions between further away cells. So this is now in this shape. Hence I can say that the new coupling constant is related to the old coupling constant by this form. This is my RG equation. What does it say? It says by the bellocary summation of Kadanov and the triangular lattice the shape of the i's in Hamiltonian doesn't change but the coefficient the coupling constant changes and the coupling constant changes by this law. So this calculation although a little involved gives me an answer to Michael Fisher that it's not really all that non-trivial. Although I have used a lot of tricks. He meant without using tricks. So I'm going to rub everything off so that we now have an RG equation. And this RG equation has happened in making A go to root 3 times A. So a scale has been enlarged as a result coupling constant has changed. If you like you can say that these are coupling constants at different scales and this is the result of changing the scale coupling constant changes as a result of the change of a scale. It is not a differential equation as I showed you before because I have changed the scale by a finite amount not by an infinitesimal amount. So the first thing I have to find the fixed points. Why do I have to find the fixed points? Because the fixed points correspond to the points of the flow where the Hamiltonian doesn't change. And if the Hamiltonian doesn't change then I have a critical point. So what is the obvious fixed point? There is an obvious face fixed point at K star equal to 0. K star equal to 0 0 equals to 0 is a fixed point. And then there is another fixed point at infinity of course. For at finite interaction strength these correspond to 0 and infinity temperatures. So this is T equal to 0 and this is T equal to infinity. So these are not interesting. So we now look for a fixed point in a finite fixed point somewhere in the middle of these two extremes. So there must be a point where this equation is satisfied at a value between 0 and infinity. The little algebra shows you that you can find this fixed point. Let's not do the algebra. K star I have it here if somebody wants to see the algebra. I'll give you later. You take logarithm and then you juggle it. Now, you can immediately ask is it correct or not? Because we know what K has to be from on Zager's solution. Of course on Zager's rectangular but similar solution for triangular we know the exact K star. So you see it's not that bad. We have about 0.06 of difference between the obtained result and the exact result. It is to actually validate this method you have to do the next kind of perturbation which these guys did the guys who I wrote their name down. And if you go to the second order of approximation then this K star approximation comes out. So if I call this K star 1 that will be K star 2 will come out to be 0.3 something. And the approximation I think 0.301 something. So the approximation improves which is the answer to your question. Whether this is a perturbation or not only now I can say that it is because you can see that the approximation is apparently converging to the exact solution. Okay, what I can do next is to take a derivative of this term let's do this company precisely. So K prime is a function of K. What I write it as K prime as a function of K star at an expand around here. Our K prime at K star is K star itself because that's the fixed point and this equation can be reorganized in this shape. So what does it say? It says that the distance that the coupling constant has to the fixed point the distance of the coupling constant as a result of each renormalization step changes by this factor it changes by this factor so if I calculate this factor it will give me the factor change of the coupling constant near the fixed point. So dK prime dK at K star this has to be calculated what is negative? Maybe you can tell me afterwards I don't see any problem. Okay, this is a calculation which eventually gives you 0.883 So how do I interpret this 0.883 how? I'm asking you it's a repulsive point but what is the exponent of repulsion? What I need to interpret this is as if you if this is exactly like what I obtained in the abstract in the abstract rG I said that this m, a stability is e to the power y1 e to the power y2 00 so this is y1 sorry not e thank you very much lambda to the power y thank you so this is the delta T is the repulsion in the direction of delta T so that it's actually T prime is equal sorry, beta prime is equal to e lambda to the power minus 1, beta this but this is interpreted as that now I have exactly the same shape but K prime delta K prime is related to delta K with a coefficient so this has to be equal to lambda to the power yt this is the amount by which this coupling constant is re-escaped as a result of Arch exactly I just want them to do a little thinking they are not supposed to just listen it's not a theater what is lambda lambda is given by this relationship that a prime is root 3 times a so this is my lambda so yt is equal to log of 0.883 divided by log of root 3 which is approximately what sorry a lot of errors here a lot of errors here 1.624 1.624 0. 0.883 and yt exact is equal to 1 so this is not this is off by 12% which is of course reflected in this as well now you can calculate one of the exponents nu is 1 over yt and that is equal to 1.13 and it should have been 1 and alpha is equal to 2 minus 2 over yt which comes out to be minus 0.26 and it should be 0 so you can if you are if you are if you are able to do the next order of approximation these things all improve the next order of approximation is to keep the second power of interaction Hamiltonian interaction in there now to complete the calculation I have to also do the h hsi which goes to an h prime si prime we will do it tomorrow ok thank you